question
stringlengths
37
38.8k
group_id
stringlengths
2
6
sentence_embeddings
listlengths
768
768
<p><strong>EDITED AND SOLUTION</strong>: In fact my stupid mistake was to take the wrong value for my $P_1$ and I was getting an 1.2998 that finally is a 1,9178 within just a difference about 7%. So at the end they are not equal but it is not a $1.9\neq1.3$, but $1,9\neq1,9278$. </p> <p>In spite of everything, <em>it has been profitable to me to discuss</em> the possible conditions where the ideal gas law can be a good aproximation. </p> <p>Thank you very much for your useful answers. </p> <hr> <p>I have made an experiment that consist of a gas inside a cylinder and I have a piston. I have this experiment connected to a computer and I can graph the temperature and the pressure. This system can lose temperature so when I push in the cylinder I can see that my temperature increases and estabilizes to my lab temperature after 5 seconds. </p> <p>So, my question is: </p> <p>Why am I getting a factor $\frac{V_1}{V_2}=1,9 \pm 0,1$ and a factor $\frac{P_1\ T_2}{P_2\ T_1}=1,2998\pm0,0001$?</p> <p><strong>I know that they have to be different but I don't know why, so why I shouldn't be expecting them to be equal</strong> (taking in account the uncertainties)<strong>?</strong> <strong>$$\frac{V_1}{V_2}=\frac{P_1\ T_2}{P_2\ T_1}?$$</strong></p> <p>Thank you in advance. </p> <p><em><strong>PLUS</em></strong>! I have added the image of the experiment. I pushed in the piston and stay making force for about 20 sec until I released the piston free</p> <p><img src="http://i.stack.imgur.com/wDzPX.jpg" alt="I pushed in the piston and stay making force for about 20 sec until I released the piston free"></p> <p>M. </p>
g5376
[ 0.028691796585917473, -0.05976591631770134, -0.0037266453728079796, 0.031758714467287064, 0.03254695609211922, -0.021655583754181862, 0.009597503580152988, 0.014556767418980598, -0.0667160376906395, -0.017085198312997818, -0.00875065941363573, 0.05526819825172424, -0.007473979145288467, -0.024969201534986496, 0.03267132490873337, 0.04701772704720497, 0.11088473349809647, -0.020644841715693474, 0.048464298248291016, 0.0010858154855668545, -0.0614166222512722, -0.005919105838984251, -0.0422673337161541, -0.07346013933420181, 0.0318276584148407, -0.0541926845908165, -0.008951887488365173, 0.03181324526667595, -0.07746779173612595, 0.014637933112680912, -0.03275052085518837, 0.008572733961045742, 0.03896775841712952, -0.023432733491063118, -0.04245111346244812, -0.023803068324923515, 0.043445054441690445, 0.03881160914897919, 0.014586668461561203, -0.06145590916275978, 0.011505736038088799, -0.025595907121896744, 0.032877299934625626, 0.02851206064224243, -0.01866033859550953, 0.005372520070523024, -0.06685099005699158, -0.03792019560933113, 0.020441940054297447, 0.0001899868220789358, 0.036004792898893356, 0.00159833999350667, -0.029545046389102936, -0.012348582036793232, 0.015351517125964165, 0.056571200489997864, -0.00762304337695241, -0.026691850274801254, 0.03062559850513935, -0.007730148267000914, -0.009437701664865017, -0.039561428129673004, 0.021701892837882042, -0.010372629389166832, -0.018821174278855324, -0.01856275461614132, -0.03560945391654968, 0.02109004370868206, -0.037588924169540405, 0.007310574408620596, -0.02974507212638855, 0.004805825650691986, 0.0005798032507300377, -0.03546964377164841, -0.030035139992833138, -0.021518085151910782, -0.0071259066462516785, -0.043711792677640915, 0.015113013796508312, -0.024097857996821404, 0.037224180996418, 0.010158405639231205, -0.01849702186882496, 0.0451076477766037, 0.043338578194379807, -0.027814330533146858, 0.01386541873216629, 0.00032862956868484616, 0.010577347129583359, 0.022449377924203873, -0.027767691761255264, -0.0036617363803088665, 0.09248004108667374, 0.033605728298425674, 0.019987931475043297, 0.011888545006513596, 0.004244010895490646, 0.07524243742227554, 0.009974448010325432, 0.02809324860572815, 0.034029245376586914, -0.023823924362659454, -0.005847535561770201, 0.029400654137134552, -0.06676172465085983, -0.011616808362305164, 0.014167927205562592, 0.01937897503376007, -0.0803011879324913, -0.04247620329260826, -0.02657116763293743, -0.04260137677192688, -0.09462696313858032, -0.07380574196577072, -0.03059626929461956, -0.045767974108457565, 0.02210516668856144, -0.014548178762197495, -0.01126545388251543, -0.007865840569138527, 0.035800542682409286, -0.0003381853166501969, 0.07761858403682709, 0.07568300515413284, 0.010015871375799179, -0.04425632581114769, 0.05672764405608177, -0.04230066016316414, 0.020078331232070923, -0.04982421547174454, -0.015846243128180504, -0.0014789702836424112, -0.009302712045609951, 0.03463521599769592, -0.023185068741440773, -0.01599970832467079, -0.030072025954723358, 0.05390617251396179, -0.006883843801915646, -0.017269596457481384, -0.029562639072537422, 0.028733860701322556, 0.0010735964169725776, -0.014395732432603836, -0.07560410350561142, -0.033351607620716095, -0.0798872783780098, -0.007276712916791439, 0.04638545587658882, -0.041356492787599564, 0.06910038739442825, 0.048161547631025314, -0.0028068707324564457, 0.03627094253897667, -0.015542573295533657, -0.024658283218741417, 0.0078088450245559216, 0.02308555506169796, 0.012694885954260826, 0.021822519600391388, 0.0071304067969322205, 0.004250776953995228, 0.020128941163420677, 0.020323995500802994, -0.063601553440094, 0.05805162712931633, -0.007061239797621965, -0.019388005137443542, 0.008158313110470772, 0.0015486960764974356, -0.0691002756357193, -0.008998638018965721, -0.001186759676784277, -0.012868588790297508, 0.017200356349349022, 0.024830123409628868, 0.060298264026641846, 0.023268332704901695, 0.02311663329601288, -0.00482954503968358, 0.03895598649978638, 0.0018574711866676807, -0.00863768719136715, -0.05892790108919144, -0.08734157681465149, 0.027771083638072014, -0.03806073218584061, -0.025468003004789352, -0.12798184156417847, 0.011218909174203873, -0.039418354630470276, 0.006116560194641352, -0.021755987778306007, 0.008891123346984386, -0.048812802881002426, 0.007283192593604326, 0.002526033902540803, -0.08941731601953506, -0.05285809189081192, 0.06640221178531647, -0.0405203253030777, 0.05732446908950806, -0.015619068406522274, 0.022546088322997093, -0.04701503366231918, -0.01792883686721325, 0.0007557102362625301, 0.017936479300260544, 0.03874879702925682, 0.027439819648861885, -0.03453940153121948, 0.028435897082090378, -0.04281451553106308, 0.054891437292099, 0.01936976984143257, -0.04040643572807312, 0.05286341905593872, 0.018397318199276924, 0.004080636892467737, -0.0012079980224370956, 0.03511292487382889, 0.01905873231589794, 0.03421219065785408, -0.02250649593770504, -0.06504806876182556, -0.04909123480319977, 0.0005661254981532693, 0.016729852184653282, -0.042636673897504807, 0.0480281300842762, -0.03368249163031578, -0.02829655259847641, -0.0116184176877141, 0.021651655435562134, 0.0172733087092638, 0.05206776037812233, -0.006566682364791632, 0.017947345972061157, -0.0056848470121622086, 0.043879926204681396, 0.011832109652459621, -0.01965751126408577, -0.04434344172477722, 0.03339606150984764, -0.003847469575703144, 0.016430886462330818, -0.0008909328607842326, 0.0010833776323124766, 0.004513034131377935, 0.01744108647108078, 0.0013002551859244704, 0.05686843767762184, 0.0163078922778368, 0.04563667252659798, -0.09053147584199905, 0.010097782127559185, -0.04132038354873657, 0.01633019745349884, -0.013994650915265083, -0.028264449909329414, -0.009983071126043797, -0.006736461538821459, 0.002664172789081931, 0.029989037662744522, -0.04008951783180237, 0.017069509252905846, -0.022291094064712524, -0.037533145397901535, -0.001326311263255775, -0.005292410496622324, -0.022360261529684067, 0.0012519767042249441, -0.004251981619745493, 0.07886990904808044, 0.007528260350227356, 0.012397736310958862, 0.0216502882540226, -0.0024204289074987173, 0.03945617005228996, -0.040860772132873535, -0.01397270429879427, 0.028689347207546234, -0.049117911607027054, 0.02673538774251938, 0.02873527631163597, -0.03428949788212776, 0.05191066116094589, 0.0315522700548172, -0.003379872301593423, -0.029352685436606407, -0.03522045910358429, 0.08701467514038086, 0.01976691372692585, 0.043769992887973785, 0.028193585574626923, 0.05944110080599785, 0.055829212069511414, -0.06717272102832794, 0.06465556472539902, 0.023106073960661888, 0.00524850282818079, 0.002317533129826188, -0.035824891179800034, 0.030157867819070816, 0.015870003029704094, -0.06573837995529175, -0.03464283049106598, -0.021296940743923187, -0.02396927960216999, 0.035779088735580444, -0.0048891655169427395, 0.006310508120805025, 0.01872125081717968, -0.07621479779481888, -0.030583715066313744, -0.002782810013741255, -0.009697633795440197, 0.0070955101400613785, -0.00028595805633813143, 0.02582179196178913, -0.02597125433385372, -0.07575856894254684, -0.022582480683922768, -0.020821020007133484, 0.0326111800968647, 0.003915817942470312, -0.049436479806900024, -0.03584618121385574, -0.0016300639836117625, -0.007262351457029581, 0.041575632989406586, 0.0635911300778389, -0.0457913875579834, -0.03941566124558449, -0.015772854909300804, -0.046245645731687546, -0.04143292084336281, 0.08326294273138046, -0.020481599494814873, -0.04028653725981712, -0.06061917543411255, -0.019363870844244957, 0.02176867239177227, 0.017796818166971207, -0.006797594018280506, -0.009241088293492794, -0.0053705438040196896, 0.04879987984895706, 0.048597630113363266, -0.006690175738185644, 0.04993077740073204, -0.017298327758908272, 0.015266155824065208, 0.01665063574910164, 0.018663890659809113, 0.009312774986028671, 0.048533711582422256, 0.0016444093780592084, -0.03806570917367935, 0.0019340133294463158, -0.013808044604957104, -0.023380061611533165, 0.02588082104921341, 0.05058338865637779, -0.050364114344120026, -0.013192219659686089, 0.019647346809506416, 0.11171840876340866, 0.032221656292676926, -0.03288597986102104, 0.014005071483552456, -0.0014588143676519394, -0.00835675559937954, 0.0391724556684494, 0.03860681876540184, -0.034019019454717636, 0.022833114489912987, 0.02987014129757881, -0.010998817160725594, 0.05124865844845772, 0.08248542994260788, 0.027624791488051414, -0.03150616213679314, -0.025297798216342926, 0.05333378538489342, 0.0015746316639706492, 0.03355775400996208, 0.038232892751693726, 0.06270106136798859, -0.05616636574268341, -0.019361402839422226, 0.029451847076416016, -0.04321316257119179, 0.0853995606303215, -0.0064185019582509995, 0.008993432857096195, 0.005355412606149912, -0.0008392002782784402, -0.004515402019023895, -0.03934159874916077, 0.011405782774090767, -0.010624219663441181, 0.0041458397172391415, 0.02584872953593731, -0.0009462782763876021, -0.011442701332271099, 0.026738429442048073, 0.0008746340172365308, 0.0175272598862648, -0.02722758799791336, -0.024098141118884087, -0.002813978586345911, -0.017802581191062927, -0.03811830282211304, 0.034246742725372314, -0.03588908910751343, 0.02822243794798851, -0.0019182702526450157, 0.03705228120088577, -0.0387151837348938, -0.007615263108164072, 0.06699027866125107, -0.00595736363902688, -0.04621317982673645, 0.028929607942700386, 0.035738974809646606, 0.008841300383210182, -0.003840146353468299, 0.04140658676624298, -0.06767250597476959, 0.023519333451986313, -0.0277592483907938, -0.04592721909284592, -0.014401135966181755, -0.014515435323119164, 0.09222061187028885, -0.028860807418823242, 0.022238116711378098, -0.024559874087572098, 0.10103528201580048, -0.005943214055150747, 0.0254611037671566, 0.03694553300738335, 0.04418566823005676, 0.01822550967335701, 0.0009252136223949492, -0.040467120707035065, -0.014817641116678715, 0.003298764117062092, -0.03235149756073952, -0.03417950123548508, -0.00633604358881712, 0.03193254768848419, -0.00609162263572216, 0.03068716451525688, -0.013697247952222824, -0.03899480774998665, 0.08461181819438934, -0.004532755818217993, 0.04306074231863022, -0.02718418836593628, 0.010192271322011948, -0.02609330229461193, 0.03270459175109863, -0.011770103126764297, 0.0008762991637922823, -0.04384472593665123, 0.005022252444177866, -0.011151119135320187, -0.0031576920300722122, 0.0057071722112596035, -0.026196202263236046, 0.0022695476654917, 0.009873680770397186, 0.02047230862081051, -0.023102693259716034, 0.025719856843352318, -0.02900790609419346, 0.07168518751859665, -0.06854233145713806, -0.037563882768154144, 0.038881734013557434, 0.04752169921994209, 0.02674124762415886, 0.02134803682565689, -0.01306067779660225, -0.053702808916568756, -0.013267569243907928, 0.00553483422845602, -0.03823571652173996, 0.02238878794014454, 0.07355280965566635, 0.020041925832629204, -0.038897011429071426, 0.034526050090789795, -0.004170047119259834, 0.033204127103090286, -0.010386058129370213, 0.015030198730528355, 0.0000788525358075276, -0.09138292819261551, 0.016441185027360916, -0.0369197353720665, -0.012746342457830906, -0.03217927739024162, 0.03675409406423569, 0.000638617028016597, -0.009579668752849102, -0.004920508246868849, 0.014351149089634418, 0.00923942867666483, -0.031867388635873795, 0.032551512122154236, 0.022503208369016647, -0.0011224080808460712, -0.017882974818348885, 0.010780280455946922, 0.008223118260502815, -0.03975434601306915, -0.05354738608002663, 0.11394580453634262, -0.050371669232845306, 0.0695122554898262, 0.015243491157889366, -0.037752605974674225, 0.008669967763125896, -0.022939933463931084, -0.07503622770309448, -0.0025984179228544235, 0.017393771559000015, -0.01462019793689251, 0.03647363558411598, 0.07421572506427765, 0.016906697303056717, -0.012605651281774044, 0.04528409242630005, 0.02526029758155346, -0.03576987236738205, 0.055052705109119415, -0.06577731668949127, 0.023960573598742485, 0.0005888622836209834, 0.005524047184735537, 0.006971363443881273, -0.012992482632398605, 0.03711683675646782, -0.0015214034356176853, 0.020132068544626236, 0.03701137378811836, -0.021602101624011993, 0.03981589525938034, 0.036806706339120865, -0.02633971907198429, -0.014806329272687435, 0.06678354740142822, 0.029343215748667717, 0.029394937679171562, 0.003578547853976488, 0.02624651975929737, 0.018918169662356377, -0.02146773599088192, 0.0403251014649868, 0.0031219576485455036, 0.014739242382347584, 0.0146946357563138, -0.03811561316251755, -0.0050760479643940926, 0.000686932704411447, -0.018721675500273705, 0.07806459814310074, 0.020448114722967148, 0.03709295019507408, 0.02586296573281288, -0.0009755229693837464, 0.029521064832806587, 0.02395966835319996, -0.06768077611923218, -0.008849270641803741, 0.023622864857316017, 0.012727301567792892, -0.03398841246962547, -0.017849329859018326, 0.017509769648313522, -0.02559058554470539, -0.0025044912472367287, -0.018409116193652153, -0.03508327156305313, 0.007925847545266151, 0.05595581233501434, -0.03070434182882309, -0.010265865363180637, -0.014455728232860565, -0.013356060720980167, -0.007063019089400768, 0.009153621271252632, -0.055047184228897095, -0.03664383664727211, -0.047388236969709396, 0.00411588279530406, 0.035006843507289886, 0.05070812255144119, 0.04679665341973305, 0.0234818235039711, -0.0108653474599123, 0.0018823815044015646, 0.0051885731518268585, 0.023280316963791847, 0.041211288422346115, -0.007379603106528521, 0.07401305437088013, -0.021625010296702385, 0.019001320004463196, 0.016224661841988564, 0.018436932936310768, 0.04939595237374306, -0.028545957058668137, 0.02504785545170307, 0.04009542241692543, 0.008863226510584354, -0.016261762008070946, 0.01791933923959732, 0.009926916100084782, 0.02634890377521515, -0.07516495883464813, 0.022839771583676338, 0.05983065068721771, -0.04779498279094696, 0.02905343659222126, 0.0513002946972847, -0.01749974489212036, 0.026598354801535606, -0.022934069857001305, -0.04339553043246269, 0.03191772475838661, -0.03233198821544647, 0.03844540938735008, -0.03934711217880249, 0.022494157776236534, 0.049758702516555786, 0.02897150069475174, -0.008686794899404049, 0.02066875249147415, 0.015973364934325218, 0.0008246963261626661, -0.012424535118043423, 0.009088819846510887, 0.037786006927490234, -0.06354586780071259, -0.08215423673391342, 0.050126850605010986, 0.0008930700714699924, -0.06124870851635933, -0.040636010468006134, 0.03663550689816475, 0.027108952403068542, 0.030860867351293564, 0.014122557826340199, -0.05143800750374794, 0.0031878771260380745, -0.055679891258478165, -0.04693843051791191, -0.028201695531606674, -0.003741539316251874, 0.03072545677423477, 0.03222410008311272, 0.03951389715075493, -0.05362500250339508, -0.06347408145666122, 0.0014830484287813306, -0.04972199350595474, 0.04357831925153732, 0.00843862909823656, -0.03369003161787987, -0.03031594306230545, 0.042763080447912216, 0.04355000704526901, -0.021977612748742104, 0.01773429475724697, -0.010196560062468052, -0.020208153873682022, -0.008021983318030834, -0.0632404312491417, -0.020851099863648415, -0.01345658116042614, -0.02367646060883999, 0.02258426509797573, -0.025323452427983284, -0.04219840094447136, -0.04738331586122513, 0.0013339953729882836, -0.018142476677894592, -0.011434371583163738, 0.05019798129796982, -0.00003381550050107762, -0.02156476117670536, 0.02002161182463169, -0.022158553823828697, -0.00003121260306215845, 0.018728984519839287, -0.03293171525001526, 0.023737015202641487, -0.0019847331568598747, -0.026224786415696144, 0.012077595107257366, 0.0016108474228531122, 0.06173707917332649, -0.0024061116855591536, 0.018136566504836082, -0.017528727650642395, -0.06689991801977158, 0.03112400881946087, -0.02412058226764202, 0.04608609899878502, -0.03817948326468468, 0.08508995175361633, -0.048439957201480865, -0.03181774541735649, -0.05937853083014488, 0.017387697473168373, -0.02005048654973507, -0.035131849348545074, -0.03688835725188255, -0.008600165136158466, -0.047469500452280045, -0.051102571189403534, -0.07462277263402939, -0.0411762110888958, -0.0467730313539505, -0.022955631837248802, 0.015228583477437496, -0.02449812740087509, -0.03052186407148838, -0.019261006265878677, 0.04042476788163185, -0.03971396014094353, 0.0071693891659379005, 0.0856422558426857, 0.026383737102150917, -0.011861706152558327, 0.03463965654373169, -0.02052680402994156, -0.04699309170246124, -0.015384200029075146, -0.006320606917142868, 0.03945189714431763, -0.028329113498330116, -0.0786614716053009, 0.08343878388404846, -0.0010499019408598542, -0.009674427099525928, -0.02749275229871273, -0.004498384892940521, -0.03324844688177109, 0.005683707073330879, 0.012759526260197163, -0.08439023047685623, 0.010319417342543602, 0.05680481716990471, 0.025080619379878044, -0.05040426924824715, -0.004435730632394552, 0.015245855785906315, -0.047425925731658936, 0.03582390397787094, 0.011345874518156052, 0.03664855659008026, 0.017810115590691566, -0.007055702619254589 ]
<p>How to show that $$ \int d\Psi d\bar {\Psi}e^{i \int d^{4}x\bar {\Psi} \hat {A} \Psi} = det (\hat {A})? $$ $\Psi , \bar {\Psi}$ refers to Dirac spinors (the second is $\bar {\Psi} = \Psi^{\dagger}\gamma^{0}$).</p>
g5377
[ 0.0066856155171990395, -0.03469700738787651, -0.022120457142591476, -0.048248086124658585, 0.09057533740997314, -0.00628117797896266, 0.02660728245973587, -0.0274822898209095, -0.050432927906513214, 0.018013734370470047, -0.016446668654680252, 0.0031504337675869465, -0.01742236502468586, -0.007566542364656925, 0.05571534112095833, -0.0009615819435566664, -0.005630346946418285, -0.059026286005973816, -0.0020251574460417032, -0.03108799271285534, 0.002401381731033325, -0.0603872574865818, 0.006269881967455149, -0.07165413349866867, 0.11333326995372772, -0.07461974024772644, 0.015973620116710663, -0.0155100766569376, -0.03639950603246689, 0.018579337745904922, 0.0030369546730071306, 0.03730328008532524, 0.0467769131064415, -0.004961428232491016, -0.011091534048318863, -0.040947336703538895, 0.1027054414153099, 0.07366140931844711, -0.024738414213061333, 0.02301127463579178, -0.04491955414414406, 0.028341712430119514, 0.0286124125123024, -0.013130748644471169, 0.05501972883939743, 0.05015334486961365, 0.0068220715038478374, 0.045781683176755905, -0.10730993747711182, 0.013836393132805824, -0.002726413542404771, 0.03706881403923035, 0.03752899914979935, 0.00867877621203661, -0.047987744212150574, 0.014244590885937214, -0.013029208406805992, -0.01929304748773575, 0.05067446827888489, 0.053535498678684235, 0.03696234151721001, -0.06898795068264008, 0.03695984184741974, 0.041213929653167725, 0.020099284127354622, 0.028290696442127228, -0.019319219514727592, -0.009985946118831635, 0.03013899363577366, -0.034246597439050674, -0.037288956344127655, -0.07973221689462662, 0.09095685184001923, -0.00818596314638853, -0.007234368473291397, 0.007138475310057402, 0.02391911670565605, -0.031277451664209366, -0.02669050544500351, -0.03673567995429039, -0.031009923666715622, -0.03417716547846794, 0.026787128299474716, -0.03331909701228142, 0.027129393070936203, 0.038276176899671555, -0.024865901097655296, 0.029273567721247673, 0.0206189826130867, 0.043323080986738205, 0.0606401227414608, -0.012722579762339592, 0.03264662250876427, 0.02408941648900509, -0.0035203255247324705, -0.04439205676317215, 0.03455958142876625, 0.047627586871385574, 0.003026606049388647, -0.04430152103304863, 0.0007011545822024345, 0.014777960255742073, 0.02601800486445427, 0.04484550282359123, 0.010064581409096718, 0.01381581649184227, 0.016707206144928932, -0.023753641173243523, -0.0025901535991579294, 0.006856672465801239, -0.026723485440015793, 0.017801359295845032, -0.054450567811727524, -0.004783368669450283, -0.005175716709345579, -0.012118268758058548, -0.04036054387688637, -0.05895473062992096, -0.06077522784471512, 0.030481910333037376, 0.052831657230854034, 0.04473887383937836, 0.019681043922901154, 0.02376173809170723, 0.04358130693435669, 0.001411114470101893, -0.022507058456540108, 0.0015789323952049017, 0.08526745438575745, -0.002746624406427145, 0.03284447640180588, 0.02298818901181221, -0.016400931403040886, 0.015235977247357368, 0.0046881805174052715, 0.10934048146009445, 0.011275902390480042, -0.059580106288194656, 0.018955614417791367, 0.0031440467573702335, -0.04117386415600777, -0.006357456557452679, 0.0407729409635067, 0.009104394353926182, -0.06355530768632889, -0.02272142842411995, 0.006178423296660185, -0.0709076002240181, -0.016905957832932472, -0.011730081401765347, 0.011332439258694649, 0.07554817944765091, 0.011308779008686543, -0.01548523735255003, 0.004791894927620888, -0.001982983434572816, 0.024490658193826675, -0.05217067524790764, -0.008218967355787754, 0.02418280392885208, -0.01176756713539362, 0.03046286851167679, -0.02764713577926159, -0.000049177710025105625, 0.022876840084791183, -0.019931085407733917, 0.05068017542362213, -0.00353635405190289, -0.08747385442256927, -0.04441899433732033, -0.03227495774626732, 0.05313972011208534, 0.06821876764297485, -0.056395966559648514, 0.0008693215204402804, 0.05625884607434273, -0.09377181529998779, -0.02118649333715439, -0.017011160030961037, 0.012822176329791546, 0.024296846240758896, -0.036876995116472244, 0.029807619750499725, -0.025963041931390762, 0.016156518831849098, 0.007664654869586229, 0.023261243477463722, 0.029748471453785896, 0.0499785915017128, -0.01933254301548004, 0.024447845295071602, -0.0015585498185828328, 0.009915083646774292, 0.02686510980129242, 0.04578152298927307, -0.02523563988506794, 0.015560920350253582, -0.056227441877126694, 0.008187428116798401, 0.07103578001260757, -0.02633257955312729, -0.00134456274099648, -0.008053828030824661, -0.007904425263404846, -0.021084031090140343, 0.00155827053822577, 0.0013442442286759615, -0.024145647883415222, 0.07971974462270737, 0.001189221628010273, 0.047171760350465775, -0.029497798532247543, -0.043870676308870316, -0.01692158542573452, -0.01596604287624359, -0.01552968192845583, 0.058958299458026886, -0.008615768514573574, 0.008843005634844303, 0.07479845732450485, -0.07430415600538254, 0.015775416046380997, 0.03994685411453247, 0.011791680939495564, -0.0029018144123256207, 0.04188762232661247, -0.06116773188114166, 0.022874509915709496, -0.003022158285602927, 0.018157759681344032, -0.038941655308008194, 0.03251603618264198, -0.01709783263504505, 0.0006032419623807073, 0.04642338305711746, 0.009390133433043957, 0.0016939070774242282, 0.015942104160785675, 0.02813178300857544, -0.006752573419362307, 0.03822953999042511, -0.08440656960010529, -0.04916548728942871, -0.004353411495685577, 0.0027665437664836645, 0.006796947680413723, -0.014765503816306591, 0.027140550315380096, -0.07538647204637527, 0.021722838282585144, -0.005089207552373409, -0.02006431110203266, -0.0565999411046505, 0.032506637275218964, 0.02204863354563713, -0.0541226752102375, -0.020025404170155525, -0.02577173337340355, -0.03979847952723503, -0.005884014070034027, -0.0014105667360126972, -0.009672308340668678, 0.0317692831158638, 0.01481321919709444, -0.05848690867424011, -0.010333755984902382, 0.04613194242119789, 0.016450170427560806, 0.0410526841878891, -0.01595299504697323, -0.04248020052909851, 0.07379825413227081, -0.013042908161878586, -0.03354659676551819, -0.003254747949540615, -0.04341893270611763, 0.03780496492981911, -0.019106335937976837, -0.013321775943040848, -0.05905411019921303, -0.014134617522358894, 0.0010545048862695694, -0.033151593059301376, -0.01254863478243351, 0.07540681213140488, -0.01374184899032116, -0.018989864736795425, -0.0047133918851614, -0.010172822512686253, 0.00034003399196080863, 0.02717680297791958, 0.019237598404288292, -0.01615060865879059, -0.028629811480641365, -0.011143045499920845, -0.010875148698687553, 0.016731049865484238, 0.022932201623916626, -0.008372475393116474, 0.022635066881775856, -0.020382506772875786, 0.02756231650710106, -0.03398587554693222, -0.05861784890294075, 0.05172458291053772, -0.021922238171100616, -0.04774118587374687, -0.026777341961860657, -0.01627771183848381, 0.004454800859093666, 0.007959301583468914, 0.026747988536953926, 0.03290417417883873, -0.0060494025237858295, -0.04475928470492363, -0.0035624548327177763, -0.0037910155951976776, -0.018021106719970703, 0.021356582641601562, -0.034358806908130646, 0.02719097211956978, -0.04287409037351608, 0.032870836555957794, 0.01446565706282854, -0.006071083247661591, -0.011873772367835045, -0.04631178453564644, 0.05674360692501068, 0.009604956954717636, 0.016252193599939346, 0.024444153532385826, 0.01654619351029396, 0.02353854477405548, 0.020846104249358177, -0.08307021856307983, 0.03053014539182186, -0.00265615270473063, 0.020788835361599922, -0.023960085585713387, 0.036580462008714676, -0.0017251536482945085, -0.07136012613773346, -0.042341575026512146, 0.01437299232929945, 0.00397329218685627, 0.05199619010090828, -0.012866473756730556, 0.023706428706645966, -0.002771877683699131, 0.025082342326641083, -0.048069603741168976, -0.013400526717305183, 0.018418872728943825, 0.05939853936433792, 0.005282583646476269, -0.037457965314388275, 0.042530521750450134, 0.01875205896794796, 0.03439157456159592, -0.05393156409263611, 0.0051035149954259396, 0.022228766232728958, 0.016332797706127167, -0.07706432044506073, -0.029892385005950928, 0.015471142716705799, 0.01213875412940979, 0.012743503786623478, -0.01814502850174904, 0.021825363859534264, -0.006028466392308474, 0.03513217717409134, 0.03685316443443298, -0.0010952998418360949, -0.0172239001840353, -0.06439017504453659, -0.032811153680086136, -0.009150123223662376, -0.01236527319997549, 0.0341215543448925, -0.032928261905908585, 0.029081124812364578, 0.020594075322151184, -0.0038775368593633175, 0.0055763437412679195, 0.03785386681556702, 0.011820133775472641, 0.0073831956833601, 0.023480692878365517, -0.01643834263086319, 0.006668752525001764, 0.031078770756721497, -0.02614741399884224, 0.07737623155117035, 0.009288717061281204, 0.0516589991748333, 0.01963738724589348, -0.012708866037428379, -0.12333773076534271, 0.00559943588450551, -0.07658983767032623, -0.009959179908037186, 0.10650128871202469, -0.034956369549036026, -0.06005614623427391, -0.008214710280299187, 0.0075499676167964935, 0.026401793584227562, 0.12228865176439285, -0.007174175698310137, 0.030237602069973946, -0.021742621436715126, 0.010930142365396023, -0.0385998897254467, -0.003185408655554056, 0.012857307679951191, -0.019689876586198807, -0.04755872115492821, 0.01972372829914093, 0.004262501373887062, 0.00008299220644403249, 0.011074850335717201, 0.05460986867547035, 0.0029466005507856607, 0.0724634975194931, 0.06899171322584152, 0.06918184459209442, 0.05444711446762085, -0.042240507900714874, 0.010655615478754044, -0.007467586547136307, 0.006832166574895382, 0.003969853278249502, 0.08876814693212509, -0.0437786728143692, 0.03804933652281761, -0.030885396525263786, -0.03027726151049137, -0.04052275791764259, 0.010974228382110596, 0.007754061836749315, 0.012732075527310371, -0.01817065104842186, -0.011152416467666626, -0.049781568348407745, 0.013582209125161171, -0.06330755352973938, -0.053990088403224945, -0.030128182843327522, 0.00704912981018424, 0.0054987892508506775, 0.022107617929577827, -0.01457384042441845, -0.00953990314155817, 0.036588843911886215, -0.01774775981903076, -0.009842786006629467, -0.024347495287656784, -0.008752605877816677, 0.010104265995323658, -0.04264656454324722, -0.004387960769236088, -0.05292854458093643, 0.0010133832693099976, -0.018212705850601196, -0.009539034217596054, -0.05086176097393036, 0.024164259433746338, -0.05007746070623398, -0.015501351095736027, 0.026803696528077126, -0.0059448410756886005, -0.07043289393186569, -0.048008497804403305, 0.032061364501714706, 0.018019037321209908, -0.020161008462309837, -0.04647893086075783, -0.05396223068237305, -0.007255793549120426, 0.007885012775659561, -0.07896114885807037, -0.040006909519433975, 0.018829725682735443, -0.010703299194574356, 0.020794184878468513, -0.028855979442596436, -0.07605317234992981, -0.04852455481886864, -0.00022820408048573881, -0.006639386527240276, 0.02903519570827484, -0.02702140063047409, -0.0027994466945528984, -0.013989729806780815, -0.0032591172493994236, 0.024563834071159363, -0.03771605342626572, 0.017179133370518684, 0.07495152950286865, -0.020380431786179543, 0.000793002313002944, -0.0037576910108327866, 0.002225878881290555, 0.005306133069097996, 0.016404349356889725, 0.10117648541927338, 0.0058763474225997925, -0.008616740815341473, 0.027916505932807922, -0.02584514394402504, -0.030204981565475464, 0.05183211341500282, 0.020632149651646614, 0.008232444524765015, 0.022062664851546288, -0.015932714566588402, 0.05586407706141472, 0.010593490675091743, -0.03367600589990616, 0.025508809834718704, 0.01033356599509716, 0.01936080865561962, -0.011150223203003407, 0.009514466859400272, 0.0464782640337944, -0.017148273065686226, -0.007855571806430817, -0.0033156611025333405, 0.012155041098594666, 0.059404417872428894, -0.039682742208242416, -0.016656912863254547, -0.024354873225092888, 0.009712086990475655, -0.03162311762571335, -0.012841061688959599, 0.04183221608400345, 0.0010948999552056193, 0.025067677721381187, 0.016925429925322533, -0.05799465999007225, -0.0008475364302285016, 0.04791025072336197, -0.017317764461040497, 0.010109124705195427, -0.009955649264156818, -0.005163125228136778, 0.019495747983455658, 0.0065932003781199455, 0.020309967920184135, -0.0494198352098465, 0.0011435920605435967, -0.024890068918466568, 0.027483860030770302, -0.008129283785820007, 0.008367319591343403, -0.015176250599324703, 0.00007992295286385342, -0.008482008241117, 0.007927465252578259, -0.009742657653987408, 0.022409185767173767, 0.09101183712482452, -0.03371116518974304, -0.09273366630077362, -0.000565677706617862, -0.030900420621037483, 0.033853668719530106, -0.03285682201385498, -0.05100230127573013, 0.053725019097328186, -0.005863645579665899, 0.041848890483379364, 0.007915311492979527, 0.023700004443526268, 0.05681880563497543, 0.004262986592948437, -0.005611700937151909, -0.0053581059910357, 0.01910000666975975, 0.03277230262756348, 0.01695930026471615, -0.04789350926876068, -0.05071037635207176, 0.07248344272375107, 0.0014313822612166405, 0.016551921144127846, -0.019988084211945534, 0.0777776762843132, -0.022976722568273544, -0.03738747909665108, -0.04467233270406723, 0.017251428216695786, -0.00030823907582089305, 0.02861839346587658, -0.041353292763233185, 0.0024379873648285866, 0.006368794944137335, -0.014831053093075752, 0.031644538044929504, 0.005090384278446436, 0.04949574917554855, 0.012214087881147861, -0.03437293320894241, -0.020795930176973343, -0.0598788857460022, 0.0010209231404587626, -0.05704091861844063, 0.03754844516515732, 0.014830633997917175, -0.027156297117471695, -0.02861434780061245, 0.028328051790595055, -0.019515184685587883, -0.040268633514642715, 0.019329985603690147, 0.05023274943232536, -0.02686360664665699, 0.04343567416071892, 0.03876706212759018, -0.006746069062501192, 0.017046641558408737, -0.06017739698290825, 0.011890895664691925, 0.046033039689064026, -0.03174948692321777, -0.03469559922814369, 0.006564183160662651, 0.023348791524767876, -0.02369685098528862, -0.024705059826374054, 0.003026070771738887, 0.007324088364839554, -0.04575107991695404, 0.014770359732210636, -0.08997560292482376, 0.07200193405151367, 0.002130309585481882, 0.04188697412610054, -0.012662512250244617, 0.0012403471628203988, 0.014288094826042652, -0.014030163176357746, -0.04817117750644684, 0.021816207095980644, 0.050027646124362946, -0.0003125045623164624, -0.07658247649669647, 0.0017589488998055458, 0.058255016803741455, -0.0014439680380746722, 0.060650527477264404, 0.03336341306567192, -0.05316903814673424, 0.02304205484688282, 0.05099447816610336, -0.005556766875088215, 0.04007361829280853, -0.06787034124135971, 0.031685736030340195, -0.022984933108091354, -0.04851613938808441, -0.06641397625207901, 0.022911028936505318, -0.003400725545361638, -0.015585945919156075, -0.01884823851287365, 0.04554104432463646, -0.03872069716453552, -0.04478705674409866, -0.017249947413802147, -0.06941728293895721, 0.025753339752554893, -0.014161575585603714, 0.0021869654301553965, 0.06043282523751259, -0.013719399459660053, 0.0024719913490116596, -0.014751073904335499, -0.058763179928064346, 0.009487831965088844, -0.0028269209433346987, -0.000852961849886924, -0.0508636049926281, 0.11929744482040405, -0.017752911895513535, -0.03392605483531952, -0.033167529851198196, 0.05554819852113724, -0.011049014516174793, -0.01153994258493185, -0.0023191520012915134, 0.010694943368434906, -0.02128906361758709, -0.01764216460287571, 0.04978298768401146, -0.023435933515429497, -0.02866181917488575, 0.00132721196860075, 0.005672002211213112, -0.01793261058628559, 0.014884775504469872, 0.019369352608919144, 0.025875158607959747, 0.04419439658522606, 0.027831729501485825, 0.02784387581050396, 0.025136929005384445, 0.023802094161510468, 0.04472525045275688, -0.030114728957414627, -0.04649076983332634, 0.022420307621359825, -0.005343311931937933, 0.008149093016982079, -0.08545521646738052, -0.00959205161780119, 0.04558313265442848, -0.04837087541818619, 0.02120138891041279, -0.047898005694150925, -0.034566085785627365, -0.04722191020846367, -0.006459683179855347, -0.08663078397512436, 0.004754119087010622, -0.006081676576286554, 0.06996040046215057, 0.015226603485643864, 0.001126796123571694, 0.015653859823942184, -0.0287094134837389, -0.025965923443436623, -0.0483909510076046, 0.03621916100382805, 0.004296039696782827, -0.008180789649486542, 0.0287708081305027, -0.010837683454155922, -0.026592334732413292, -0.025525476783514023, -0.03093932569026947, -0.004015117883682251, -0.01774856075644493, -0.03134738653898239, -0.0006377467652782798, -0.004419253207743168, 0.046300776302814484, 0.01738799549639225, -0.0175396129488945, 0.04289931431412697, -0.017682677134871483, 0.06176634132862091, 0.049497656524181366, -0.046354036778211594, 0.017081454396247864, 0.03849327564239502, 0.031039796769618988, 0.06186605244874954, 0.026437951251864433, -0.008706961758434772, -0.026723070070147514, 0.027545494958758354, -0.017820850014686584, -0.03405546769499779, -0.029637182131409645, 0.003861223114654422 ]
<p>In a lecture (<a href="http://teorica.fis.ucm.es/TAE2012/CHARLAS.DIR/MEISSNER.DIR/part2.pdf" rel="nofollow">look</a> at the chapter "The fermion determinant in a constant field", p. 5) I found some strange transformation, which is given by eq. 18. How to prove it? Exactly, I don't understand the appearance of some crossed symbols, especially in denominator.</p>
g5378
[ 0.011224672198295593, 0.02784258872270584, 0.0029152589850127697, -0.08939146995544434, 0.0757802426815033, 0.010007712990045547, 0.033107902854681015, 0.046486884355545044, -0.001078138593584299, -0.05657612532377243, -0.0936361625790596, 0.05064576491713524, -0.0003229006542824209, -0.0031312485225498676, 0.009312983602285385, 0.002042139647528529, 0.04525367170572281, -0.010052314028143883, 0.015399784781038761, -0.016477791592478752, 0.007688022684305906, 0.03447214141488075, 0.001812920905649662, -0.0383189432322979, 0.08271550387144089, -0.046975813806056976, 0.03835420310497284, 0.058890946209430695, -0.019142193719744682, -0.023309804499149323, 0.07635828107595444, 0.025015655905008316, 0.05717785656452179, -0.01334217470139265, 0.05481882765889168, -0.02860180474817753, 0.08707457780838013, 0.06332790106534958, 0.05028257519006729, 0.04299072548747063, -0.031280767172575, 0.043750450015068054, -0.032463718205690384, 0.028593536466360092, 0.0014081797562539577, 0.03261012211441994, -0.019518859684467316, 0.06498152017593384, -0.0018446638714522123, -0.00033570051891729236, -0.028169898316264153, -0.0016348741482943296, 0.05422946438193321, -0.04047828167676926, 0.010554059408605099, 0.005210706498473883, 0.01225760206580162, -0.004616722464561462, 0.02886408194899559, 0.016132008284330368, -0.01894964836537838, -0.07788790017366409, 0.062208231538534164, -0.025020210072398186, 0.05715181306004524, -0.03866158425807953, 0.013610130175948143, 0.04619365930557251, -0.07433007657527924, -0.009512847289443016, -0.02906242199242115, -0.03886498883366585, 0.025289474055171013, -0.029743697494268417, -0.006252001039683819, 0.047640539705753326, 0.016718605533242226, 0.027281837537884712, 0.005710842553526163, -0.06481041759252548, 0.011289073154330254, -0.04277502000331879, 0.0048813545145094395, 0.0028489853721112013, 0.025733524933457375, -0.01066670659929514, 0.010029722936451435, -0.014461593702435493, -0.0502442792057991, -0.016965489834547043, -0.04559490829706192, -0.03210507705807686, 0.020976699888706207, 0.018736010417342186, -0.007180933840572834, -0.048044897615909576, 0.003977871499955654, 0.02221912331879139, -0.025105025619268417, -0.057081438601017, 0.005613426677882671, 0.027311604470014572, 0.012067548930644989, 0.007952648214995861, -0.022671153768897057, -0.011288252659142017, 0.03592953830957413, -0.026543544605374336, -0.009851230308413506, -0.02485358528792858, -0.023012790828943253, -0.030978664755821228, -0.011722047813236713, -0.07114249467849731, 0.022869430482387543, 0.02029847539961338, 0.028634194284677505, 0.019083276391029358, -0.02511121891438961, -0.00754886120557785, 0.00556295458227396, 0.004650402814149857, 0.029931772500276566, 0.011736330576241016, -0.011595095507800579, -0.05633668974041939, 0.010265868157148361, 0.00618468364700675, 0.03843759745359421, -0.0019963113591074944, 0.02159217558801174, 0.010064249858260155, 0.023264454677700996, 0.031220754608511925, -0.00631273677572608, 0.022773075848817825, 0.02614257112145424, 0.02271478995680809, -0.040137629956007004, -0.0016575435874983668, 0.011899215169250965, 0.005852106958627701, 0.04891646280884743, -0.01946398988366127, -0.021814018487930298, -0.06720244884490967, 0.020759306848049164, -0.06254000216722488, 0.0621805414557457, -0.03988462686538696, 0.02081329934298992, 0.05046708881855011, -0.043388381600379944, 0.013195516541600227, -0.02550118789076805, -0.0026141719426959753, 0.02437378466129303, -0.022630035877227783, -0.005488209892064333, 0.051854826509952545, 0.032397206872701645, -0.05595366656780243, -0.0977289155125618, 0.0077736275270581245, -0.00865031499415636, 0.012042490765452385, 0.009830279275774956, -0.03823060542345047, -0.010720902122557163, -0.0037886619102209806, -0.06662806868553162, 0.04138428345322609, -0.008617585524916649, 0.027149202302098274, -0.0006262924871407449, 0.022281968966126442, -0.03082495555281639, -0.03116406686604023, 0.024857154116034508, -0.006036654114723206, -0.03219807520508766, 0.008804220706224442, 0.06080438941717148, 0.03945450112223625, 0.020066095516085625, -0.02728165127336979, -0.0436246395111084, 0.042418017983436584, -0.010048149153590202, 0.00697060814127326, 0.04633938893675804, -0.0029807041864842176, -0.0169683787971735, 0.06173844262957573, 0.028462804853916168, -0.02424110658466816, 0.05394739285111427, -0.05263102799654007, -0.03272072598338127, -0.04663750156760216, -0.0008290546829812229, 0.02304546907544136, 0.021647755056619644, 0.011569199152290821, -0.00044744357001036406, 0.008668242022395134, -0.039589133113622665, -0.018683213740587234, 0.011776248924434185, -0.013060997240245342, -0.00010166831634705886, -0.013207347132265568, 0.005720668472349644, 0.022637788206338882, -0.003013228066265583, 0.030273139476776123, -0.004940081853419542, -0.05183403939008713, -0.01245637983083725, 0.0729689672589302, -0.0021170680411159992, -0.016910238191485405, 0.030250390991568565, 0.030178047716617584, -0.007590285502374172, 0.06136923283338547, -0.007316549774259329, -0.019610829651355743, -0.00794643722474575, -0.03755246847867966, -0.05392127111554146, -0.0002033639175351709, 0.008017022162675858, -0.03615528345108032, -0.008344823494553566, 0.010486654937267303, 0.02747630700469017, 0.04628957062959671, 0.025595733895897865, 0.10521586239337921, 0.014303200878202915, -0.03139626979827881, -0.03719092905521393, -0.017589900642633438, 0.03306640312075615, 0.0021036898251622915, 0.04554057866334915, 0.006818088702857494, 0.01118868961930275, 0.015336780808866024, 0.022022806107997894, -0.030269352719187737, -0.03133093938231468, 0.05181801691651344, -0.057323575019836426, -0.002105183433741331, -0.003534062532708049, 0.08984626084566116, 0.007827200926840305, -0.020427487790584564, -0.03465475142002106, -0.049452006816864014, 0.008159919641911983, 0.035558320581912994, -0.04817858338356018, -0.021338781341910362, -0.036573514342308044, 0.029795631766319275, -0.018605651333928108, -0.0005075162625871599, -0.08278355002403259, 0.059262920171022415, 0.035395022481679916, 0.013415713794529438, -0.081061452627182, -0.06318870931863785, -0.013479955494403839, -0.030061790719628334, 0.02854417823255062, -0.0037711833138018847, 0.012598047964274883, 0.038530413061380386, -0.010593317449092865, 0.06673452258110046, 0.05505768582224846, 0.014047868549823761, -0.05130711942911148, -0.009363172575831413, -0.02006540074944496, 0.05135488137602806, 0.007943150587379932, -0.03376970812678337, -0.02130904234945774, 0.01958853006362915, -0.0225061122328043, -0.03635402396321297, 0.04908958449959755, -0.008619643747806549, -0.006722186226397753, 0.040872108191251755, 0.009427705779671669, -0.04637560993432999, -0.021944308653473854, 0.03274202346801758, 0.07359903305768967, -0.05191728100180626, -0.01997317373752594, -0.05786876752972603, -0.030994491651654243, -0.029613163322210312, -0.018999869003891945, -0.0009775040671229362, -0.02670459635555744, 0.012394209392368793, -0.039854489266872406, 0.023233385756611824, -0.029614590108394623, 0.010903710499405861, 0.025370677933096886, -0.030650153756141663, 0.012540976516902447, -0.010984049178659916, 0.01639818400144577, -0.006780900061130524, 0.052095480263233185, -0.049360789358615875, -0.028863709419965744, 0.042160388082265854, -0.06540515273809433, -0.05181426554918289, -0.011662391945719719, 0.021195458248257637, -0.0594332180917263, -0.06163646653294563, -0.02883228473365307, 0.021551238372921944, 0.007640559691935778, 0.06042471155524254, 0.0366646982729435, -0.05902150645852089, -0.022735409438610077, 0.023717492818832397, -0.10374245792627335, 0.026954999193549156, 0.038780298084020615, -0.03230573982000351, -0.018345454707741737, -0.03558550402522087, 0.03240067884325981, 0.03911925479769707, -0.036224208772182465, -0.020007478073239326, 0.06633338332176208, 0.0206218920648098, -0.013294809497892857, 0.005146839655935764, 0.008541417308151722, -0.0035411410499364138, 0.01425799448043108, -0.007901174016296864, 0.04142327979207039, 0.0016413655830547214, 0.02026061713695526, -0.02056480571627617, -0.009059680625796318, 0.01190891768783331, -0.04180331155657768, 0.06456809490919113, 0.07838719338178635, 0.005359889008104801, -0.005565381608903408, -0.01619904860854149, -0.024128034710884094, 0.03791828453540802, -0.023777689784765244, -0.005161612760275602, -0.00028714933432638645, 0.022604547441005707, -0.05462472140789032, -0.005721096880733967, 0.045641958713531494, 0.03331805393099785, 0.012821940705180168, 0.04345640912652016, 0.051797907799482346, 0.04576492682099342, -0.026829129084944725, -0.007415060885250568, 0.04123888909816742, 0.007704074028879404, 0.04967884719371796, 0.0728660300374031, 0.028208669275045395, 0.02362091839313507, -0.0632094219326973, 0.03076285310089588, 0.007933950051665306, -0.0005865987623110414, -0.002183647360652685, 0.009319906122982502, -0.0015964761842042208, -0.020798776298761368, -0.033658336848020554, -0.06319007277488708, -0.035085227340459824, -0.04566861689090729, 0.05567626282572746, 0.003590456210076809, 0.013073582202196121, -0.07045461982488632, -0.032214000821113586, 0.060769278556108475, -0.020065270364284515, -0.04743117839097977, -0.008380070328712463, 0.01282088365405798, 0.006792024709284306, -0.02982845902442932, 0.0019725917372852564, -0.06850182265043259, -0.0029467428103089333, 0.0377756729722023, -0.0034501482732594013, 0.009763926267623901, 0.0435500368475914, 0.045732975006103516, 0.008320997469127178, 0.06266295164823532, -0.0549975149333477, -0.0377732515335083, -0.023158328607678413, 0.045863330364227295, -0.04471432790160179, 0.06322120875120163, -0.045659344643354416, 0.057934995740652084, -0.08389818668365479, 0.029632210731506348, 0.019585317000746727, 0.04276434704661369, 0.03364681825041771, -0.019740324467420578, 0.0009448247728869319, -0.019487570971250534, -0.04484077915549278, 0.020697912201285362, -0.04418136551976204, 0.002117516240105033, -0.00809017475694418, -0.050209932029247284, -0.023299504071474075, 0.02986152097582817, 0.0011144416639581323, 0.012340754270553589, -0.0080722039565444, -0.09176792204380035, -0.05990325286984444, 0.0032294655684381723, -0.0005608575884252787, 0.04270989075303078, -0.06804542988538742, -0.04744485765695572, 0.011601016856729984, 0.010546098463237286, 0.03674605116248131, 0.06173517554998398, -0.03588541969656944, -0.0208484698086977, 0.030493706464767456, -0.020895689725875854, 0.009171941317617893, -0.0033671814016997814, -0.01374977920204401, -0.05530228838324547, -0.023265119642019272, 0.01389875914901495, -0.017772100865840912, 0.012240356765687466, -0.02078566700220108, -0.03154435008764267, -0.006102709099650383, -0.045552924275398254, 0.0005858009681105614, -0.006567075382918119, -0.02524684928357601, 0.07063566893339157, -0.014364078640937805, 0.020003903657197952, 0.01252206414937973, -0.03695274889469147, 0.009977915324270725, -0.0049090199172496796, 0.06653521955013275, -0.005355524830520153, -0.0044993325136601925, 0.017227236181497574, 0.018094656988978386, -0.0010092727607116103, 0.06288886815309525, -0.014452056027948856, -0.03914426267147064, 0.029164036735892296, -0.004856659099459648, 0.05740291252732277, -0.01924460381269455, 0.04921090230345726, 0.08322437107563019, -0.018017444759607315, 0.0017981412820518017, 0.01864795945584774, 0.030259771272540092, -0.03353451192378998, 0.013669650070369244, -0.01883302628993988, -0.007045647595077753, 0.023776531219482422, -0.041993264108896255, -0.056129537522792816, -0.020250927656888962, -0.04066896438598633, 0.016712060198187828, 0.06399030983448029, 0.001550258370116353, -0.06527918577194214, 0.036870185285806656, -0.026608243584632874, -0.010846356861293316, -0.05614788457751274, -0.03790508210659027, 0.016107121482491493, 0.07597988843917847, -0.0008388333371840417, -0.03847012296319008, 0.015547284856438637, 0.014903509989380836, -0.016428956761956215, 0.0031722451094537973, -0.0024107052013278008, -0.02076755091547966, -0.002912579569965601, 0.05413125455379486, -0.0486111156642437, -0.011224797926843166, -0.030628016218543053, -0.03408697992563248, -0.033227358013391495, 0.0015697783092036843, 0.02008892595767975, 0.03683394566178322, -0.03174714371562004, 0.012480702251195908, 0.0019206850556656718, 0.018976634368300438, -0.026829896494746208, 0.051892489194869995, 0.0021075194235891104, -0.025230295956134796, 0.01813756301999092, -0.038766879588365555, -0.010214699432253838, 0.04596694931387901, 0.032563429325819016, 0.04241296276450157, 0.002017793245613575, 0.0021043214946985245, 0.0042765261605381966, -0.02030624821782112, 0.034673165529966354, 0.03003743290901184, 0.03470766544342041, 0.06956199556589127, 0.03717515617609024, 0.006999250501394272, 0.015574539080262184, -0.02884778194129467, 0.028203878551721573, -0.025065138936042786, -0.027008499950170517, 0.010754385031759739, -0.03182722255587578, 0.04273882135748863, -0.0404256209731102, -0.03161114454269409, -0.07610079646110535, -0.05400605872273445, 0.04284873232245445, -0.05045492574572563, -0.014102946035563946, 0.005967643577605486, -0.015267416834831238, -0.07896047830581665, 0.005364856217056513, -0.01608463190495968, 0.03220834583044052, 0.017985792830586433, -0.05381336435675621, -0.048256274312734604, -0.0006351644988171756, -0.03125079348683357, -0.027066344395279884, 0.01658623106777668, -0.009334897622466087, 0.03889406472444534, 0.016966329887509346, 0.04564882069826126, 0.08133987337350845, 0.0389404371380806, 0.03338542580604553, -0.03406192734837532, -0.04193982109427452, 0.024462928995490074, -0.04218553379178047, -0.09729404002428055, 0.025429490953683853, -0.023926878347992897, -0.049143437296152115, -0.061321742832660675, 0.031856656074523926, -0.04017890617251396, 0.00520728062838316, 0.04890380799770355, -0.01816314086318016, -0.015896840021014214, -0.07011282444000244, 0.011170116253197193, 0.0677112489938736, -0.021084845066070557, -0.0018121348693966866, 0.10737558454275131, -0.010284568183124065, -0.02070239745080471, 0.0343109630048275, 0.03766794130206108, -0.01704512909054756, -0.02310130000114441, 0.019869361072778702, -0.052829157561063766, 0.10306300967931747, 0.026771550998091698, 0.047415077686309814, -0.019568078219890594, 0.021269574761390686, 0.02900116890668869, 0.003152844961732626, 0.026616279035806656, 0.038524191826581955, 0.03772894665598869, 0.006647907663136721, -0.023428885266184807, -0.017121270298957825, 0.039506785571575165, 0.03196129575371742, -0.04555618762969971, 0.037606626749038696, -0.028350023552775383, -0.02724095620214939, 0.04075713828206062, 0.030552050098776817, -0.020067553967237473, -0.05297572538256645, -0.05202416330575943, -0.002975488780066371, -0.040068529546260834, -0.007224659901112318, 0.04518543556332588, -0.000961644109338522, -0.04166088253259659, 0.003917036112397909, 0.0719495490193367, -0.026193806901574135, -0.03572063520550728, -0.06421784311532974, 0.0020610720384866, -0.023333024233579636, 0.0012778171803802252, 0.04192553088068962, -0.020733902230858803, 0.07912817597389221, 0.007743652909994125, -0.04514781013131142, -0.039195772260427475, -0.0030319588258862495, -0.007316094357520342, -0.02662290446460247, -0.012243873439729214, 0.009573686867952347, -0.025447113439440727, 0.0130614647641778, -0.00016868184320628643, 0.021675582975149155, 0.033757589757442474, -0.06117546185851097, 0.03451881930232048, -0.0038894996978342533, -0.0003101194743067026, -0.013003535568714142, 0.000590001349337399, -0.0020568722393363714, -0.0000410104330512695, -0.0023493673652410507, 0.02864805981516838, 0.03410409390926361, -0.024072691798210144, 0.0626276433467865, -0.022253284230828285, -0.005179919768124819, 0.001977659296244383, -0.0173996239900589, -0.05252467840909958, 0.004109272267669439, 0.002869636518880725, -0.04669729992747307, -0.018690327182412148, -0.0010276796529069543, 0.011405347846448421, 0.04770062491297722, 0.01751948520541191, 0.027231229469180107, -0.004356842953711748, -0.02177169732749462, -0.024029763415455818, 0.004047584254294634, -0.039887767285108566, 0.0012099810410290956, -0.10265115648508072, -0.004916052334010601, 0.011617087759077549, 0.07419560104608536, 0.004769445396959782, 0.055255670100450516, -0.006254084873944521, -0.019474932923913002, -0.07314977049827576, -0.0027640738990157843, -0.05798766016960144, 0.020302532240748405, -0.01236574724316597, -0.07155148684978485, -0.021149136126041412, 0.01005502324551344, -0.0008441602694801986, -0.02587103471159935, -0.0086869141086936, 0.014849231578409672, -0.013010654598474503, -0.03565533459186554, -0.04357435181736946, 0.044479552656412125, -0.0040635294280946255, -0.015169116668403149, -0.02070029452443123, -0.036727674305438995, -0.031731780618429184, 0.0736958459019661, 0.06168484687805176, -0.008966467343270779, -0.021001547574996948, 0.03995215520262718, 0.0413019172847271, 0.0387544259428978, -0.030248768627643585, 0.012347843497991562, -0.020853647962212563, 0.09620992094278336, -0.01700028032064438, 0.024883514270186424, -0.040403254330158234, 0.0373595766723156 ]
<p>If I had a static thin (a few mm) film of water lying on a surface and I tried to push a squeegee across the surface in order to move the water. Would the water rise up in front of the squeegee? Would the angle be possible to calculate if the speed were to increase and or the force of gravity were to increase?</p>
g5379
[ 0.01567828096449375, 0.048849523067474365, 0.010285835713148117, 0.017785094678401947, -0.012210597284138203, 0.03692105785012245, 0.011547946371138096, 0.02824179269373417, -0.059702496975660324, -0.0002994622918777168, 0.018090033903717995, 0.002700262004509568, -0.0020629556383937597, 0.02789241261780262, -0.015499650500714779, 0.029895421117544174, 0.010516421869397163, -0.06462894380092621, -0.035388968884944916, 0.0323038250207901, 0.033496055752038956, -0.01680406741797924, -0.005903294309973717, 0.0006984036299400032, -0.006628807168453932, -0.011978350579738617, 0.006704481318593025, -0.0037238402292132378, -0.057031773030757904, 0.003616298083215952, -0.00351178040727973, 0.01844138093292713, -0.01529747899621725, 0.0034323728177696466, -0.040929943323135376, -0.01993386447429657, -0.011332233436405659, -0.016592402011156082, 0.04223908856511116, -0.047746870666742325, -0.01253035943955183, -0.03392689302563667, -0.02476564794778824, 0.008447597734630108, -0.019796214997768402, -0.03684861212968826, 0.015711989253759384, -0.030817897990345955, -0.043554749339818954, -0.03980883210897446, -0.052469607442617416, -0.036049433052539825, 0.00032818817999213934, -0.00206704530864954, -0.025831615552306175, 0.031230753287672997, 0.021439673379063606, -0.01546973455697298, 0.04437214881181717, 0.04376409575343132, -0.07720565795898438, -0.01574406772851944, 0.03907524049282074, -0.05113347992300987, 0.05631396919488907, 0.043070413172245026, 0.05173484981060028, -0.028595367446541786, -0.014176084659993649, 0.022880321368575096, -0.018122348934412003, -0.040920063853263855, 0.006054323632270098, -0.00048039760440588, -0.02609100565314293, 0.017988599836826324, -0.027618104591965675, -0.005388721823692322, -0.04148941859602928, -0.03362152725458145, -0.016009250655770302, 0.03855850547552109, -0.0026612880174070597, -0.04275761544704437, 0.015164948999881744, -0.02220580354332924, 0.026563391089439392, 0.02190706878900528, -0.01402487326413393, -0.0009353546192869544, -0.03800542652606964, -0.00003725864735315554, 0.02903684787452221, 0.041708022356033325, -0.021393775939941406, -0.07594934105873108, -0.019398069009184837, 0.03527028113603592, -0.000785654119681567, 0.03102925978600979, -0.07252653688192368, -0.02954365313053131, 0.11725916713476181, -0.022870568558573723, -0.019032398238778114, 0.025812286883592606, 0.00043172130244784057, 0.044423673301935196, 0.049341779202222824, -0.06783472001552582, 0.05765661224722862, -0.04930812120437622, 0.009122656658291817, 0.0015937841963022947, 0.030113646760582924, -0.0395105704665184, 0.03379363566637039, 0.01556085143238306, 0.022820062935352325, 0.04329153522849083, -0.003088288474828005, 0.037009067833423615, 0.00045008474262431264, 0.08843042701482773, 0.047352418303489685, -0.016621485352516174, -0.03279181942343712, 0.012492538429796696, 0.006613429170101881, 0.012355483137071133, -0.0054450505413115025, 0.00986017007380724, -0.014372928068041801, -0.002513875486329198, 0.010650750249624252, 0.03439515456557274, -0.052147477865219116, 0.023673245683312416, -0.002716825343668461, -0.03435220196843147, 0.05636113882064819, -0.030749917030334473, 0.005324089899659157, 0.005152427591383457, 0.03746955841779709, -0.021118253469467163, 0.0086461640894413, 0.05858868733048439, 0.012751061469316483, -0.02938203327357769, -0.0065977731719613075, 0.02691546641290188, 0.002542132046073675, -0.03396787494421005, 0.05477984994649887, 0.01817282661795616, 0.007888168096542358, 0.03829841688275337, 0.033382169902324677, -0.05668042600154877, 0.08835193514823914, -0.04398336634039879, 0.05131754279136658, 0.008802192285656929, -0.04400208964943886, 0.0515715517103672, -0.00562407448887825, -0.013688668608665466, -0.0032372770365327597, 0.009420394897460938, -0.021624818444252014, -0.008470618166029453, -0.014193662442266941, 0.03632418066263199, -0.024987446144223213, 0.043226391077041626, 0.06304489076137543, -0.036379896104335785, 0.02764817886054516, 0.006273643113672733, -0.007476613856852055, 0.009378938935697079, 0.021251197904348373, -0.022770298644900322, -0.011190839111804962, -0.03464170917868614, 0.05649485066533089, -0.04363640770316124, -0.0907100960612297, -0.02633967623114586, -0.017222896218299866, -0.028228001669049263, -0.026574717834591866, 0.0625336542725563, -0.026399273425340652, -0.046117089688777924, 0.035163749009370804, 0.017881037667393684, 0.042197082191705704, -0.004732235334813595, -0.015437462367117405, 0.03806858882308006, 0.016762439161539078, -0.0035465634427964687, -0.0069878618232905865, -0.0033707749098539352, 0.027653798460960388, -0.02797766961157322, 0.02085302583873272, -0.00375923328101635, 0.021789999678730965, 0.06393776088953018, -0.04006179794669151, -0.012264375574886799, -0.012544378638267517, 0.04841323569417, -0.01655217818915844, -0.02106567472219467, 0.006481310818344355, -0.01668320782482624, 0.0014930504839867353, -0.016940969973802567, -0.02318376861512661, 0.046244293451309204, -0.029900237917900085, -0.05596857890486717, -0.02046150714159012, 0.009502480737864971, -0.04019210487604141, 0.02440207451581955, 0.04071035608649254, -0.002441810443997383, 0.004094959702342749, -0.020671356469392776, 0.0251653790473938, 0.025180388242006302, -0.00862920843064785, 0.04086257144808769, 0.028590241447091103, -0.028514984995126724, 0.017414884641766548, 0.018319765105843544, -0.037763915956020355, -0.04440591111779213, 0.04248872026801109, 0.0065234205685555935, 0.032613612711429596, 0.0011328129330649972, 0.0649987980723381, 0.10019224137067795, 0.04096672311425209, -0.08876501768827438, -0.04643802344799042, 0.054595161229372025, -0.01611434482038021, 0.010876963846385479, -0.042476192116737366, 0.03753542900085449, -0.046254947781562805, 0.05490514263510704, -0.015070514753460884, -0.002627325477078557, -0.04996723309159279, 0.03667016327381134, -0.03778093680739403, 0.024996355175971985, -0.10270679742097855, 0.020975761115550995, 0.03302183002233505, 0.03639816492795944, -0.03007636032998562, 0.025303078815340996, -0.006178463809192181, 0.07281975448131561, -0.057644322514534, -0.05973226577043533, 0.07463967055082321, 0.003972120117396116, -0.0016387056093662977, -0.01116938330233097, -0.03440139815211296, 0.014440723694860935, -0.05251430720090866, 0.04223152995109558, 0.03475283086299896, -0.01480085588991642, 0.04060877487063408, -0.02329188399016857, -0.04441621154546738, 0.023893196135759354, 0.0032652514055371284, 0.014607785269618034, 0.005123191047459841, 0.03501002863049507, 0.012216521427035332, 0.05547875538468361, 0.018570277839899063, -0.030331861227750778, 0.008044774644076824, 0.016733020544052124, -0.04571346938610077, 0.01331746019423008, -0.011484304443001747, -0.0005186074995435774, -0.022946462035179138, -0.016754521057009697, 0.007696443237364292, -0.018346108496189117, -0.003512541763484478, 0.0010343899484723806, -0.04066145047545433, 0.046141017228364944, -0.018170086666941643, -0.007735760882496834, -0.04834391549229622, -0.01826830767095089, 0.03853568062186241, -0.0006328665767796338, -0.018450988456606865, 0.01631423458456993, -0.007733088918030262, -0.01911710388958454, -0.06634388118982315, -0.006927279755473137, -0.007227192632853985, 0.055426616221666336, 0.010507686994969845, 0.0410233773291111, -0.04833998903632164, -0.016331130638718605, 0.025026552379131317, 0.011843756772577763, -0.0377371646463871, -0.0613870844244957, 0.026779241859912872, 0.00567095959559083, 0.03919493407011032, 0.024073734879493713, 0.032587602734565735, 0.07450324296951294, -0.01286837924271822, -0.0066030193120241165, -0.04995645955204964, -0.009885262697935104, -0.06850213557481766, 0.04276684671640396, 0.0054424479603767395, -0.018869711086153984, -0.04457060992717743, -0.016992224380373955, 0.05019175261259079, -0.01156549621373415, 0.004202275071293116, -0.017816925421357155, -0.010654467158019543, -0.01882319338619709, 0.011516871862113476, 0.03314417228102684, -0.038072504103183746, -0.043684136122465134, 0.01962120272219181, 0.03231346234679222, -0.04077765345573425, -0.01747106947004795, -0.031059779226779938, 0.007839365862309933, -0.032396893948316574, 0.0652298629283905, -0.0773603618144989, 0.003190406830981374, -0.0003715768689289689, -0.03330497816205025, -0.03503928333520889, 0.05081325024366379, -0.013209429569542408, 0.01945299655199051, 0.01029252726584673, -0.05078570917248726, -0.01781058870255947, -0.0005600762669928372, 0.08498354256153107, 0.043324436992406845, -0.006684354972094297, 0.038269080221652985, -0.06066663935780525, 0.04000375047326088, -0.05242031067609787, -0.0014819670468568802, 0.07538797706365585, -0.022639548406004906, -0.006294766440987587, -0.06425755470991135, -0.036835867911577225, 0.0044447286054492, -0.024556266143918037, -0.01393947284668684, 0.02183011919260025, 0.00240051606670022, -0.04321209341287613, -0.003055758774280548, 0.03217724710702896, 0.031571559607982635, -0.032209161669015884, 0.06763504445552826, -0.06339123100042343, -0.019172048196196556, 0.09550835192203522, -0.02899320423603058, -0.05583905428647995, -0.02436280995607376, 0.0010774346301332116, -0.07379606366157532, -0.014733907766640186, -0.07918333262205124, 0.00204502884298563, 0.011919365264475346, -0.007209716830402613, 0.038323987275362015, -0.028276152908802032, -0.0016669241013005376, 0.015370138920843601, 0.055195245891809464, 0.04599522426724434, 0.017852511256933212, -0.03088737092912197, 0.03607708588242531, -0.0023026918061077595, -0.0547451376914978, 0.02781662344932556, -0.0850972831249237, -0.03537553921341896, 0.034081291407346725, -0.01744048483669758, 0.0745442658662796, -0.008024563081562519, 0.06534349173307419, 0.023905297741293907, -0.01241611409932375, -0.020440315827727318, -0.004440531134605408, 0.0137417521327734, 0.051047515124082565, -0.019156059250235558, 0.007140780799090862, 0.034852638840675354, 0.09960217773914337, -0.02760946936905384, -0.00018768463633023202, -0.01243885513395071, 0.007834773510694504, -0.08744428306818008, 0.020141584798693657, -0.0001187963061966002, -0.0015710137085989118, 0.002482422860339284, -0.02162381075322628, -0.062494367361068726, -0.009080386720597744, -0.011555993929505348, 0.03110131248831749, 0.0028517297469079494, 0.04741142690181732, 0.009147541597485542, 0.043356142938137054, 0.02979142777621746, -0.026602456346154213, 0.022065026685595512, -0.042735807597637177, -0.0253287386149168, 0.029347768053412437, 0.01619032584130764, 0.028278155252337456, 0.0532810278236866, 0.06046408414840698, -0.032818179577589035, 0.00964124221354723, 0.019085198640823364, 0.010573949664831161, 0.013989381492137909, -0.01538938656449318, -0.021353937685489655, 0.06935707479715347, -0.0033604754135012627, 0.016211610287427902, -0.025186043232679367, -0.031091030687093735, -0.06076430156826973, 0.06822334229946136, 0.018679112195968628, -0.02663908153772354, 0.03418978676199913, -0.023073391988873482, 0.009772691875696182, -0.009030645713210106, -0.06413988023996353, 0.06479350477457047, 0.006852557882666588, 0.016183217987418175, 0.006111393682658672, 0.0025273971259593964, -0.012596438638865948, 0.04277785122394562, 0.013388162478804588, 0.053604841232299805, 0.053422197699546814, 0.006973132956773043, 0.03943081945180893, -0.03431789204478264, 0.026402313262224197, 0.12420404702425003, 0.009021636098623276, 0.0043348404578864574, 0.015203887596726418, -0.013294645585119724, 0.07232825458049774, 0.005958713125437498, 0.030048465356230736, -0.02084876038134098, -0.05979729816317558, 0.05256182327866554, 0.0903894379734993, 0.022516509518027306, 0.0033606993965804577, -0.010747949592769146, -0.04362304136157036, 0.03210199251770973, -0.06558407843112946, 0.020966237410902977, -0.028741128742694855, 0.012293754145503044, 0.04303721711039543, 0.0042227329686284065, -0.020730432122945786, -0.04209821671247482, 0.002493515145033598, -0.04162806645035744, 0.04418577998876572, 0.02664407528936863, 0.047336652874946594, -0.02178710326552391, -0.019478674978017807, -0.010442995466291904, 0.02488485723733902, 0.05567071586847305, 0.0009584457729943097, 0.008824213407933712, -0.05392155423760414, -0.0040882485918700695, 0.020562786608934402, -0.004339094273746014, -0.052612096071243286, 0.08034925907850266, -0.04569610580801964, 0.03449103981256485, -0.043812524527311325, 0.030616089701652527, -0.013553579337894917, -0.039351388812065125, 0.00011720592738129199, -0.0634220615029335, 0.034478336572647095, 0.011549301445484161, 0.03264053910970688, 0.01029779389500618, 0.0053583974950015545, -0.05168969929218292, -0.012949159368872643, -0.0034576321486383677, 0.10122037678956985, 0.044394414871931076, -0.0862927958369255, 0.0037448580842465162, -0.021530289202928543, -0.049113888293504715, -0.023137200623750687, -0.03992842137813568, -0.015689032152295113, -0.0054871211759746075, -0.03839435055851936, 0.018899280577898026, -0.04657730087637901, 0.02652311883866787, -0.010229241102933884, -0.011970778927206993, -0.0016335543477907777, 0.01713527925312519, -0.08933558315038681, 0.01551667507737875, 0.06592150777578354, -0.03307382017374039, -0.026561135426163673, 0.02683171071112156, 0.03459583967924118, 0.008040967397391796, 0.011252865195274353, -0.02473939210176468, -0.00037490716204047203, 0.03484516218304634, 0.005660257302224636, 0.08595725893974304, 0.030759962275624275, 0.05572020262479782, 0.05277860909700394, -0.005556077230721712, -0.053579606115818024, 0.007306240499019623, -0.024841811507940292, 0.05138590931892395, 0.04237925261259079, -0.06378639489412308, 0.008208885788917542, 0.024387065321207047, 0.04190247133374214, -0.018243366852402687, -0.016863372176885605, -0.04845792055130005, 0.0020534046925604343, -0.03914265334606171, 0.0657820999622345, -0.04394460469484329, 0.009991730563342571, -0.011884404346346855, 0.03209364786744118, -0.0645548552274704, -0.014535404741764069, -0.02204987406730652, -0.04295692220330238, 0.01698409952223301, 0.01792541705071926, -0.004067678470164537, 0.02701747417449951, 0.0008659418672323227, -0.04121646657586098, 0.009129303507506847, 0.0013151359744369984, 0.03804804012179375, -0.0025012625847011805, 0.025925882160663605, -0.010720910504460335, 0.08793047815561295, 0.02636897750198841, 0.01980111375451088, 0.011671517044305801, 0.024570249021053314, -0.004756004083901644, 0.005141792818903923, 0.0077753919176757336, -0.010557384230196476, 0.004972612019628286, 0.013161379843950272, 0.02592196688055992, -0.07621408253908157, -0.05438400059938431, -0.006706406828016043, -0.03847363591194153, 0.014164184220135212, -0.037071507424116135, -0.004624710418283939, 0.015453513711690903, -0.0015851480420678854, -0.043371353298425674, -0.02691422961652279, -0.024584975093603134, -0.06543735414743423, -0.008052420802414417, 0.0828121230006218, -0.0057920836843550205, 0.060877326875925064, -0.024220934137701988, -0.0004688578483182937, 0.018494196236133575, -0.03993783891201019, -0.00861814059317112, 0.0413653701543808, 0.02352808602154255, 0.0023442262317985296, -0.03434058651328087, -0.0076680295169353485, -0.018347585573792458, 0.0429127998650074, 0.035786308348178864, 0.034921687096357346, -0.03122716024518013, -0.008726010099053383, -0.0407126247882843, -0.03423905745148659, -0.01452744472771883, 0.04666634649038315, 0.01826070435345173, -0.019361445680260658, 0.01909872330725193, 0.004420804791152477, -0.10349376499652863, 0.019899513572454453, -0.0218373853713274, -0.02223603054881096, -0.049881722778081894, 0.011333147063851357, 0.0597161129117012, 0.013948001898825169, -0.03639869764447212, -0.0020688711665570736, -0.03392889350652695, -0.005172728095203638, 0.0028011929243803024, 0.016788380220532417, -0.04881662130355835, -0.031159786507487297, 0.0025148862041532993, -0.05642234534025192, -0.04207305237650871, 0.0375426709651947, -0.01445028930902481, 0.01452803798019886, 0.06212707236409187, -0.002664519939571619, -0.0444449782371521, -0.006628877017647028, -0.027397222816944122, -0.005477378610521555, -0.007276511751115322, 0.014568095095455647, -0.06755254417657852, -0.08098217099905014, 0.00008226174395531416, 0.053706567734479904, -0.005716333631426096, 0.006309774704277515, -0.014861761592328548, -0.02649976685643196, 0.00782320462167263, -0.08642858266830444, -0.019604401662945747, -0.04109513759613037, -0.03779202327132225, 0.013278945349156857, 0.01566159538924694, -0.05231471732258797, -0.06894900649785995, 0.01232603844255209, -0.0062967524863779545, -0.010571790859103203, 0.04180498048663139, -0.015231270343065262, 0.03237934038043022, 0.01305284071713686, 0.06561736762523651, 0.019049447029829025, 0.016629476100206375, -0.018749216571450233, 0.06882089376449585, 0.007304140832275152, 0.000849408854264766, 0.003916849382221699, 0.01286777388304472, 0.0017369212582707405, -0.06149766221642494, 0.011030677706003189, 0.027443483471870422, -0.052258510142564774, -0.06497908383607864, 0.00306817633099854, 0.026757540181279182, -0.04907293617725372, -0.031106330454349518, -0.031702734529972076, -0.0330500490963459, -0.02385406568646431 ]
<p>What is the physical constraint that gauge invariance is a required condition for electromagnetic fields? What would happen if the electromagnetic fields were not gauge invariant?</p>
g5380
[ -0.015200180932879448, 0.005339575931429863, -0.01713727042078972, -0.022539589554071426, 0.04491843655705452, 0.12145962566137314, 0.030273815616965294, 0.013043573126196861, -0.03737247735261917, -0.029228469356894493, 0.009906560182571411, -0.034147072583436966, -0.05355756729841232, -0.009096400812268257, -0.017236102372407913, 0.06015804037451744, 0.042802903801202774, -0.008006771095097065, 0.01117612048983574, 0.00925427209585905, -0.019697492942214012, 0.028234893456101418, -0.028356146067380905, -0.06889358907938004, 0.005537617951631546, 0.00774577958509326, 0.08038721978664398, -0.06993934512138367, 0.04143159091472626, -0.04668808728456497, 0.0281852874904871, 0.007579644676297903, 0.06280090659856796, -0.027894532307982445, -0.013049283064901829, -0.05448977276682854, 0.0283516813069582, 0.0625159963965416, 0.055586956441402435, 0.03593314811587334, 0.06505418568849564, 0.02739682048559189, -0.04321061447262764, -0.004238677676767111, -0.03465498611330986, 0.027479387819767, 0.0190457571297884, 0.016232797876000404, -0.02796197682619095, -0.008649714291095734, -0.009177125990390778, -0.0544707328081131, 0.07015913724899292, -0.0419074110686779, -0.02981470339000225, 0.03572310507297516, 0.05639265850186348, 0.01729472540318966, 0.02974572591483593, -0.017985962331295013, 0.012993022799491882, 0.0008662764448672533, 0.018777115270495415, -0.010275729931890965, 0.012304727919399738, -0.04794560745358467, -0.04601748287677765, -0.07317259907722473, -0.00815777387470007, -0.011401299387216568, -0.04655439779162407, -0.000211186648812145, -0.052745260298252106, 0.03161318972706795, -0.004309289623051882, 0.04529498517513275, 0.020415116101503372, -0.006488734390586615, -0.02263067103922367, -0.005518573801964521, -0.003881604177877307, 0.037422433495521545, 0.048775382339954376, 0.005128839053213596, 0.049416959285736084, -0.05100824311375618, -0.007625962141901255, -0.045287299901247025, -0.005764590110629797, -0.016858641058206558, -0.020990783348679543, -0.03234705701470375, 0.024526230990886688, 0.011113503016531467, 0.07142071425914764, -0.008915112353861332, 0.009593328461050987, 0.06369844079017639, -0.029733477160334587, 0.04143869876861572, -0.04613620042800903, -0.01328214816749096, 0.023159224539995193, -0.01790396310389042, -0.0009891362860798836, -0.01855918951332569, 0.0896022692322731, 0.0488913431763649, 0.043687280267477036, -0.061856143176555634, -0.01640273630619049, 0.025044141337275505, -0.03499416634440422, -0.018111780285835266, -0.06839509308338165, -0.03464147821068764, 0.07890370488166809, -0.002471520798280835, 0.002779138507321477, 0.06093617528676987, -0.02048095129430294, -0.0188603438436985, 0.02149055153131485, 0.053894199430942535, -0.04029357433319092, 0.0007691171485930681, -0.020494012162089348, 0.029885834082961082, 0.03726805001497269, -0.06442272663116455, 0.06802387535572052, -0.030729049816727638, -0.012387458235025406, 0.0035369889810681343, -0.011051256209611893, -0.037050772458314896, 0.05255516618490219, -0.02279701642692089, 0.0001652311475481838, 0.01650634966790676, -0.024740446358919144, -0.01140954066067934, 0.01540434081107378, -0.018080778419971466, 0.01749308593571186, 0.017831703647971153, 0.022909995168447495, -0.016548234969377518, 0.07204150408506393, 0.04901253432035446, -0.01244303584098816, 0.034901320934295654, 0.017522964626550674, -0.022918570786714554, 0.03602024167776108, -0.04671430587768555, 0.04419974610209465, 0.0323476567864418, 0.024075470864772797, -0.015435540117323399, 0.09651660174131393, 0.04722597822546959, 0.012116743251681328, 0.021625781431794167, -0.014845466241240501, 0.00025862938491627574, -0.01665636897087097, 0.002947141183540225, -0.015859106555581093, -0.054386820644140244, -0.0429970920085907, 0.024313176050782204, 0.05303395912051201, 0.018411023542284966, -0.02207065001130104, 0.07385260611772537, -0.03575363755226135, -0.0009501003078185022, 0.03658697381615639, -0.04856952652335167, 0.008316420949995518, 0.02622266672551632, 0.02747756987810135, -0.006159795913845301, -0.03532668575644493, -0.005202564410865307, -0.04379924014210701, 0.019884726032614708, -0.05981295555830002, -0.017939401790499687, 0.03147387132048607, -0.019784070551395416, -0.013560574501752853, 0.05003838986158371, -0.009177870117127895, -0.015583330765366554, 0.016668671742081642, -0.00974180269986391, 0.0294958408921957, 0.017315490171313286, 0.04223817586898804, 0.05104555934667587, 0.050788551568984985, -0.0016385286580771208, -0.02094925381243229, -0.034365441650152206, -0.03287151828408241, 0.005977902561426163, 0.05131853371858597, -0.03408299386501312, 0.02712639607489109, -0.04082643240690231, -0.005045540630817413, -0.05536163970828056, -0.03952941298484802, -0.01510763168334961, -0.01546355988830328, 0.011280261911451817, -0.10662034898996353, 0.04181870445609093, -0.023632323369383812, -0.035812847316265106, 0.01715308427810669, 0.004563156049698591, -0.06745780259370804, -0.020428866147994995, -0.04093176871538162, -0.005629721097648144, 0.04069022461771965, -0.02204606682062149, 0.02280120924115181, 0.03614351525902748, -0.008077968843281269, -0.009866164065897465, -0.014580999501049519, 0.10579182952642441, -0.03241332992911339, -0.03546687960624695, 0.036351099610328674, -0.06038476899266243, 0.011229356750845909, 0.04178142547607422, 0.027562148869037628, 0.045073650777339935, 0.058722592890262604, -0.019366160035133362, 0.01564779132604599, 0.01957203820347786, -0.04698945954442024, 0.08135709166526794, 0.03258317708969116, -0.03645161911845207, 0.04431614652276039, -0.00781935453414917, -0.010894453153014183, -0.04115075618028641, 0.050646573305130005, 0.03229976072907448, -0.050809845328330994, 0.05584477633237839, 0.00780608132481575, -0.050736553966999054, 0.0077821784652769566, 0.03184071183204651, -0.050876371562480927, 0.0334150604903698, 0.06086845323443413, 0.0031959430780261755, 0.024765070527791977, -0.0076172491535544395, -0.015865452587604523, 0.030573656782507896, -0.002232852391898632, 0.008910643868148327, 0.07265245914459229, 0.003846718929708004, -0.0240117609500885, -0.03311355039477348, 0.004559016320854425, -0.05047893896698952, -0.014691918157041073, 0.006649171933531761, -0.01045416109263897, -0.003646702505648136, 0.07355690002441406, -0.057645902037620544, -0.006251615937799215, -0.06585052609443665, -0.019873380661010742, 0.054471105337142944, -0.034627724438905716, 0.0026279326993972063, 0.04181301221251488, -0.02504594437777996, -0.05298175290226936, -0.0442337691783905, -0.01553221233189106, -0.08771082758903503, -0.002892451360821724, 0.05067132040858269, 0.03915055841207504, 0.035802438855171204, -0.037905219942331314, -0.025074461475014687, 0.01801685243844986, -0.030556542798876762, -0.03747745603322983, -0.015575116500258446, 0.000802127062343061, -0.03656161576509476, -0.032408952713012695, 0.07967030256986618, -0.035068925470113754, 0.03503958135843277, -0.029535403475165367, 0.012309263460338116, -0.020583340898156166, -0.025998450815677643, -0.04042189568281174, -0.009040359407663345, -0.04284228757023811, -0.0380810871720314, 0.037217602133750916, -0.03134213015437126, 0.05558963865041733, 0.003863012185320258, 0.007936937734484673, -0.007094298489391804, -0.016513140872120857, -0.007924885489046574, -0.005407539661973715, -0.016360504552721977, -0.02591480314731598, 0.01199918333441019, 0.0007998169749043882, -0.011519262567162514, -0.019195115193724632, -0.021759768947958946, 0.017451496794819832, -0.002368462970480323, 0.04454943910241127, -0.050548382103443146, -0.08582337200641632, 0.005852417554706335, -0.04734877124428749, 0.03340331092476845, -0.0136927030980587, -0.043747927993535995, 0.06263430416584015, 0.00044690040522255003, 0.026123318821191788, -0.03844057768583298, 0.023302186280488968, -0.017679406329989433, -0.037570495158433914, 0.030298443511128426, 0.042940039187669754, -0.020161442458629608, 0.009446127340197563, -0.006581453140825033, -0.03189215064048767, -0.026975182816386223, -0.016600724309682846, -0.03129470720887184, -0.008889003656804562, 0.06882057338953018, -0.011392628774046898, 0.00045092508662492037, 0.05025032162666321, 0.028240922838449478, 0.003896558191627264, -0.0004638490208890289, -0.01934647560119629, 0.022634219378232956, -0.01734119839966297, -0.03152144327759743, 0.03857967257499695, -0.049083784222602844, -0.0007867850945331156, -0.0022700352128595114, -0.011588184162974358, 0.0250522680580616, -0.0014279289171099663, 0.018667425960302353, -0.002551000565290451, -0.022488325834274292, 0.020372770726680756, 0.08100448548793793, -0.011144984513521194, 0.007983817718923092, -0.028802908957004547, -0.029160315170884132, -0.039763860404491425, -0.0028000483289361, 0.022872429341077805, -0.031785279512405396, 0.0055180019699037075, -0.016886664554476738, 0.04934055730700493, -0.03257884085178375, 0.06968462467193604, 0.03513023629784584, 0.010921713896095753, -0.004543454851955175, 0.01428779773414135, -0.042254261672496796, -0.009828913025557995, -0.02461289055645466, 0.004768981598317623, -0.012325849384069443, -0.014849115163087845, -0.023399515077471733, -0.005232001189142466, -0.05066416785120964, -0.013017447665333748, 0.03264015540480614, -0.040418580174446106, -0.02067556045949459, 0.025590995326638222, -0.03638792410492897, 0.031065668910741806, 0.010912912897765636, 0.059075333178043365, -0.0437828004360199, 0.0707710012793541, 0.12235013395547867, 0.06565486639738083, -0.06619245558977127, -0.026029199361801147, -0.011987190693616867, 0.00481801200658083, 0.019293149933218956, -0.005102173425257206, -0.005830036476254463, -0.012392101809382439, 0.027092628180980682, -0.09651720523834229, 0.008060777559876442, -0.014051279053092003, 0.0032641515135765076, 0.0464082770049572, -0.039606235921382904, 0.04949024319648743, -0.06217442452907562, -0.08605869114398956, 0.046638745814561844, 0.00330066354945302, -0.041216328740119934, -0.0237808208912611, -0.003799257567152381, 0.015424439683556557, -0.025192955508828163, -0.04736194387078285, -0.017412379384040833, -0.03702175244688988, -0.052539974451065063, -0.02428489364683628, 0.04870434105396271, 0.013787873089313507, 0.020315341651439667, -0.0070985667407512665, -0.0554543100297451, 0.011296285316348076, 0.027428967878222466, 0.012189194560050964, -0.04229142144322395, -0.027376046404242516, -0.005182937253266573, -0.0634932667016983, 0.017221828922629356, 0.024267783388495445, 0.017961125820875168, 0.005582683254033327, 0.0166410431265831, 0.05729353427886963, 0.053433552384376526, 0.00045502776629291475, 0.015225732699036598, 0.0011629376094788313, -0.07658898830413818, -0.025471622124314308, 0.01662067323923111, 0.005812052171677351, 0.03487710282206535, -0.03793436288833618, -0.00781563762575388, -0.004396108444780111, 0.03184766322374344, -0.009051023982465267, -0.0503348633646965, 0.011138655245304108, 0.02315894328057766, 0.0520353764295578, 0.040180157870054245, -0.003959235735237598, -0.007629409432411194, -0.05531736835837364, 0.05265404284000397, -0.021628569811582565, -0.0468025729060173, -0.01367187686264515, -0.012609418481588364, 0.02955845557153225, 0.012265519239008427, -0.028958966955542564, 0.051944613456726074, 0.052252285182476044, 0.01113197486847639, 0.0030369427986443043, -0.016782071441411972, -0.013003089465200901, 0.020418480038642883, 0.012086775153875351, 0.023298315703868866, 0.04254789277911186, 0.013465221971273422, -0.019581517204642296, 0.010792256332933903, -0.03396499156951904, -0.1143941730260849, 0.040549177676439285, -0.025078432634472847, 0.027893872931599617, -0.05751734599471092, -0.0005673224804922938, 0.025748375803232193, -0.013969974592328072, -0.032631803303956985, 0.03181920945644379, 0.05145817622542381, 0.058977995067834854, 0.005174526013433933, -0.029134031385183334, -0.026694120839238167, 0.03440471738576889, -0.019473165273666382, 0.02681204117834568, -0.029197385534644127, -0.0044256155379116535, 0.05019741505384445, -0.010312751866877079, 0.004927567671984434, 0.025678494945168495, -0.01895640604197979, -0.001615819986909628, -0.010549156926572323, -0.002250853693112731, 0.01923350989818573, 0.005154875107109547, -0.045715585350990295, -0.0148167684674263, 0.016979984939098358, -0.0235529113560915, -0.02248295582830906, 0.005298143718391657, 0.0038951036985963583, 0.01336609572172165, -0.012363102287054062, 0.0046604410745203495, -0.03316830098628998, 0.04736442118883133, 0.04288826137781143, 0.000753777741920203, -0.01753186248242855, 0.006517849862575531, 0.00025210031890310347, 0.017782878130674362, -0.029377538710832596, 0.047470323741436005, 0.02028159610927105, 0.0003185340901836753, 0.018247148022055626, 0.022613223642110825, 0.04351499676704407, -0.016661254689097404, 0.010089369490742683, -0.03712077811360359, -0.023279352113604546, -0.022534720599651337, -0.019578883424401283, 0.010768637992441654, 0.022268936038017273, 0.028329908847808838, -0.09229175746440887, 0.008776344358921051, 0.009071515873074532, -0.053678520023822784, 0.022308116778731346, 0.08622875064611435, -0.014136256650090218, -0.038134992122650146, -0.06272506713867188, 0.024941671639680862, 0.03080742061138153, -0.04092976450920105, 0.02840544655919075, -0.01926974207162857, 0.0026878323405981064, -0.023336971178650856, 0.03176085650920868, 0.04259921610355377, -0.008986669592559338, 0.015625517815351486, 0.0019183391705155373, 0.026847226545214653, 0.034990228712558746, -0.04817516356706619, -0.05428265407681465, -0.007281873840838671, -0.016472261399030685, -0.011264135129749775, -0.08593824505805969, -0.01087735965847969, -0.0011164244497194886, -0.018912266939878464, 0.030307123437523842, -0.007502539083361626, -0.010435816831886768, -0.03781796991825104, -0.005706948693841696, -0.013428060337901115, -0.029851969331502914, -0.01659504510462284, -0.017356570810079575, -0.05985797196626663, 0.04995011165738106, -0.030214713886380196, 0.025991778820753098, 0.02225634641945362, -0.02549990825355053, -0.026114236563444138, -0.002342252293601632, -0.02511264570057392, 0.030355866998434067, 0.024176647886633873, 0.009346305392682552, 0.03767266497015953, 0.025603756308555603, 0.09033042937517166, -0.007814048789441586, 0.057341091334819794, 0.03191068395972252, 0.08045835047960281, 0.012050257064402103, -0.016951436176896095, 0.05041435360908508, 0.001982820685952902, -0.055431216955184937, -0.041974395513534546, 0.031610555946826935, -0.05280343070626259, 0.03337683528661728, -0.03360199183225632, -0.010188051499426365, -0.01902363821864128, -0.023832576349377632, -0.00770442234352231, 0.0034619069192558527, -0.0669216588139534, 0.02258836105465889, 0.007160663139075041, -0.034150827676057816, -0.03246637433767319, 0.019345581531524658, 0.02799290604889393, -0.028208596631884575, -0.006274340208619833, -0.1382889747619629, 0.013187190517783165, 0.005562503822147846, -0.0049274093471467495, -0.05300523713231087, 0.01974061131477356, 0.050812818109989166, 0.007313679438084364, -0.03828362002968788, -0.03028227761387825, 0.03554072976112366, 0.03012746199965477, -0.004837258718907833, -0.04169769957661629, 0.031849611550569534, 0.05194128677248955, -0.01765969581902027, -0.004138942342251539, -0.024617858231067657, -0.018906233832240105, -0.031293272972106934, 0.0507083535194397, -0.005504668690264225, -0.011785847134888172, 0.007163531146943569, 0.06176890432834625, -0.03900017589330673, -0.05355297774076462, -0.05896326154470444, 0.021898701786994934, 0.022325336933135986, 0.039773259311914444, -0.0076964194886386395, -0.02114291302859783, 0.0029469167347997427, 0.010337891057133675, 0.008984954096376896, 0.02015666663646698, 0.022013461217284203, 0.0016785392072051764, -0.05286011844873428, -0.061262838542461395, 0.0379863940179348, -0.008498397655785084, 0.07011611014604568, 0.03501088544726372, 0.02340412139892578, 0.10052654147148132, -0.008587784133851528, -0.06432809680700302, 0.0018991312244907022, 0.036131277680397034, 0.0008258412126451731, 0.025213250890374184, 0.024317150935530663, -0.004985596984624863, 0.01705850288271904, -0.020793914794921875, 0.001404757029376924, 0.016052648425102234, -0.05422374606132507, 0.04900269955396652, -0.021355070173740387, -0.03570161014795303, 0.004767999053001404, -0.052564725279808044, 0.04860280454158783, -0.024756677448749542, 0.016254356130957603, -0.007488767150789499, 0.031314827501773834, -0.021426232531666756, 0.0011574288364499807, 0.038357559591531754, -0.03760802745819092, -0.04924542456865311, -0.016840679571032524, -0.017976658418774605, 0.02624143660068512, -0.006469540297985077, 0.03714660555124283, 0.014507917687296867, 0.015491556376218796, -0.022026540711522102, -0.03696564584970474, -0.01475038006901741, 0.05770832300186157, 0.05650177225470543, -0.07105753570795059, 0.021018825471401215, -0.005593390669673681, 0.07310674339532852, 0.09833312779664993, 0.011881982907652855, 0.010441785678267479, 0.0038536295760422945, 0.01527189090847969, -0.07626182585954666, -0.02590077929198742, -0.0028862913604825735, -0.007462639361619949 ]
<p>There was an announcement at a recent UCLA symposium on dark matter by the <a href="http://fermi.gsfc.nasa.gov/" rel="nofollow">FERMI collaboration</a> which hints at some evidence of dark matter. The results aren't yet published, but the <a href="http://m.ucla.edu/newsroom/item.php?name=News&amp;path=http%3A%2F%2Fnewsroom.ucla.edu%2Fportal%2Fucla%2Ffiles%2Fmobile.xml&amp;article=Possible+evidence+for+dark+matter+particle+presented&amp;signature=18ef784085eaa0c6a3c40872eac84dbe&amp;no_server_init" rel="nofollow">symposium news release is here</a>. Most of the news release is just general dark matter fluff, but it says that</p> <blockquote> <p>One search technique involves using the vast amount of dark matter in our galaxy. The NASA Fermi Satellite Telescope, an international collaboration involving NASA, the Goddard Space Flight Center and the SLAC National Accelerator Laboratory, searches for gamma rays — very high-energy light particles — from this dark matter.</p> <p>There are models of dark matter that would allow a signal in the galactic dark matter consistent with the claims at the meeting and provide a small interaction consistent with the "null results" in the direct dark matter searches all over the world.</p> </blockquote> <p>This obviously doesn't contain much information. Can anyone closer to the field expound on the findings?</p>
g5381
[ 0.01292348001152277, 0.03052230179309845, 0.006613933946937323, -0.05842557176947594, 0.07526864111423492, -0.022460833191871643, -0.06879402697086334, -0.01461971364915371, -0.01768535189330578, -0.03359482064843178, 0.07549931108951569, 0.012625333853065968, 0.009016076102852821, -0.0018167499219998717, -0.01552504487335682, 0.036553774029016495, 0.08788681775331497, -0.002588641829788685, -0.06465252488851547, 0.01635598950088024, 0.031575363129377365, -0.04624807834625244, 0.03379753604531288, -0.05370814725756645, -0.09726513922214508, 0.004225256387144327, 0.0027078581042587757, 0.0020385016687214375, -0.02920331433415413, -0.023308590054512024, 0.04083273559808731, -0.09736931324005127, 0.024162190034985542, -0.008866287767887115, -0.04133496806025505, -0.02166353166103363, 0.07470185309648514, 0.05552501231431961, -0.00723998574540019, 0.03198501467704773, -0.052159905433654785, 0.011256464757025242, -0.03162360191345215, 0.024866152554750443, 0.010770200751721859, 0.06062092259526253, -0.006865072064101696, -0.013620267622172832, -0.02442508563399315, -0.028532953932881355, -0.012214135378599167, 0.013873930089175701, -0.013682853430509567, 0.015441427007317543, -0.008654529228806496, -0.05218308046460152, 0.033619802445173264, 0.02096153423190117, 0.08568400144577026, -0.022542541846632957, 0.030635593459010124, 0.03202376142144203, 0.012234616093337536, -0.006450268905609846, -0.019803348928689957, 0.03941098600625992, -0.008535241708159447, -0.035281386226415634, 0.001764576300047338, -0.021042630076408386, 0.002482981188222766, -0.0020810330752283335, 0.002584535162895918, -0.003960307687520981, -0.04429224878549576, 0.02148968167603016, 0.005098144523799419, 0.00502272043377161, -0.024795999750494957, -0.02846631594002247, -0.0006317039951682091, -0.002861475571990013, -0.018107229843735695, 0.008667496964335442, 0.029079774394631386, -0.00709923729300499, -0.0592627190053463, 0.04260757192969322, 0.046659503132104874, 0.059736691415309906, 0.05025884881615639, 0.030380869284272194, -0.00982180330902338, -0.020191406831145287, 0.02192576229572296, 0.06491067260503769, 0.03266368806362152, 0.02627749927341938, -0.03972088173031807, -0.04758329316973686, -0.07156717032194138, 0.027532553300261497, 0.005713416263461113, 0.05460488423705101, 0.027624567970633507, 0.075892373919487, -0.037341468036174774, 0.0030543371103703976, -0.02317333035171032, 0.02938864566385746, -0.08042054623365402, 0.02996741607785225, -0.012837548740208149, -0.0643748939037323, 0.018044395372271538, -0.07833975553512573, 0.012992850504815578, 0.030343424528837204, 0.01678452640771866, 0.030846575275063515, -0.0016546623082831502, -0.014800945296883583, 0.0277397483587265, 0.032851044088602066, -0.011426020413637161, -0.053930576890707016, 0.03198891505599022, -0.009712629951536655, -0.016346285119652748, -0.04464517906308174, -0.028276843950152397, -0.055601298809051514, -0.01652703434228897, 0.07614948600530624, 0.012481439858675003, -0.012200766243040562, -0.0389663465321064, 0.0367610938847065, 0.034429967403411865, 0.024211805313825607, -0.03462054207921028, -0.027818243950605392, 0.007899727672338486, 0.024539625272154808, -0.011849485337734222, 0.006523282267153263, -0.0016953417798504233, 0.0330827422440052, 0.007185329683125019, 0.014831235632300377, 0.02043747529387474, 0.035396017134189606, -0.01101358700543642, -0.028482679277658463, -0.03875322639942169, -0.002346120774745941, -0.02331552281975746, -0.019293656572699547, -0.007854267954826355, -0.002736973576247692, 0.0308257844299078, 0.028232993558049202, -0.03025686740875244, -0.047844137996435165, -0.03845006972551346, -0.007719273678958416, 0.04306066781282425, -0.0067362478002905846, -0.007577138487249613, -0.016877008602023125, -0.0724216178059578, -0.020171521231532097, 0.021583715453743935, 0.02090325392782688, 0.008445200510323048, 0.02312699519097805, 0.037166327238082886, -0.05334565043449402, -0.015124374069273472, -0.03996101766824722, -0.016607755795121193, -0.03366107866168022, -0.008511525578796864, -0.02852296642959118, 0.05453626811504364, -0.005034500267356634, 0.022324712947010994, 0.029953427612781525, 0.04038180410861969, 0.02746015600860119, -0.03335901349782944, -0.044987037777900696, 0.05525868386030197, -0.03162848576903343, 0.055229224264621735, 0.0033934214152395725, 0.05366187170147896, -0.05805959552526474, -0.037060629576444626, 0.033276092261075974, 0.035865359008312225, 0.021146699786186218, 0.02042500488460064, -0.011401878669857979, 0.052434518933296204, -0.0459015853703022, -0.024794936180114746, -0.009948567487299442, 0.0702921524643898, 0.017906036227941513, 0.01716918870806694, -0.018751809373497963, 0.01728145405650139, -0.010929189622402191, 0.023685650900006294, -0.024580052122473717, -0.03351271152496338, 0.015771113336086273, 0.012133236043155193, 0.030353950336575508, -0.05183348432183266, -0.027800727635622025, -0.04923299327492714, 0.011546027846634388, 0.00928119383752346, 0.02937837690114975, 0.005496555007994175, -0.09380952268838882, -0.07516797631978989, 0.06601480394601822, -0.01184061449021101, 0.05817839503288269, -0.061802297830581665, 0.0028444556519389153, 0.018708163872361183, -0.0073283156380057335, 0.025614703074097633, -0.018176982179284096, -0.012208055704832077, 0.056283824145793915, -0.051738664507865906, -0.07626274973154068, -0.054135482758283615, -0.014301791787147522, 0.023206325247883797, -0.08368387073278427, 0.002916477620601654, 0.017945274710655212, 0.03735347092151642, -0.0034047639928758144, 0.013226890936493874, 0.0015826403396204114, -0.0063508618623018265, -0.004564870148897171, 0.008651252835988998, -0.016541307792067528, -0.037778228521347046, 0.09520348906517029, -0.06135554984211922, -0.01110018603503704, 0.03990436717867851, -0.024867834523320198, 0.009405256249010563, 0.0033188166562467813, 0.02742832712829113, -0.015692874789237976, -0.008690237998962402, -0.020815588533878326, -0.02143419347703457, 0.0017713465495035052, 0.011262411251664162, 0.0014323638752102852, 0.05557430535554886, -0.06462763249874115, -0.01045925635844469, 0.050116609781980515, -0.008814184926450253, 0.07112983614206314, 0.027570191770792007, -0.052244022488594055, -0.02281796559691429, 0.011519948951900005, -0.019555218517780304, -0.015872115269303322, 0.010743958875536919, 0.0006562311318702996, -0.024352718144655228, -0.014266963116824627, -0.05376417934894562, -0.018027998507022858, 0.035563524812459946, -0.020517349243164062, 0.05501607060432434, 0.00798750575631857, -0.0006509352824650705, 0.004351952113211155, -0.042984575033187866, 0.010694237425923347, 0.016699614003300667, 0.03792041540145874, 0.05341839790344238, -0.05772000923752785, -0.027469376102089882, 0.05660632625222206, 0.05046670883893967, 0.012366151437163353, -0.0434134304523468, 0.0052305422723293304, -0.04410087689757347, -0.053527574986219406, 0.0453900545835495, -0.007381371688097715, 0.026272734627127647, -0.01199655793607235, -0.019534248858690262, 0.041368741542100906, -0.009852978400886059, 0.050249695777893066, -0.0009252235759049654, 0.046337224543094635, 0.06232622638344765, 0.00557785714045167, -0.032849956303834915, -0.10339043289422989, 0.03152487054467201, 0.054068759083747864, 0.02418101206421852, -0.030734799802303314, -0.029467128217220306, 0.029179904609918594, 0.015857767313718796, -0.011439661495387554, -0.025429192930459976, 0.00934749748557806, -0.009939438663423061, 0.027593882754445076, -0.028374159708619118, 0.04594958573579788, 0.020997632294893265, -0.010430091992020607, -0.04539214074611664, 0.021842699497938156, -0.04092702642083168, 0.03492674231529236, -0.014256367459893227, 0.0198774803429842, -0.04650185629725456, -0.011283149011433125, -0.02503465674817562, 0.06337478011846542, 0.008313676342368126, -0.00888037495315075, 0.025044037029147148, -0.026944104582071304, 0.022832881659269333, -0.045506466180086136, 0.028238171711564064, 0.031165482476353645, 0.020184265449643135, 0.012221704237163067, -0.008573693223297596, -0.0005580023862421513, -0.0005929493345320225, -0.0496470145881176, 0.03713947534561157, 0.0024795655626803637, 0.04381222277879715, -0.04315569996833801, 0.05837438255548477, -0.0011690714163705707, 0.034149982035160065, -0.017218714579939842, 0.016796376556158066, 0.03933427855372429, 0.0008684171480126679, -0.00313015328720212, 0.03502506762742996, 0.03217015042901039, -0.04276145622134209, -0.021810267120599747, 0.029126711189746857, 0.09156414866447449, 0.020287098363041878, 0.05104562267661095, 0.032794248312711716, 0.019126923754811287, -0.020869405940175056, 0.003617282956838608, -0.049188051372766495, -0.07453648000955582, -0.0020817804615944624, 0.010126983746886253, -0.03716111555695534, 0.09585269540548325, -0.01711389794945717, -0.021366093307733536, 0.0036239931359887123, 0.014767342247068882, 0.023987198248505592, -0.0021053182426840067, -0.00974351167678833, 0.049670182168483734, 0.03531854972243309, -0.02775423415005207, -0.0334300622344017, 0.0025220687966793776, -0.03222343698143959, -0.015808099880814552, 0.006235784385353327, 0.0043933941051363945, -0.017990007996559143, 0.026368698105216026, 0.014547200873494148, 0.0022220215760171413, 0.04721803590655327, -0.02806505188345909, -0.050678279250860214, -0.04623646289110184, 0.024426782503724098, 0.021465247496962547, 0.0038447072729468346, 0.031021513044834137, -0.06772700697183609, 0.007874792441725731, -0.00962371937930584, 0.04412218928337097, -0.012928604148328304, 0.05021238699555397, 0.025440942496061325, 0.008113198913633823, 0.03205309063196182, -0.013579289428889751, -0.03513526916503906, 0.06790176779031754, -0.010849977843463421, 0.05717917159199715, 0.002183726755902171, -0.005766041576862335, 0.009605767205357552, 0.02249663695693016, 0.03111843578517437, -0.06737736612558365, 0.019382651895284653, 0.00021106985514052212, 0.048965733498334885, 0.06876888871192932, -0.018299413844943047, 0.023764969781041145, 0.0006201985524967313, 0.02935810387134552, 0.020410895347595215, -0.0475509949028492, -0.009122773073613644, -0.010462397709488869, 0.01002147700637579, 0.04470093548297882, -0.02885359339416027, 0.047576580196619034, -0.03450401872396469, 0.03300546482205391, -0.04364318773150444, 0.02884095534682274, 0.03626806661486626, 0.04738283529877663, 0.08302630484104156, -0.048599373549222946, -0.020528174936771393, -0.07721442729234695, -0.02759329415857792, -0.043849024921655655, -0.027546003460884094, -0.026376694440841675, 0.04420678690075874, 0.03493103012442589, -0.0010122996754944324, -0.03658020496368408, -0.07444443553686142, -0.05009545758366585, -0.023919764906167984, -0.014096200466156006, -0.02936326153576374, 0.013177106156945229, 0.03863179683685303, -0.058247342705726624, -0.002633066847920418, 0.1013292670249939, -0.055798497051000595, -0.0000028382858090481022, -0.025916215032339096, -0.07116633653640747, -0.029293110594153404, -0.03724969923496246, 0.001789879985153675, -0.06644592434167862, -0.040427614003419876, 0.02391102910041809, -0.011966587975621223, -0.02861686609685421, 0.0032584285363554955, 0.009312531910836697, 0.05590520799160004, 0.019553476944565773, 0.02955802157521248, -0.045620474964380264, -0.03580104559659958, 0.043187178671360016, -0.0037363094743341208, -0.0189548060297966, 0.042811594903469086, -0.04349999874830246, -0.014637374319136143, 0.0010538058122619987, 0.013911384157836437, 0.05764172598719597, -0.06819579750299454, 0.004234567284584045, 0.0426051989197731, 0.05303332954645157, 0.024428099393844604, -0.001374739222228527, -0.037472181022167206, -0.0576796792447567, -0.02896113693714142, -0.026237010955810547, 0.09122943133115768, -0.04540664702653885, -0.013299377635121346, 0.04658970609307289, 0.024918977171182632, 0.00819927267730236, 0.007571513764560223, -0.013314493000507355, 0.04239755868911743, 0.0444062314927578, 0.04613497108221054, -0.055027641355991364, 0.0620594285428524, -0.004339968785643578, 0.005246043670922518, -0.017441868782043457, 0.017210453748703003, 0.005092719104140997, 0.07623641937971115, 0.037786196917295456, 0.024422062560915947, -0.006004695780575275, 0.03413115069270134, -0.033536240458488464, -0.0009348169551230967, -0.08880335837602615, 0.03548893332481384, -0.025439182296395302, 0.03120036981999874, 0.01645750179886818, -0.0026481819804757833, -0.026622122153639793, -0.012408709153532982, -0.007438569329679012, -0.021697167307138443, 0.014288836158812046, 0.0097190635278821, -0.004046110436320305, 0.025556860491633415, 0.040809281170368195, -0.022090673446655273, 0.033956799656152725, 0.0026675667613744736, -0.06438691169023514, -0.00817372277379036, -0.05020369589328766, -0.004721000324934721, 0.026827234774827957, -0.06026829779148102, 0.04423575848340988, -0.009580961428582668, -0.05169862508773804, 0.047032810747623444, 0.005506574641913176, -0.04522516205906868, -0.04133515805006027, 0.05510862171649933, -0.020894791930913925, 0.06449112296104431, -0.03061160072684288, 0.01667860895395279, 0.033816784620285034, -0.07067104429006577, 0.023206450045108795, -0.01648985594511032, -0.003458665683865547, 0.009620887227356434, -0.024352168664336205, 0.010106229223310947, 0.06147400289773941, -0.11870763450860977, -0.0794328972697258, -0.01579282432794571, 0.008617222309112549, -0.004310783930122852, 0.01743244379758835, -0.029246410354971886, 0.007125210482627153, -0.005514432210475206, 0.02641480602324009, 0.02617606893181801, -0.04698643833398819, -0.005060954950749874, -0.0014915263745933771, -0.02074405737221241, 0.012651990167796612, 0.021275483071804047, 0.03616838902235031, -0.08624821156263351, 0.019532499834895134, 0.015742462128400803, -0.020025692880153656, -0.0388999842107296, -0.04634534940123558, -0.05821941792964935, 0.008957017213106155, 0.0023748690728098154, 0.003459837520495057, -0.051425278186798096, -0.05604758858680725, -0.036641448736190796, 0.038997575640678406, -0.02644583210349083, -0.03523552417755127, 0.0661526545882225, 0.05589546263217926, -0.000201110087800771, 0.00890804547816515, 0.053240228444337845, 0.006744597107172012, -0.05530077964067459, -0.034180719405412674, 0.03289822116494179, 0.010681885294616222, 0.04094809666275978, -0.023984083905816078, 0.02268122509121895, -0.04411452263593674, -0.0051837703213095665, -0.00005988097473164089, -0.004460431635379791, -0.038667138665914536, -0.016471078619360924, 0.06328292936086655, -0.0655321478843689, -0.019411612302064896, 0.023610875010490417, -0.008706588298082352, 0.014917748048901558, -0.07363898307085037, -0.05477491766214371, 0.014336644671857357, 0.024075979366898537, -0.028336437419056892, 0.023297684267163277, -0.03685665503144264, -0.01954641006886959, -0.038644012063741684, -0.031337443739175797, -0.006198365241289139, 0.010984385386109352, 0.006760980933904648, -0.0627153292298317, -0.01927693374454975, 0.007331447210162878, -0.042124539613723755, 0.02706804871559143, -0.04930600896477699, -0.04339926689863205, 0.005240186583250761, -0.02839508466422558, -0.00810164399445057, -0.006827018689364195, -0.027007048949599266, 0.0198640376329422, -0.002725933212786913, 0.04639771953225136, -0.019410550594329834, -0.02132594957947731, 0.06559834629297256, -0.04084695130586624, 0.049943894147872925, -0.012144078500568867, 0.011459560133516788, -0.04072529450058937, 0.06335697323083878, -0.017714980989694595, 0.0072269015945494175, 0.0015484914183616638, -0.06961355358362198, -0.014697035774588585, -0.007377204019576311, 0.021545834839344025, 0.057415928691625595, -0.05295570194721222, 0.05731114745140076, -0.016018986701965332, 0.040723010897636414, -0.0013573201140388846, 0.023666391149163246, 0.01860865019261837, 0.018067963421344757, 0.04316249117255211, -0.038798876106739044, 0.01474367268383503, 0.025654826313257217, -0.020272236317396164, 0.010305431671440601, -0.01610579341650009, 0.046149399131536484, -0.034460317343473434, 0.04045066609978676, 0.01959259808063507, 0.022349923849105835, 0.07512503117322922, 0.02954142354428768, -0.016792787238955498, -0.022718118503689766, -0.031062886118888855, 0.011313988827168941, -0.010228919796645641, -0.03691454976797104, 0.011835538782179356, 0.0705789253115654, 0.07480321079492569, 0.04035582020878792, 0.010387127287685871, -0.0020276065915822983, -0.012555095367133617, -0.0379110686480999, 0.00017994604422710836, 0.010006023570895195, 0.02143029309809208, -0.020365647971630096, -0.014509227126836777, 0.053019002079963684, 0.006056285463273525, -0.012575529515743256, -0.04147329553961754, -0.03498263284564018, -0.018962888047099113, -0.02566707320511341, -0.016289807856082916, 0.04385075718164444, 0.017815206199884415, -0.017901897430419922, 0.0014180453727021813, 0.0006371581694111228, 0.011557897552847862, 0.018514549359679222, 0.02623690851032734, -0.03930458426475525, -0.029486367478966713, -0.02190440706908703, 0.02377280592918396, -0.02625897154211998, 0.030682463198900223, -0.007269843947142363, 0.04483729600906372, 0.08840982615947723, 0.03280992433428764, -0.012645380571484566, 0.006234341766685247, -0.011360571719706059 ]
<ul> <li>Suppose there is a habitable star with a significantly large mass, and thus a huge gravitation field. It has a clock on it that ticks each local second. And it also has a mirror. This is Star A.</li> <li>Suppose there is another habitable star with a much smaller mass, also with a clock, called Star B. </li> <li>Finally, suppose that these two stars somehow maintain a fixed distance between them. (Eg: the two stars have perfectly calibrated rocket thrusters pointing toward one another).</li> </ul> <p>Please correct me if I'm wrong: An observer on Star A looking through a telescope at clock B would see it ticking quickly. Likewise, an observer on Star B looking at the clock on Star A would see it ticking slowly.</p> <p>Now, suppose a person on A sends a light pulse towards B and starts a clock. They measure it takes 10 seconds for it to come back.</p> <p>Now, a person on B sends a pulse to A, and measures how long it takes to get back. Does it also take 10 seconds? If so, there's a pretty clear paradox. If not, how could it take light different times to travel the same distance?</p> <p>Thanks</p>
g5382
[ 0.03752198442816734, 0.06340128928422928, -0.0159296952188015, -0.03260891139507294, 0.03885888680815697, -0.0027585048228502274, 0.02810620330274105, -0.01890760287642479, -0.022447366267442703, -0.0005155803519301116, -0.021940380334854126, 0.045175325125455856, 0.04663172736763954, -0.04997904226183891, 0.0013084798119962215, -0.00497056869789958, 0.14474667608737946, -0.059250835329294205, 0.04734096676111221, 0.04784451425075531, 0.05189044028520584, 0.062140919268131256, -0.02081657387316227, -0.02942206896841526, -0.014416173100471497, -0.033419519662857056, 0.053169168531894684, -0.017754223197698593, -0.05195702239871025, -0.030700350180268288, 0.036080241203308105, -0.04590455815196037, 0.03989377245306969, -0.10217422991991043, 0.011637073010206223, -0.028348926454782486, 0.019291633740067482, -0.002000593114644289, 0.003495601937174797, 0.07081104069948196, 0.06499981880187988, 0.02849763073027134, 0.06747215241193771, -0.04226772114634514, 0.04478580877184868, 0.024263931438326836, 0.0069916732609272, -0.007564662955701351, 0.05603267624974251, -0.05088411644101143, -0.013947270810604095, 0.019124750047922134, -0.0020964061841368675, 0.05816347524523735, -0.0017799567431211472, 0.05647454783320427, 0.011519617401063442, -0.0344042107462883, 0.05329415574669838, -0.020921099931001663, 0.008058552630245686, -0.0575077123939991, -0.0165853314101696, 0.035739630460739136, 0.008165719918906689, 0.0071148620918393135, 0.0052848136983811855, 0.0022985641844570637, 0.044156357645988464, -0.03689024969935417, -0.046955883502960205, -0.017599593847990036, -0.033596523106098175, -0.07525597512722015, -0.022075891494750977, 0.03953451290726662, 0.013787795789539814, 0.02681601047515869, -0.013259723782539368, 0.028183354064822197, -0.08298150449991226, -0.04187973588705063, 0.004288762342184782, 0.05370336398482323, 0.05555249750614166, -0.00011524391447892413, -0.020079826936125755, 0.01257189642637968, -0.0061907959170639515, 0.03496187552809715, 0.01863604597747326, -0.034311387687921524, 0.06728158891201019, 0.017314530909061432, -0.054065071046352386, 0.009242921136319637, -0.015639152377843857, 0.0427623987197876, -0.009708305820822716, 0.028458423912525177, -0.032301757484674454, 0.013613234274089336, -0.014567198231816292, 0.025715280324220657, 0.02935604192316532, -0.046303559094667435, 0.003894304158166051, 0.011513793841004372, -0.00861351191997528, -0.00988444872200489, 0.01488750521093607, -0.09325569123029709, 0.01731259748339653, 0.014453849755227566, 0.0049200537614524364, -0.02579924836754799, 0.048310332000255585, -0.0230157021433115, 0.008666892535984516, 0.01745563931763172, -0.026602327823638916, 0.01924951933324337, -0.05616012215614319, 0.039443619549274445, -0.06274066120386124, -0.01398934330791235, -0.02324082888662815, 0.02629559487104416, 0.032733771950006485, 0.046094365417957306, -0.00139000010676682, 0.05460008978843689, -0.018092859536409378, -0.006480115931481123, -0.06753455102443695, 0.010724637657403946, 0.020499445497989655, -0.0027278533671051264, -0.025165539234876633, 0.032846689224243164, -0.004758136812597513, -0.03604953736066818, -0.0062273163348436356, -0.007039480376988649, -0.04511632025241852, 0.042822614312171936, -0.005312545690685511, -0.020450539886951447, 0.034873541444540024, -0.0024097429122775793, 0.009235791862010956, 0.08382152020931244, -0.02024487406015396, 0.033808037638664246, 0.01724209077656269, 0.016126491129398346, -0.010683493688702583, 0.010343496687710285, 0.006871548946946859, 0.003214973257854581, 0.06638428568840027, -0.02812531217932701, -0.002356455195695162, -0.007231070660054684, -0.02329559624195099, 0.03753413259983063, 0.047647859901189804, -0.012232741340994835, -0.024358678609132767, -0.04475286230444908, -0.06524550914764404, -0.023714710026979446, 0.04582958295941353, 0.06107645109295845, 0.02028437703847885, 0.01831577531993389, -0.011578382924199104, -0.010217820294201374, -0.09090079367160797, -0.009610648266971111, -0.048779454082250595, -0.06899652630090714, -0.01144404150545597, -0.07156870514154434, -0.007733394857496023, -0.04335416108369827, -0.009227891452610493, -0.05507710203528404, -0.07113178074359894, 0.017772164195775986, -0.01895166002213955, -0.01862058788537979, -0.015000749379396439, 0.07090190052986145, 0.0029050535522401333, -0.023246653378009796, 0.03476805239915848, -0.01515935268253088, -0.01957462728023529, 0.010103583335876465, -0.01844320259988308, 0.019241157919168472, 0.049122050404548645, -0.017603032290935516, 0.021933594718575478, 0.012691289186477661, -0.013494809158146381, 0.029433464631438255, 0.02976333349943161, -0.022227413952350616, 0.001718686195090413, 0.01728495955467224, -0.017465999349951744, 0.033040113747119904, -0.018515685573220253, -0.03695540875196457, 0.006214500404894352, 0.0031669638119637966, 0.029509209096431732, -0.01020769588649273, 0.013225657865405083, -0.0046964590437710285, 0.08982839435338974, -0.10442177951335907, -0.007549304515123367, 0.006424384657293558, -0.026403890922665596, -0.010628695599734783, 0.009381132200360298, 0.05698010325431824, -0.005650360137224197, -0.0175919272005558, 0.03992732614278793, 0.01770113967359066, 0.03330087289214134, 0.029196299612522125, 0.016501033678650856, 0.015429923310875893, -0.003935782704502344, 0.008821913972496986, 0.027080776169896126, -0.03027472458779812, -0.021006470546126366, 0.04184582084417343, 0.006143888924270868, -0.018396766856312752, 0.010717722587287426, -0.013693180866539478, -0.008729681372642517, 0.051409464329481125, 0.023092828691005707, 0.01844072714447975, -0.06281649321317673, -0.03829712048172951, -0.01189788430929184, -0.07587247341871262, 0.03735041618347168, 0.036607351154088974, -0.08561308681964874, 0.023366251960396767, 0.017419062554836273, -0.02029598318040371, 0.0195216853171587, -0.010993392206728458, 0.031960394233465195, -0.039084166288375854, -0.021015942096710205, 0.03516644239425659, -0.01651735231280327, 0.0045361947268247604, 0.006418142467737198, -0.013748123310506344, 0.06382307410240173, 0.036469489336013794, -0.028642164543271065, 0.0011665334459394217, 0.016566189005970955, -0.02453812211751938, -0.00003285055936430581, 0.016645144671201706, -0.012536556459963322, -0.012488073669373989, -0.0976080596446991, -0.038350045680999756, 0.04275285080075264, -0.015273340046405792, -0.007983443327248096, 0.06373356282711029, 0.03697923570871353, 0.013247113674879074, -0.024151986464858055, 0.03329145535826683, 0.03554539754986763, 0.03420049324631691, -0.020099306479096413, 0.06259320676326752, 0.01706002466380596, -0.010165373794734478, -0.032362811267375946, -0.01388484239578247, 0.04651074483990669, -0.053380630910396576, 0.023059140890836716, 0.01610608585178852, 0.07042714953422546, -0.03561612218618393, -0.05135141685605049, -0.034716181457042694, -0.003325690981000662, -0.022575052455067635, 0.07181286066770554, 0.07049116492271423, 0.00595842394977808, -0.018527794629335403, 0.02877643145620823, -0.0319102518260479, -0.02194765768945217, 0.01690801978111267, 0.007865623570978642, 0.005766424350440502, 0.030020399019122124, -0.024273402988910675, -0.03797761723399162, -0.024147039279341698, 0.017181476578116417, -0.026081643998622894, -0.04590819031000137, 0.00903838500380516, -0.05317525938153267, 0.01577952317893505, -0.03317319229245186, 0.0499618798494339, -0.04820306971669197, -0.011855746619403362, -0.01962844654917717, 0.0003901029995176941, -0.02365884743630886, 0.05656436085700989, -0.0020435231272131205, 0.051160648465156555, -0.035823095589876175, 0.02729482762515545, -0.053905174136161804, 0.021980073302984238, 0.006616080179810524, 0.02942369319498539, 0.018363473936915398, 0.00512333307415247, 0.02562948688864708, -0.045186545699834824, 0.005608364008367062, -0.0352497436106205, 0.019135162234306335, -0.021367596462368965, 0.00239691068418324, 0.023150285705924034, -0.01206093467772007, 0.023027541115880013, 0.05330802500247955, -0.04775230213999748, 0.01264578104019165, 0.009906780906021595, 0.007914296351373196, 0.06216379255056381, 0.010588466189801693, -0.03251592069864273, 0.0178386103361845, 0.015559229999780655, 0.020596537739038467, -0.008044597692787647, -0.032552748918533325, 0.024869292974472046, -0.040002185851335526, -0.03655548393726349, 0.1348423957824707, -0.05151978135108948, 0.0546845868229866, -0.007902913726866245, -0.04837128147482872, 0.03845807909965515, 0.012360702268779278, 0.022652164101600647, 0.02832568809390068, -0.05670757591724396, 0.09455559402704239, -0.012201918289065361, 0.02205650694668293, -0.037348948419094086, 0.012500620447099209, -0.06745703518390656, 0.03258806839585304, -0.07294154167175293, -0.015479817055165768, -0.02025386318564415, 0.01930304244160652, -0.004071731120347977, 0.01911027543246746, 0.012172427959740162, 0.04017724096775055, -0.025413189083337784, -0.026490267366170883, 0.016950208693742752, 0.011492034420371056, -0.006581047549843788, -0.025661781430244446, -0.0030658748000860214, -0.017307652160525322, 0.02206313982605934, -0.015713917091488838, 0.035208769142627716, -0.015390732325613499, -0.006952236872166395, -0.02125556766986847, -0.0706733912229538, 0.007337725255638361, 0.053825076669454575, 0.023421619087457657, 0.039728496223688126, 0.023011086508631706, 0.005356820300221443, -0.012067480944097042, 0.04160713404417038, 0.038505565375089645, -0.019049828872084618, 0.006305714137852192, 0.10770214349031448, 0.04350357502698898, -0.013953189365565777, -0.030034760013222694, -0.06881766021251678, 0.07494347542524338, 0.03484727442264557, 0.008655130863189697, 0.03682282567024231, -0.04053632915019989, 0.06341886520385742, 0.006364237051457167, 0.02086855284869671, -0.004011593759059906, 0.03960055485367775, 0.01870189979672432, -0.024049174040555954, -0.0020894750487059355, 0.013069812208414078, -0.01590392366051674, 0.060350969433784485, -0.05357643961906433, -0.11402204632759094, -0.032854605466127396, -0.07644394040107727, -0.023497136309742928, 0.016326552256941795, -0.016240889206528664, -0.005768091883510351, -0.015359905548393726, -0.027616385370492935, 0.04153233394026756, 0.06797061115503311, 0.049365632236003876, -0.014764639548957348, -0.02011071890592575, 0.001182597829028964, 0.05139404162764549, 0.011317755095660686, 0.027047453448176384, 0.00646885996684432, -0.02817535400390625, -0.04972188547253609, -0.03486044704914093, -0.008069640025496483, -0.045204970985651016, 0.019857307896018028, -0.020379120483994484, 0.06479150056838989, -0.02745305933058262, -0.02458488568663597, -0.017245881259441376, 0.03667021915316582, 0.029204726219177246, -0.035235028713941574, -0.03782365471124649, 0.0120341582223773, 0.016747241839766502, 0.0369870699942112, -0.016016991809010506, -0.031021185219287872, -0.027293290942907333, 0.011375032365322113, 0.04532351717352867, -0.03432528302073479, -0.010447630658745766, -0.022593209519982338, 0.0535741001367569, -0.0048439581878483295, 0.021778691560029984, -0.014430522918701172, 0.03761276230216026, 0.03019079752266407, 0.00606548972427845, -0.032163143157958984, -0.034728363156318665, 0.06930231302976608, 0.01004377007484436, -0.010448692366480827, -0.03274979442358017, 0.06409909576177597, 0.009049968793988228, 0.017056772485375404, 0.018555833026766777, 0.049154795706272125, -0.05791865661740303, 0.017946070060133934, -0.01653832569718361, 0.03910589963197708, 0.03107392229139805, -0.05223727226257324, -0.02897271327674389, -0.028547948226332664, 0.01462603360414505, -0.03514857962727547, 0.009404025971889496, -0.005878586322069168, -0.00193211215082556, -0.009599666111171246, 0.003852417226880789, -0.018583400174975395, -0.028435278683900833, -0.009756974875926971, -0.016009477898478508, -0.007152494043111801, 0.057321783155202866, -0.034135907888412476, 0.019286364316940308, -0.018417004495859146, -0.008447833359241486, 0.009413368068635464, 0.020802969112992287, -0.006026369985193014, -0.002093339106068015, 0.0009121665498241782, -0.04003406688570976, -0.0350128635764122, 0.03566158562898636, 0.057519663125276566, 0.026583418250083923, -0.03456626459956169, 0.0036156591959297657, -0.017814436927437782, 0.07413717359304428, -0.007355744019150734, -0.014911827631294727, -0.008818387985229492, -0.005184051115065813, 0.05576147139072418, -0.015808148309588432, 0.01955067738890648, -0.01823313534259796, -0.02939578890800476, -0.040366802364587784, -0.026622693985700607, 0.04231545701622963, 0.011523609980940819, 0.02061101607978344, -0.060737624764442444, 0.029934706166386604, -0.08512087166309357, -0.0015075481496751308, -0.00003532083428581245, 0.0855591893196106, 0.011207799427211285, 0.0388694629073143, 0.01216394267976284, -0.007389243692159653, -0.013724098913371563, -0.02815709263086319, 0.021708495914936066, -0.04830577224493027, -0.0047866045497357845, -0.03508185222744942, -0.014369715936481953, -0.04569343850016594, 0.015247201547026634, -0.021450147032737732, -0.027949433773756027, 0.005203721113502979, 0.01602485403418541, 0.01853487640619278, -0.00990954041481018, 0.028661005198955536, -0.013134541921317577, -0.02004189044237137, -0.0629316046833992, -0.00841925572603941, -0.0858556255698204, -0.016352828592061996, -0.016366487368941307, -0.04533219709992409, -0.009561531245708466, -0.05210788547992706, 0.02791781909763813, -0.010317988693714142, -0.03487994521856308, 0.06238800659775734, -0.024681581184267998, 0.009644654579460621, 0.056485679000616074, -0.08983834087848663, 0.02330399863421917, 0.10949613153934479, 0.015223132446408272, 0.007108122110366821, 0.005886014085263014, 0.0632094293832779, 0.054987967014312744, -0.0354415662586689, -0.0031063994392752647, -0.005346664693206549, 0.0032984022982418537, -0.03200003132224083, 0.07592690736055374, 0.05427923798561096, -0.024746663868427277, -0.01736551523208618, -0.06114727631211281, 0.003947839606553316, 0.028430450707674026, -0.014732755720615387, -0.0058095986023545265, 0.0030856351368129253, 0.02751019038259983, -0.0412265919148922, -0.009884866885840893, -0.05584195628762245, 0.007026416715234518, 0.05168721824884415, 0.026902517303824425, -0.04906468093395233, 0.02294926904141903, 0.027481703087687492, -0.017558597028255463, 0.03101298399269581, 0.006807377561926842, -0.020072678104043007, 0.0261321272701025, 0.0001584099663887173, -0.007180063985288143, 0.04788836091756821, 0.003510891692712903, -0.0010043821530416608, 0.019579138606786728, -0.0301055945456028, 0.004570429679006338, -0.0031030047684907913, 0.008015075698494911, -0.018799567595124245, -0.033135831356048584, -0.0009029491920955479, -0.012016044929623604, 0.03334460407495499, -0.036843191832304, 0.005988351069390774, -0.03251028433442116, -0.08971516042947769, -0.0278027206659317, 0.031486522406339645, 0.0006450326764024794, -0.015912801027297974, -0.0650295540690422, -0.019858771935105324, -0.048179663717746735, 0.02743416279554367, -0.003973254468291998, -0.035088784992694855, -0.010542388074100018, 0.02940310724079609, -0.005457604303956032, -0.02736702933907509, -0.02217940241098404, -0.004177015274763107, -0.035175878554582596, 0.030292687937617302, 0.004960293881595135, -0.008677350357174873, 0.028429269790649414, -0.012350695207715034, 0.06988038122653961, -0.013634578324854374, -0.01922120526432991, 0.019561076536774635, -0.04900854080915451, -0.025099197402596474, 0.03703542798757553, 0.019530730322003365, -0.0010686323512345552, 0.055928442627191544, -0.014125926420092583, 0.0447760708630085, -0.00183787290006876, 0.00676319794729352, -0.025612391531467438, -0.03989413380622864, 0.02883104793727398, 0.02046305313706398, 0.008060572668910027, 0.05332973599433899, 0.016864588484168053, -0.041907913982868195, -0.022587690502405167, -0.046823833137750626, -0.02287028729915619, 0.001980565022677183, 0.040326159447431564, -0.04726666957139969, -0.06417493522167206, 0.0363277792930603, -0.0666651800274849, -0.05238601192831993, 0.012631870806217194, 0.02396276406943798, 0.026193400844931602, -0.02357455901801586, -0.07202029228210449, -0.008133836090564728, -0.059292022138834, 0.028991516679525375, 0.0152059281244874, 0.027255356311798096, -0.04137173295021057, -0.004818175453692675, -0.04005306214094162, 0.010674414224922657, 0.019415507093071938, -0.02931598760187626, -0.00789430271834135, 0.005624912213534117, 0.024387890473008156, 0.005486690439283848, -0.027646061033010483, -0.05785081535577774, -0.0032607526518404484, -0.015923598781228065, -0.06778247654438019, 0.061730120331048965, -0.004217054229229689, 0.0068740881979465485, -0.015438849106431007, 0.001102513400837779, 0.03252394497394562, 0.039565324783325195, -0.06941826641559601, 0.024131570011377335, 0.06813123822212219, -0.08113910257816315, -0.033660631626844406, 0.09391160309314728, -0.0001319131115451455, 0.023800048977136612, -0.014874439686536789, -0.06654708087444305, -0.038057975471019745, -0.03788667172193527, -0.018751826137304306, -0.02458440512418747, -0.026163436472415924, -0.0021990553941577673, -0.018206147477030754, 0.007632267661392689, 0.06116967275738716 ]
<p>Does the photino in super-symmetry have a mass, Or is this different in different super symmetric models?</p>
g5383
[ 0.01010875590145588, 0.05528288334608078, 0.005508077330887318, -0.005274211522191763, 0.062338557094335556, 0.032015152275562286, -0.03360114246606827, 0.04687855392694473, -0.03215710446238518, -0.005467479582875967, -0.05441422015428543, -0.06882001459598541, 0.011544196866452694, -0.04024259373545647, -0.022218506783246994, -0.014644804410636425, 0.03132867068052292, -0.05037922412157059, -0.0021811905317008495, 0.011847015470266342, -0.01848750188946724, -0.045898184180259705, -0.029434286057949066, 0.006034553982317448, 0.048934515565633774, 0.07278573513031006, -0.0014886062126606703, -0.06603599339723587, -0.007208685856312513, -0.03088255599141121, 0.02845950797200203, -0.006898174993693829, -0.0029641585424542427, -0.05207648128271103, 0.0035309947561472654, -0.03336542844772339, 0.009120508097112179, 0.016516363248229027, 0.051071617752313614, -0.013002447783946991, 0.04854688048362732, -0.006310801021754742, -0.015074685215950012, -0.016716787591576576, -0.07473594695329666, -0.0528390035033226, -0.006399739533662796, -0.03127782791852951, -0.1067858412861824, 0.0044070053845644, 0.054745543748140335, 0.04780202731490135, 0.06027792766690254, -0.021697796881198883, 0.0021745446138083935, -0.0032820210326462984, 0.06308600306510925, -0.02341367118060589, -0.022857826203107834, 0.0764092206954956, -0.0007982501410879195, -0.006208241451531649, 0.06325079500675201, 0.05424314737319946, 0.08703209459781647, 0.006755265407264233, -0.005338346119970083, -0.024170272052288055, 0.0027832407504320145, -0.012517395429313183, 0.007759257685393095, 0.05657366290688515, 0.04410194233059883, 0.021276380866765976, -0.05265185609459877, -0.013455424457788467, -0.023502502590417862, -0.008910570293664932, -0.03735492005944252, -0.028774721547961235, 0.017609847709536552, 0.038458727300167084, 0.04132256284356117, 0.016674574464559555, 0.009446833282709122, -0.009300312958657742, -0.017001880332827568, 0.012128415517508984, -0.033837128430604935, -0.02839699573814869, -0.0012877037515863776, -0.004462622571736574, -0.0035461208317428827, 0.017327291890978813, -0.004619292914867401, 0.03427638113498688, -0.007288489490747452, 0.052015967667102814, -0.03297670930624008, -0.020615071058273315, 0.009966743178665638, 0.01288052648305893, 0.005705318413674831, 0.0025129751302301884, 0.04585675895214081, 0.014667919836938381, 0.029456092044711113, -0.09032198041677475, 0.046481478959321976, 0.0021197206806391478, -0.04144379869103432, -0.04440848156809807, -0.04976637661457062, 0.01565087027847767, -0.10459950566291809, -0.02438821829855442, 0.07048646360635757, -0.013335785828530788, 0.01907593384385109, -0.0262347012758255, 0.05949324369430542, -0.04369957745075226, -0.026581954210996628, 0.07122109830379486, -0.008166207000613213, -0.019480949267745018, -0.019694175571203232, -0.0000886841953615658, -0.021487802267074585, -0.03586001321673393, -0.023821428418159485, 0.026280682533979416, 0.0007751474040560424, -0.0029451085720211267, 0.006603440269827843, -0.03705941140651703, -0.006220744922757149, 0.06983529031276703, 0.011243053711950779, -0.055940572172403336, -0.012262574397027493, 0.04115941375494003, 0.03878074884414673, -0.00831100158393383, 0.0023787720128893852, -0.06574086099863052, 0.026546627283096313, 0.007938277907669544, -0.012727824039757252, 0.06002870574593544, -0.008161177858710289, 0.02273435890674591, -0.02267387881875038, 0.007862268947064877, -0.07505611330270767, -0.01889192685484886, 0.02869071252644062, 0.052390389144420624, 0.0290708988904953, -0.08336671441793442, -0.05896918848156929, -0.03188017010688782, 0.03452811390161514, -0.06701377779245377, -0.009365005418658257, -0.05227840319275856, 0.03392770513892174, -0.002879238221794367, -0.05425528436899185, 0.006903359666466713, -0.028615610674023628, 0.05598783865571022, -0.02500140853226185, 0.08314919471740723, 0.01642593927681446, -0.03259047493338585, -0.053206246346235275, 0.007585451938211918, 0.0815194696187973, 0.04503314569592476, 0.03600836545228958, -0.01648489385843277, 0.02052890881896019, -0.0022936267778277397, -0.00020330031111370772, 0.032463863492012024, 0.010640248656272888, 0.043980300426483154, 0.007995021529495716, 0.007398128043860197, 0.018675168976187706, 0.03361556679010391, 0.010576475411653519, 0.04003145173192024, 0.02414405718445778, -0.015429300256073475, 0.007800689898431301, -0.026030749082565308, -0.049349721521139145, -0.013165361247956753, -0.019614188000559807, 0.027029747143387794, 0.04850137606263161, -0.05265988036990166, 0.0026054326444864273, -0.0012988375965505838, -0.03820094093680382, 0.035431355237960815, 0.02665129490196705, 0.01300449762493372, -0.010852946899831295, 0.026039550080895424, -0.03190607205033302, -0.013135874643921852, -0.07157028466463089, -0.03449007868766785, 0.01983621157705784, 0.03674466162919998, 0.008013480342924595, 0.004979397635906935, -0.019501943141222, -0.023946864530444145, 0.03532079979777336, 0.043187372386455536, 0.009476915933191776, 0.05030371621251106, 0.036466725170612335, -0.0111516322940588, 0.010488883592188358, -0.01540799904614687, -0.032167449593544006, 0.011876288801431656, 0.04175316542387009, -0.012106604874134064, 0.03410371020436287, -0.005654802080243826, 0.01931067556142807, -0.014934701845049858, 0.02746555022895336, -0.04540863260626793, 0.0061542680487036705, -0.008896967396140099, -0.014873472042381763, 0.0454418919980526, 0.004607215523719788, -0.00825559627264738, -0.010919756256043911, 0.05282194912433624, 0.015643944963812828, 0.070200115442276, -0.03666850924491882, -0.013362335041165352, 0.030342629179358482, -0.05763988196849823, -0.003976711072027683, -0.004130048211663961, 0.010065953247249126, -0.018669024109840393, -0.05856680870056152, 0.008453751914203167, 0.021321119740605354, 0.0008769598207436502, -0.03529217094182968, -0.021611327305436134, -0.011989658698439598, -0.02617182768881321, 0.016176415607333183, -0.01189282163977623, -0.004236506763845682, -0.0482158362865448, -0.013677936047315598, 0.13933980464935303, 0.04306294396519661, 0.05242035165429115, -0.07269980013370514, 0.027131173759698868, -0.0291555505245924, -0.011335086077451706, 0.07293876260519028, -0.026837307959794998, -0.023104462772607803, -0.019946597516536713, -0.011818685568869114, -0.05336907505989075, 0.02162773907184601, -0.02536185085773468, -0.08556081354618073, -0.04915206506848335, -0.05721134692430496, 0.011401832103729248, -0.04433465376496315, -0.02094794251024723, 0.028060732409358025, -0.03436264768242836, 0.006262326613068581, -0.0006613300065509975, 0.02193988673388958, -0.03992627561092377, 0.00622002175077796, 0.07377807796001434, 0.09728506207466125, -0.011624851264059544, -0.008120990358293056, 0.030100636184215546, 0.06887538731098175, 0.045913342386484146, -0.008024954237043858, -0.02597111463546753, 0.016785770654678345, -0.04400360584259033, 0.006429075263440609, 0.09372881799936295, 0.059446342289447784, 0.03525564447045326, 0.019875958561897278, 0.004654400050640106, -0.039690352976322174, 0.017819063737988472, 0.03032710589468479, -0.04320041835308075, -0.08125516027212143, 0.011254061944782734, 0.048228438943624496, 0.003001754404976964, -0.02577151358127594, 0.007813130505383015, 0.005356827285140753, 0.031302426010370255, -0.04272214323282242, -0.06092352792620659, -0.03951304405927658, -0.03570438548922539, -0.019656574353575706, 0.017230069264769554, -0.05319227650761604, 0.053573090583086014, -0.004522937349975109, -0.04116159677505493, 0.007000096142292023, 0.02805037423968315, -0.02904948592185974, -0.026321399956941605, 0.005259528290480375, -0.053258586674928665, 0.009329007938504219, -0.013438425026834011, -0.0132532250136137, -0.048565223813056946, 0.04654446989297867, 0.06705061346292496, 0.024797489866614342, 0.03709797561168671, 0.01951523870229721, 0.005708490498363972, 0.026716796681284904, -0.0004625486908480525, 0.017360690981149673, 0.03710179775953293, -0.027161942794919014, -0.004324703942984343, 0.06733018904924393, 0.015586345456540585, 0.04318007081747055, -0.06887827068567276, 0.013504360802471638, 0.060193855315446854, -0.03514491394162178, -0.03208846226334572, 0.023586606606841087, -0.007184730377048254, -0.020489957183599472, -0.053720515221357346, 0.014560668729245663, -0.04698309302330017, 0.04122322052717209, -0.004202563781291246, 0.004425039514899254, -0.047878433018922806, -0.08464139699935913, -0.018977859988808632, 0.03970780968666077, -0.024690134450793266, -0.036866478621959686, -0.03731392323970795, 0.014890209771692753, 0.011359279043972492, -0.02318555675446987, 0.011173116974532604, -0.025626489892601967, -0.04189501330256462, 0.034802474081516266, -0.013027498498558998, -0.0025006718933582306, -0.024395952001214027, 0.018273908644914627, -0.005424991250038147, 0.04405266419053078, -0.0789843425154686, -0.018060024827718735, 0.04372970387339592, -0.004023350775241852, 0.046037446707487106, 0.028968455269932747, -0.05839115008711815, 0.012066002003848553, 0.015254530124366283, 0.010666356422007084, -0.016735808923840523, -0.0850122794508934, 0.01109236292541027, 6.579842874998576e-7, 0.04260243847966194, 0.0011984113370999694, -0.009476750157773495, 0.02891641855239868, 0.016530126333236694, -0.05060781538486481, -0.045342303812503815, 0.018521418794989586, 0.0043738544918596745, 0.035122741013765335, 5.364944399843807e-7, -0.04053778201341629, -0.026937317103147507, 0.007141025271266699, 0.036571428179740906, 0.036694880574941635, -0.014401573687791824, -0.06362545490264893, 0.00870035495609045, 0.06447690725326538, -0.030451076105237007, 0.09181762486696243, 0.04874479025602341, -0.0014958379324525595, 0.01487714797258377, -0.037238627672195435, 0.0006847000331617892, 0.005362558178603649, 0.05437764525413513, 0.08227340131998062, 0.054361097514629364, 0.01624116860330105, -0.06475043296813965, 0.04531605914235115, -0.05719123035669327, 0.0011289826361462474, 0.002163176890462637, -0.050509653985500336, 0.007527839858084917, -0.032640282064676285, 0.025406626984477043, -0.04039819538593292, -0.029913879930973053, -0.04574907571077347, 0.032210804522037506, -0.004899647552520037, 0.06781582534313202, 0.06314513832330704, 0.01980491541326046, 0.0009212436270900071, -0.05184640735387802, 0.020181262865662575, -0.015101373195648193, 0.061826445162296295, 0.006560119334608316, -0.022841084748506546, 0.0032312802504748106, 0.028490513563156128, -0.06421162933111191, 0.026954706758260727, 0.01515157800167799, -0.01023773942142725, -0.0028213453479111195, -0.031701743602752686, 0.043478984385728836, -0.04112093523144722, -0.017978155985474586, 0.028362197801470757, 0.020538918673992157, -0.0027646019589155912, 0.06999610364437103, -0.020543089136481285, -0.028267737478017807, 0.017167313024401665, 0.002926239976659417, -0.021593665704131126, -0.033561237156391144, -0.030950594693422318, -0.07600278407335281, -0.02371177449822426, 0.00533661525696516, 0.00004736125629278831, -0.006748332642018795, -0.010617896914482117, -0.01160195842385292, 0.01778554730117321, -0.016777321696281433, 0.011142478324472904, 0.023875322192907333, -0.020596224814653397, 0.03403237462043762, 0.035449378192424774, -0.009943793527781963, 0.026225535199046135, 0.04341518506407738, 0.044777847826480865, 0.006769086234271526, -0.00850430317223072, 0.01915328949689865, 0.0058414810337126255, 0.03068968653678894, -0.02864590287208557, 0.07295447587966919, 0.0049432446248829365, 0.01319910679012537, -0.005929277744144201, 0.0061604720540344715, -0.00769755570217967, -0.06955251097679138, -0.0006918638246133924, -0.022931218147277832, 0.0547042116522789, -0.020875556394457817, 0.00044708483619615436, 0.035338468849658966, -0.05241725966334343, -0.040434304624795914, 0.026440216228365898, 0.0062233456410467625, 0.003755574580281973, -0.008882017806172371, 0.06887806951999664, 0.05840272828936577, 0.05496298521757126, -0.05259450897574425, 0.045033421367406845, -0.010935435071587563, -0.0072394926100969315, 0.02210710197687149, 0.022266708314418793, -0.024562353268265724, 0.03196718171238899, 0.03862214460968971, 0.043117452412843704, 0.03395861014723778, 0.0009034266695380211, 0.032857708632946014, -0.01529519259929657, -0.000593596778344363, -0.06771732866764069, 0.07389336824417114, -0.03833102434873581, 0.04328403249382973, -0.005341473966836929, 0.02247956022620201, -0.05835113674402237, -0.028081415221095085, -0.00920047052204609, -0.03559907153248787, -0.01654883660376072, 0.021068215370178223, 0.021237479522824287, -0.07616003602743149, -0.01735631376504898, -0.06731579452753067, -0.02348172850906849, -0.07398873567581177, 0.010290008969604969, -0.0016164345433935523, 0.017089780420064926, 0.03254901245236397, -0.0057142022997140884, -0.011213520541787148, -0.012661519460380077, 0.028544463217258453, -0.018658829852938652, -0.025801967829465866, 0.023935068398714066, -0.003447833703830838, 0.025598201900720596, -0.025489691644906998, 0.008864698000252247, 0.026634613052010536, 0.02836296521127224, 0.007331731263548136, -0.025526873767375946, -0.0040602427907288074, 0.041416868567466736, 0.09915096312761307, -0.013499530032277107, -0.047134555876255035, -0.05386364459991455, -0.0227580014616251, -0.05128167197108269, 0.09453390538692474, -0.013880030252039433, -0.03267171233892441, -0.005277087911963463, 0.048340145498514175, 0.05692741647362709, -0.022104648873209953, 0.03888050466775894, -0.016260117292404175, 0.023579474538564682, 0.044489335268735886, 0.03150773420929909, 0.0673694908618927, -0.02985578589141369, -0.004477929789572954, 0.025972720235586166, -0.006504664197564125, -0.04208168759942055, 0.029867805540561676, 0.03275521472096443, -0.040676675736904144, 0.008060724474489689, 0.027571244165301323, -0.04705061763525009, 0.017398281022906303, 0.006030896678566933, -0.019719086587429047, -0.03963478282094002, -0.028648070991039276, 0.036550987511873245, -0.04128233715891838, -0.021194912493228912, 0.031828053295612335, 0.011702761985361576, -0.01789991930127144, -0.0059338100254535675, -0.013112817890942097, 0.01030826848000288, 0.009348982013761997, -0.02235587127506733, -0.008305974304676056, -0.0322088897228241, 0.013800951652228832, 0.007363240700215101, 0.006725706625729799, 0.01078719925135374, 0.015399177558720112, -0.04324907809495926, -0.059442561119794846, -0.047138918191194534, 0.062406379729509354, -0.01500991266220808, 0.026113631203770638, -0.006448653526604176, -0.02446724846959114, -0.00895147304981947, 0.0013927556574344635, -0.06250666081905365, -0.033067893236875534, -0.004668062087148428, -0.007109643425792456, 0.032705485820770264, 0.035141944885253906, 0.0218486487865448, -0.01883108541369438, -0.08462759107351303, 0.0075128404423594475, -0.007856528274714947, -0.042441222816705704, 0.03440006077289581, 0.04922875016927719, 0.03426341712474823, -0.041557427495718, -0.02851836569607258, 0.03277283161878586, -0.01863141916692257, 0.025122320279479027, -0.008865194395184517, -0.03247113525867462, 0.0395803302526474, -0.07334435731172562, -0.02049781195819378, -0.030694959685206413, -0.010393957607448101, -0.02198813296854496, 0.03279300034046173, 0.03308699280023575, -0.02258402109146118, 0.06373527646064758, 0.02110510878264904, 0.006190816406160593, 0.01668865978717804, -0.015703927725553513, 0.04427291825413704, 0.015785448253154755, 0.008460679091513157, -0.010807711631059647, 0.00480732973664999, 0.026129087433218956, -0.04842045158147812, 0.015396354719996452, 0.004381218925118446, 0.040695469826459885, 0.02975265495479107, 0.060339704155921936, -0.04182404279708862, 0.023845592513680458, -0.016020914539694786, 0.034480806440114975, 0.0647265613079071, 0.008000913076102734, -0.023235918954014778, -0.023571647703647614, -0.01630978472530842, 0.015756672248244286, -0.004655730444937944, 0.03502336144447327, 0.011898769065737724, 0.010489072650671005, 0.03911023959517479, 0.025545064359903336, -0.08591677993535995, -0.037180326879024506, 0.00688052037730813, -0.03289808705449104, -0.033029451966285706, -0.009474336169660091, 0.03887743875384331, -0.03396819904446602, -0.004485659766942263, -0.08011221140623093, 0.0007258330006152391, 0.023654531687498093, 0.0400121808052063, 0.031300466507673264, 0.012052242644131184, -0.012089623138308525, -0.06154603883624077, -0.023937221616506577, -0.009476326406002045, 0.04648131877183914, 0.023646319285035133, -0.09742465615272522, 0.01894351653754711, -0.01620202511548996, 0.032623160630464554, -0.06299137324094772, 0.0016209244495257735, -0.013901252299547195, -0.019539957866072655, 0.03344166651368141, -0.019909609109163284, -0.06020989269018173, 0.02576099894940853, 0.001507856766693294, 0.026494286954402924, -0.014868561178445816, -0.015382684767246246, 0.04969422146677971, -0.058103494346141815, 0.01033067051321268, 0.0413004495203495, -0.038749810308218, -0.019824964925646782, -0.030566252768039703, 0.010852417908608913, -0.04285680130124092, 0.006651155184954405, -0.024965506047010422, 0.011132447980344296, 0.01804816909134388, 0.010487575083971024, -0.007090274710208178 ]
<p>Quantum entanglement bridges space and time: entangled particles show correlations independently of where and when they are measured. This is most evident in "delayed choice quantum eraser" experiments, where the outcome of single measurments <em>now</em> depends on which measurements are done <em>in the future</em> (though there is no retro-causality in the strict sense).</p> <p>I am looking for realistic interpretations which directly address this topic, i.e. discussions of underlying physical mechanisms or basic structures of the universe on which this correlations may be built.</p> <p>So far I found John Cramers "Transactional Interpretation" of 1986; Bohmian mechanics may also be considered. Are there other physical interpretations or philosophical papers on this topic of correlations over spacetime?</p>
g5384
[ 0.03000093251466751, 0.02450472302734852, 0.0025380917359143496, -0.022787952795624733, 0.020348524674773216, 0.04461855813860893, 0.029951784759759903, 0.05032059922814369, 0.009479341097176075, 0.013942448422312737, 0.03744236379861832, -0.012710140086710453, -0.014679662883281708, 0.025891287252306938, -0.0029251007363200188, -0.010148406028747559, 0.018498467281460762, 0.022910403087735176, 0.03753088042140007, -0.015400642529129982, 0.014493105001747608, 0.04152394458651543, -0.06145036220550537, -0.010837630368769169, -0.05039427801966667, -0.03142835572361946, 0.037754956632852554, -0.04456891492009163, 0.009562191553413868, -0.03270537406206131, 0.04925796017050743, -0.06508150696754456, 0.032574612647295, -0.0684489980340004, -0.05208798125386238, -0.05788945406675339, -0.04086356237530708, -0.02509104646742344, 0.01998322643339634, -0.007559869904071093, 0.04121684283018112, 0.026040295138955116, -0.04797748476266861, -0.020618101581931114, 0.023638732731342316, 0.06775949150323868, 0.004403609316796064, 0.03839436545968056, 0.036202266812324524, -0.002892352407798171, -0.03836096450686455, 0.019926877692341805, 0.03428816422820091, 0.03393905237317085, 0.04600978270173073, 0.03458324074745178, 0.10541988164186478, 0.030180754140019417, 0.07106022536754608, 0.023626554757356644, 0.00072052440373227, -0.00933141727000475, 0.03431480750441551, 0.00021305317932274193, 0.08689779788255692, 0.02397305518388748, -0.04900316148996353, 0.007219288963824511, 0.05361352488398552, -0.04552502557635307, 0.034930333495140076, -0.03603516146540642, -0.030205274000763893, 0.001649264944717288, 0.07513444125652313, 0.0513642281293869, -0.012426857836544514, -0.0018899358110502362, 0.04804029315710068, -0.008984120562672615, -0.07012069970369339, -0.010825946927070618, -0.03210136294364929, 0.017632294446229935, 0.09158772975206375, -0.026850182563066483, -0.027689281851053238, -0.03743347153067589, -0.006146703381091356, -0.012024922296404839, 0.0005937417154200375, 0.011370450258255005, 0.04929853975772858, -0.009878150187432766, -0.02683264948427677, -0.0014464401174336672, -0.029297636821866035, 0.01816975325345993, -0.012723153457045555, -0.005926819052547216, -0.06223708763718605, 0.015086938627064228, 0.07008236646652222, -0.02817482315003872, -0.0333855040371418, -0.040903691202402115, -0.00846346840262413, 0.0034801552537828684, -0.01725848764181137, -0.02204286679625511, -0.04419736936688423, 0.02042831853032112, -0.02263450436294079, 0.02285483293235302, -0.022801171988248825, -0.03147603198885918, 0.00010842300252988935, -0.04473121091723442, -0.04769398272037506, -0.003991990350186825, 0.004494067747145891, 0.019449196755886078, 0.010711338371038437, 0.033295828849077225, -0.02839931845664978, 0.005685269366949797, -0.042137470096349716, -0.03753690421581268, 0.005798737984150648, 0.028735974803566933, 0.021696990355849266, -0.0023968787863850594, -0.02706304006278515, 0.06979791820049286, -0.06526650488376617, 0.03418297320604324, 0.034208185970783234, -0.06583157926797867, -0.02207929641008377, -0.014576503075659275, 0.0005699225002899766, -0.06368697434663773, 0.02479030378162861, 0.01858779788017273, -0.020206904038786888, 0.0038324559573084116, 0.02950434945523739, -0.011700313538312912, 0.003543891478329897, -0.017906805500388145, 0.010121870785951614, 0.017269838601350784, -0.044085074216127396, -0.0029484869446605444, -0.009684519842267036, 0.05023029446601868, -0.01971556805074215, -0.028376340866088867, 0.017565950751304626, 0.030900463461875916, 0.026813752949237823, -0.0009921276941895485, 0.02475324273109436, 0.03572183847427368, -0.0027626364026218653, -0.015162828378379345, 0.005499713122844696, -0.04771079495549202, 0.03723073750734329, -0.02388051711022854, -0.060339946299791336, -0.04456453397870064, -0.040354445576667786, 0.012421678751707077, 0.014106152579188347, 0.07441318780183792, -0.025069529190659523, -0.04366134852170944, -0.007550831884145737, 0.029876351356506348, 0.0007526628905907273, -0.018655819818377495, 0.005418144632130861, -0.00597170228138566, -0.023486001417040825, -0.028927216306328773, -0.03952028229832649, -0.025260355323553085, -0.0374223031103611, 0.01598028466105461, 0.00001638407411519438, -0.07999753206968307, -0.05436856672167778, -0.007527244742959738, -0.014724011532962322, -0.00013117381604388356, 0.061551716178655624, 0.006592250429093838, 0.027286745607852936, -0.024162329733371735, -0.02730243094265461, 0.048365987837314606, 0.04086055979132652, 0.07057395577430725, 0.04285202547907829, 0.02378775179386139, 0.00008307763346238062, -0.004249777644872665, -0.042630765587091446, -0.02590438351035118, 0.019493071362376213, 0.048027168959379196, -0.029710553586483, -0.02343386597931385, -0.032230179756879807, -0.06747961789369583, -0.00926122535020113, -0.023344669491052628, 0.03475828468799591, 0.013825277797877789, -0.025159679353237152, -0.023735977709293365, 0.04245586693286896, -0.04410959780216217, 0.034457843750715256, -0.0030222663190215826, -0.014915808103978634, -0.06477510929107666, -0.0447254404425621, 0.028096169233322144, -0.07466406375169754, 0.06317738443613052, -0.038381427526474, -0.03362331911921501, 0.06553975492715836, 0.0544942282140255, 0.04221130535006523, -0.005094653926789761, 0.014598023146390915, 0.03341769427061081, 0.05182347074151039, 0.06014912202954292, -0.07075786590576172, 0.00583222322165966, 0.016529394313693047, -0.041993286460638046, 0.021621432155370712, -0.04093721881508827, -0.018403619527816772, -0.03647948428988457, 0.029135622084140778, 0.0026138396933674812, -0.011943385004997253, -0.004147531930357218, -0.023217400535941124, -0.009129902347922325, 0.04190632700920105, 0.043949663639068604, -0.09032964706420898, -0.035857245326042175, 0.007695470005273819, -0.004770822823047638, -0.031068630516529083, 0.021524138748645782, 0.02686309441924095, -0.04728906601667404, -0.017647337168455124, -0.0016518555348739028, -0.02640172466635704, 0.005792461801320314, 0.005016200244426727, -0.01008475013077259, -0.012260648421943188, 0.0041410960257053375, 0.0354466438293457, -0.013192381709814072, -0.05072130635380745, -0.04391933232545853, 0.009718481451272964, -0.006078267004340887, 0.01629413105547428, 0.03863142058253288, -0.020908471196889877, 0.058950528502464294, 0.019147278741002083, -0.053178586065769196, -0.004753774031996727, 0.019233006983995438, 0.07971388846635818, 0.0717637687921524, 0.020577186718583107, 0.032244548201560974, -0.021290937438607216, 0.04119591414928436, -0.026837991550564766, 0.02279742993414402, 0.00019643976702354848, 0.024104740470647812, -0.0024615670554339886, 0.004784512333571911, -0.014682724140584469, -0.030221354216337204, -0.009719395078718662, 0.0694759264588356, 0.03187418356537819, -0.026908455416560173, -0.06710963696241379, -0.024589281529188156, -0.020963292568922043, -0.03180518001317978, -0.025672348216176033, -0.001604665070772171, 0.011753618717193604, -0.01206978503614664, -0.03482489287853241, -0.026185760274529457, -0.0035612420178949833, 0.05561248958110809, 0.024986958131194115, -0.04845556989312172, 0.031113775447010994, 0.0034021518658846617, 0.0022854418493807316, -0.04093818739056587, 0.046368420124053955, -0.025205330923199654, 0.0020503373816609383, 0.010469293221831322, -0.11051667481660843, 0.013477063737809658, 0.009220066480338573, -0.053559206426143646, 0.07734782993793488, -0.029808277264237404, -0.08880569040775299, -0.09031195193529129, -0.0369478240609169, 0.008990861475467682, -0.03900616243481636, -0.0016693014185875654, -0.001358492998406291, 0.008830283768475056, 0.018015092238783836, 0.06230972334742546, 0.06283301115036011, 0.036016885191202164, 0.01907077617943287, 0.02604164555668831, 0.06320672482252121, -0.055031225085258484, 0.027184808626770973, 0.05417332425713539, 0.044151756912469864, -0.001404859940521419, -0.0014731275150552392, 0.07956879585981369, 0.04740248993039131, 0.00272650015540421, 0.02400193177163601, -0.0299716554582119, -0.008273358456790447, 0.03573114424943924, -0.015803489834070206, -0.014846596866846085, -0.008776861242949963, -0.011839878745377064, 0.01710396818816662, 0.027150483801960945, 0.07887186855077744, 0.058770813047885895, 0.01577834226191044, 0.0728081613779068, -0.033530037850141525, 0.03502971678972244, 0.012903161346912384, -0.0048150476068258286, 0.04047161340713501, 0.021095404401421547, 0.05691540613770485, 0.025294488295912743, 0.014516101218760014, 0.02574283443391323, 0.054935697466135025, 0.01308382023125887, 0.08095501363277435, -0.011097189038991928, -0.044144973158836365, 0.009775995276868343, -0.08259646594524384, -0.05026990920305252, 0.038986995816230774, 0.024105286225676537, -0.0007590691675432026, -0.041060999035835266, -0.005873451009392738, -0.019489793106913567, 0.02918659895658493, 0.009090730920433998, 0.08917772769927979, -0.05464503914117813, -0.016597352921962738, 0.008930802345275879, -0.010683512315154076, -0.011768206022679806, 0.015473570674657822, -0.016869524493813515, -0.007468550466001034, -0.04711450636386871, -0.060291897505521774, -0.04853084683418274, 0.008778568357229233, 0.040686219930648804, -0.0004514171741902828, -0.06778523325920105, -0.015593746677041054, 0.012613446451723576, 0.03217971324920654, -0.022681865841150284, 0.012759316712617874, -0.006558071821928024, 0.01663903146982193, 0.09220600128173828, 0.055940233170986176, -0.007633457891643047, -0.004155924078077078, -0.003387221833691001, -0.01726796105504036, -0.02206658013164997, -0.009140538051724434, -0.004013274796307087, 0.008115524426102638, -0.020680002868175507, -0.027793316170573235, -0.0023987661115825176, -0.038965579122304916, 0.02088518999516964, 0.009675730019807816, 0.06201677396893501, -0.01704265922307968, 0.0006722940597683191, 0.09711886942386627, 0.0022094454616308212, 0.05781826749444008, 0.035055167973041534, -0.010327132418751717, 0.008341371081769466, -0.06396198272705078, -0.04584735259413719, 0.010562146082520485, -0.02832651138305664, -0.033169638365507126, 0.08836325258016586, 0.003953758627176285, -0.03713054955005646, -0.053691498935222626, -0.046412598341703415, -0.002047349466010928, 0.02093507908284664, 0.0349099263548851, -0.00966573040932417, -0.05505041778087616, 0.015182887203991413, 0.001822517835535109, 0.015586656518280506, -0.01676693744957447, 0.012015391141176224, -0.0029397231992334127, 0.01106277946382761, -0.06615366041660309, -0.005271818954497576, -0.02268856391310692, 0.007696032989770174, 0.002205053810030222, -0.014975260943174362, -0.005211560521274805, -0.04614989459514618, 0.01775132305920124, -0.037082232534885406, 0.019755149260163307, -0.03021753765642643, -0.01746603101491928, 0.009865500032901764, -0.001821016427129507, -0.019610008224844933, -0.030775858089327812, 0.03291201591491699, 0.013020044192671776, -0.021268697455525398, 0.006235912907868624, 0.009524318389594555, 0.041655510663986206, -0.0542534664273262, 0.0052437977865338326, 0.003827723441645503, -0.024114293977618217, -0.00731409527361393, -0.021100977435708046, 0.03133131563663483, 0.024886492639780045, -0.02097087912261486, 0.01797831803560257, 0.03482021018862724, 0.03748463839292526, 0.011204961687326431, -0.011179715394973755, 0.02060895785689354, 0.024851717054843903, -0.023644067347049713, -0.056726276874542236, 0.02198369987308979, -0.026955364271998405, 0.08048132807016373, -0.07852593064308167, 0.05043306201696396, 0.015115813352167606, 0.032528866082429886, -0.03931372985243797, -0.02716992050409317, -0.0016817457508295774, -0.016852131113409996, -0.052096955478191376, 0.028963953256607056, 0.041932348161935806, 0.024975817650556564, 0.0039169760420918465, -0.002948923734948039, 0.020465053617954254, 0.01585138402879238, 0.007819805294275284, -0.016890874132514, 0.022079791873693466, 0.04576573520898819, 0.09822241216897964, 0.026520589366555214, 0.0075395479798316956, 0.0005394740146584809, 0.001217820798046887, 0.012228956446051598, 0.04840394854545593, 0.020527509972453117, -0.011036265641450882, 0.02193574607372284, 0.006571434438228607, 0.05591621994972229, -0.013542969711124897, 0.046144332736730576, -0.035103850066661835, 0.04074929282069206, 0.038041695952415466, -0.03747780993580818, -0.02230069413781166, -0.03210599720478058, -0.07169464975595474, -0.0303142499178648, -0.015857668593525887, -0.01161503978073597, 0.003404512070119381, -0.010348846204578876, -0.06005364656448364, 0.039940331131219864, 0.024649687111377716, 0.025617120787501335, 0.06017432361841202, 0.020686522126197815, 0.01265745796263218, -0.0015202645445242524, -0.018250105902552605, -0.018183458596467972, 0.06587833911180496, 0.09983686357736588, 0.04182298108935356, 0.04093382507562637, 0.011970264837145805, -0.018401218578219414, -0.021560119464993477, 0.01136296521872282, -0.034798216074705124, -0.09218375384807587, -0.05442196503281593, -0.011755740270018578, 0.008411899209022522, 0.011129056103527546, 0.04396183043718338, -0.03133569657802582, -0.05317814275622368, 0.006384780164808035, -0.04259057343006134, -0.0002865667047444731, 0.007495737634599209, 0.01110121887177229, -0.03712235391139984, -0.006534324958920479, -0.0067383539862930775, -0.08082960546016693, -0.04952874407172203, 0.0321989469230175, 0.05312563106417656, 0.03769056499004364, -0.048135820776224136, 0.0013297698460519314, -0.06964055448770523, -0.018564505502581596, 0.010883860290050507, -0.008216693066060543, 0.0375000536441803, 0.024908339604735374, -0.06080133467912674, 0.04262734204530716, 0.034593723714351654, 0.004884225316345692, 0.03465033695101738, -0.04835856333374977, 0.02405373565852642, 0.020122883841395378, -0.013095003552734852, -0.03377951681613922, -0.03365926817059517, 0.005081928800791502, -0.07411962002515793, 0.017294984310865402, 0.031523529440164566, 0.007841468788683414, -0.04832252860069275, 0.01722937822341919, -0.021549589931964874, 0.05188583955168724, 0.024007607251405716, -0.023797905072569847, 0.020588893443346024, 0.016588322818279266, -0.029323669150471687, -0.03589993342757225, 0.025246264412999153, 0.03060489520430565, -0.03333663567900658, 0.04234543442726135, 0.00011303700011922047, 0.013928539119660854, 0.021359901875257492, 0.020208468660712242, 0.06230274215340614, 0.00892862118780613, 0.027905814349651337, 0.0020160148851573467, -0.021816778928041458, -0.02134122885763645, 0.040615878999233246, 0.016384603455662727, -0.05535692349076271, -0.01484582107514143, 0.040105003863573074, -0.01050143875181675, -0.011199724860489368, -0.022027328610420227, -0.02794789895415306, -0.005158829968422651, -0.032100941985845566, -0.0024211667478084564, 0.07990749925374985, -0.06850513070821762, -0.011475672014057636, -0.04463110491633415, -0.047151222825050354, 0.033309970051050186, -0.0091641740873456, 0.012673962861299515, 0.036556120961904526, -0.02884213998913765, 0.01457501482218504, -0.03602912649512291, -0.018725352361798286, -0.05423688516020775, -0.008297373540699482, -0.00686775054782629, -0.028110723942518234, -0.0015460868598893285, -0.045580439269542694, 0.04370053485035896, -0.06644000113010406, 0.03147514536976814, 0.007408704608678818, 0.012943997979164124, 0.035051144659519196, 0.04627759009599686, -0.030496951192617416, 0.07682827115058899, 0.018887272104620934, 0.026319606229662895, -0.08999555557966232, -0.05532384291291237, 0.021655958145856857, -0.06030400097370148, -0.02658006176352501, -0.03160500526428223, 0.04558856785297394, -0.04234629124403, 0.09889911860227585, -0.012195590883493423, -0.016526998952031136, -0.019269822165369987, -0.0309754628688097, 0.0068597011268138885, -0.020626813173294067, 0.011363046243786812, -0.028961744159460068, -0.028868500143289566, 0.0015234441962093115, -0.04747685417532921, 0.026461146771907806, 0.02030566893517971, -0.037730664014816284, -0.013795974664390087, -0.02488728053867817, 0.02131027728319168, 0.005604469683021307, -0.018215777352452278, 0.0012963040499016643, -0.033776186406612396, 0.024835526943206787, 0.040027741342782974, 0.004690215457230806, 0.003487670561298728, -0.040416449308395386, -0.06421388685703278, -0.04505942761898041, -0.01352209784090519, -0.01095784641802311, 0.03683502599596977, -0.03620953857898712, 0.010513911955058575, 0.05297502130270004, -0.09777197241783142, -0.03663070499897003, 0.01649453490972519, -0.020371904596686363, 0.051970187574625015, 0.004620108753442764, 0.04979250952601433, -0.06671985238790512, -0.01175676379352808, 0.012370496056973934, -0.04739418998360634, -0.02393789403140545, 0.007660317700356245, -0.007317752111703157, -0.06904827058315277, -0.04348265379667282, -0.011122334748506546, -0.005827326327562332, -0.029436619952321053, -0.0013826761860400438, 0.04556393250823021, 0.015273364260792732, 0.027253633365035057, 0.0010704222368076444, -0.01726984605193138, -0.019473476335406303, -0.013357680290937424, 0.07466226816177368, -0.02082785591483116, 0.014685074798762798, -0.01866852305829525, -0.0026427609845995903, 0.004239467903971672, -0.05693887919187546, -0.012009542435407639, 0.019111644476652145, 0.053413890302181244 ]
<p>Why capacitors are used in flashlights of cameras instead of attaching the light directly to the battery? How this leads more light?</p>
g5385
[ 0.020801449194550514, 0.009642318822443485, -0.014586870558559895, 0.06528519839048386, 0.03569682314991951, 0.023434657603502274, 0.037441134452819824, -0.007326954510062933, 0.004959157668054104, -0.03203495219349861, -0.03928269445896149, 0.022236386314034462, 0.08345930278301239, 0.022711854428052902, -0.030308550223708153, 0.01649109460413456, 0.027118422091007233, 0.00937321875244379, 0.024626174941658974, 0.056128330528736115, -0.027985120192170143, -0.008848105557262897, -0.021739229559898376, 0.013810394331812859, -0.05950796604156494, 0.03533085435628891, 0.017529340460896492, -0.028419403359293938, 0.00018714145699050277, -0.03068654239177704, 0.047949716448783875, -0.018987858667969704, 0.04705177992582321, -0.010747109539806843, -0.012101764790713787, -0.06621699780225754, 0.0582064613699913, 0.08415007591247559, 0.03760850802063942, 0.06180863454937935, -0.038980577141046524, 0.0773373395204544, -0.022911876440048218, 0.01113254763185978, -0.003486966248601675, -0.05706612393260002, 0.025374317541718483, -0.029663963243365288, -0.01972862519323826, -0.08162279427051544, -0.015299138613045216, 0.009050406515598297, -0.006423331331461668, 0.04842396080493927, 0.0981704518198967, -0.014243762008845806, -0.010362616740167141, -0.009569165296852589, 0.07018136233091354, 0.00450899638235569, -0.005052533000707626, -0.02141917683184147, 0.03702223300933838, -0.002287458162754774, 0.015588068403303623, -0.04484637454152107, 0.018836012110114098, -0.03294908255338669, 0.0559171698987484, 0.05198298394680023, -0.0005598023417405784, -0.03234686329960823, -0.0030506281182169914, 0.0002493213687557727, 0.05495749041438103, -0.0401863157749176, -0.003222094150260091, -0.0015628527617082, -0.07071586698293686, -0.020116755738854408, 0.012607093900442123, -0.0464203916490078, -0.009608483873307705, -0.04361923784017563, 0.01800258830189705, 0.014913259074091911, -0.0005141611909493804, 0.028461258858442307, -0.030576340854167938, -0.054520655423402786, 0.08710113912820816, -0.004930730909109116, 0.07895205914974213, -0.019858181476593018, -0.042975764721632004, 0.002421534387394786, 0.07106492668390274, -0.016919121146202087, 0.04647592455148697, 0.018869413062930107, -0.015607453882694244, 0.01844221167266369, 0.023434948176145554, 0.0612943135201931, 0.005833652336150408, 0.029706371948122978, 0.014749888330698013, 0.01382929552346468, -0.029668577015399933, -0.04137611389160156, -0.04541606828570366, 0.0064097060821950436, 0.019685102626681328, -0.016176456585526466, -0.03308752551674843, 0.022247036918997765, 0.0792107880115509, -0.08998004347085953, 0.04758564382791519, 0.018408535048365593, -0.024998998269438744, 0.007417591288685799, -0.05448092147707939, -0.00798353273421526, 0.016595300287008286, -0.012309189885854721, 0.08197441697120667, -0.009893421083688736, 0.009748991578817368, -0.0036608781665563583, 0.035553935915231705, 0.018675899133086205, -0.06449365615844727, -0.021048564463853836, 0.08043136447668076, 0.04086502641439438, -0.000015381410776171833, -0.05594390630722046, 0.032091256231069565, -0.0033750601578503847, 0.02286425605416298, -0.004509918391704559, 0.022664865478873253, 0.04269755259156227, 0.0056954026222229, 0.007833846844732761, -0.042159490287303925, 0.053738757967948914, 0.030135612934827805, 0.01768381893634796, 0.024853868409991264, 0.03411310911178589, 0.019814465194940567, -0.05592440068721771, 0.03257640451192856, -0.03452553600072861, 0.02534385211765766, -0.0334366075694561, -0.03360513225197792, -0.03926754370331764, 0.02281038649380207, 0.04986089468002319, -0.0584893524646759, -0.015134962275624275, -0.04107696935534477, -0.02471992000937462, 0.05662206932902336, 0.0011319296900182962, -0.051396504044532776, -0.03813047707080841, 0.03779807314276695, -0.03932882845401764, -0.05436459928750992, 0.01759285293519497, 0.04512506723403931, 0.03649912402033806, 0.07552842795848846, 0.043869346380233765, 0.06338395923376083, -0.00447413045912981, -0.01825818046927452, -0.00826448667794466, -0.03122299537062645, -0.04883432388305664, 0.00415680231526494, 0.02683825045824051, 0.007443718612194061, -0.016759658232331276, 0.005125421565026045, 0.018934475257992744, -0.047178544104099274, -0.0016596128698438406, -0.0475664883852005, 0.05186145380139351, -0.057468123733997345, -0.019519565626978874, -0.04575156047940254, -0.05784858763217926, -0.0009007863118313253, -0.0036551509983837605, -0.07556255161762238, -0.04652371630072594, 0.00043706814176402986, 0.004168817773461342, 0.051686182618141174, -0.012488228268921375, -0.007229883689433336, -0.061461061239242554, 0.026835935190320015, 0.0026454266626387835, -0.03021218813955784, 0.03060922957956791, 0.019418897107243538, 0.015316590666770935, -0.04538287967443466, -0.0667773112654686, -0.03231172263622284, 0.028703350573778152, 0.013946741819381714, 0.0034884046763181686, -0.040203701704740524, 0.021418098360300064, 0.023219574242830276, 0.0017627265769988298, -0.029349427670240402, 0.019009873270988464, -0.030305199325084686, 0.015160824172198772, -0.024296121671795845, 0.010914640501141548, -0.03332360461354256, -0.005749584641307592, -0.025868766009807587, -0.0033100955188274384, -0.01907130517065525, 0.034279871731996536, 0.012929736636579037, -0.025773024186491966, 0.0023099887184798717, 0.022625494748353958, 0.0034901429899036884, -0.03568630293011665, 0.025708887726068497, -0.015257474035024643, -0.008934983983635902, 0.029541227966547012, 0.013670559041202068, 0.02169773355126381, -0.07371173053979874, 0.013497959822416306, -0.0023345663212239742, 0.012189040891826153, -0.033920884132385254, -0.03963609039783478, 0.025633160024881363, -0.027927806600928307, 0.025576578453183174, 0.030053086578845978, -0.011352472007274628, 0.05510614439845085, -0.03395899385213852, -0.05167011171579361, -0.08878908306360245, -0.02820337750017643, -0.00811751838773489, 0.059091560542583466, -0.03398788347840309, -0.026651225984096527, 0.06221945956349373, -0.009923433884978294, -0.011352915316820145, 0.09014421701431274, -0.02473273314535618, -0.04817725718021393, 0.014102828688919544, -0.008992607705295086, 0.038743410259485245, -0.008810462430119514, 0.038363322615623474, -0.09164846688508987, 0.03138711676001549, -0.026953641325235367, -0.05449488013982773, -0.06344862282276154, 0.022781256586313248, 0.006657149642705917, 0.01655513234436512, -0.05018521472811699, 0.03576966002583504, -0.05231437832117081, 0.019305629655718803, -0.025288868695497513, 0.02048860862851143, -0.06759458035230637, 0.09123846888542175, 0.019767018035054207, 0.06848736852407455, 0.07017791271209717, 0.017271503806114197, 0.03209201991558075, 0.04276922345161438, 0.07852596044540405, -0.039198681712150574, -0.019265135750174522, 0.015582993626594543, 0.016673238947987556, -0.021799826994538307, -0.04406976327300072, -0.015102609060704708, 0.08593835681676865, 0.023617194965481758, -0.010883435606956482, -0.0005986146861687303, 0.024606946855783463, -0.007480785250663757, -0.04616231098771095, -0.022569689899683, 0.038881853222846985, -0.04909887909889221, -0.07090136408805847, 0.021873733028769493, 0.02933541312813759, 0.004626639652997255, 0.005158992484211922, -0.014678889885544777, -0.02861803211271763, -0.01076429057866335, 0.030408084392547607, 0.05568407103419304, -0.011065307073295116, 0.023411883041262627, 0.04460640624165535, -0.0023342720232903957, -0.01382559072226286, -0.03271642327308655, -0.00880235806107521, 0.017824817448854446, 0.04227326065301895, -0.006350972689688206, -0.04743208736181259, -0.015504187904298306, 0.017145857214927673, -0.09839613735675812, -0.04988037049770355, 0.018008770421147346, -0.04312387481331825, 0.012583640404045582, 0.04351452738046646, -0.01522522047162056, -0.021841121837496758, 0.017912007868289948, 0.012467898428440094, 0.0014454764313995838, 0.014125388115644455, -0.0818590447306633, 0.046322014182806015, -0.027079297229647636, 0.05284423753619194, 0.014400992542505264, -0.020758284255862236, 0.06047233194112778, 0.03553098067641258, 0.021513503044843674, -0.005846573505550623, -0.010587146505713463, 0.024579595774412155, 0.0018961287569254637, 0.04849619045853615, -0.06718866527080536, -0.018288595601916313, -0.037481777369976044, -0.005140203982591629, -0.0480983629822731, 0.04677551984786987, -0.0037444548215717077, -0.02958521619439125, -0.029304727911949158, -0.0466957613825798, -0.03728414699435234, 0.022428521886467934, -0.03981956094503403, 0.013664083555340767, 0.06367748975753784, -0.048963721841573715, 0.03750931844115257, -0.022353651002049446, 0.02057621255517006, 0.048721760511398315, -0.0016772092785686255, -0.008324841968715191, -0.03770814090967178, 0.024366063997149467, -0.003166274167597294, -0.015827784314751625, -0.027837632223963737, -0.008575165644288063, -0.05272082984447479, -0.02549162693321705, 0.03449118882417679, -0.03856584429740906, -0.020625155419111252, 0.004853844176977873, 0.012760975398123264, -0.0007346352213062346, -0.02360123209655285, -0.004988092463463545, 0.043134044855833054, -0.02452061139047146, 0.042688753455877304, -0.010468066670000553, 0.026171265169978142, 0.014957317151129246, 0.012415633536875248, -0.025016963481903076, 0.036721207201480865, -0.014767718501389027, 0.03807656466960907, 0.07252596318721771, 0.04281993210315704, 0.037801437079906464, -0.0021434316877275705, -0.01583326980471611, -0.025138430297374725, 0.025460248813033104, 0.04593389853835106, 0.010469639673829079, -0.017865044996142387, -0.02986019290983677, 0.026329563930630684, -0.011676999740302563, -0.021716542541980743, 0.004970149137079716, 0.053757186979055405, 0.055136196315288544, 0.003373718122020364, 0.08110092580318451, 0.02242240309715271, 0.11606073379516602, 0.013621688820421696, 0.09269339591264725, 0.04718120023608208, -0.05263233929872513, -0.0009246608824469149, -0.06663023680448532, 0.062269046902656555, 0.03644770383834839, -0.06708478182554245, 0.05079461634159088, -0.015878023579716682, -0.0660870149731636, -0.040529560297727585, 0.017484962940216064, 0.005696968175470829, -0.025191279128193855, 0.061033785343170166, -0.02703475020825863, 0.001969690667465329, -0.010597508400678635, 0.030057338997721672, 0.04045015573501587, -0.08704448491334915, -0.014242276549339294, 0.03187369927763939, -0.0409734882414341, 0.032377421855926514, 0.007641601376235485, -0.08745720982551575, -0.06301312148571014, -0.009973831474781036, 0.0029648360796272755, -0.028800416737794876, 0.05866777524352074, -0.009815019555389881, 0.020532719790935516, 0.029297133907675743, -0.03493664786219597, -0.004277084954082966, 0.012680916115641594, -0.08807255327701569, -0.03571046516299248, -0.00849507749080658, -0.003355988534167409, -0.07047443836927414, -0.057677965611219406, -0.047054994851350784, -0.04048505425453186, -0.05600184202194214, -0.04980337992310524, 0.025791125372052193, -0.06419090181589127, 0.04827292263507843, 0.050014678388834, -0.02469456009566784, -0.021284056827425957, -0.028927698731422424, 0.02668648585677147, 0.05457606539130211, 0.007912720553576946, -0.014370942488312721, 0.008167950436472893, -0.01375938393175602, 0.003372856415808201, -0.05335628241300583, 0.03520625829696655, -0.01768339052796364, 0.01187315583229065, -0.0019519267370924354, 0.018817847594618797, 0.03999895229935646, -0.007289355155080557, 0.012786266393959522, -0.030065082013607025, -0.0003481649328023195, 0.03581669181585312, 0.04076557978987694, 0.016728391870856285, 0.012493736110627651, -0.0005035006906837225, 0.002625129884108901, 0.022158291190862656, 0.050131309777498245, -0.04451581835746765, -0.012057148851454258, 0.01178341917693615, 0.03641841560602188, 0.009970144368708134, 0.0020858219359070063, -0.0343274287879467, 0.0735810399055481, -0.028983816504478455, -0.01886676624417305, -0.002231250749900937, 0.07161402702331543, -0.019237719476222992, -0.02822565846145153, 0.007991740480065346, -0.010197288356721401, 0.023156648501753807, 0.02093811333179474, -0.006726368796080351, -0.006203352939337492, -0.035704147070646286, -0.006612597499042749, 0.11083370447158813, 0.02720540575683117, -0.05919058620929718, 0.06266497075557709, -0.0165182426571846, 0.032030437141656876, 0.012942544184625149, 0.059187788516283035, 0.05554106459021568, -0.045514848083257675, -0.03306026756763458, 0.0008669125963933766, -0.03236420825123787, 0.019602589309215546, -0.05030956119298935, -0.004685806576162577, -0.028614815324544907, 0.046677686274051666, 0.044270824640989304, 0.01866946555674076, 0.00359004782512784, 0.007762818597257137, -0.023118970915675163, 0.018943142145872116, -0.00884929671883583, -0.005521169397979975, -0.0018716107588261366, 0.0008903213893063366, -0.05874975398182869, 0.0392538458108902, -0.00776189798489213, -0.05433277785778046, 0.01759185455739498, 0.0027711056172847748, 0.02451941929757595, -0.05301625281572342, 0.013507510535418987, -0.06275469064712524, 0.010526586323976517, 0.004201806616038084, -0.07789047062397003, 0.01087712962180376, -0.03139123320579529, 0.052582353353500366, -0.021182121708989143, 0.0056765410117805, -0.037677131593227386, -0.004999164491891861, -0.022207915782928467, 0.046542949974536896, -0.040961917489767075, -0.020669078454375267, -0.01176542043685913, 0.04659348353743553, 0.03035982884466648, -0.001352485385723412, -0.038319069892168045, 0.003353340784087777, -0.01317570824176073, 0.03185943886637688, 0.015336391516029835, 0.007906650193035603, -0.037235382944345474, -0.007771840784698725, -0.007702813018113375, 0.023719534277915955, 0.023973854258656502, -0.0323479101061821, 0.01614624261856079, -0.05326257646083832, -0.0034613008610904217, 0.019651053473353386, 0.03803682327270508, -0.01577451452612877, 0.009274194948375225, -0.019278762862086296, 0.06093977019190788, -0.035940758883953094, 0.019528565928339958, 0.024444913491606712, 0.038875993341207504, -0.027338797226548195, 0.030046135187149048, -0.006351690273731947, 0.016271989792585373, -0.047330304980278015, 0.02293119765818119, -0.05987520143389702, 0.07592309266328812, 0.005309849977493286, 0.029214274138212204, 0.02566881850361824, 0.02133411169052124, -0.050143979489803314, -0.057191818952560425, -0.008487220853567123, -0.02903647907078266, 0.009581439197063446, 0.022788304835557938, -0.03400074318051338, 0.022049104794859886, -0.01867048069834709, 0.04191576689481735, 0.027032993733882904, -0.001860610325820744, -0.002515394240617752, -0.008728357031941414, -0.010856429114937782, -0.026677584275603294, -0.0307614728808403, 0.016152385622262955, 0.04652271047234535, 0.028185993432998657, 0.031592726707458496, -0.00845492072403431, -0.010975751094520092, -0.022426288574934006, -0.05235927551984787, -0.007373780012130737, 0.005427128169685602, -0.034322384744882584, 0.05683990567922592, 0.0020396460313349962, -0.003246632870286703, -0.033187385648489, -0.002890646690502763, 0.029994167387485504, 0.028049524873495102, -0.03562082722783089, -0.029404863715171814, -0.03835763409733772, -0.0131558021530509, 0.0334843210875988, 0.02031550742685795, 0.01628226786851883, -0.031122660264372826, -0.011476180516183376, -0.04207088425755501, -0.041235558688640594, -0.04404068365693092, -0.022158373147249222, -0.039388034492731094, 0.012184539809823036, -0.025744833052158356, -0.024454066529870033, 0.03791284188628197, -0.05285627767443657, -0.008898334577679634, -0.031235292553901672, 0.024111732840538025, -0.02545693702995777, 0.00209953379817307, 0.009136473760008812, -0.04291631281375885, -0.04146441072225571, 0.007059005089104176, 0.07616516202688217, 0.016347071155905724, -0.04952971264719963, 0.011521156877279282, 0.00474573764950037, -0.01372674573212862, 0.012920462526381016, -0.0009475783444941044, 0.00975891761481762, 0.019539931789040565, 0.00907889287918806, -0.057649679481983185, 0.004601265769451857, -0.008334580808877945, 0.05362707003951073, -0.01878741942346096, 0.01580195128917694, -0.013862940482795238, 0.07646191120147705, -0.017125578597187996, 0.0347939059138298, -0.05723688006401062, -0.04819381609559059, -0.02563154697418213, 0.019270053133368492, 0.007442111615091562, -0.01643100567162037, 0.059462498873472214, -0.006179760210216045, 0.027012687176465988, -0.025808412581682205, 0.030567875131964684, -0.019024234265089035, -0.013866747729480267, -0.04077006131410599, -0.03800499066710472, -0.02258583903312683, 0.008895715698599815, -0.013331861235201359, 0.010316966101527214, -0.017703821882605553, -0.04843279346823692, -0.014263040386140347, -0.00029600103152915835, -0.06081445515155792, -0.003264621365815401, 0.00379453063942492, -0.017174631357192993, 0.010203121230006218, 0.05342501029372215, -0.011938480660319328, 0.028680087998509407, 0.007271029986441135, -0.024770867079496384, 0.0018846566090360284, 0.05817651003599167, -0.040527988225221634, 0.00953197292983532, -0.006129160523414612, 0.06151667237281799, 0.023590058088302612, 0.008811495266854763, 0.0035844517406076193, -0.046808887273073196, -0.02178596332669258, 0.037145502865314484, -0.029290126636624336, -0.014547253958880901, -0.015794945880770683 ]
<p>I talked to a professor about solar panels and their efficiency. It seemed that the main reason solar panels aren't that efficient is because it can only accept a single energy input size. Anything below is ignored and anything above only gives the energy of that single limit.</p> <p>That is, say the limit is 1W. A photon with 0.999W energy wouldn't give any voltage. A photon with 10W energy would give the same voltage as a 1W photon.</p> <p>Does this mean I can get very high efficiency from a light source with a specific frequency? For example a solar-powered calculator in a room with only sodium lights. How high?</p> <p>How does the efficiency change depending on the amount of light or the temperature of the solar cell? How about an extremely small amount of light, like 1nW, close to 0K?</p> <p>This could be terribly wrong as there was quite a language barrier between us. I want to learn, so please point out any misstakes.</p>
g5386
[ 0.005114101339131594, 0.12241783738136292, 0.01629830338060856, 0.048987142741680145, 0.0030359760858118534, -0.041258808225393295, 0.041489388793706894, 0.016983559355139732, -0.026751581579446793, -0.03674537315964699, 0.029355419799685478, 0.051567770540714264, 0.006817998364567757, 0.018612615764141083, -0.007951597683131695, 0.005452485289424658, 0.0987812876701355, 0.008942239917814732, 0.07907213270664215, 0.07753801345825195, -0.02613729238510132, -0.0034766860771924257, -0.019551867619156837, -0.05859791859984398, -0.07688305526971817, 0.08707355707883835, 0.021057024598121643, -0.02555139735341072, -0.03356238082051277, -0.05505705624818802, -0.0258528720587492, -0.04824339598417282, 0.029737401753664017, 0.032326143234968185, -0.06453736126422882, 0.046476565301418304, 0.08843133598566055, -0.03069455921649933, 0.012257221154868603, 0.012136638164520264, -0.020449165254831314, 0.001936033251695335, 0.01862455904483795, -0.04023709520697594, 0.012787360697984695, -0.023907136172056198, 0.012673317454755306, -0.021826516836881638, 0.011778668500483036, -0.04219122976064682, 0.005064106546342373, -0.03631730377674103, 0.04059888422489166, 0.019124839454889297, 0.021492550149559975, 0.026849785819649696, -0.019987301900982857, -0.040068767964839935, 0.048623308539390564, 0.024310773238539696, 0.003985534887760878, 0.03475954383611679, 0.003127060364931822, -0.018833473324775696, -0.04195592924952507, 0.03333872929215431, 0.005822648294270039, -0.0314822681248188, 0.0025015471037477255, -0.012251836247742176, 0.023373940959572792, -0.032176729291677475, -0.022177819162607193, -0.05743195116519928, 0.02967733144760132, -0.035589367151260376, 0.02351296879351139, 0.013622391037642956, -0.005689674988389015, 0.029440516605973244, -0.004979860503226519, -0.04927976429462433, 0.000684355734847486, -0.008937289007008076, 0.05178846791386604, 0.0177055224776268, -0.01575661264359951, -0.030306126922369003, -0.03810948505997658, -0.0009434957755729556, 0.013108805753290653, 0.017017558217048645, 0.06549733877182007, 0.0074170674197375774, 0.002695937640964985, 0.035298120230436325, 0.037497006356716156, 0.001829380402341485, 0.002242681570351124, 0.005630155093967915, -0.0375584177672863, -0.022132975980639458, 0.004992862232029438, 0.01521438080817461, -0.016768604516983032, 0.03452372923493385, 0.04443959891796112, -0.05050557851791382, -0.029980091378092766, -0.003677629167214036, -0.008329403586685658, -0.01601606421172619, -0.005678546614944935, -0.06965464353561401, -0.09669680148363113, 0.009039495140314102, 0.03953612968325615, -0.0024670392740517855, 0.02088998258113861, 0.027306579053401947, 0.051702551543712616, 0.04865036904811859, 0.005599873140454292, 0.035899125039577484, 0.002101586665958166, -0.0055050537921488285, 0.06160512939095497, 0.03601454943418503, -0.007689371705055237, -0.0014673469122499228, 0.008452457375824451, -0.004778533708304167, -0.041930925101041794, -0.008392997086048126, 0.05433035269379616, 0.024812908843159676, 0.04393839091062546, -0.0024595491122454405, 0.06501534581184387, -0.012672457844018936, 0.008920859545469284, -0.013084170408546925, -0.01913340762257576, -0.0032325617503374815, -0.0000540617220394779, -0.0019080240745097399, -0.05042282119393349, 0.01713687554001808, -0.026273898780345917, 0.039040371775627136, 0.07271142303943634, 0.016132595017552376, 0.020562605932354927, -0.044481467455625534, 0.007492204196751118, 0.048640575259923935, 0.04493037238717079, -0.00307140639051795, -0.044541459530591965, -0.0010938324267044663, 0.07220254838466644, 0.04961434006690979, 0.0015527006471529603, -0.03555132448673248, -0.07332132756710052, -0.04717842489480972, 0.013974069617688656, -0.06787450611591339, -0.04679020866751671, 0.0010257859248667955, -0.050238024443387985, -0.012255566194653511, 0.047154415398836136, 0.023897893726825714, -0.020165205001831055, 0.018004098907113075, 0.05302859842777252, -0.020122535526752472, -0.026930373162031174, 0.018634721636772156, -0.017395205795764923, -0.02238168939948082, 0.028439493849873543, -0.04461373761296272, -0.052901048213243484, 0.0009717351058498025, -0.013118479400873184, -0.04009971395134926, -0.009753306396305561, 0.03509972244501114, -0.041649457067251205, -0.00010554755135672167, 0.044417448341846466, -0.05299649015069008, -0.03384104371070862, -0.0026792800053954124, -0.03971008211374283, -0.016305875033140182, -0.06220775842666626, -0.0310091320425272, -0.03506090119481087, 0.01324518397450447, 0.010833075270056725, -0.0034268912859261036, 0.041480693966150284, 0.0667046383023262, -0.025395603850483894, -0.047140318900346756, -0.011104503646492958, -0.03524084761738777, 0.02923745848238468, -0.041661862283945084, -0.03602880612015724, 0.0728909820318222, 0.007543963845819235, -0.011492740362882614, -0.08511854708194733, -0.07504034042358398, 0.02787562645971775, -0.01623591221868992, 0.005287260748445988, 0.0006269731093198061, 0.07142670452594757, 0.040987927466630936, -0.048144370317459106, 0.0630650445818901, -0.04134643077850342, -0.01280028373003006, 0.027062132954597473, 0.025863926857709885, -0.07673434913158417, 0.04333136975765228, -0.027202198281884193, -0.04544835165143013, -0.029972760006785393, 0.03703008219599724, -0.01254965178668499, 0.024824118241667747, -0.010641193948686123, -0.016667364165186882, 0.017245670780539513, -0.058790769428014755, -0.029950030148029327, -0.028589829802513123, -0.055624913424253464, -0.0801239088177681, 0.012093768455088139, -0.02015698328614235, -0.05449530482292175, 0.015019482001662254, 0.04358822852373123, 0.014829223044216633, 0.033442795276641846, 0.05401148647069931, -0.05953904986381531, -0.02057412639260292, -0.009804247878491879, 0.02309170365333557, -0.03483886644244194, -0.045483484864234924, 0.008319171145558357, -0.0247632022947073, 0.009045727550983429, 0.03779222071170807, 0.016259700059890747, -0.0022894716821610928, -0.028987931087613106, -0.0638774186372757, 0.019155941903591156, -0.017318062484264374, 0.006486124359071255, 0.05959640070796013, 0.02472696825861931, -0.013262496329843998, 0.006021049339324236, -0.007229857612401247, -0.018225185573101044, -0.012886349111795425, 0.06606801599264145, -0.09837248176336288, 0.028496619313955307, -0.032526835799217224, -0.0700603574514389, -0.031156273558735847, 0.0008379881619475782, -0.03718148171901703, 0.016830718144774437, 0.019150985404849052, 0.027363833039999008, -0.013632003217935562, -0.06685987114906311, -0.007085451390594244, 0.03798036649823189, -0.015285885892808437, -0.010664560832083225, -0.03601473197340965, 0.032047949731349945, 0.003292001783847809, -0.053276561200618744, 0.009942993521690369, -0.019047176465392113, 0.019490493461489677, -0.01398315466940403, -0.025147119536995888, -0.058601561933755875, 0.04383574426174164, -0.033196136355400085, -0.023696493357419968, 0.015265272930264473, 0.033759910613298416, -0.00037551255081780255, 0.02520364709198475, 0.009596293792128563, 0.06487499177455902, -0.06506597250699997, 0.013950983993709087, 0.004723455291241407, -0.06112222000956535, -0.044530414044857025, -0.010607989504933357, 0.008155564777553082, 0.0028801399748772383, 0.03282972052693367, -0.007262145169079304, 0.0069611575454473495, 0.040279146283864975, 0.005254118237644434, -0.03847359120845795, -0.02796575054526329, -0.006072639022022486, 0.03010423295199871, 0.008662342093884945, -0.08714268356561661, -0.01797294244170189, 0.017711076885461807, -0.04001547768712044, -0.015037856064736843, 0.02034907042980194, 0.01566844806075096, -0.00030732195591554046, -0.01780240796506405, 0.0503116175532341, -0.07864595204591751, -0.01253100112080574, 0.002812853315845132, 0.02249678038060665, -0.009346325881779194, -0.07834641635417938, -0.036659181118011475, -0.01874692179262638, 0.04573339596390724, -0.0348714143037796, -0.023224245756864548, 0.01556706428527832, -0.027414552867412567, 0.048687927424907684, -0.016622742637991905, 0.03216627240180969, 0.016296178102493286, 0.03776156157255173, 0.010184218175709248, -0.015027838759124279, 0.06923523545265198, -0.036150626838207245, -0.054986488074064255, 0.05584388226270676, -0.00018151324184145778, 0.04479930177330971, -0.01903592050075531, -0.011659517884254456, -0.007153935264796019, -0.0028907633386552334, -0.003289522137492895, 0.022290106862783432, -0.02916461043059826, -0.04686273634433746, 0.03830951824784279, -0.000009885955478239339, 0.012708593159914017, 0.029051773250102997, 0.02357448823750019, -0.02567577362060547, -0.007234487216919661, -0.035102128982543945, 0.028430545702576637, 0.001560758682899177, -0.04120760038495064, 0.005204923916608095, 0.008526721969246864, -0.020373934879899025, -0.009627231396734715, -0.08587604761123657, -0.0024341552052646875, 0.0376829095184803, 0.018446683883666992, -0.02190965600311756, 0.06534083187580109, -0.011274288408458233, 0.025337783619761467, 0.03845128044486046, 0.01856108382344246, 0.03999808803200722, 0.010935896076261997, -0.049443770200014114, 0.0245775505900383, 0.004349774681031704, 0.019526749849319458, -0.04920162260532379, -0.047514885663986206, 0.006453953217715025, 0.029736917465925217, -0.005095364060252905, 0.05613156780600548, -0.03167666494846344, 0.043540071696043015, 0.046565134078264236, 0.02638045698404312, -0.01671050302684307, 0.09594638645648956, 0.059832822531461716, -0.03165535256266594, 0.0034946328960359097, -0.03614203631877899, -0.04396068677306175, 0.017706647515296936, 0.11218848824501038, 0.01428257767111063, -0.020269716158509254, 0.0029262977186590433, -0.029502879828214645, 0.07452481985092163, 0.03008340671658516, -0.01533790584653616, -0.006829488091170788, -0.0022609771694988012, 0.03874756023287773, 0.0015979448799043894, 0.02962789312005043, 0.031901292502880096, 0.02932889387011528, 0.01789255253970623, 0.02272171527147293, 0.008820254355669022, 0.034412041306495667, 0.025756729766726494, -0.0293864868581295, -0.006143820937722921, -0.00404489366337657, -0.026980841532349586, -0.020068224519491196, -0.04612502083182335, -0.009619939140975475, -0.055865075439214706, -0.04135122522711754, 0.017128264531493187, 0.03870852664113045, -0.03856689855456352, 0.016888223588466644, 0.029061632230877876, 0.05170384421944618, -0.02938993088901043, 0.006507888436317444, 0.03220491483807564, -0.006002798676490784, -0.024081354960799217, 0.043021298944950104, -0.06031038239598274, -0.04205239564180374, -0.05565856397151947, -0.006268942728638649, -0.017662251368165016, 0.025571102276444435, 0.024693259969353676, -0.022469157353043556, -0.04287119209766388, -0.06293381750583649, -0.020998859778046608, -0.047885581851005554, -0.02581312134861946, 0.021196676418185234, 0.007360950578004122, -0.005927952937781811, 0.018084436655044556, 0.0561397559940815, 0.04119975492358208, 0.0022821761667728424, -0.06643436849117279, 0.027494266629219055, 0.03435451164841652, -0.030158257111907005, -0.05384783819317818, 0.044603727757930756, 0.010865837335586548, 0.005181888118386269, 0.008525814861059189, 0.05094418674707413, 0.07420071959495544, -0.0346696674823761, 0.0147754717618227, 0.045164626091718674, 0.002697537885978818, 0.0005832031602039933, -0.037959225475788116, -0.04397159069776535, 0.016896547749638557, 0.03119276836514473, 0.0022133009042590857, -0.060588542371988297, 0.04656099155545235, 0.041125670075416565, -0.05195226892828941, 0.001141522079706192, -0.004538365174084902, 0.053755830973386765, 0.025521468371152878, -0.0467805489897728, -0.03514573723077774, 0.015820911154150963, -0.005568422377109528, 0.012754257768392563, 0.002197816502302885, -0.05064404010772705, -0.012751412577927113, 0.012300916016101837, 0.029512811452150345, -0.031281501054763794, -0.12624958157539368, -0.04320482537150383, 0.0431586317718029, -0.005905539728701115, 0.06562095880508423, 0.03968213498592377, -0.05181684345006943, 0.01291828602552414, -0.004571935627609491, 0.034663133323192596, 0.046888869255781174, -0.05866418406367302, 0.046138446778059006, 0.016223613172769547, -0.0054977103136479855, -0.029353676363825798, 0.014889298938214779, 0.006035470403730869, 0.006622149143368006, 0.019428236410021782, 0.01258502621203661, -0.0007015078444965184, -0.013532177545130253, -0.015936894342303276, -0.005883741658180952, 0.03882720693945885, 0.05707589164376259, -0.010024133138358593, -0.0009735692292451859, 0.062448952347040176, -0.023562166839838028, 0.0005481218686327338, 0.06848280131816864, -0.01587110571563244, 0.014486484229564667, 0.06770500540733337, -0.0066332644782960415, -0.04803486168384552, 0.007901199162006378, -0.040439579635858536, -0.024847853928804398, -0.07558366656303406, -0.005275217350572348, 0.050846636295318604, 0.023721763864159584, 0.0406433530151844, 0.020250989124178886, 0.001864679274149239, 0.024950124323368073, -0.05106205865740776, 0.05522098019719124, -0.01650797389447689, -0.04248415678739548, -0.0711338073015213, 0.0029668111819773912, 0.016166726127266884, -0.0013332675443962216, -0.012655389495193958, 0.023334389552474022, 0.028120189905166626, -0.010132054798305035, -0.010691652074456215, -0.011394774541258812, -0.03911753371357918, -0.02354240231215954, -0.015549866482615471, 0.04074157029390335, 0.028571613132953644, -0.011903967708349228, -0.08104917407035828, -0.00275827432051301, 0.008879618719220161, -0.0015775973442941904, -0.032116882503032684, 0.0024268452543765306, 0.00022334055393002927, -0.014085003174841404, -0.02211536467075348, 0.017356546595692635, -0.007273809053003788, -0.007833603769540787, 0.031659066677093506, 0.0014712972333654761, -0.008013500832021236, -0.0582648329436779, 0.018784189596772194, -0.004309431649744511, 0.03067154437303543, -0.006621139124035835, -0.08451218158006668, -0.02062886767089367, -0.003959862049669027, 0.060035575181245804, -0.009978974238038063, 0.037546705454587936, -0.07236035168170929, 0.04492330923676491, -0.05526227131485939, 0.0003886748745571822, 0.09091062098741531, 0.024678910151124, 0.07273366302251816, 0.09306700527667999, -0.019610924646258354, 0.0071929022669792175, 0.03037712536752224, -0.025295907631516457, 0.06813658028841019, 0.005051635205745697, 0.053970035165548325, -0.07051023095846176, -0.01734803430736065, 0.030701952055096626, 0.025148866698145866, -0.02424783632159233, 0.02417072281241417, -0.004794674459844828, 0.0710151419043541, 0.006727661471813917, 0.059120845049619675, -0.016754377633333206, -0.011016719043254852, -0.03769850358366966, 0.008066656067967415, 0.0027377137448638678, -0.034413132816553116, -0.0380704402923584, 0.007296609692275524, -0.011288671754300594, 0.062151119112968445, -0.02797362394630909, 0.06265006214380264, 0.0004754848778247833, -0.02341422811150551, 0.02434082329273224, 0.06512138247489929, -0.020272625610232353, 0.0405689999461174, 0.061655811965465546, 0.038186874240636826, 0.014181302860379219, -0.04748576134443283, -0.031241675838828087, -0.037586551159620285, 0.032262563705444336, -0.006113753654062748, -0.02310802787542343, -0.0017708130180835724, 0.004951794631779194, -0.03101687878370285, -0.07012677937746048, 0.01619178242981434, -0.01503461692482233, -0.044885728508234024, 0.018035300076007843, 0.009703517891466618, 0.004349023103713989, -0.008578145876526833, 0.03196815028786659, -0.004014803096652031, -0.04799145832657814, -0.006433307658880949, -0.0043607475236058235, 0.0183273795992136, -0.07495767623186111, -0.00751967029646039, 0.03547964245080948, 0.016389664262533188, 0.009964626282453537, 0.04243915528059006, 0.03905375674366951, -0.010855359956622124, 0.03765265643596649, 0.013274549506604671, 0.026860129088163376, -0.03463971987366676, -0.04424677789211273, -0.014821285381913185, -0.029598120599985123, 0.0365542471408844, -0.03706325218081474, -0.013964866288006306, 0.017574334517121315, 0.01563074067234993, 0.019004948437213898, -0.005148075986653566, -0.00468476302921772, 0.02941351756453514, 0.04575289785861969, 0.01912287250161171, -0.042404673993587494, 0.005147968418896198, -0.01152015570551157, 0.016806483268737793, -0.038799334317445755, 0.02034526690840721, 0.016235826537013054, -0.04791198670864105, 0.024424567818641663, -0.01892082951962948, 0.045258261263370514, -0.009312745183706284, 0.04680820181965828, 0.0287671759724617, -0.002776936162263155, -0.03703245893120766, -0.0030875131487846375, -0.06498366594314575, -0.043363604694604874, -0.01881619170308113, -0.0015373688656836748, -0.011784905567765236, 0.005064845085144043, 0.015194263309240341, 0.037367865443229675, 0.002381838858127594, -0.024598436430096626, -0.03655696660280228, 0.0006293811602517962, 0.030496593564748764, -0.07955943048000336, 0.0020081917755305767, 0.03764178603887558, -0.054579589515924454, -0.06925898790359497, 0.040218472480773926, -0.010478324256837368, 0.041017401963472366, 0.07249026745557785, -0.035546425729990005, 0.0027075689285993576, 0.015378063544631004, -0.007753998041152954, -0.0006223897216841578, -0.01644672080874443, 0.039242129772901535, 0.020207809284329414, 0.023635102435946465, -0.033931370824575424, -0.006787620950490236, 0.022706594318151474, -0.05772341787815094 ]
<p>I know the magnetic field strength increases as the number of turns in the solenoid increases.</p> <p>However, I've learnt the field inside the solenoid is usually nearly uniform.</p> <p>So, does the number of turns in the solenoid effect the uniformity of the field inside the solenoid? Does the field gets closer to uniform as the number of turns increases?</p>
g5387
[ -0.0009456349653191864, 0.06641116738319397, 0.00889026653021574, -0.0671873688697815, 0.06442558765411377, -0.0001303242170251906, 0.04855718836188316, 0.031184779480099678, -0.03030918724834919, -0.02248828299343586, -0.0756828784942627, -0.0021220329217612743, -0.03369758278131485, 0.0010413660202175379, 0.05421065911650658, -0.030813798308372498, -0.009584936313331127, 0.009169286116957664, 0.02706344611942768, -0.014693191275000572, 0.024241700768470764, 0.04783763736486435, 0.0037458327133208513, 0.04057854041457176, -0.004579920321702957, -0.013325341045856476, -0.003697374602779746, -0.05719083547592163, 0.009371520020067692, -0.031245265156030655, -0.026712339371442795, -0.009700814262032509, 0.038193605840206146, -0.006201381329447031, -0.08682004362344742, -0.025787103921175003, -0.013438379392027855, 0.07375789433717728, 0.012509895488619804, -0.028008395805954933, 0.029915671795606613, 0.01576678268611431, 0.016042377799749374, -0.01231333613395691, -0.02886275202035904, -0.048695169389247894, -0.07801000773906708, -0.0026532376650720835, -0.043611329048871994, 0.03547169268131256, -0.05373956635594368, -0.08490928262472153, 0.03276194632053375, 0.06378908455371857, 0.0349719412624836, 0.007511295843869448, -0.003543310100212693, -0.07168638706207275, 0.008839203044772148, 0.05457596853375435, 0.0038985591381788254, 0.016111239790916443, 0.006759410724043846, -0.011828736402094364, -0.03860355168581009, -0.009691997431218624, -0.03533506020903587, 0.01761271245777607, -0.015414799563586712, 0.030440950766205788, -0.07256150245666504, -0.05332699790596962, 0.001682481961324811, -0.04990025982260704, 0.016490459442138672, 0.06711044907569885, 0.06666948646306992, 0.0068769981153309345, -0.014116743579506874, 0.07270241528749466, -0.06514143198728561, 0.015727100893855095, -0.024560440331697464, 0.0053444127552211285, 0.0493793711066246, -0.030854346230626106, 0.006007414776831865, 0.010790069587528706, 0.019838795065879822, 0.016702257096767426, 0.04290543124079704, 0.031255025416612625, 0.01834070309996605, 0.01627950929105282, -0.02910386398434639, -0.03944171965122223, -0.007409825921058655, 0.018753817304968834, -0.040886372327804565, 0.05053437873721123, -0.03514937311410904, -0.03763341158628464, -0.00015468521451111883, -0.02326304093003273, 0.006209299433976412, 0.009013492614030838, -0.016537493094801903, 0.0191156305372715, -0.005119534209370613, 0.00477906409651041, -0.04907936230301857, -0.05640166252851486, -0.004044842906296253, 0.009125170297920704, -0.046483490616083145, 0.023617256432771683, 0.026733819395303726, -0.0058885072357952595, -0.0005946663441136479, 0.0428522452712059, 0.03199146315455437, 0.007213817909359932, -0.06038977950811386, 0.032678041607141495, 0.019420234486460686, 0.03349243849515915, 0.017886042594909668, 0.022940291091799736, 0.01912899687886238, 0.01697414182126522, 0.00709677767008543, -0.0012230576248839498, 0.03699305281043053, -0.013094175606966019, 0.006366916466504335, 0.02893674187362194, 0.026495125144720078, 0.011620670557022095, -0.004118276294320822, 0.022632651031017303, 0.010966264642775059, -0.04425078257918358, 0.057351429015398026, -0.04942091181874275, 0.012435764074325562, -0.029408859089016914, 0.06993436068296432, 0.012182480655610561, 0.012675033882260323, 0.01649983413517475, 0.028531143441796303, -0.011491933837532997, 0.03170591592788696, -0.004259177017956972, -0.02524266578257084, 0.02124209515750408, 0.01972062513232231, 0.03478727862238884, 0.06325963139533997, -0.04076602682471275, 0.015582221560180187, -0.009483966045081615, 0.039186835289001465, -0.03260287642478943, -0.07967732846736908, 0.02016846276819706, 0.016810676082968712, 0.01028648391366005, 0.0023589469492435455, -0.022786974906921387, -0.0031326045282185078, -0.012725774198770523, 0.0019070961279794574, 0.09866266697645187, 0.000056965458497870713, 0.002576566068455577, 0.07846873998641968, -0.012841477058827877, 0.026127316057682037, 0.036086298525333405, 0.003769343253225088, 0.0209200419485569, -0.02985202707350254, -0.060282252728939056, -0.004694319795817137, 0.027427639812231064, -0.0017057869117707014, 0.01833971031010151, -0.07123134285211563, -0.006955401971936226, -0.017784258350729942, 0.033731210976839066, 0.03349006175994873, 0.06765033304691315, -0.044253669679164886, -0.035682082176208496, -0.05417242273688316, -0.04892917722463608, -0.03768575191497803, -0.03283405676484108, -0.046459347009658813, 0.03624250367283821, 0.062340013682842255, -0.008245613425970078, 0.03943318873643875, -0.02825482003390789, -0.0004309730138629675, 0.023822925984859467, 0.10395970940589905, -0.013015399686992168, 0.026267126202583313, 0.07150274515151978, 0.0007372975815087557, -0.03656134009361267, -0.034123342484235764, 0.00486445939168334, -0.010438562370836735, 0.014665845781564713, 0.03718838468194008, 0.022701114416122437, 0.030059445649385452, -0.02353791706264019, 0.06160417199134827, 0.0049289739690721035, -0.06934656202793121, -0.030441273003816605, -0.010970461182296276, 0.014609523117542267, -0.033013466745615005, -0.015418553724884987, -0.06479132920503616, -0.061576955020427704, -0.01496856939047575, -0.023929757997393608, -0.04804086685180664, -0.03781626373529434, 0.05231348052620888, -0.00700907688587904, -0.0010072631994262338, 0.0026022878009825945, 0.015581839717924595, 0.009966915473341942, -0.0015053327661007643, -0.014818753115832806, 0.012655675411224365, -0.04185236245393753, -0.0033313308376818895, -0.03061135672032833, 0.0063779037445783615, 0.08585786819458008, 0.01668202318251133, -0.01243132259696722, -0.006330713629722595, 0.07860624045133591, -0.050736792385578156, 0.04060687869787216, -0.005530790891498327, 0.07182347774505615, 0.009425511583685875, 0.008164568804204464, 0.0036339154466986656, -0.04709193855524063, 0.0032157369423657656, 0.03548929840326309, -0.024477673694491386, 0.03895871341228485, -0.001969266217201948, -0.011089453473687172, 0.02425290271639824, 0.0007407687953673303, -0.06963428854942322, 0.05557749792933464, -0.0026509773451834917, 0.02212595008313656, 0.024341832846403122, -0.03549840673804283, 0.03462613746523857, -0.006291926372796297, -0.0170005913823843, -0.02125096693634987, -0.03701368346810341, -0.026702437549829483, 0.01593862846493721, -0.0036099853459745646, 0.005912985652685165, -0.028843842446804047, -0.02561102993786335, -0.05616127327084541, -0.03214738890528679, 0.042533617466688156, -0.024165078997612, -0.03137996420264244, 0.0932341068983078, -0.057146959006786346, 0.060216642916202545, -0.018957912921905518, -0.016983799636363983, -0.026537006720900536, 0.006838275585323572, -0.003290820401161909, -0.01707090623676777, 0.01681261882185936, -0.014381974935531616, -0.0737379640340805, -0.018931590020656586, 0.02925042062997818, -0.01705893874168396, -0.08070775121450424, 0.00998065434396267, 0.01638784445822239, -0.07487507909536362, 0.0066747418604791164, 0.01022601593285799, -0.010958907194435596, -0.014599775895476341, 0.0066645508632063866, 0.03204428032040596, 0.09249952435493469, -0.013807689771056175, 0.015963351354002953, 0.002775318454951048, -0.04898788407444954, 0.017619168385863304, -0.011013462208211422, 0.04751202091574669, 0.005004977807402611, 0.0696086660027504, 0.02522536739706993, -0.04937572777271271, -0.010854726657271385, 0.022694647312164307, 0.009205023758113384, -0.007453700061887503, -0.0286052655428648, -0.09874288737773895, 0.0590023510158062, 0.019204096868634224, 0.017233597114682198, -0.012410799041390419, -0.008556024171411991, 0.020381711423397064, -0.05846032872796059, -0.05696052685379982, -0.05276649072766304, -0.0400867685675621, 0.08765692263841629, 0.010285737924277782, -0.03532717004418373, 0.03276927024126053, 0.03265218436717987, 0.08365467190742493, -0.027932370081543922, -0.005036270711570978, 0.006830662023276091, 0.024248970672488213, -0.041030291467905045, -0.05861417576670647, 0.024229569360613823, 0.01746813952922821, 0.015501515939831734, 0.06191964074969292, -0.03423253819346428, 0.01206091046333313, 0.010143439285457134, -0.01700464077293873, 0.0008281501359306276, 0.010799509473145008, 0.0594460666179657, -0.009041165001690388, 0.0012564476346597075, -0.07802529633045197, 0.04273177310824394, 0.0025907913222908974, 0.005212961696088314, -0.004450206179171801, -0.01604413613677025, 0.010051828809082508, -0.0116521455347538, 0.01635272428393364, -0.026034675538539886, 0.025207048282027245, 0.026291746646165848, -0.014276135712862015, -0.012712341733276844, 0.06513006240129471, 0.059195809066295624, 0.023972732946276665, -0.018000230193138123, -0.0031900748144835234, -0.02906438708305359, -0.005493224132806063, -0.007808002643287182, -0.011291591450572014, -0.037928950041532516, -0.009688496589660645, -0.025158852338790894, -0.005332993809133768, 0.015025941655039787, -0.014225875958800316, 0.00732925720512867, 0.015421383082866669, 0.03171997144818306, -0.013330809772014618, 0.04147122800350189, 0.010875185951590538, -0.02001180686056614, 0.03606290742754936, 0.020440181717276573, -0.0216851644217968, -0.05902933329343796, 0.02466442435979843, 0.008269348181784153, -0.06588812172412872, -0.0670449286699295, 0.05205800384283066, -0.012733722105622292, 0.05377386510372162, 0.0020443438552320004, 0.01855543628334999, -0.044325072318315506, -0.011843141168355942, -0.01767815090715885, -0.005642750766128302, -0.01682864874601364, -0.0270573440939188, -0.030817171558737755, 0.00006295857019722462, -0.013744446448981762, 0.0029689364600926638, -0.04965755343437195, -0.015309102833271027, 0.011367009952664375, 0.008798581548035145, 0.0045882463455200195, -0.017812838777899742, 0.05931974947452545, 0.009287276305258274, 0.00648382818326354, -0.035096555948257446, 0.030072061344981194, -0.005820012651383877, 0.015982434153556824, -0.009228064678609371, -0.029235705733299255, -0.050752557814121246, 0.03705747798085213, -0.07687436789274216, -0.011249600909650326, -0.04080610349774361, -0.04459484666585922, -0.06225399672985077, 0.005477074533700943, -0.008506027050316334, 0.0093223350122571, -0.018821468576788902, -0.032382089644670486, -0.03988978639245033, 0.028978221118450165, 0.07723001390695572, 0.004019722808152437, -0.07320429384708405, 0.10072185099124908, -0.04940032586455345, 0.07573673129081726, -0.03175794333219528, 0.00603590440005064, 0.01100101973861456, -0.015947328880429268, -0.05105375498533249, 0.03521992638707161, 0.08238163590431213, -0.012855319306254387, 0.03889360651373863, -0.024822916835546494, 0.008181427605450153, -0.010017944499850273, 0.04431740567088127, -0.02549193799495697, -0.014174791984260082, -0.02948574163019657, -0.02255980670452118, -0.02088838815689087, 0.043073490262031555, -0.001759141101501882, -0.06963355094194412, -0.020353641360998154, -0.012837078422307968, -0.008331133984029293, 0.007250830065459013, -0.02831849828362465, -0.0007491527358070016, 0.03991743549704552, 0.05519905313849449, 0.014241667464375496, -0.013685262762010098, 0.027886655181646347, 0.020673532038927078, -0.03370334580540657, -0.07072115689516068, -0.016311801970005035, -0.04505842179059982, -0.007967106066644192, -0.01235758513212204, -0.04021506384015083, -0.07630577683448792, 0.04316621273756027, 0.01677880808711052, -0.0667329803109169, -0.01587645895779133, 0.002207942772656679, -0.004746335558593273, -0.015553159639239311, 0.013590160757303238, 0.04103343188762665, 0.018674198538064957, 0.005820116959512234, -0.024970535188913345, 0.03364189714193344, 0.05220774561166763, -0.04929333180189133, 0.04247528687119484, 0.04015936329960823, 0.016037696972489357, -0.037746354937553406, -0.024750398471951485, -0.06253471970558167, -0.049527358263731, -0.027244800701737404, 0.03730006888508797, 0.06047181785106659, 0.06997337937355042, 0.05407508835196495, 0.028476817533373833, 0.04233657196164131, -0.003832913003861904, 0.03284328430891037, 0.06639997661113739, -0.07391229271888733, -0.018812740221619606, 0.05586707219481468, -0.017097212374210358, -0.009605864994227886, 0.008786019869148731, 0.007516469806432724, -0.020910117775201797, -0.03568563237786293, 0.02037530019879341, -0.0177908968180418, 0.035409167408943176, 0.025905877351760864, -0.0687408521771431, 0.05042189359664917, -0.04234293848276138, 0.0035243064630776644, -0.052344910800457, 0.07790444046258926, -0.013887842185795307, -0.0068652015179395676, 0.0835186243057251, 0.009878820739686489, 0.02136462740600109, -0.015062662772834301, -0.014054221101105213, -0.05653347820043564, -0.04320449009537697, -0.05300181731581688, -0.04654509201645851, -0.01942313276231289, 0.08308200538158417, 0.05063941329717636, 0.05385278910398483, -0.020119255408644676, -0.021276257932186127, -0.007932905107736588, -0.022190187126398087, 0.009151207283139229, -0.07370692491531372, -0.026269186288118362, -0.024329660460352898, 0.015329316258430481, 0.001148359035141766, 0.02078787423670292, -0.02386053092777729, -0.05813102051615715, 0.002129778964444995, 0.028505263850092888, -0.04987766966223717, 0.044458553194999695, 0.040250033140182495, -0.012359981425106525, 0.013739380054175854, 0.03716989606618881, 0.04771440476179123, 0.015709666535258293, -0.006870681419968605, 0.029168272390961647, -0.024784831330180168, 0.04337912052869797, -0.00946942251175642, 0.03399960696697235, 0.04670959338545799, -0.014456158503890038, 0.01416159700602293, 0.011416414752602577, -0.00008878649532562122, 0.0087724719196558, 0.008324218913912773, -0.023858241736888885, -0.006505946628749371, 0.019616320729255676, 0.03147615119814873, -0.041652265936136246, -0.006124534644186497, 0.01648271642625332, -0.009402142837643623, -0.00048147147754207253, 0.03187735751271248, -0.039577681571245193, -0.025230158120393753, 0.009464990347623825, 0.01539380382746458, -0.042613230645656586, -0.03533465415239334, 0.04136794060468674, -0.0032735848799347878, 0.04609009996056557, 0.011323816142976284, -0.049236152321100235, 0.03195048123598099, -0.07947767525911331, -0.005834815092384815, 0.02960527502000332, -0.036942631006240845, 0.06569056212902069, 0.021675994619727135, 0.008642083033919334, 0.0038442062214016914, -0.0870957151055336, 0.022034265100955963, 0.04493168368935585, -0.019560551270842552, 0.03285829722881317, 0.05149514973163605, 0.0612572617828846, -0.005495049990713596, -0.037044890224933624, 0.0235026516020298, 0.05674987658858299, 0.0005981522845104337, 0.017629435285925865, 0.023535162210464478, 0.003281342564150691, 0.05032186582684517, 0.002606905996799469, 0.0219784677028656, 0.04168142378330231, 0.01432831957936287, -0.014923255890607834, -0.002198226749897003, 0.01523515023291111, -0.03300516679883003, 0.009668625891208649, -0.09620972722768784, -0.004247182980179787, -0.017695577815175056, 0.03263584151864052, 0.01968337595462799, 0.004058169201016426, 0.016589539125561714, -0.023047633469104767, 0.023671787232160568, -0.003193297190591693, -0.033171143382787704, 0.008137726224958897, 0.03623572364449501, -0.004861818626523018, -0.08999605476856232, -0.03211773559451103, 0.00501202791929245, -0.009117170237004757, -0.020145755261182785, -0.007187198847532272, 0.026921173557639122, -0.05769318714737892, 0.02805323153734207, 0.042021192610263824, -0.10065453499555588, 0.004416392184793949, 0.035672880709171295, -0.03576373681426048, 0.012697834521532059, -0.004598351661115885, 0.0054462323896586895, -0.0037269066087901592, -0.06946682929992676, 0.06499077379703522, -0.06730843335390091, 0.03239383175969124, 0.048878464847803116, -0.0016638364177197218, 0.00939895212650299, 0.028586603701114655, 0.022232379764318466, -0.006116695702075958, 0.07993707805871964, 0.0012841244461014867, -0.02081572636961937, 0.020244846120476723, -0.06419453024864197, -0.005526446737349033, 0.017336491495370865, 0.030827727168798447, -0.007900470867753029, -0.004316928330808878, 0.018754327669739723, 0.0058997515588998795, -0.015983236953616142, -0.05922560393810272, -0.017347237095236778, 0.04472696781158447, -0.024203600361943245, 0.04356292262673378, 0.0321388877928257, 0.02942664362490177, -0.017292823642492294, -0.04579925909638405, -0.030503325164318085, -0.0023155342787504196, 0.024686483666300774, -0.01844779960811138, 0.02784191258251667, -0.04395752027630806, -0.06401889026165009, -0.024342088028788567, -0.055939942598342896, -0.020673509687185287, 0.015209856443107128, -0.058449260890483856, -0.01694423519074917, -0.018232043832540512, 0.0020460588857531548, -0.010880856774747372, 0.04250136762857437, 0.005938732530921698, -0.020617373287677765, 0.06200404092669487, -0.006886268965899944, 0.04153389111161232, -0.00601910799741745, -0.016050143167376518, 0.0009417156688869, 0.041404493153095245, -0.038380689918994904, 0.007285099010914564, 0.0640372708439827, -0.007685793098062277, -0.04935554787516594, 0.017320724204182625, 0.015154407359659672, -0.0076118637807667255, 0.01716732047498226, 0.03531869128346443, 0.02608652412891388, 0.017424045130610466, -0.045609667897224426, 0.011918226256966591, -0.04830542951822281, 0.05160302296280861 ]
<p>Anthropic principle, at least in laymen explanations that I have encountered so far, sounds something like "the physical universe suits us exceptionally well because among all the possibilities we, the observers, tautologically encounter the one that can support us."</p> <p>I was wondering whether this principle can be applied to specific observers. That is, suppose that Shroedinger performs his thought experiment with himself, rather than his cat. Would the anthropic principle imply <strong>from Shroedinger's viewpoint</strong> that he would always survive, at least according to many-worlds interpretation?</p> <p>How about this setting, assuming many-worlds interpretation: two people decided to divorce by proceeding with their lives as window&amp;widower in separate universes. They create a setup similar with Shroedingers, except that 2 boxes have been created in such a way that a person in exactly one of them would get killed, depending how a certain superposition collapses. Then the unhappy couple enters the chambers. Does the anthropic principle imply that <strong>each</strong> of them would experience the exiting the chamber as the sole surviving spouse?</p>
g5388
[ -0.025017086416482925, 0.020840749144554138, 0.024068312719464302, -0.06712280213832855, -0.0032206515315920115, 0.035069070756435394, -0.03333203122019768, 0.012212160043418407, -0.023912658914923668, 0.035600822418928146, 0.008912483230233192, -0.026895124465227127, 0.04259095340967178, 0.04102248325943947, -0.05739597603678703, 0.029678920283913612, 0.09757888317108154, -0.018864315003156662, 0.05172733962535858, 0.08431269973516464, -0.06070530787110329, 0.021093158051371574, -0.0028277996461838484, -0.010041218250989914, -0.08532942831516266, -0.018145248293876648, -0.018316600471735, -0.0007592985639348626, -0.060744430869817734, 0.057444024831056595, 0.010567202232778072, -0.009153010323643684, 0.02526445873081684, -0.07726316899061203, -0.0008221551543101668, -0.055090729147195816, 0.044156286865472794, 0.01296484936028719, -0.022547390311956406, -0.022091766819357872, -0.03609222546219826, -0.011540777049958706, -0.016004158183932304, -0.04170960187911987, -0.02972242422401905, 0.011263696476817131, -0.015256758779287338, -0.0685846284031868, 0.0538395419716835, -0.060666315257549286, -0.028288694098591805, 0.020085765048861504, 0.015472306869924068, 0.0247123371809721, 0.049311596900224686, 0.05571475625038147, 0.029145946726202965, 0.026163777336478233, -0.05634254962205887, -0.04145378991961479, -0.009264812804758549, 0.017138971015810966, 0.0039006650913506746, 0.04574311897158623, 0.017048703506588936, 0.02279515750706196, -0.040032751858234406, 0.01547545287758112, 0.04478846490383148, -0.01910409890115261, -0.009567774832248688, -0.07893344759941101, -0.09938491880893707, -0.018546773120760918, 0.025823010131716728, 0.03691298887133598, -0.045636098831892014, 0.008949942886829376, 0.07241319119930267, 0.07913431525230408, -0.039091866463422775, -0.03908403217792511, -0.021503187716007233, 0.08338165283203125, 0.010433106683194637, -0.0071491883136332035, 0.015538624487817287, -0.052282460033893585, -0.048636019229888916, -0.00503391632810235, 0.04880324751138687, 0.008463799953460693, 0.06286376714706421, 0.0496441014111042, -0.026123611256480217, 0.04333964362740517, -0.03167090564966202, 0.031382836401462555, -0.03320522606372833, 0.022698501124978065, -0.061054740101099014, 0.011216619051992893, 0.03996483236551285, -0.013530305586755276, -0.06485540419816971, 0.01624874956905842, 0.011968571692705154, 0.03917943313717842, 0.01644013449549675, 0.0022100985515862703, -0.01748085767030716, -0.012164648622274399, -0.06780348718166351, -0.01006881520152092, 0.0146383848041296, -0.06381098181009293, 0.04409485310316086, 0.023521654307842255, 0.020929692313075066, 0.06479950994253159, 0.03528352826833725, 0.031879719346761703, -0.017122240737080574, 0.029755141586065292, -0.041207510977983475, 0.03583288937807083, -0.04102402180433273, -0.002198029775172472, 0.019900064915418625, 0.016190676018595695, 0.0492328405380249, -0.006212305743247271, 0.018779847770929337, 0.015880577266216278, 0.03688422590494156, -0.00877972412854433, 0.011047407053411007, -0.0027176772709935904, 0.04865263029932976, -0.023380320519208908, 0.039503518491983414, 0.019162798300385475, -0.007466480135917664, 0.003953226376324892, -0.02539747580885887, 0.03709855675697327, 0.01270494144409895, -0.02120795287191868, 0.01211007684469223, 0.03715413808822632, -0.014878977090120316, 0.0613144189119339, -0.025708334520459175, 0.019511306658387184, -0.003959171939641237, 0.008597100153565407, -0.02465951442718506, 0.026191215962171555, -0.019778022542595863, -0.025019971653819084, 0.05199024826288223, -0.005289094522595406, -0.009065852500498295, 0.03342422470450401, 0.018896915018558502, 0.023152709007263184, -0.03561639413237572, -0.09229782968759537, 0.03520437702536583, 0.0008930375333875418, -0.014074145816266537, -0.027916476130485535, 0.039974331855773926, 0.03434407338500023, 0.009723245166242123, 0.03495325148105621, 0.024076540023088455, -0.009465386159718037, -0.06278249621391296, 0.0325985886156559, -0.003603951307013631, 0.021934395655989647, -0.03024025447666645, -0.01111340057104826, 0.043913327157497406, -0.046681903302669525, -0.01180677767843008, 0.03150881454348564, -0.037260107696056366, -0.040054067969322205, 0.03972785174846649, -0.012289721518754959, 0.037941765040159225, 0.052383583039045334, -0.018590686842799187, -0.044860415160655975, 0.011413322761654854, 0.022787703201174736, 0.00434676231816411, -0.038199663162231445, 0.053172219544649124, 0.009369101375341415, -0.016886988654732704, -0.019044462591409683, -0.04457658529281616, -0.0025885580107569695, -0.05783754959702492, 0.0054480950348079205, -0.016760481521487236, -0.019887028262019157, 0.034586820751428604, -0.021082064136862755, -0.048929840326309204, 0.003149472875520587, -0.0787397101521492, -0.024224981665611267, 0.012381120584905148, 0.014661996625363827, -0.0521729439496994, -0.02956169657409191, 0.05133943259716034, -0.019365552812814713, -0.012248637154698372, -0.005035522393882275, 0.04183058813214302, -0.00007350019586738199, -0.09250853955745697, -0.01875174045562744, -0.01946689747273922, -0.000056764198234304786, 0.005572452209889889, 0.007935908623039722, 0.025906266644597054, -0.05343242734670639, 0.02134496532380581, 0.0010826416546478868, 0.021164970472455025, 0.05412931367754936, 0.006107889581471682, 0.02216801419854164, 0.040560126304626465, -0.05276647210121155, -0.06982801854610443, 0.00954483076930046, 0.02779197134077549, -0.0033931571524590254, -0.016273807734251022, -0.02307582087814808, 0.009069508872926235, 0.04091666638851166, -0.030419865623116493, 0.003701218171045184, 0.045567966997623444, -0.06712894141674042, -0.026802372187376022, -0.05809897184371948, 0.003988461568951607, 0.021834706887602806, -0.04127472639083862, -0.021518558263778687, 0.02114020846784115, 0.026648053899407387, -0.012222076766192913, 0.03908953443169594, 0.026916636154055595, -0.032095685601234436, 0.009518561884760857, 0.04502144828438759, -0.0051542287692427635, 0.026693042367696762, 0.011668145656585693, 0.020162101835012436, -0.0272044874727726, 0.028425464406609535, 0.007116601802408695, 0.014536518603563309, -0.03610389307141304, -0.03260165825486183, 0.03978223726153374, -0.0407324843108654, 0.01725374534726143, -0.005736475810408592, -0.03573893755674362, -0.014289727434515953, 0.08940951526165009, -0.011034050956368446, 0.04811530560255051, 0.025798728689551353, -0.0008881579851731658, 0.037945181131362915, -0.013651576824486256, -0.05113514885306358, 0.008607537485659122, 0.0013743494637310505, 0.01534482091665268, 0.009569683112204075, -0.007720771711319685, -0.0049809557385742664, 0.008132433518767357, 0.01550605334341526, -0.01244918443262577, -0.04590708017349243, 0.010520720854401588, 0.027118327096104622, 0.015095759183168411, 0.039299748837947845, -0.05132713168859482, -0.009492466226220131, -0.03560539335012436, -0.0568096749484539, -0.014975149184465408, 0.051778264343738556, -0.005317546892911196, -0.04008591175079346, -0.05027586594223976, 0.002433735178783536, -0.01710594817996025, 0.017723828554153442, 0.04175429791212082, -0.045811962336301804, -0.007586171850562096, 0.021766478195786476, -0.0038302531465888023, 0.008653734810650349, 0.05435636267066002, -0.02711782231926918, -0.058995604515075684, 0.014151756651699543, -0.01988542638719082, -0.03402283042669296, -0.013280393555760384, 0.022563770413398743, -0.015342186205089092, 0.010250135324895382, -0.08300555497407913, 0.007568759843707085, -0.05243450030684471, -0.05116777867078781, -0.017227796837687492, 0.02333611436188221, 0.06073588505387306, 0.012289818376302719, 0.06423086673021317, -0.02451702393591404, 0.016596999019384384, 0.010404452681541443, 0.03603164851665497, 0.04253191873431206, 0.08288954943418503, 0.0042991540394723415, 0.006870257668197155, 0.034951016306877136, 0.03564388304948807, 0.029019761830568314, -0.0033573543187230825, -0.0272018201649189, 0.03645426407456398, 0.016549447551369667, 0.024829726666212082, -0.02491014637053013, -0.006319008767604828, 0.05280953645706177, -0.01748821511864662, -0.005039704032242298, 0.0026619259733706713, -0.0008476979564875364, 0.0015364201972261071, 0.03878844529390335, 0.0389944352209568, -0.007387428544461727, 0.056087251752614975, -0.00010691140778362751, -0.03955311328172684, 0.05876978859305382, 0.05585814267396927, 0.004751210566610098, 0.04514674097299576, -0.016794264316558838, -0.06559712439775467, 0.03261854127049446, 0.04823916032910347, 0.059192411601543427, -0.0039004983846098185, 0.0038036564365029335, 0.042376838624477386, -0.009600923396646976, -0.0033218245953321457, 0.011724820360541344, -0.037893399596214294, -0.0026345287915319204, -0.008049573749303818, -0.022122923284769058, -0.06882479041814804, -0.014537745155394077, 0.03850081190466881, 0.03207317367196083, -0.05481484532356262, -0.06693834066390991, 0.006032551638782024, 0.015455418266355991, 0.0319962352514267, 0.009991501457989216, 0.023788124322891235, -0.0010868317913264036, 0.013516884297132492, 0.0038765640929341316, -0.01540825329720974, -0.0653834268450737, -0.04128402844071388, -0.022731224074959755, -0.020191553980112076, 0.044248130172491074, 0.0028744193259626627, -0.07639528065919876, 0.008595503866672516, -0.007165722083300352, 0.02103205770254135, -0.013386809267103672, 0.04266776517033577, -0.009431599639356136, 0.02195124141871929, -0.01795162260532379, -0.0377129390835762, -0.004500345326960087, -0.08259516954421997, 0.011144270189106464, -0.04538872092962265, -0.03841252997517586, -0.048689816147089005, 0.008771873079240322, -0.016827469691634178, 0.011376705020666122, 0.030612537637352943, 0.027589309960603714, -0.007774312049150467, -0.02200303226709366, -0.007873749360442162, -0.019042110070586205, 0.049294449388980865, 0.03388440981507301, 0.018903985619544983, -0.021915622055530548, 0.0308509711176157, -0.022791581228375435, 0.02852468565106392, 0.02738686464726925, -0.00016501393110956997, -0.047410573810338974, 0.016490114852786064, -0.022503400221467018, -0.0412619523704052, 0.012412244454026222, -0.022868439555168152, 0.06425310671329498, 0.03759034350514412, 0.015087366104125977, -0.0031293730717152357, -0.0021535123232752085, 0.03896792605519295, 0.028846973553299904, -0.022075995802879333, -0.004925892222672701, -0.050090353935956955, 0.034546107053756714, 0.03394824638962746, 0.08200929313898087, -0.040391433984041214, -0.02713409811258316, 0.00977339781820774, 0.024225031957030296, -0.0443890281021595, 0.024019816890358925, -0.003954307641834021, 0.016595415771007538, -0.03475352004170418, -0.06403759866952896, -0.03755330666899681, -0.03292861208319664, 0.012759282253682613, 0.046385541558265686, -0.001049803919158876, -0.038046590983867645, 0.05850360915064812, -0.0178982000797987, 0.046244774013757706, -0.014067484065890312, -0.015517186373472214, 0.04171782359480858, -0.01646612212061882, -0.010996678844094276, -0.0765916258096695, -0.02600000984966755, 0.052568066865205765, 0.03754054009914398, -0.04409640654921532, -0.006426073145121336, 0.04625050723552704, -0.044352173805236816, -0.0007308872300200164, 0.028438281267881393, 0.014569608494639397, -0.02744816057384014, 0.03962680697441101, -0.004921891260892153, 0.03454664722084999, -0.025413352996110916, 0.057732127606868744, -0.013469952158629894, 0.005019287578761578, -0.019986510276794434, -0.04346037656068802, 0.01191042922437191, 0.017913183197379112, 0.05259452760219574, 0.02827184833586216, -0.018798233941197395, -0.036681678146123886, 0.023421306163072586, -0.006066920701414347, -0.08247806131839752, 0.04789229482412338, 0.06759091466665268, 0.011050422675907612, -0.027577057480812073, 0.01447051391005516, 0.01044679805636406, -0.032723743468523026, -0.0014245333150029182, 0.018518775701522827, -0.009380113333463669, 0.0006646362598985434, 0.06067937612533569, 0.020395249128341675, 0.02421576902270317, 0.023845858871936798, -0.12453803420066833, -0.024036966264247894, -0.006545258220285177, 0.04355543851852417, -0.005095430184155703, -0.015608042478561401, 0.002448556013405323, 0.040232427418231964, 0.040987350046634674, -0.025269117206335068, 0.04448826238512993, -0.09376945346593857, 0.006371127441525459, 0.01334042102098465, 0.07890042662620544, -0.07755820453166962, 0.026547301560640335, -0.05336815491318703, 0.011233089491724968, -0.004936353303492069, 0.057551681995391846, 0.012014485895633698, 0.04776021093130112, -0.01069906447082758, 0.01241970807313919, -0.012224683538079262, 0.05282488837838173, 0.03572385758161545, 0.0070910085923969746, -0.04950149729847908, 0.0019237465457990766, -0.00997282937169075, -0.03665785863995552, -0.009996579959988594, 0.06238814815878868, 0.0350060760974884, 0.039873186498880386, -0.0010361114982515574, 0.02911725640296936, 0.02687549963593483, 0.04874071478843689, -0.039779745042324066, -0.05540100485086441, 0.022910939529538155, -0.04208637773990631, -0.006880446802824736, -0.011962175369262695, 0.002565584145486355, -0.017968080937862396, -0.01959945261478424, 0.06401994824409485, -0.0427154079079628, 0.006972688250243664, 0.019473237916827202, 0.01399027369916439, 0.037109337747097015, -0.012867944315075874, 0.009744967333972454, 0.013031847774982452, -0.029237832874059677, 0.005808656569570303, 0.018884550780057907, -0.0007721966248936951, -0.07072030007839203, 0.020227940753102303, -0.0071589150466024876, 0.026795458048582077, 0.05843714252114296, -0.016885660588741302, -0.005148202180862427, 0.04801587015390396, -0.017724979668855667, -0.010666580870747566, 0.06639467179775238, -0.026619352400302887, -0.05392036959528923, 0.04807019978761673, 0.007579145021736622, 0.11023112386465073, 0.004940410610288382, -0.03004068322479725, 0.036479026079177856, -0.007076330948621035, -0.055672790855169296, 0.021709440276026726, -0.01274132076650858, -0.03271866962313652, 0.04043179377913475, 0.021961741149425507, -0.016914675012230873, 0.036363404244184494, -0.025551127269864082, 0.006356507074087858, 0.06059381738305092, 0.049326952546834946, -0.01176575105637312, -0.008429755456745625, 0.08753541111946106, -0.03680400550365448, -0.0025325752794742584, 0.013703537173569202, -0.0728774443268776, 0.019678911194205284, 0.0010249398183077574, 0.007835307158529758, 0.0322476327419281, 0.04244023561477661, 0.021709078922867775, -0.02835792675614357, -0.06244945153594017, 0.030982164666056633, -0.0018268664134666324, 0.005048003513365984, -0.0013006507651880383, -0.03108270838856697, 0.036961592733860016, -0.03367627412080765, -0.031796686351299286, 0.02620997652411461, 0.017203718423843384, 0.028666313737630844, -0.03936835005879402, 0.02922544814646244, -0.05154693126678467, -0.04431683570146561, -0.00039355442277155817, 0.002789444522932172, -0.05576082319021225, -0.025142623111605644, -0.06423598527908325, 0.004048080649226904, 0.030426330864429474, -0.038901880383491516, -0.06119348481297493, 0.015177330933511257, -0.00963940192013979, -0.012815886177122593, -0.01260669156908989, -0.07818633317947388, -0.020358918234705925, -0.09112852811813354, -0.0006129869725555182, -0.006281235255300999, 0.04181075096130371, -0.006772212218493223, -0.012173724360764027, 0.033636391162872314, 0.06608054786920547, -0.012777390889823437, 0.001847049337811768, -0.04588782414793968, 0.012636248953640461, -0.022033074870705605, -0.07677414268255234, -0.012588515877723694, -0.00675481092184782, -0.042494554072618484, -0.019723942503333092, -0.030038215219974518, -0.007572182919830084, 0.05170737951993942, 0.014731867238879204, 0.03951260447502136, 0.03762703388929367, 0.05882830545306206, -0.008374388329684734, -0.016927184537053108, -0.013970392756164074, 0.0009412736399099231, 0.09334317594766617, -0.03629497438669205, -0.06461133062839508, -0.00028476674924604595, -0.011675537563860416, -0.015847858041524887, 0.041675884276628494, 0.07181389629840851, -0.005734275560826063, 0.023543406277894974, 0.03009232133626938, -0.04340416193008423, -0.035366035997867584, 0.01502490695565939, 0.024710416793823242, 0.02121463231742382, 0.04710463806986809, -0.007159754633903503, 0.006426119711250067, -0.005471176467835903, 0.0030501559376716614, 0.05647653713822365, -0.026385946199297905, -0.006106419023126364, -0.02682683616876602, -0.03872198611497879, 0.0009628926636651158, -0.00497957831248641, -0.0412142276763916, 0.035653941333293915, -0.04213916137814522, 0.01668483205139637, -0.0690569132566452, 0.04248826205730438, -0.055159855633974075, -0.04080522432923317, 0.07328805327415466, -0.038210541009902954, 0.01310608722269535, 0.028428375720977783, -0.046632226556539536, -0.030398165807127953, -0.03549898415803909, -0.010258504189550877, -0.011315224692225456, 0.020645199343562126, -0.0022385912016034126, -0.04723089560866356, -0.07624151557683945, -0.020360086113214493, 0.04163346812129021, -0.025067884474992752, 0.007952539250254631, 0.02003827691078186, -0.029980169609189034, -0.024989059194922447, -0.0314694419503212, -0.008431530557572842, -0.08955046534538269, -0.07746938616037369, -0.02113407477736473, 0.003528602421283722, 0.04613206163048744, -0.06004699692130089 ]
<p>while studying scattering formula for the supercurrent (<a href="http://arxiv.org/abs/cond-mat/9611162" rel="nofollow">Beenakker</a>) I encountered that the density of states for discrete and continuous spectrum can be simultaneously described by taking $\epsilon\ -&gt;\ \epsilon + i\delta $ in the following formula: $\rho(\epsilon) = -\frac{1}{\pi}Im\frac{d}{d\epsilon}\left\{lnDet\left[1 - S_{A}(\epsilon)S_{N}(\epsilon) \right] - \frac{1}{2}lnDet\left[S_{A}(\epsilon)S_{N}(\epsilon)\right]\right\}$.</p> <p>I am wondering if one could argument this by referring to scattering theory and Green's function - eg. <a href="http://newton.phy.bme.hu/~szunyogh/Elszerk/Kkr-slides.pdf" rel="nofollow">Laszlo Szunyogh</a>.</p>
g5389
[ -0.0043217032216489315, 0.011570998467504978, -0.02662588283419609, -0.03077641688287258, 0.04298260807991028, 0.03346213325858116, 0.016957776620984077, 0.016712429001927376, -0.03145308047533035, -0.0349636971950531, -0.010433724150061607, -0.04577118158340454, 0.06180582940578461, 0.0064224740490317345, 0.024700788781046867, -0.021325087174773216, -0.002316483063623309, 0.022441329434514046, -0.04977644234895706, 0.01595711149275303, -0.08544965088367462, -0.03378095105290413, 0.04984801635146141, -0.06674465537071228, 0.020672785118222237, 0.005039065610617399, 0.018005764111876488, -0.01885838992893696, -0.01789057068526745, -0.03910820931196213, -0.010223200544714928, -0.010808484628796577, 0.0019080309430137277, -0.0036580131854861975, -0.014559409581124783, 0.033547293394804, 0.01817907951772213, -0.029813168570399284, 0.002875419333577156, -0.002297496423125267, -0.007015838287770748, -0.00014171525253914297, -0.0009609003318473697, 0.004883677698671818, -0.040499232709407806, 0.00025154196191579103, -0.01978207379579544, 0.04936422407627106, -0.08820758014917374, 0.000766340468544513, -0.014233901165425777, 0.09587126970291138, 0.019610250368714333, 0.03295048698782921, -0.01320258341729641, 0.013995901681482792, 0.004780222661793232, -0.030949631705880165, -0.011094479821622372, 0.006463291123509407, -0.01087313424795866, -0.02924199402332306, -0.014863801188766956, -0.016313832253217697, 0.09248240292072296, 0.0014994497178122401, -0.012157384306192398, -0.0031972015276551247, -0.0342421792447567, -0.04288806766271591, 0.023633282631635666, -0.06383766978979111, 0.022470049560070038, -0.030828023329377174, -0.010543644428253174, -0.026546170935034752, 0.0003948120283894241, -0.029044074937701225, -0.02907761186361313, 0.039928119629621506, -0.017102321609854698, -0.048867251724004745, 0.04433507099747658, -0.05040819197893143, 0.04149060323834419, -0.014559551142156124, 0.014816494658589363, -0.003982677590101957, 0.005157872568815947, -0.020933425053954124, -0.019842451438307762, -0.05822727456688881, -0.008776704780757427, 0.02836904674768448, 0.04158041626214981, -0.035200200974941254, -0.005244180094450712, 0.062321554869413376, -0.05237980931997299, -0.032414332032203674, 0.009330686181783676, 0.05174238607287407, 0.01620832271873951, 0.005805391352623701, 0.003811066271737218, 0.011626043356955051, 0.019316362217068672, -0.025743674486875534, 0.02493721805512905, -0.018494362011551857, -0.06332068890333176, -0.06028474494814873, -0.02196340635418892, 0.02977062202990055, -0.012113422155380249, 0.0073156640864908695, 0.04441491514444351, -0.05817938968539238, -0.04683113470673561, 0.007914520800113678, 0.012058863416314125, 0.02165970392525196, 0.07650420814752579, 0.0748911052942276, 0.017900574952363968, 0.03349604457616806, 0.013293550349771976, 0.05200900509953499, 0.07114353030920029, -0.007625727914273739, 0.01850389875471592, 0.03695731982588768, 0.028494225814938545, 0.02650231309235096, 0.04269895702600479, -0.03295743092894554, -0.04867979511618614, 0.06401503831148148, -0.024942271411418915, -0.007088107988238335, 0.05114222690463066, 0.02343609556555748, -0.004944945219904184, -0.03888290748000145, -0.016149502247571945, -0.007704432122409344, -0.0731525868177414, -0.08131516724824905, -0.03616560995578766, -0.025904111564159393, 0.02314751408994198, -0.005662468262016773, -0.013430817984044552, -0.03393832594156265, -0.011453982442617416, 0.039616845548152924, 0.07451912760734558, 0.030874283984303474, 0.0051095085218548775, 0.006046563386917114, -0.029735295102000237, -0.01451111026108265, -0.007148609962314367, 0.055481452494859695, -0.019686482846736908, -0.014204513281583786, 0.0510859489440918, -0.060560766607522964, -0.0013522037770599127, -0.07799255847930908, -0.012305878102779388, 0.04381418973207474, -0.010529115796089172, -0.004460946191102266, 0.07022975385189056, 0.0384942851960659, 0.0032515800558030605, -0.033996276557445526, 0.049244146794080734, -0.014842442236840725, -0.009960705414414406, 0.0026821568608283997, -0.008358964696526527, -0.02443661540746689, 0.04251766577363014, 0.013063345104455948, -0.032825812697410583, -0.0021597889717668295, -0.05858242139220238, 0.0003436094557400793, -0.03680163621902466, 0.008282857947051525, 0.005974709987640381, 0.08980503678321838, 0.031958576291799545, 0.03222876414656639, 0.023390937596559525, -0.020065315067768097, -0.011761799454689026, 0.00027323790709488094, -0.0014484361745417118, 0.030336901545524597, 0.04810355603694916, -0.019082941114902496, 0.03001985512673855, 0.06275247782468796, -0.021612178534269333, -0.06625630706548691, -0.017848309129476547, -0.03672473132610321, -0.013615855947136879, -0.10196054726839066, -0.0556870773434639, 0.04425444453954697, -0.016790999099612236, -0.043845485895872116, -0.030343709513545036, -0.024890637025237083, -0.026665441691875458, 0.06853139400482178, -0.06266029924154282, -0.02862468548119068, 0.0181999821215868, 0.0703500509262085, 0.009824059903621674, -0.027034690603613853, 0.04337647184729576, 0.014356523752212524, 0.024442223832011223, -0.04427900165319443, -0.038699015974998474, -0.019319476559758186, 0.006140965968370438, -0.020067496225237846, -0.029699129983782768, 0.0849524661898613, 0.0009338365634903312, -0.027768753468990326, -0.007016858551651239, 0.0010747455526143312, 0.02454671636223793, -0.01966722123324871, -0.028914501890540123, 0.020460082218050957, 0.004027164075523615, 0.008275024592876434, 0.015091313049197197, 0.02782595343887806, 0.03688609227538109, 0.029087794944643974, -0.07169485092163086, 0.019561534747481346, 0.0018819113029167056, 0.03643951565027237, -0.014667353592813015, -0.037947218865156174, -0.015797944739460945, 0.018685918301343918, 0.01377224363386631, -0.0031403200700879097, 0.00807970017194748, -0.027241749688982964, 0.022271793335676193, -0.03763628005981445, -0.04022766277194023, -0.050558749586343765, -0.01659615896642208, 0.012088365852832794, -0.0422171875834465, -0.025798365473747253, -0.008926681242883205, 0.05286812782287598, 0.08382057398557663, 0.008615309372544289, -0.02216515503823757, -0.016262803226709366, 0.0029467083513736725, -0.016914114356040955, 0.07238330692052841, 0.005975817330181599, -0.02596847526729107, 0.029923435300588608, 0.023291945457458496, 0.02612147107720375, 0.0477554090321064, -0.05598067492246628, -0.007124969270080328, 0.05079594627022743, 0.007350503467023373, 0.02770858071744442, 0.050528451800346375, 0.05173877626657486, 0.044535454362630844, -0.025157712399959564, -0.06716582924127579, 0.023306572809815407, 0.019212592393159866, -0.07419770956039429, 0.03589679300785065, 0.08357195556163788, -0.025324421003460884, -0.010182295925915241, 0.025121618062257767, 0.011175028048455715, 0.09738406538963318, 0.01492635440081358, -0.07458091527223587, -0.0010241479612886906, 0.021492034196853638, -0.036185093224048615, 0.02996845170855522, 0.017723826691508293, -0.009792903438210487, -0.018156375735998154, 0.0010738394921645522, -0.009584739804267883, 0.008468487299978733, 0.034512959420681, 0.07759200781583786, 0.008750672452151775, 0.014264692552387714, -0.03937166929244995, 0.004069034941494465, -0.014294607564806938, 0.01121472381055355, 0.014087749645113945, -0.09718511998653412, 0.004158891271799803, -0.02088850364089012, 0.01676054112613201, 0.004759559407830238, -0.031195318326354027, 0.015372035093605518, -0.030765721574425697, -0.0939888060092926, -0.000751514220610261, -0.06095723807811737, 0.028835225850343704, 0.022571349516510963, 0.08097998052835464, -0.028908897191286087, -0.01641763374209404, -0.08210636675357819, -0.0003479801816865802, -0.006086922716349363, -0.014256076887249947, 0.019346684217453003, 0.023152267560362816, 0.0002956319658551365, -0.010377462953329086, -0.03803503140807152, 0.036099884659051895, 0.04298117011785507, 0.002161547774448991, -0.04779181256890297, 0.023786362260580063, 0.00699663907289505, 0.003589217783883214, 0.012913334183394909, 0.017002202570438385, -0.003750618314370513, -0.052551355212926865, 0.03738253191113472, -0.05396714434027672, 0.05164613574743271, 0.0236289631575346, 0.0027323709800839424, 0.041496045887470245, 0.020795879885554314, 0.05566037446260452, -0.01998107135295868, -0.022105757147073746, 0.06722494959831238, -0.01734066940844059, 0.04567892104387283, -0.017254192382097244, -0.033336058259010315, 0.012421985156834126, -0.07244227826595306, 0.11097443848848343, 0.01246719341725111, 0.029355447739362717, 0.0334947444498539, 0.014722074382007122, -0.0060466015711426735, -0.022985730320215225, 0.04578828811645508, 0.009486133232712746, 0.013986611738801003, -0.03225375711917877, 0.06593097746372223, -0.027428844943642616, 0.017662744969129562, -0.024084707722067833, -0.046271804720163345, 0.040312036871910095, 0.00021840265253558755, -0.0034845322370529175, -0.10351306200027466, 0.06765249371528625, -0.0003338491078466177, -0.0548141673207283, -0.01155139785259962, -0.0837312638759613, -0.004030770156532526, 0.005154358223080635, 0.021805349737405777, 0.01306031085550785, 0.030956365168094635, -0.05601322278380394, -0.03213081881403923, 0.01165513601154089, -0.03374181315302849, -0.021682273596525192, -0.014277166686952114, -0.0034033048432320356, 0.09161453694105148, -0.10040559619665146, 0.0052789426408708096, 0.014200438745319843, 0.024182990193367004, -0.0028008115477859974, -0.014568236656486988, -0.026106951758265495, -0.004415626637637615, 0.02036125957965851, 0.06816469877958298, 0.002666761865839362, 0.007327921688556671, -0.004439112730324268, -0.0002603827160783112, 0.05684388801455498, 0.037850406020879745, 0.04711202532052994, -0.06943805515766144, 0.06756418943405151, -0.05431797355413437, 0.030771898105740547, -0.021132919937372208, -0.02717769518494606, 0.011215601116418839, -0.04638364538550377, 0.023272555321455002, 0.04438973590731621, 0.030959490686655045, 0.028032997623085976, -0.0412278026342392, -0.053494006395339966, -0.014159617945551872, -0.04742402955889702, 0.020429687574505806, -0.0040060835890471935, -0.016818370670080185, -0.005511815194040537, 0.015508883632719517, -0.032256513833999634, -0.023755863308906555, 0.01485096663236618, 0.05614110454916954, 0.03957001119852066, 0.01373396534472704, 0.03579745069146156, -0.02822888270020485, -0.03975171968340874, 0.10884076356887817, -0.006290235091000795, -0.014125139452517033, 0.02696833945810795, -0.05730278417468071, -0.02269924245774746, 0.02977866120636463, 0.02255740575492382, 0.046532731503248215, -0.06011534109711647, 0.049989450722932816, -0.0708933100104332, -0.011588909663259983, 0.07364415377378464, -0.07327593863010406, 0.021268805488944054, -0.01935829408466816, -0.05132918432354927, -0.007645517122000456, 0.009610177017748356, 0.007750396151095629, 0.05832727253437042, 0.010842223651707172, -0.009254002943634987, -0.04827407747507095, 0.006820822134613991, 0.007361179683357477, -0.02151312492787838, 0.07570261508226395, 0.002222831593826413, 0.039202336221933365, -0.01683444157242775, 0.02247975766658783, -0.07479289174079895, -0.03765984997153282, 0.035002753138542175, -0.03451994061470032, -0.017521779984235764, -0.024607449769973755, 0.008878040127456188, 0.039232343435287476, 0.10663427412509918, 0.030079709365963936, 0.053217608481645584, 0.003910978324711323, -0.03268055245280266, -0.013164514675736427, 0.05995353311300278, 0.023710301145911217, 0.028462424874305725, -0.026783261448144913, -0.014101354405283928, -0.08214632421731949, -0.012649600394070148, -0.02935711294412613, -0.0564233772456646, 0.04807731509208679, 0.04908065125346184, -0.002512559527531266, -0.019315917044878006, -0.017911063507199287, 0.02972986176609993, -0.03306921198964119, -0.0006066947244107723, 0.0660247802734375, 0.007002160884439945, 0.02348959445953369, -0.020268317312002182, -0.0005139301647432148, -0.07103168964385986, 0.024944191798567772, -0.022364022210240364, -0.06167903169989586, 0.04627259448170662, -0.013134189881384373, 0.02048112265765667, -0.007987787015736103, -0.010086110793054104, 0.044847048819065094, 0.05481896176934242, -0.01774907112121582, -0.04144083335995674, -0.015761783346533775, 0.008746556006371975, 0.003460198175162077, 0.0010909598786383867, -0.02689696103334427, 0.01914389804005623, -0.02978489361703396, -0.014020695351064205, 0.03345956280827522, 0.039745133370161057, 0.05269796401262283, -0.015570955350995064, 0.001206764834932983, 0.022785069420933723, -0.052358437329530716, 0.01965312846004963, 0.01573842205107212, 0.036587756127119064, 0.01065794751048088, -0.041745007038116455, 0.03814864903688431, -0.017799966037273407, 0.03157973289489746, 0.0016965907998383045, -0.004388172645121813, -0.03417821228504181, 0.017133241519331932, 0.021969739347696304, -0.022915221750736237, 0.009346931241452694, 0.0010953503660857677, -0.051348183304071426, 0.02787100337445736, -0.005727343261241913, 0.05429929122328758, -0.0032989976461976767, 0.02070031873881817, 0.00428415322676301, -0.037259701639413834, 0.005178330931812525, -0.035084839910268784, -0.031801849603652954, -0.05443669110536575, 0.02532803826034069, -0.033999279141426086, -0.03138864412903786, 0.037782344967126846, -0.014395254664123058, -0.04801056534051895, 0.013521783985197544, -0.027713030576705933, 0.013530341908335686, -0.009293562732636929, 0.025384990498423576, 0.052376653999090195, 0.011665229685604572, 0.025069216266274452, 0.0053114863112568855, -0.020441094413399696, 0.006546447053551674, -0.006259782239794731, -0.042374808341264725, -0.02043979801237583, -0.003640285460278392, 0.005582489538937807, -0.01163432002067566, 0.009192653000354767, -0.04037782549858093, 0.008354021236300468, -0.030716707929968834, -0.003405521856620908, 0.01752803660929203, -0.006345393601804972, 0.03609256446361542, 0.07331296801567078, -0.015674075111746788, -0.03166249394416809, -0.017448822036385536, 0.005726799368858337, 0.06266923248767853, -0.008055967278778553, -0.023195860907435417, 0.05616259202361107, 0.04502299427986145, 0.05228866636753082, -0.0010698334081098437, 0.03063143789768219, 0.03356311097741127, -0.02277444675564766, 0.04880343750119209, -0.005294375587254763, 0.024553192779421806, 0.03707372024655342, 0.01642213948071003, -0.01976226083934307, 0.02382354810833931, 0.05167323723435402, -0.04328013211488724, -0.0349077545106411, -0.006988065782934427, 0.0122126005589962, -0.019055500626564026, -0.07536006718873978, 0.018572788685560226, 0.0725579708814621, -0.007352177985012531, 0.00004429147156770341, 0.018480299040675163, -0.04139741137623787, -0.019373366609215736, 0.026543719694018364, -0.003306793048977852, -0.03422555327415466, 0.003832717426121235, -0.017876669764518738, -0.011834600009024143, -0.0017199580324813724, 0.016800791025161743, -0.005092380568385124, 0.005283899139612913, 0.059828028082847595, -0.019232366234064102, -0.010836124420166016, -0.06372671574354172, 0.016858499497175217, -0.07756180316209793, -0.002867309609428048, -0.034926459193229675, 0.010140418075025082, -0.03426486253738403, 0.00887778028845787, 0.012052047997713089, -0.03442436084151268, -0.027012992650270462, 0.034602075815200806, 0.021980514749884605, 0.017393775284290314, -0.0012344166170805693, -0.032544445246458054, 0.056490458548069, -0.06202726066112518, -0.00471612298861146, 0.02720157615840435, -0.023737430572509766, 0.0048634931445121765, -0.016716763377189636, -0.021339254453778267, 0.012022243812680244, -0.02727736160159111, 0.049839217215776443, 0.025066984817385674, 0.010193223133683205, 0.019656596705317497, 0.03365541249513626, 0.021595459431409836, -0.019231515005230904, -0.009102662093937397, -0.02792396768927574, 0.005550180561840534, -0.03603964298963547, -0.0010780437150970101, -0.045500390231609344, 0.009092752821743488, -0.019286826252937317, -0.018688155338168144, -0.022259654477238655, -0.02550695464015007, -0.00870332308113575, 0.03134263679385185, 0.020936250686645508, -0.00962222833186388, 0.022597109898924828, -0.025260675698518753, 0.02794657088816166, -0.00250858161598444, -0.013281096704304218, 0.005505033768713474, 0.014767407439649105, -0.0010231052292510867, -0.014562015421688557, -0.07534134387969971, 0.006081223022192717, -0.008305197581648827, 0.04729174077510834, -0.06887419521808624, 0.035261474549770355, -0.039892204105854034, -0.06430205702781677, -0.0842735543847084, -0.0042775399051606655, 0.013316567055881023, 0.022564085200428963, 0.07875935733318329, 0.05060053616762161, -0.009824457578361034, -0.048673734068870544, 0.015768513083457947, -0.00222261855378747, 0.011204639449715614, 0.009577801451086998, -0.04530252888798714, -0.06381247937679291, 0.030837925150990486, 0.0333988256752491, -0.0043228608556091785, -0.03884131461381912, -0.004157121293246746, 0.04553172364830971, 0.05556042864918709, 0.01249319314956665, 0.05049176514148712, -0.03898637741804123, 0.05463898554444313, 0.03804090991616249, -0.013579627498984337, -0.02423848956823349, -0.042106714099645615, -0.013104508630931377, -0.05327414721250534, -0.06359735131263733, 0.0030287792906165123, 0.006499886978417635 ]
<p>How to show with Maxwells Equations that nonaccelerating charges don't radiate?</p>
g5390
[ 0.018764780834317207, -0.008019533939659595, -0.007502816151827574, 0.0030514495447278023, 0.08038005232810974, 0.01045059785246849, 0.00540886539965868, -0.010348208248615265, 0.011394629254937172, 0.04137127473950386, -0.0006189078558236361, 0.0677700862288475, -0.0038954743649810553, 0.061219461262226105, -0.04893776774406433, -0.01628197729587555, 0.06499024480581284, -0.02976289391517639, 0.06334623694419861, 0.06637822091579437, -0.047398991882801056, -0.009621815755963326, 0.0554807111620903, -0.020271960645914078, -0.026536066085100174, 0.029349714517593384, -0.02720460668206215, 0.012929149903357029, -0.053231753408908844, -0.046616554260253906, 0.02803729847073555, 0.03183206915855408, 0.04351721704006195, -0.0017238017171621323, 0.022457968443632126, -0.05483203008770943, 0.030282750725746155, -0.019750578328967094, -0.025937393307685852, 0.014261290431022644, 0.013325773179531097, -0.012960498221218586, 0.0012973465491086245, 0.04216904938220978, -0.021538274362683296, -0.011912519112229347, -0.007545270025730133, 0.047274112701416016, -0.05896656960248947, -0.018645428121089935, 0.011892956681549549, 0.011085623875260353, 0.06635012477636337, -0.023682309314608574, 0.024609215557575226, 0.0013040417106822133, -0.023934371769428253, -0.0025231908075511456, 0.09061338007450104, 0.0227797981351614, -0.007153146434575319, 0.006774622946977615, 0.010127566754817963, 0.04480166360735893, -0.024697890505194664, -0.007008600048720837, 0.003502629464492202, -0.07610270380973816, -0.041103966534137726, -0.015618831850588322, 0.0031219315715134144, -0.0042763338424265385, -0.015835469588637352, -0.04210576042532921, -0.015731913968920708, -0.05827660486102104, -0.0007210515905171633, 0.005007285624742508, -0.028653739020228386, -0.0018972752150148153, 0.0009947343496605754, 0.006271743215620518, 0.05430685356259346, -0.03085574321448803, 0.07211237400770187, 0.009321358054876328, 0.01620967499911785, -0.03244413807988167, -0.015855278819799423, -0.02744269371032715, -0.005938934627920389, 0.03892975300550461, 0.07599847763776779, -0.034167882055044174, 0.04451422020792961, -0.038429491221904755, 0.0352354533970356, 0.034305673092603683, 0.0012614899314939976, -0.0375966839492321, -0.044803719967603683, 0.025946801528334618, -0.027282942086458206, 0.048889871686697006, 0.05757443606853485, -0.019543075934052467, -0.011616797186434269, 0.013908370397984982, -0.008076698519289494, -0.006411067675799131, -0.007917964830994606, -0.0426894910633564, -0.06960423290729523, -0.03336392715573311, -0.03783472254872322, -0.017880361527204514, 0.04983047768473625, -0.06180647760629654, 0.028897276148200035, 0.054590530693531036, 0.009450461715459824, 0.03132456913590431, 0.02426818013191223, 0.043136995285749435, -0.0058379932306706905, 0.03418796509504318, 0.025311216711997986, 0.016885381191968918, 0.018677448853850365, -0.018740413710474968, 0.03822653368115425, -0.014565284363925457, 0.008496969006955624, 0.04308135434985161, 0.01713882014155388, 0.031666435301303864, -0.011018873192369938, -0.05029434338212013, -0.018602846190333366, -0.07099596410989761, 0.016968803480267525, -0.013742759823799133, 0.017881104722619057, 0.0044884467497467995, -0.003468458540737629, -0.014707284048199654, 0.0009690388687886298, -0.06068311259150505, 0.05426614359021187, 0.07520546019077301, 0.00818582996726036, 0.06655016541481018, 0.0159462820738554, -0.05104499310255051, -0.010087771341204643, -0.04261069744825363, 0.08760106563568115, -0.04352876916527748, -0.049304522573947906, 0.003914404660463333, 0.036881111562252045, 0.007383580785244703, 0.022938469424843788, 0.0062843929044902325, -0.04234076663851738, 0.017622582614421844, -0.04284435510635376, -0.01882294937968254, 0.014844055287539959, -0.054103169590234756, -0.04211090877652168, 0.019950654357671738, 0.059292059391736984, -0.019996874034404755, -0.005408338736742735, 0.10177178680896759, -0.020635006949305534, -0.03655503690242767, 0.042202070355415344, 0.014305243268609047, -0.05626876652240753, 0.03302901238203049, 0.0565948449075222, -0.010729115456342697, -0.03023218922317028, -0.020351964980363846, -0.08298763632774353, 0.01018703542649746, -0.0408431775867939, -0.01005279179662466, -0.03337724506855011, -0.009271645918488503, -0.005213162396103144, 0.008775472640991211, -0.004016582388430834, 0.015418913215398788, -0.0018059727735817432, -0.010971094481647015, 0.03247785568237305, -0.008588869124650955, 0.020809100940823555, 0.03722600266337395, -0.017583787441253662, 0.026939161121845245, -0.002357945777475834, 0.010596212930977345, -0.03155826777219772, -0.05218835547566414, 0.05059276893734932, -0.016647128388285637, 0.011842058040201664, -0.05726754665374756, 0.00365224527195096, 0.02628498524427414, -0.0333583690226078, 0.021094057708978653, -0.008517686277627945, 0.01653849147260189, -0.07014010101556778, -0.021931953728199005, -0.0677400678396225, 0.025736352428793907, 0.01724332943558693, 0.008966123685240746, 0.024254674091935158, 0.018255565315485, -0.02382640354335308, 0.04444792866706848, -0.015971703454852104, -0.03149882331490517, -0.030518943443894386, -0.0031691743060946465, -0.020029596984386444, -0.015561932697892189, 0.05498651787638664, 0.02411614917218685, -0.06666978448629379, 0.012325420044362545, 0.04143650084733963, -0.03309999406337738, -0.08075781166553497, 0.005781353916972876, -0.0034491962287575006, 0.014037171378731728, 0.03179781138896942, -0.03183958679437637, 0.0198514424264431, 0.007769901305437088, -0.024853279814124107, 0.017141148447990417, 0.020628636702895164, 0.023535652086138725, 0.045435432344675064, 0.06372517347335815, -0.018633650615811348, -0.00725537771359086, 0.005894634407013655, 0.010951405391097069, -0.05209740996360779, -0.006250410806387663, -0.021959669888019562, -0.02102075330913067, 0.003900970332324505, -0.007446870673447847, -0.07376822084188461, -0.026079315692186356, -0.011199850589036942, -0.020033732056617737, 0.028402157127857208, 0.015013514086604118, -0.03324878215789795, 0.10742925107479095, 0.015562429092824459, -0.03317337483167648, -0.0209022406488657, 0.02095460146665573, -0.011966411955654621, 0.04117129370570183, 0.02635936066508293, -0.04286909103393555, -0.003278658026829362, 0.0005026753060519695, 0.016946980729699135, 0.0070077539421617985, 0.020627126097679138, -0.049995291978120804, -0.00013144334661774337, 0.029894797131419182, 0.023856591433286667, 0.0285357553511858, -0.016459181904792786, -0.018586324527859688, 0.007656573783606291, -0.02177637815475464, -0.08694102615118027, -0.022635510191321373, 0.08398380875587463, -0.025814784690737724, 0.02560264617204666, -0.008845378644764423, 0.0010689530754461884, 0.059521909803152084, -0.054518017917871475, -0.006007806397974491, 0.014882797375321388, 0.0352570042014122, -0.005717621184885502, -0.10744642466306686, 0.07460066676139832, -0.0026235724799335003, -0.014490248635411263, 0.014760085381567478, 0.018710073083639145, -0.016000237315893173, 0.026250792667269707, -0.08542638272047043, -0.011355593800544739, -0.02558126300573349, 0.04633334279060364, 0.044089872390031815, -0.016913462430238724, -0.05013863369822502, 0.05366716906428337, -0.04645324498414993, -0.023306487128138542, -0.011345281265676022, 0.017831876873970032, 0.020176755264401436, 0.05178442224860191, 0.0003049671940971166, 0.021694689989089966, 0.04315944388508797, 0.03419075906276703, -0.05144421383738518, -0.039222780615091324, -0.06720861047506332, 0.007768453098833561, 0.021728066727519035, 0.004791061859577894, 0.045888110995292664, -0.006950210314244032, -0.022429421544075012, -0.11023610085248947, 0.004823832772672176, -0.0366535484790802, -0.004842822905629873, -0.029965827241539955, -0.03707246854901314, 0.007246525026857853, -0.0622476302087307, 0.010957160033285618, 0.004382620565593243, 0.019135402515530586, -0.02514834702014923, -0.1151028573513031, 0.019976992160081863, 0.024023747071623802, 0.021891124546527863, -0.004192084539681673, 0.017467614263296127, 0.01190416980534792, -0.03824646398425102, 0.01572817750275135, -0.04697389528155327, 0.04191230237483978, 0.06370248645544052, 0.029103858396410942, 0.0799822136759758, -0.0007279326673597097, -0.054911840707063675, 0.03812074288725853, 0.02163984440267086, -0.00482482323423028, 0.03904042765498161, -0.01046564057469368, -0.013058322481811047, -0.020287146791815758, -0.031719453632831573, -0.003654974978417158, 0.03038298897445202, -0.03272121027112007, -0.0009458141284994781, 0.006652806419879198, -0.05201008915901184, -0.004731510765850544, 0.04184476286172867, 0.008420909754931927, 0.04023870825767517, -0.02178231067955494, -0.011853511445224285, -0.0058182659558951855, 0.004983624443411827, -0.010095426812767982, 0.029117431491613388, 0.00411536218598485, -0.10268126428127289, 0.04016721248626709, -0.04338976740837097, 0.06538071483373642, -0.006204118952155113, 0.06581028550863266, 0.03314148634672165, 0.04925910755991936, -0.04160776734352112, 0.028252875432372093, 0.02298806421458721, 0.04490043222904205, -0.015771280974149704, -0.0021335873752832413, 0.0179650466889143, -0.01099606417119503, -0.0391266755759716, 0.01735812798142433, -0.03056265600025654, 0.014458158053457737, -0.028263341635465622, 0.0056124040856957436, 0.027412883937358856, -0.05137474834918976, 0.03929945454001427, 0.015256882645189762, 0.0396576002240181, 0.004404939711093903, -0.014519602991640568, 0.03712650388479233, 0.08959150314331055, 0.060999613255262375, -0.04974094033241272, 0.04383379593491554, 0.010410145856440067, -0.059741050004959106, -0.03928543999791145, -0.047244928777217865, 0.024451589211821556, -0.05171554908156395, 0.03681537136435509, -0.033656444400548935, 0.10334280878305435, 0.00008175992115866393, 0.022568147629499435, 0.06768793612718582, -0.013280035927891731, 0.05998103693127632, -0.0542040690779686, -0.00022797698329668492, 0.0733853206038475, -0.019410869106650352, -0.00022246615844778717, -0.021655526012182236, 0.00011768153490265831, -0.02227104641497135, 0.004183694254606962, -0.06899482011795044, -0.017993943765759468, 0.0031550019048154354, -0.027854973450303078, -0.0208141952753067, -0.006050754338502884, 0.029963746666908264, 0.032969363033771515, -0.03966880589723587, -0.044103797525167465, 0.04338465631008148, -0.017833085730671883, 0.031043831259012222, -0.038467247039079666, 0.018089691177010536, -0.0009901028824970126, -0.022502556443214417, -0.07822591066360474, 0.03049280308187008, 0.05373635143041611, 0.048148833215236664, -0.06405599415302277, -0.0007181646069511771, -0.03474289923906326, 0.0367414616048336, 0.012550076469779015, -0.11366895586252213, 0.018016178160905838, 0.022761549800634384, 0.009416300803422928, -0.05510586500167847, 0.0010764788603410125, 0.03452508524060249, 0.05296733230352402, -0.038163922727108, 0.058320581912994385, -0.05394629016518593, -0.045267704874277115, 0.00024364319688174874, 0.010521609336137772, -0.052322350442409515, -0.04984384775161743, -0.00040429140790365636, 0.020742150023579597, -0.006239442620426416, 0.06484551727771759, -0.041805244982242584, 0.04101123660802841, -0.02057279460132122, -0.022048266604542732, -0.024221334606409073, 0.06675123423337936, -0.0369877964258194, 0.014840511605143547, 0.005418013781309128, -0.0037122764624655247, 0.02139785885810852, 0.007781556807458401, -0.01134340651333332, -0.025622423738241196, 0.06002555042505264, -0.0015608405228704214, -0.013961581513285637, 0.014934985898435116, -0.10322997719049454, 0.024756386876106262, -0.05049848556518555, -0.028774891048669815, 0.01990325003862381, -0.017025593668222427, 0.03622262179851532, -0.003393534803763032, 0.027512256056070328, -0.014374530874192715, -0.015869811177253723, -0.060322970151901245, 0.03682351112365723, 0.022801842540502548, -0.015410056337714195, 0.010765394195914268, 0.011964622884988785, 0.003146323375403881, 0.037257615476846695, -0.04011636599898338, 0.08670143038034439, -0.01614956557750702, -0.0007395506254397333, -0.03273411840200424, -0.036268651485443115, 0.03236880898475647, 0.03583398833870888, 0.0071782758459448814, -0.0024726244155317545, 0.025865841656923294, -0.06158514320850372, 0.012257461436092854, 0.017942562699317932, -0.02333190105855465, 0.008808914572000504, 0.045445311814546585, 0.006788808386772871, -0.017873601987957954, 0.06319261342287064, -0.020884552970528603, -0.015951234847307205, -0.07414247840642929, -0.013685090467333794, 0.0030356035567820072, 0.017252042889595032, -0.017382077872753143, 0.059298641979694366, 0.06328964233398438, 0.009423271752893925, -0.055006012320518494, 0.0021215472370386124, 0.018313005566596985, 0.027806997299194336, -0.045950353145599365, 0.004976129159331322, 0.03927009925246239, 0.028977856040000916, -0.046616069972515106, 0.03596481308341026, 0.010661903768777847, -0.0019541557412594557, 0.021275943145155907, 0.032157741487026215, 0.0021479546558111906, 0.0229418333619833, 0.034881141036748886, 0.07582370191812515, 0.0016638955567032099, 0.008639171719551086, -0.03257075324654579, 0.010264215059578419, 0.027054961770772934, 0.021598542109131813, -0.012220548465847969, -0.04840877279639244, -0.06548263132572174, -0.002596951089799404, -0.020933128893375397, 0.00498761935159564, -0.02577746845781803, -0.0024523145984858274, -0.023470640182495117, 0.015449774451553822, -0.015958257019519806, 0.029893718659877777, 0.021243803203105927, 0.01865261048078537, -0.028819285333156586, 0.021617233753204346, -0.04375798627734184, -0.002146014478057623, -0.02159705199301243, -0.024850288406014442, 0.012607055716216564, -0.09459520131349564, 0.010249428451061249, -0.02105635777115822, 0.0024785776622593403, 0.02402331866323948, -0.037052400410175323, -0.017522677779197693, 0.0405694879591465, 0.017612148076295853, -0.0021261440124362707, -0.011972540058195591, 0.022515684366226196, 0.03518184646964073, 0.008823282085359097, 0.024000059813261032, 0.06309311836957932, -0.048042505979537964, 0.03478485718369484, 0.04159573093056679, -0.044294074177742004, -0.01438015978783369, 0.018832789734005928, 0.0032426007091999054, 0.007776904385536909, 0.04404260218143463, 0.04114476591348648, 0.011333188973367214, -0.008387455716729164, -0.0021387464366853237, -0.007614157162606716, -0.04476243630051613, 0.05855187401175499, 0.07557713240385056, -0.005342199932783842, -0.03170793130993843, -0.023961689323186874, -0.03398875147104263, -0.019857047125697136, -0.03696778044104576, 0.039250440895557404, 0.008845057338476181, -0.012299740687012672, 0.009131462313234806, 0.043837010860443115, -0.04049254581332207, 0.0035418043844401836, -0.04339522495865822, 0.046749722212553024, -0.03362796828150749, -0.0006510962266474962, -0.051482826471328735, -0.06885021179914474, 0.0006288381409831345, 0.006647856440395117, -0.0028868867084383965, 0.014695865102112293, -0.011392081156373024, -0.08675295859575272, -0.003188386559486389, -0.005070425570011139, -0.0024506335612386465, -0.04383229464292526, 0.020519796758890152, 0.003993114456534386, -0.02993747778236866, -0.07199663668870926, 0.013848192058503628, 0.030840380117297173, -0.010635620914399624, -0.025699084624648094, 0.023226356133818626, 0.023969143629074097, 0.01591569185256958, 0.03921055793762207, 0.020089220255613327, -0.018567144870758057, -0.02651628665626049, -0.015698587521910667, 0.04472101479768753, 0.0023688445799052715, -0.018497034907341003, -0.021717602387070656, 0.06095914915204048, 0.0058915880508720875, -0.016915565356612206, 0.007483560126274824, 0.029916862025856972, 0.00174035900272429, 0.02686452493071556, -0.029595768079161644, 0.01661682315170765, 0.02473221905529499, 0.026244772598147392, -0.007876146584749222, -0.08154354244470596, 0.009356560185551643, -0.019260751083493233, -0.029710719361901283, -0.030874263495206833, -0.04219997674226761, -0.03562110662460327, 0.05473065376281738, -0.023675180971622467, 0.03847609832882881, -0.0181247778236866, 0.021229736506938934, -0.058987535536289215, 0.058689042925834656, 0.034385986626148224, -0.005670619662851095, -0.035172149538993835, -0.0257539264857769, -0.039641112089157104, -0.01788814179599285, 0.02589263953268528, -0.032535478472709656, -0.018975479528307915, 0.06022077798843384, -0.015509053133428097, 0.007643311284482479, -0.009647311642765999, 0.07301430404186249, -0.020022448152303696, 0.03560049459338188, -0.039942823350429535, -0.023294854909181595, 0.03112344816327095, 0.014844466000795364, 0.051779236644506454, -0.012666803784668446, -0.0491957813501358, -0.003949572332203388, -0.01703350618481636, -0.051016002893447876, 0.011883677914738655, 0.013002930209040642, -0.0270206518471241, -0.0215982086956501, 0.05077940225601196, 0.034644778817892075, -0.005952845327556133, 0.003898462513461709, -0.020930463448166847, 0.010750307701528072, 0.08044450730085373, 0.014679964631795883, 0.02088753692805767, -0.0009857339318841696, 0.04319017753005028, -0.007097829598933458, 0.0029496627394109964, -0.04732469096779823, -0.023954320698976517, 0.006976456381380558, 0.052343182265758514, -0.07747329026460648, -0.04545171558856964, -0.07039952278137207 ]
<p>A wedge of mass $M$ rests on a rough horizontal surface with coefficient of static friction $\mu$. The face of the wedge is a smooth plane inclined at an angle $ \alpha$ to the horizontal. A mass $m_1$ hangs from a light string which passes over a smooth peg at the upper end of the wedge and attaches to a mass $m_2$ which slides without friction on the face of the wedge.</p> <p>A) Find the accelerations of $ m_1, m_2 $ and the tension in the string when $ \mu $ is very large.</p> <p>B)Find the smallest coefficient of friction such that the wedge will remain at rest.</p> <p>Attempts:</p> <p>No specification on whether or not any of the masses $m_i$ are bigger than the others, so let us assume that $m_1$ goes down and $m_2$ goes up the slope. Then A) is fine. (a minus error in the final answer for A) is introduced if I assume the other orientation)</p> <p>As for B) if we consider the wedge+masses as a system, then to conserve linear momentum if the masses move as above, then the wedge must move rightwards. So the frictional force acts leftwards until the wedge slips. The only other force acting on the wedge is via the normal contact force from $m_2$. A component of this force acts to accelerate the wedge horizontally. Let's write this relative to some fixed inertial frame of reference with $x$ rightwards. Then the above recast into symbols gives $$-\mu (M+m_1+m_2)g - m_2 g \cos \alpha \sin \alpha = 0 $$ at the point of slip of the wedge. However, solving this for $\mu$ gives a negative result. Where did I go wrong?</p> <p><img src="http://i.stack.imgur.com/IQBDT.png" alt="enter image description here"></p>
g5391
[ 0.016125556081533432, 0.011907787062227726, 0.008282839320600033, -0.010765105485916138, 0.031127475202083588, 0.017666766420006752, 0.08896596729755402, -0.020823193714022636, -0.05791465938091278, 0.00025566929252818227, -0.004968938417732716, 0.004447711165994406, -0.009513295255601406, -0.0042812153697013855, 0.028040248900651932, 0.06454164534807205, 0.08793110400438309, 0.01392753142863512, 0.023371528834104538, -0.030855368822813034, -0.03948301449418068, 0.028455091640353203, -0.027560994029045105, -0.026125343516469002, 0.04356048256158829, -0.04877239838242531, 0.014864902943372726, 0.018717603757977486, -0.01820402219891548, 0.004700039513409138, 0.02050197124481201, -0.035788632929325104, 0.015784312039613724, -0.019483020529150963, -0.0035867872647941113, 0.0036894436925649643, 0.052219782024621964, 0.006095295771956444, 0.02513018250465393, 0.0018847599858418107, 0.020609166473150253, -0.059254590421915054, 0.04056142270565033, 0.00649271672591567, 0.03914947435259819, -0.02694370597600937, 0.013881286606192589, -0.014717485755681992, -0.006142045371234417, -0.018046077340841293, 0.01387490052729845, 0.06974203884601593, 0.009100532159209251, -0.05730454623699188, -0.06285500526428223, 0.057095322757959366, 0.031248167157173157, -0.02398643083870411, 0.03432108461856842, 0.09487976133823395, -0.01442133542150259, -0.057125359773635864, 0.016763659194111824, -0.042524948716163635, 0.013694379478693008, -0.04512631148099899, -0.021566426381468773, -0.0026219470892101526, 0.0546758808195591, -0.01129761803895235, -0.027972809970378876, -0.007162757683545351, 0.03456069156527519, -0.07513310760259628, -0.08032184094190598, -0.00929984636604786, -0.012584298849105835, -0.017357250675559044, -0.05146117880940437, -0.02177358791232109, -0.05052361637353897, 0.015202960930764675, 0.004841020796447992, 0.008392595686018467, 0.047527287155389786, -0.05127318575978279, 0.04573488235473633, 0.0441763810813427, -0.044229332357645035, -0.0048142289742827415, 0.06260722130537033, 0.0036080817226320505, 0.032588548958301544, 0.0735621377825737, 0.040789831429719925, -0.027658749371767044, -0.039544835686683655, 0.10258890688419342, -0.0049026599153876305, 0.00496677914634347, 0.002351393923163414, -0.03294314071536064, -0.02430690824985504, -0.018358176574110985, 0.07513728737831116, -0.014733705669641495, -0.005491938907653093, 0.06894459575414658, -0.00310957501642406, 0.022136317566037178, 0.024119852110743523, -0.009037245996296406, -0.0381835475564003, -0.12985478341579437, 0.004414914175868034, -0.09178569912910461, 0.030274050310254097, 0.03424261510372162, -0.012304996140301228, 0.037325453013181686, -0.06556489318609238, -0.05836450308561325, 0.00933501124382019, 0.08766095340251923, 0.03986694663763046, -0.027418306097388268, -0.010665040463209152, 0.023642998188734055, -0.005249418783932924, 0.008848922327160835, -0.035149406641721725, 0.0210251621901989, 0.05385696887969971, -0.011654789559543133, -0.001820666715502739, 0.036192525178194046, -0.04941412806510925, 0.03988082334399223, 0.0197015218436718, 0.0143633633852005, -0.016941603273153305, 0.008059937506914139, -0.024330953136086464, 0.014774821698665619, -0.06519792973995209, 0.03375876694917679, -0.0645207092165947, 0.028854867443442345, 0.07141287624835968, 0.030009889975190163, 0.02929745800793171, 0.058937735855579376, -0.010822227224707603, 0.007431527599692345, 0.03356999158859253, 0.012009150348603725, 0.08871296048164368, -0.035618435591459274, -0.0446816012263298, 0.031724028289318085, 0.02563418634235859, -0.046839628368616104, 0.042799212038517, 0.008573280647397041, -0.006429592613130808, 0.004961813800036907, -0.030753901228308678, -0.07026058435440063, 0.015162263996899128, -0.010979276150465012, -0.05692214518785477, -0.020230663940310478, 0.04409494623541832, 0.017988858744502068, -0.026000594720244408, 0.02933797612786293, 0.05409795418381691, -0.05343671143054962, 0.06521953642368317, 0.009970075450837612, 0.0024625486694276333, -0.015683840960264206, 0.00854444969445467, 0.021784447133541107, -0.009596328251063824, 0.017244983464479446, 0.03425578773021698, 0.04917651042342186, 0.03453871235251427, -0.0034356359392404556, -0.0032919354271143675, -0.015273102559149265, -0.020504867658019066, -0.0034871594980359077, -0.03028569370508194, 0.01906566321849823, 0.02549738436937332, -0.05544438585639, 0.0022178194485604763, -0.0005460565444082022, -0.004672378301620483, 0.018283577635884285, 0.02668427862226963, -0.017342455685138702, -0.001955481246113777, -0.008461498655378819, 0.019721217453479767, -0.037427980452775955, 0.011371560394763947, 0.01939399167895317, 0.03526486083865166, 0.028489332646131516, 0.009466111660003662, 0.012341718189418316, -0.023922530934214592, -0.07798741012811661, 0.01213408075273037, -0.02237924188375473, 0.018601130694150925, 0.013839120976626873, -0.05052272975444794, -0.02255599945783615, -0.002334913006052375, -0.03418995812535286, -0.031393855810165405, 0.01214275136590004, -0.03754696622490883, -0.027678783982992172, 0.013680188916623592, 0.03342384099960327, -0.03900865092873573, 0.004424749407917261, 0.025367382913827896, 0.008706234395503998, 0.025712043046951294, 0.00414557009935379, 0.02127145603299141, 0.018571482971310616, 0.024169884622097015, 0.04133244976401329, 0.0004982214304618537, -0.01924707368016243, -0.03795843943953514, -0.03873753920197487, 0.00247895997017622, -0.01570277102291584, 0.00017442632815800607, 0.034595031291246414, 0.00616516824811697, 0.058585409075021744, 0.036785438656806946, 0.03719237819314003, -0.018452981486916542, 0.008649704046547413, 0.021765395998954773, -0.027383722364902496, -0.07259472459554672, -0.03053385019302368, 0.04659290984272957, -0.032235726714134216, -0.03323616832494736, -0.02978229522705078, -0.025695962831377983, 0.024630403146147728, -0.09098605066537857, -0.003880976000800729, -0.04678737744688988, -0.023830289021134377, 0.041774895042181015, 0.05264845862984657, -0.01095851045101881, -0.004533954430371523, -0.019821491092443466, 0.05052395164966583, 0.010708156041800976, -0.02683924324810505, -0.008101309649646282, 0.04047221317887306, -0.05270541459321976, 0.01376846618950367, 0.025221874937415123, 0.023505859076976776, -0.006107343826442957, -0.01119527593255043, 0.000271767406957224, -0.05047307536005974, -0.0008959301630966365, -0.012675062753260136, -0.03353840485215187, 0.0073537505231797695, -0.04163598269224167, 0.02318493090569973, 0.07655586302280426, 0.05067470297217369, 0.06875555217266083, 0.057422488927841187, -0.02176525630056858, -0.036895062774419785, -0.01607930287718773, 0.018746905028820038, -0.007008625194430351, -0.02846350334584713, 0.012639121152460575, -0.015964753925800323, 0.0202017854899168, -0.0011262038024142385, -0.025118837133049965, -0.04871854931116104, 0.0368565209209919, -0.00639291200786829, 0.0174932312220335, 0.05155159905552864, 0.034500326961278915, -0.07819490134716034, -0.04923095181584358, 0.00935981422662735, 0.009662210941314697, -0.005656703840941191, 0.009756946936249733, 0.0007227208698168397, -0.06330458074808121, -0.057396456599235535, -0.016575399786233902, 0.0004960874211974442, -0.017894715070724487, 0.03931311517953873, -0.05243020877242088, 0.02676122635602951, -0.00907550286501646, -0.006747382692992687, 0.04181971773505211, 0.06669404357671738, -0.007481805514544249, -0.024252554401755333, 0.03204682096838951, -0.04924424737691879, 0.032465506345033646, 0.004223356954753399, 0.031722016632556915, 0.02908162586390972, -0.05631330981850624, -0.0373561754822731, -0.025946611538529396, -0.0018972811521962285, 0.0006978914025239646, -0.003221193328499794, 0.02154972031712532, 0.012265890836715698, 0.0272695142775774, -0.002007115166634321, 0.04443458095192909, -0.08264489471912384, -0.03554490953683853, 0.012921402230858803, 0.015438775531947613, 0.056996628642082214, -0.016921071335673332, -0.006047364324331284, -0.047981493175029755, -0.022626029327511787, -0.01708989031612873, -0.031647101044654846, -0.03419233486056328, 0.03381528705358505, 0.044111721217632294, -0.026065362617373466, -0.04520386457443237, 0.012162528000772, -0.018853839486837387, 0.004990175366401672, 0.012847566045820713, -0.039385102689266205, 0.033272307366132736, -0.06054944545030594, -0.010655725374817848, -0.01670582965016365, -0.008020615205168724, -0.02701490931212902, -0.008612362667918205, 0.017973696812987328, 0.04858383908867836, -0.009918570518493652, -0.04954136908054352, -0.02465813048183918, -0.023544464260339737, 0.07892701774835587, 0.0007673350628465414, 0.01752959005534649, 0.02749471180140972, -0.012965686619281769, -0.016639430075883865, -0.045837003737688065, 0.015271227806806564, -0.0006114156567491591, 0.012519991025328636, 0.007448902353644371, -0.0015227018157020211, 0.02389313094317913, -0.0414702370762825, -0.06429292261600494, 0.01797359809279442, 0.010411306284368038, 0.004528972320258617, 0.04500381276011467, -0.0302151907235384, 0.09078355133533478, -0.014045370742678642, 0.03351328894495964, 0.008354122750461102, -0.02979455329477787, 0.07098077982664108, -0.0167908426374197, -0.034315191209316254, -0.0010514070745557547, 0.03839462995529175, -0.0028290445916354656, -0.021404128521680832, 0.033051248639822006, -0.02355951815843582, -0.012001683004200459, 0.022676244378089905, 0.08591680973768234, -0.02485625632107258, -0.03230338916182518, 0.03316769376397133, -0.03310483321547508, -0.018691059201955795, 0.07703090459108353, -0.025722643360495567, -0.000488161196699366, 0.007540835067629814, 0.032156042754650116, 0.0038681586738675833, -0.014742542989552021, -0.030624695122241974, 0.09581970423460007, 0.044502511620521545, -0.058719247579574585, -0.01286862138658762, 0.07280614227056503, -0.04112003743648529, 0.04655401408672333, 0.0018560627941042185, -0.03837389126420021, -0.006399834994226694, 0.03322504088282585, 0.005926336161792278, -0.02074226550757885, -0.005365372635424137, -0.024278849363327026, 0.00538452947512269, -0.07289586961269379, 0.015689563006162643, -0.04706546664237976, -0.0001974579063244164, 0.03329738229513168, -0.04512988030910492, 0.057364322245121, -0.04621361941099167, 0.028996823355555534, 0.04194192588329315, -0.030354220420122147, -0.007970045320689678, -0.009695255197584629, -0.008650748059153557, -0.0026357683818787336, -0.027489379048347473, 0.030928386375308037, -0.0031429424416273832, 0.005067576188594103, -0.004377072677016258, -0.00973877590149641, -0.029557203873991966, 0.0020628056954592466, 0.0006729137967340648, 0.03363747522234917, -0.015537334606051445, 0.022112367674708366, 0.02255060337483883, -0.011119097471237183, -0.040068067610263824, 0.014318433590233326, 0.03428919240832329, -0.03682554513216019, 0.03360719978809357, -0.05261547118425369, -0.025569578632712364, 0.011927657760679722, 0.006916757673025131, 0.021789340302348137, 0.019336460158228874, -0.003391555743291974, -0.04408161714673042, -0.028456633910536766, -0.019204409793019295, 0.037708498537540436, -0.03587483987212181, 0.006569379940629005, -0.010647409595549107, 0.01242438331246376, -0.048707351088523865, -0.012783888727426529, 0.053327687084674835, 0.0013042393838986754, 0.0029397921171039343, 0.012408249080181122, 0.0488932766020298, -0.06262035667896271, 0.0063298954628407955, 0.07150214165449142, -0.021196072921156883, 0.042300548404455185, 0.10161100327968597, -0.021946260705590248, -0.008486034348607063, 0.0022611303720623255, 0.049227867275476456, 0.033118341118097305, -0.06140591949224472, 0.02164706401526928, 0.05213348567485809, -0.024837134405970573, -0.004822819493710995, -0.030300648882985115, 0.000041641531424829736, 0.03891637176275253, -0.0015393159119412303, -0.03141973912715912, -0.08224799484014511, -0.02775227651000023, 0.00258128484711051, -0.07579290121793747, 0.03266778960824013, -0.024539809674024582, 0.01221230998635292, -0.024128466844558716, -0.014876295812427998, -0.038397207856178284, -0.014861135743558407, -0.09889058023691177, -0.053263433277606964, -0.043478500097990036, 0.05792393162846565, 0.001188464229926467, 0.010223817080259323, 0.046005088835954666, -0.02737642265856266, -0.018377114087343216, 0.00779064791277051, -0.06274107843637466, -0.03119441121816635, 0.06702004373073578, -0.045298367738723755, -0.005762173794209957, -0.024875521659851074, -0.03955915570259094, 0.019697347655892372, -0.04330797120928764, -0.008625063113868237, -0.01769116520881653, 0.05013831704854965, -0.08329693973064423, 0.018432172015309334, 0.0014898449881002307, 0.004056643694639206, -0.030242539942264557, 0.034052617847919464, -0.023176541551947594, 0.041774094104766846, 0.010203584097325802, -0.03549131378531456, 0.03802192211151123, -0.02337680570781231, 0.07509763538837433, 0.03290870040655136, 0.0404488705098629, -0.0831875279545784, 0.0003580463526304811, -0.012942333705723286, 0.0309405867010355, 0.0003941709001082927, 0.04738287627696991, -0.01314935740083456, -0.04233340173959732, 0.010365464724600315, -0.018077900633215904, -0.1285707801580429, -0.05565056577324867, 0.041184306144714355, -0.02263740450143814, -0.05635310336947441, 0.08462856709957123, -0.041356395930051804, 0.06762900948524475, -0.06290191411972046, -0.061268292367458344, -0.007600078359246254, 0.0352214016020298, -0.01686406135559082, 0.022343888878822327, 0.07736816257238388, 0.0318613164126873, 0.06751058250665665, -0.04295171797275543, 0.0034583366941660643, -0.026106227189302444, 0.009231887757778168, 0.012104440480470657, 0.02065618894994259, -0.046246327459812164, -0.03875264152884483, 0.07299277931451797, 0.0034770024940371513, 0.029221702367067337, 0.005373684223741293, -0.0017052076291292906, 0.0010570322629064322, 0.00436115637421608, -0.019610850140452385, -0.0788937509059906, -0.020362500101327896, 0.015609689056873322, 0.02771022915840149, -0.029401402920484543, 0.020122990012168884, -0.01217140443623066, -0.051388178020715714, 0.006546114105731249, -0.0008278321474790573, 0.0050400602631270885, 0.018119897693395615, 0.008663191460072994, -0.006901005748659372, 0.021154768764972687, 0.012694524601101875, 0.03301109001040459, -0.0615820549428463, 0.023553835228085518, -0.03336700052022934, 0.08484283089637756, 0.018218858167529106, 0.007159336004406214, -0.037624433636665344, -0.014946579933166504, -0.011766059324145317, -0.016881104558706284, 0.009218355640769005, 0.0005814672913402319, -0.03820660337805748, -0.0093340203166008, -0.028087541460990906, -0.00010538611968513578, 0.0016776988049969077, 0.038888704031705856, 0.0007685379823669791, -0.025559768080711365, 0.0212481077760458, 0.010965895839035511, 0.03820086270570755, 0.04097505286335945, -0.04318668320775032, 0.03142322972416878, 0.06781943887472153, -0.004253874532878399, -0.030137475579977036, 0.02680090069770813, -0.04205801337957382, 0.022087110206484795, 0.027821112424135208, 0.0501110814511776, -0.01932545006275177, -0.05072154104709625, 0.006475670263171196, -0.005444183014333248, 0.017283562570810318, 0.025405505672097206, 0.01732718199491501, -0.002077866345643997, -0.007080879062414169, 0.02889769710600376, 0.02814345620572567, -0.008827670477330685, 0.0007903006044216454, -0.010134258307516575, 0.02464737929403782, -0.027567759156227112, 0.03150774911046028, 0.03414818271994591, -0.05310231074690819, 0.003382400143891573, 0.005616451613605022, 0.06386402994394302, 0.01175987534224987, -0.008005081675946712, -0.04391756281256676, -0.0034077989403158426, -0.06451444327831268, 0.043793171644210815, -0.029282502830028534, -0.01777886040508747, -0.013919373974204063, -0.027880093082785606, 0.004027052782475948, 0.027650827541947365, 0.005020669661462307, 0.01859726943075657, -0.0356929637491703, -0.045265574008226395, -0.06582780182361603, 0.003915856126695871, 0.05605554208159447, 0.04250677302479744, 0.0008294897270388901, 0.014036089181900024, 0.08185321092605591, 0.0377165861427784, 0.00443514809012413, 0.03898252546787262, 0.0044432347640395164, -0.073092021048069, -0.0017598906997591257, -0.01219858042895794, 0.02393537387251854, -0.07673334330320358, -0.03854604437947273, -0.032042939215898514, -0.011539148166775703, -0.022313201799988747, 0.010079211555421352, -0.007111501879990101, -0.021846065297722816, 0.0024323160760104656, 0.04526441916823387, -0.021285725757479668, 0.02116031013429165, -0.008588189259171486, 0.01205363404005766, -0.025921791791915894, -0.019508233293890953, 0.023905383422970772, -0.011985254473984241, -0.09184432029724121, 0.013639182783663273, -0.008063679561018944, 0.07277686148881912, -0.004864702932536602, 0.05052303895354271, 0.023648273199796677, 0.03208687901496887, -0.023094695061445236, 0.03591087833046913, 0.006792015861719847, -0.0341385081410408, -0.0010515415342524648, 0.03677165508270264, -0.003023435128852725, 0.046483125537633896, 0.022314749658107758, 0.021887023001909256, -0.05058998987078667, -0.005103642586618662, -0.023282047361135483, -0.04420127347111702, -0.027668893337249756, 0.049161721020936966, -0.07963861525058746, -0.02577339857816696, 0.02777441218495369 ]
<p>What do you mean by charge? Why should a particle have a charge?</p>
g189
[ 0.07349176704883575, 0.022758811712265015, -0.027320196852087975, 0.008541198447346687, 0.10398975759744644, 0.051820531487464905, -0.04037565365433693, -0.016943147405982018, -0.05317452922463417, -0.011396362446248531, -0.007837294600903988, 0.055164486169815063, -0.026280872523784637, 0.010918687097728252, -0.08173054456710815, 0.003182056825608015, 0.048124246299266815, -0.012035510502755642, 0.04651516675949097, 0.031394168734550476, -0.008188036270439625, -0.019042735919356346, 0.02118621952831745, -0.021785065531730652, -0.008976707234978676, 0.02382737211883068, 0.01754239946603775, -0.012232545763254166, 0.024421030655503273, -0.049627985805273056, 0.07560662925243378, -0.00033262436045333743, -0.00906958244740963, -0.018831351771950722, -0.03822755068540573, -0.06234927475452423, 0.06305024027824402, -0.008181280456483364, -0.01233949325978756, 0.002580061787739396, -0.023803435266017914, -0.004240731243044138, -0.0173969566822052, -0.02257074974477291, 0.0135205602273345, 0.0033570940140634775, 0.037165943533182144, 0.01800171658396721, -0.007688636425882578, -0.014382997527718544, -0.03154117241501808, 0.0005613547982648015, -0.012684858404099941, -0.037858616560697556, 0.0848228856921196, -0.016736477613449097, 0.006333883851766586, 0.005075585562735796, 0.006930014118552208, 0.0426904670894146, -0.017134126275777817, 0.04202279821038246, 0.001836941810324788, 0.024768149480223656, 0.001250341534614563, -0.024699820205569267, -0.045171644538640976, -0.021948296576738358, 0.0032973033376038074, 0.05036601424217224, 0.023548737168312073, -0.07764455676078796, -0.024746019393205643, -0.02435065247118473, 0.005127209238708019, -0.03018692322075367, -0.04627125710248947, 0.010991356335580349, 0.06052963435649872, -0.015727804973721504, 0.014994925819337368, -0.016180485486984253, 0.06164797395467758, 0.001932553481310606, 0.09376563876867294, -0.05984038487076759, -0.026205074042081833, -0.0656667947769165, -0.012764178216457367, -0.021845689043402672, -0.01780867949128151, -0.03564390912652016, 0.04484138637781143, 0.01151534728705883, -0.013529169373214245, -0.0759204626083374, 0.0004109895380679518, 0.024577518925070763, 0.008189442567527294, 0.03469463065266609, -0.030109062790870667, 0.0019809515215456486, 0.030644865706562996, 0.0806664377450943, 0.041061002761125565, -0.01062241941690445, 0.012026139535009861, 0.05591582506895065, -0.00010416544682811946, -0.051292769610881805, 0.0539877712726593, -0.006958679296076298, 0.03260442242026329, -0.024636801332235336, -0.05569152534008026, 0.006509389728307724, 0.11191795021295547, -0.033997707068920135, -0.020466921851038933, 0.07365284860134125, -0.017098769545555115, 0.005856196396052837, -0.009190313518047333, 0.037884581834077835, -0.04914325475692749, 0.010917727835476398, 0.02324923686683178, -0.006228818092495203, 0.011653134599328041, 0.009686244651675224, 0.0010783213656395674, 0.013696365989744663, -0.08484382182359695, 0.005733752157539129, 0.0032421236392110586, 0.02677043527364731, -0.017110062763094902, -0.032320644706487656, 0.043275557458400726, -0.05097257345914841, 0.008248143829405308, 0.051861971616744995, 0.021469444036483765, -0.00400471081957221, -0.014352651312947273, -0.05058141052722931, -0.017430389299988747, -0.02417590096592903, 0.016163300722837448, 0.037915993481874466, -0.0006018845597282052, 0.03938750922679901, 0.0599132664501667, 0.0011783605441451073, 0.04735070839524269, -0.06519117206335068, 0.08403248339891434, 0.022819453850388527, -0.024227673187851906, 0.011504394002258778, 0.04955034330487251, 0.04606560245156288, -0.03942865505814552, 0.025930799543857574, -0.07262199372053146, -0.010462903417646885, 0.0176206286996603, -0.04496736824512482, -0.05409250408411026, -0.002326027723029256, 0.01727193221449852, -0.0029926474671810865, -0.016417894512414932, -0.004342440515756607, 0.022759661078453064, 0.009253786876797676, -0.08697961270809174, -0.017273057252168655, 0.07585227489471436, 0.0005873921909369528, -0.016491679474711418, -0.011273403652012348, 0.05410745367407799, -0.01696844771504402, -0.05456898361444473, 0.04275156557559967, -0.02268119342625141, -0.0027006410527974367, -0.012863300740718842, 0.0347297340631485, -0.03507429361343384, -0.0374656543135643, -0.014193510636687279, 0.04465366527438164, 0.018496612086892128, -0.023031633347272873, 0.014902148395776749, -0.02948005124926567, -0.03942766785621643, 0.03197746351361275, -0.016115428879857063, -0.037139881402254105, 0.004653779789805412, 0.02378145419061184, 0.023316746577620506, -0.022923793643712997, -0.005618242081254721, -0.013432690873742104, 0.038361210376024246, -0.013509831391274929, 0.07678569853305817, -0.027450349181890488, -0.0015038764104247093, 0.027745118364691734, -0.053459953516721725, -0.054436273872852325, -0.0004416900919750333, -0.016436094418168068, -0.04456697776913643, 0.0007933434098958969, -0.08387348055839539, -0.021709168329834938, 0.04671773687005043, 0.010763870552182198, -0.03561018779873848, 0.03267579898238182, -0.025826284661889076, -0.04522576928138733, -0.021431054919958115, 0.012174898758530617, -0.025960030034184456, -0.026090625673532486, -0.06567852199077606, 0.008385236375033855, 0.06479864567518234, 0.039530690759420395, -0.052483849227428436, -0.004539199639111757, 0.01671566255390644, -0.04397322237491608, -0.03172682598233223, -0.012021956965327263, 0.05215921252965927, -0.007627119310200214, 0.0036589661613106728, -0.02757161669433117, 0.0013475583400577307, -0.010431770235300064, -0.05987159162759781, 0.0032827970571815968, 0.026022542268037796, -0.05329720303416252, 0.027867743745446205, -0.02744860015809536, 0.05490478500723839, -0.05052534490823746, 0.008447435684502125, 0.039160460233688354, -0.02917897328734398, -0.0734390914440155, 0.040580153465270996, -0.044759638607501984, -0.07123225927352905, -0.0071189189329743385, -0.05938446521759033, 0.012853297404944897, -0.0021252227015793324, 0.04265621304512024, 0.06429135799407959, -0.021489711478352547, 0.019273560494184494, 0.09818762540817261, 0.015293586999177933, 0.004240707494318485, 0.005574003793299198, 0.01787172071635723, 0.011467636562883854, -0.01156359538435936, 0.04840549826622009, -0.08201735466718674, 0.013043488375842571, 0.03490755334496498, -0.059706225991249084, 0.03405136615037918, 0.034920621663331985, -0.029747383669018745, 0.03410482406616211, -0.01794743910431862, -0.0010278739500790834, -0.055969566106796265, 0.023392610251903534, 0.022432401776313782, 0.033672504127025604, -0.035921696573495865, 0.04528023302555084, 0.0007586055435240269, 0.060454897582530975, -0.019016221165657043, 0.028582094237208366, 0.0499318391084671, -0.024227768182754517, -0.0028544114902615547, -0.002341880928725004, -0.004590569995343685, 0.04811088740825653, 0.07198327779769897, -0.005501634906977415, -0.03942523151636124, -0.033419154584407806, 0.038020577281713486, -0.015657998621463776, 0.05813796818256378, -0.026660645380616188, 0.03642517328262329, 0.009793304838240147, -0.039679303765296936, -0.08170363306999207, 0.010378705337643623, -0.007932075299322605, -0.06037728488445282, -0.003291295375674963, 0.007478528190404177, 0.02074010856449604, -0.02287994511425495, -0.01686905510723591, 0.06528341770172119, -0.02396547980606556, -0.025005148723721504, 0.02908981963992119, -0.03540648892521858, -0.016510402783751488, 0.036415498703718185, 0.006921553052961826, -0.009327199310064316, 0.01886671409010887, -0.07601314038038254, 0.025321785360574722, 0.03423291817307472, 0.012136468663811684, 0.02778361737728119, -0.01759123057126999, 0.009371650405228138, -0.0374642089009285, -0.008548456244170666, -0.025419069454073906, -0.016439253464341164, 0.04236558824777603, -0.045486196875572205, 0.01488330028951168, -0.0059387641958892345, -0.0010976232588291168, 0.01320671383291483, 0.01309514231979847, 0.016939539462327957, -0.03991241753101349, -0.0010924384696409106, 0.02531643584370613, 0.02831130288541317, -0.0747075006365776, 0.012660536915063858, 0.04474421218037605, -0.005802659783512354, 0.0283307284116745, 0.023495187982916832, 0.027112891897559166, 0.02726851776242256, -0.056998878717422485, -0.015475748106837273, 0.01307477056980133, -0.007446346338838339, 0.009587298147380352, 0.027740897610783577, -0.03200794383883476, 0.024070773273706436, 0.004029130097478628, -0.011284965090453625, -0.002723964862525463, -0.016676785424351692, -0.044578492641448975, -0.06193079054355621, 0.006872329395264387, -0.006953791715204716, -0.02406150847673416, 0.010119552724063396, 0.005969501566141844, 0.010505435056984425, -0.007562375161796808, 0.04236764460802078, 0.0037297329399734735, -0.011484107002615929, 0.004287709482014179, -0.002013305900618434, -0.029604535549879074, -0.029291843995451927, -0.018941547721624374, -0.008520027622580528, 0.00860366690903902, -0.0827510803937912, 0.04622427001595497, -0.0568455271422863, -0.023006241768598557, 0.04273344948887825, -0.01928938739001751, -0.07406647503376007, 0.034730300307273865, 0.0027162455953657627, 0.05816925689578056, -0.06859223544597626, 0.023279422894120216, -0.012712659314274788, 0.0029644425958395004, 0.045405078679323196, 0.0011233582627028227, 0.03477850183844566, -0.062102317810058594, -0.03378067538142204, -0.024715643376111984, 0.005131636746227741, 0.02441580593585968, 0.03551068529486656, 0.01653650961816311, 0.02732788771390915, 0.05874286964535713, -0.029708482325077057, 0.0041199116967618465, 0.047862425446510315, 0.02840927615761757, -0.013142074458301067, -0.044576361775398254, -0.026398079469799995, -0.0036410714965313673, 0.06974950432777405, -0.020222529768943787, -0.025486694648861885, -0.0077430978417396545, 0.017678694799542427, -0.06992604583501816, 0.022222869098186493, -0.03309505432844162, 0.04481731727719307, 0.07956545799970627, 0.02846202813088894, 0.05819811671972275, -0.05407943204045296, 0.02204376831650734, 0.022261599078774452, -0.006629202980548143, 0.032314397394657135, -0.01733868196606636, -0.01943606697022915, 0.02009151130914688, 0.04422294348478317, -0.058986954391002655, -0.048171769827604294, 0.021365100517868996, -0.0058885011821985245, -0.031402282416820526, -0.058555200695991516, -0.025526663288474083, 0.02896769531071186, -0.07099208235740662, 0.008193762972950935, 0.04589756578207016, 0.00510224886238575, 0.0171933826059103, 0.0032551835756748915, -0.048434413969516754, -0.05516514182090759, 0.016090335324406624, -0.035463135689496994, -0.015430252999067307, 0.0027881967835128307, 0.009062548168003559, -0.01867302879691124, 0.06619016826152802, 0.023287078365683556, 0.03040027618408203, -0.019416768103837967, -0.02830485627055168, -0.02599352039396763, 0.005726792849600315, 0.007183491252362728, 0.0036324714310467243, -0.0073822615668177605, -0.058353714644908905, -0.014621416106820107, -0.05504925176501274, 0.01783713698387146, -0.023994524031877518, -0.050391316413879395, -0.021753178909420967, 0.011011147871613503, 0.03299248218536377, 0.011990092694759369, 0.017069946974515915, 0.03289738669991493, 0.01479649730026722, 0.050096891820430756, 0.02645222470164299, 0.007272734306752682, -0.005911692976951599, -0.07052772492170334, -0.026112500578165054, 0.01545403990894556, -0.04082376882433891, 0.03673269599676132, 0.042750123888254166, -0.024672875180840492, -0.007576560601592064, -0.046056341379880905, 0.016213160008192062, 0.0020177261903882027, 0.06605377793312073, 0.024651410058140755, 0.028294526040554047, 0.12009972333908081, -0.013475632295012474, -0.019912229850888252, -0.03797146677970886, 0.06006418913602829, -0.004251742735505104, -0.02443971112370491, 0.04430070146918297, -0.05571553856134415, 0.046046845614910126, 0.0010235295630991459, -0.029447609558701515, -0.060566168278455734, 0.05524974316358566, 0.0445670522749424, -0.0061162677593529224, -0.027462437748908997, 0.015307004563510418, 0.019406121224164963, -0.05475442111492157, -0.024169068783521652, -0.013872315175831318, 0.0502152293920517, 0.026310373097658157, -0.021102111786603928, -0.03293792903423309, -0.0519583523273468, -0.026533113792538643, 0.04456198215484619, 0.059567905962467194, 0.011040203273296356, -0.04229393228888512, 0.05758310481905937, 0.017341982573270798, -0.0864768922328949, 0.008724355138838291, 0.0056746038608253, -0.011199171654880047, -0.07682257890701294, 0.04333893582224846, 0.025645850226283073, 0.05924995243549347, -0.021848104894161224, -0.006203691475093365, -0.04191046208143234, -0.013142039068043232, -0.01913980022072792, -0.020572608336806297, 0.027431432157754898, 0.05831032246351242, 0.03142073005437851, 0.012674030847847462, -0.00575349573045969, 0.00478614866733551, -0.016568409278988838, -0.0039309607818722725, 0.025179028511047363, 0.03613816574215889, 0.0035499136429280043, 0.04737159609794617, -0.01437363587319851, 0.007395850960165262, 0.01834648847579956, -0.044173602014780045, -0.03869437798857689, 0.07040513306856155, -0.0225114393979311, 0.0299990251660347, -0.0018383254064247012, 0.015288242138922215, -0.00920772273093462, 0.03101852536201477, -0.022023774683475494, 0.07083262503147125, 0.009476849809288979, 0.05326773226261139, 0.003448470728471875, 0.033490102738142014, -0.02317178063094616, -0.001155917183496058, 0.007528890389949083, 0.04913579300045967, -0.03781773895025253, -0.021583890542387962, -0.015312133356928825, 0.031398460268974304, 0.02555418573319912, -0.0293140709400177, 0.030138880014419556, 0.06490734219551086, 0.017993299290537834, 0.024022845551371574, -0.024948451668024063, -0.06707267463207245, 0.04377465695142746, -0.09228119254112244, -0.03624372556805611, -0.04377935826778412, -0.021208301186561584, 0.04563600569963455, -0.03126988559961319, -0.0281466506421566, 0.04310382902622223, -0.003712260629981756, -0.00906566996127367, 0.016170745715498924, 0.015129641629755497, 0.02917570248246193, -0.012199989520013332, 0.05271630361676216, 0.019401326775550842, -0.022235557436943054, 0.10840518772602081, 0.04138505458831787, 0.012264984659850597, -0.0725916177034378, 0.00871709082275629, -0.0065851882100105286, 0.04186767339706421, -0.04432583600282669, 0.010961173102259636, 0.012444506399333477, 0.01845398172736168, 0.003289436222985387, 0.034037284553050995, 0.005986660253256559, 0.014307075180113316, 0.036735523492097855, 0.014885220676660538, -0.08599724620580673, -0.008905760012567043, 0.06745672971010208, -0.07188098877668381, -0.02164684794843197, -0.025500576943159103, -0.016261324286460876, 0.012623073533177376, 0.024114737287163734, 0.033872026950120926, 0.03608433157205582, -0.015035944059491158, 0.009581376798450947, 0.04615052789449692, 0.03053927794098854, -0.056850504130125046, -0.02590148150920868, 0.008903722278773785, -0.004633682314306498, -0.031447891145944595, 0.017940791323781013, -0.01562343630939722, -0.013605020008981228, -0.0436723493039608, 0.008124535903334618, -0.03234397619962692, -0.04300466179847717, 0.012229004874825478, -0.056802429258823395, -0.030361702665686607, -0.02344060130417347, -0.004593508318066597, 0.0299749206751585, 0.094715915620327, -0.014928207732737064, 0.00645532738417387, 0.05581036955118179, -0.004433024674654007, -0.011175379157066345, -0.004427979234606028, -0.007651406340301037, -0.042334239929914474, -0.02727845497429371, 0.009574536234140396, 0.006001567468047142, 0.01731974445283413, 0.007528845686465502, 0.00089812814258039, 0.03396868705749512, -0.042399488389492035, -0.03604746237397194, 0.049547888338565826, 0.030843574553728104, -0.006698792800307274, 0.03799804300069809, -0.055797379463911057, -0.015228144824504852, -0.014993212185800076, 0.012572617270052433, -0.021071430295705795, -0.010699150152504444, 0.020061930641531944, 0.014046008698642254, -0.0018315000925213099, -0.057558197528123856, -0.03144141659140587, -0.03376123681664467, -0.048009563237428665, 0.030274152755737305, 0.007633429951965809, 0.04280762001872063, 0.006206471938639879, 0.005668408703058958, 0.025377055630087852, -0.01935482583940029, -0.020770784467458725, 0.04748109355568886, 0.02321646176278591, -0.01039784774184227, -0.03411683812737465, -0.012036873959004879, -0.07935131341218948, 0.009589352644979954, 0.022880898788571358, 0.06066827476024628, -0.014149910770356655, -0.008003485389053822, 0.04759865254163742, -0.025589296594262123, 0.022235935553908348, -0.046145930886268616, -0.0010807301150634885, 0.03985028713941574, 0.016216957941651344, -0.015621786005795002, 0.04978200048208237, 0.0027811278123408556, -0.04467741772532463, -0.03923448175191879, -0.05826464667916298, -0.037237729877233505, -0.03195113688707352, -0.01680849678814411, 0.04580420255661011, 0.05762534588575363, 0.028497805818915367, -0.0169534794986248, 0.01589108817279339, -0.0504036583006382, 0.03281614929437637, 0.021785873919725418, -0.033835772424936295, 0.007350856903940439, 0.08542758226394653, -0.004368566442281008, -0.028418296948075294, 0.046326521784067154, 0.03683068975806236, 0.0006788070895709097, -0.022412128746509552, 0.025087902322411537, -0.029699021950364113, -0.020086204633116722, -0.043293680995702744 ]
<p>I know that the equation for it is $$v^2 = \frac{2GM}{r},$$ and with that, the rocket should be launched at that speed. But could it go much slower spending much more fuel to escape from gravity right? </p> <p>Wouldn't it be easier to calculate it with energy? </p>
g5392
[ 0.0075515941716730595, 0.07034854590892792, -0.007919206283986568, 0.07776181399822235, -0.0348920039832592, -0.011261808685958385, 0.024439344182610512, -0.016261668875813484, -0.10519583523273468, -0.0003716464852914214, 0.000682651880197227, 0.010114270262420177, 0.03291253373026848, 0.01904227025806904, 0.02205486223101616, -0.02299199439585209, 0.07393653690814972, -0.07669619470834732, 0.0004599772219080478, 0.05121135339140892, -0.0014988426119089127, -0.06202702969312668, -0.019252987578511238, -0.015168673358857632, 0.03466359153389931, -0.007222003769129515, -0.005134349688887596, -0.03221820667386055, -0.0694693997502327, 0.05263367295265198, 0.02249607816338539, -0.019716355949640274, 0.011204750277101994, -0.06770727783441544, -0.08575530350208282, 0.00105742656160146, 0.0014564882731065154, 0.029081035405397415, 0.039414141327142715, -0.036165349185466766, -0.0017256513237953186, -0.03661419078707695, 0.0011336890747770667, 0.008011091500520706, -0.017098063603043556, 0.01741846650838852, 0.012852457351982594, -0.007742154411971569, -0.018219497054815292, -0.05511605739593506, -0.045367997139692307, 0.032889753580093384, -0.020213577896356583, 0.004678291734308004, -0.04137459397315979, 0.01012155320495367, 0.00984977837651968, -0.0347185879945755, 0.04286913573741913, 0.02249325066804886, -0.022268133237957954, -0.04730299115180969, -0.004423394799232483, 0.018192339688539505, 0.08134455978870392, -0.024841809645295143, -0.05494368448853493, -0.003982170484960079, 0.058134764432907104, 0.042332541197538376, 0.04618704691529274, -0.011152682825922966, -0.03466678783297539, -0.09162980318069458, -0.04047813266515732, -0.026486894115805626, 0.016675686463713646, -0.031609028577804565, -0.023970402777194977, -0.028555655851960182, -0.027254678308963776, 0.033817753195762634, -0.033282119780778885, -0.0352369099855423, 0.03220253810286522, -0.02785504423081875, 0.04084678739309311, 0.039177775382995605, 0.013387753628194332, 0.010217322036623955, -0.004591979552060366, -0.0008730698609724641, 0.04499207064509392, -0.003940153401345015, -0.02115500345826149, -0.02667914889752865, -0.04938950017094612, 0.029572619125247, -0.018369736149907112, 0.02384454384446144, 0.052196282893419266, -0.061597008258104324, 0.01055461261421442, 0.006878248881548643, 0.02009543776512146, -0.05672239884734154, 0.022106565535068512, -0.009145330637693405, 0.027708347886800766, -0.018504437059164047, 0.028578339144587517, -0.04171858727931976, -0.014581904746592045, -0.008622538298368454, -0.008502496406435966, -0.010078401304781437, 0.037982113659381866, -0.06157631427049637, -0.020591111853718758, -0.005443484056740999, 0.03599679097533226, 0.04058011621236801, -0.0336557999253273, 0.02601274475455284, -0.0033511631190776825, -0.03448783978819847, -0.020438741892576218, -0.03253720700740814, 0.011293803341686726, 0.05384393781423569, -0.04510848596692085, -0.03346213325858116, 0.02127397432923317, -0.022450264543294907, 0.018711306154727936, 0.015981698408722878, -0.03154388815164566, 0.03856711834669113, -0.03450842946767807, 0.006312817335128784, 0.016205646097660065, -0.02101314812898636, 0.0092241782695055, -0.000022953921870794147, -0.09868362545967102, 0.0390794537961483, -0.02876211702823639, 0.054934319108724594, -0.03675562143325806, -0.01674126647412777, 0.033294934779405594, 0.06299280375242233, 0.08220801502466202, -0.022690989077091217, 0.06867920607328415, 0.005471149925142527, 0.05323852226138115, 0.020364398136734962, -0.02059938944876194, -0.011878816410899162, 0.05888980254530907, 0.016516495496034622, 0.015785058960318565, -0.00011055608047172427, -0.08633622527122498, 0.06808653473854065, 0.06067570298910141, -0.07064133882522583, -0.032409168779850006, -0.01605422981083393, -0.019335912540555, -0.028744453564286232, 0.008137424476444721, 0.06673242896795273, 0.041436370462179184, 0.008161515928804874, 0.054858725517988205, 0.02308005467057228, -0.05085407570004463, 0.040183112025260925, 0.03419055789709091, -0.04970255121588707, 0.01090912614017725, -0.02105753682553768, -0.01276053674519062, -0.028419405221939087, -0.020956574007868767, 0.0060953255742788315, -0.06527187675237656, 0.023430010303854942, -0.008111740462481976, 0.0015001187566667795, 0.009264391846954823, 0.03327149897813797, -0.05522698536515236, -0.0029669469222426414, 0.027667336165905, -0.01550211664289236, -0.05741430073976517, 0.08893375843763351, -0.005395256448537111, 0.03244480490684509, 0.03185218572616577, -0.011142777279019356, 0.05342826992273331, 0.0011725296499207616, -0.02575376071035862, -0.008439285680651665, 0.027232905849814415, -0.015010789968073368, 0.04750232398509979, 0.02357165701687336, 0.024230217561125755, 0.051934000104665756, 0.04092581942677498, 0.020006747916340828, -0.019717907533049583, 0.050798386335372925, 0.002633072901517153, 0.040594182908535004, -0.04984419420361519, 0.011266309767961502, 0.04749612510204315, 0.03124062344431877, 0.0031890743412077427, 0.017798377200961113, -0.04054015129804611, -0.011116600595414639, 0.010987930931150913, -0.03458684682846069, 0.0082505252212286, -0.004200137685984373, -0.0031992567237466574, -0.03658353537321091, 0.022869259119033813, 0.02349681593477726, -0.00687918346375227, 0.021764438599348068, -0.03822452202439308, 0.018077043816447258, 0.04715801775455475, -0.03946175053715706, 0.024242829531431198, -0.013725289143621922, 0.04257851466536522, -0.051704905927181244, 0.04131735488772392, 0.015594972297549248, -0.024308942258358, 0.021726345643401146, 0.01547282561659813, 0.00007408656529150903, -0.09449196606874466, 0.02014409750699997, -0.06616843491792679, 0.015844780951738358, -0.04813513532280922, 0.002678348682820797, -0.07155673950910568, -0.009032712318003178, -0.03068343736231327, 0.008592253550887108, 0.02323654480278492, 0.0033420089166611433, -0.04683472588658333, -0.0009589071851223707, -0.01156590785831213, 0.005593656562268734, -0.004442441742867231, -0.014901554211974144, -0.04636625200510025, 0.004626655485481024, -0.02354009449481964, 0.03553232550621033, -0.03627609834074974, -0.04066042602062225, 0.03919064626097679, -0.01852663978934288, 0.03843613341450691, 0.010177528485655785, -0.06123492866754532, -0.06312718242406845, -0.02086467295885086, 0.056301720440387726, 0.027896437793970108, -0.05126287043094635, 0.021369872614741325, 0.049363914877176285, 0.026131097227334976, -0.06306766718626022, -0.038383979350328445, 0.018285352736711502, 0.0014155267272144556, 0.024797076359391212, -0.005200940649956465, 0.04448103904724121, 0.03820513188838959, -0.0361437126994133, -0.02631504274904728, -0.051316093653440475, 0.05167658254504204, -0.004758745897561312, -0.005771046970039606, 0.022991003468632698, -0.10344087332487106, 0.011191205121576786, -0.03541850298643112, -0.0036600311286747456, -0.02094031311571598, -0.05467052757740021, 0.0590750053524971, 0.049110718071460724, 0.01249116100370884, 0.06962808221578598, -0.024486111477017403, -0.0477604977786541, -0.008694259449839592, 0.04282514005899429, -0.008909692987799644, 0.02295144647359848, -0.05130491033196449, -0.07629991322755814, -0.044155899435281754, -0.0036752934101969004, -0.03920917958021164, 0.037833843380212784, -0.0736449733376503, -0.024286329746246338, 0.007549748755991459, 0.00955467950552702, 0.03182152658700943, 0.07004424184560776, -0.05217729136347771, 0.013061057776212692, -0.047365885227918625, -0.03183760121464729, 0.015990501269698143, 0.0835409015417099, 0.013884029351174831, 0.021232515573501587, -0.07638466358184814, 0.023372402414679527, -0.0009050278458744287, 0.04686465859413147, -0.008755285292863846, 0.004619709216058254, 0.018462685868144035, 0.037308644503355026, 0.021869350224733353, -0.03635752946138382, 0.0075982254929840565, -0.08064443618059158, -0.009098219685256481, -0.009465551935136318, -0.02791815623641014, 0.022056318819522858, -0.02009047195315361, 0.011301168240606785, -0.005381331313401461, 0.003341648494824767, 0.004568459931761026, -0.015110853128135204, 0.02757892943918705, 0.06619187444448471, -0.0010663599241524935, -0.02178148180246353, -0.057121265679597855, 0.018793778494000435, -0.06363333761692047, 0.008780143223702908, 0.013453207910060883, -0.0130176255479455, -0.012204117141664028, 0.06461737304925919, 0.06572031229734421, -0.0030465959571301937, 0.027243757620453835, -0.019266027957201004, -0.013523442670702934, 0.0010075096506625414, 0.06653772294521332, -0.04913294315338135, 0.007961626164615154, 0.00957559049129486, 0.020214054733514786, 0.02697312831878662, -0.0718381330370903, -0.032049477100372314, 0.03728324919939041, 0.0054305437952280045, 0.014607416465878487, -0.03364350646734238, -0.006599639542400837, 0.038732584565877914, -0.016688352450728416, 0.022863976657390594, 0.000016908868929021992, 0.016223955899477005, -0.020749112591147423, 0.07934828847646713, -0.0095252376049757, 0.0010482624638825655, -0.02053997479379177, -0.0003401830908842385, -0.015082714147865772, 0.06536534428596497, 0.02942275069653988, -0.00987651851028204, -0.005930685438215733, -0.03284042701125145, 0.006332194432616234, -0.03863849118351936, -0.02835260145366192, -0.010882236063480377, -0.042051512748003006, -0.044692203402519226, 0.014360284432768822, 0.03359571471810341, -0.01409061811864376, 0.05738820135593414, 0.014763034880161285, -0.010486005805432796, 0.03639338165521622, -0.020004915073513985, 0.001210590242408216, 0.004850791767239571, 0.06486477702856064, 0.022926561534404755, 0.005195247009396553, -0.013152601197361946, 0.08394236862659454, 0.03577331081032753, 0.005280517973005772, 0.0709155723452568, -0.030681520700454712, 0.10311031341552734, 0.014133754186332226, 0.02500452846288681, 0.010318916290998459, 0.05070311576128006, 0.02717268466949463, -0.00604655034840107, 0.0011637973366305232, 0.020641732960939407, 0.011781280860304832, 0.04305574670433998, 0.037248510867357254, -0.016593359410762787, 0.00892062671482563, -0.03491739183664322, -0.048464447259902954, -0.012798067182302475, 0.05208070948719978, 0.04714850336313248, -0.024256203323602676, -0.01594310812652111, -0.047019992023706436, 0.011898486874997616, 0.07191838324069977, 0.029001843184232712, -0.026973245665431023, -0.03241701424121857, 0.0372283048927784, 0.007068519946187735, 0.01887783221900463, -0.038223519921302795, -0.05861322954297066, 0.004081712104380131, 0.027141787111759186, 0.023695874959230423, -0.005687011871486902, 0.0035152717027813196, 0.014814571477472782, -0.002407712396234274, -0.051016710698604584, -0.03200378268957138, 0.008523901924490929, 0.0007034676382318139, 0.07403287291526794, -0.02177688106894493, -0.05751432478427887, 0.020973237231373787, 0.006558756809681654, 0.00732424296438694, 0.035230256617069244, 0.05709032341837883, -0.045466069132089615, -0.027918878942728043, 0.018056947737932205, -0.034999728202819824, 0.011718417517840862, 0.0627574697136879, -0.03412652388215065, -0.02200775407254696, 0.04068600386381149, 0.04151507094502449, 0.04207330197095871, -0.01774236559867859, 0.009813501499593258, 0.01610563136637211, -0.031539034098386765, 0.010885896161198616, -0.053154684603214264, -0.03913555666804314, -0.01203910168260336, 0.07248985767364502, 0.03995779529213905, 0.024739861488342285, -0.03793257102370262, 0.07328395545482635, -0.02627781592309475, -0.019054872915148735, -0.027941672131419182, -0.02240614779293537, 0.030191384255886078, -0.07284380495548248, 0.037728194147348404, -0.0019276656676083803, 0.050779372453689575, -0.022841205820441246, 0.08424650132656097, -0.020351359620690346, 0.032842736691236496, 0.03321223333477974, 0.04660436883568764, 0.0011791359866037965, -0.08027947694063187, -0.0412004329264164, -0.04749458283185959, -0.011777717620134354, 0.02750546857714653, -0.06369946897029877, -0.025772158056497574, 0.0345563068985939, -0.029259860515594482, 0.03796545788645744, 0.03316972404718399, -0.002600177889689803, 0.032233621925115585, -0.07811734080314636, -0.0634877011179924, -0.007744684815406799, -0.006960148923099041, 0.10122915357351303, 0.020597664639353752, -0.0006509245722554624, -0.050590839236974716, -0.006019978318363428, -0.008677148260176182, -0.0528625026345253, -0.04118788242340088, 0.03251848369836807, 0.009742844849824905, 0.0354204960167408, 0.011606625281274319, 0.07590249180793762, -0.006068387534469366, 0.040256813168525696, -0.028648335486650467, 0.01092059537768364, -0.042655158787965775, 0.013084440492093563, 0.015474807471036911, -0.01037679985165596, 0.0054895333014428616, -0.03582344204187393, 0.044339608401060104, -0.035826489329338074, 0.043157290667295456, -0.02729918621480465, -0.0016613637562841177, 0.024169258773326874, -0.009247113950550556, 0.0026084529235959053, 0.00992901623249054, 0.023030363023281097, 0.020218376070261, -0.04564061388373375, -0.013785811141133308, -0.036963507533073425, 0.008302424103021622, -0.021607656031847, 0.02132040075957775, -0.03675799071788788, -0.009444120340049267, 0.0380840003490448, -0.01775464043021202, -0.014840240590274334, 0.01371796615421772, -0.03553108498454094, 0.041666798293590546, 0.020454907789826393, 0.013851269148290157, -0.021282484754920006, -0.044499721378088, -0.013004097156226635, -0.05414191260933876, 0.008939525112509727, -0.021438270807266235, 0.02765423059463501, 0.07969420403242111, 0.06735086441040039, 0.039103828370571136, 0.002034128177911043, 0.0121860820800066, 0.020643340423703194, 0.01592307910323143, 0.03652294725179672, 0.026370810344815254, -0.006420142017304897, -0.03171898052096367, 0.02786990813910961, 0.0644662156701088, 0.0017372899455949664, 0.008560131303966045, 0.0014838771894574165, -0.001492512528784573, 0.033375080674886703, 0.08470887690782547, -0.0050362697802484035, 0.04895365610718727, 0.005633246153593063, 0.015420878306031227, -0.05809934437274933, 0.021177466958761215, -0.004464020021259785, -0.0326460562646389, 0.03303048387169838, 0.03719444200396538, -0.03868405520915985, 0.026800725609064102, -0.017720047384500504, -0.0462125800549984, 0.018431462347507477, 0.047653403133153915, -0.010835608467459679, -0.01375710777938366, 0.005346663761883974, -0.04773793742060661, -0.0007169075543060899, -0.02321827970445156, -0.028884541243314743, 0.006288612727075815, 0.020844105631113052, -0.05318025127053261, 0.06304292380809784, 0.0005815777694806457, -0.04920275881886482, 0.05481037124991417, -0.020871970802545547, -0.038392506539821625, -0.02423740364611149, -0.05275741219520569, -0.008457059971988201, -0.018750743940472603, -0.006011091638356447, -0.047866784036159515, 0.014880606904625893, 0.02657369151711464, -0.022011851891875267, 0.0028535076417028904, 0.003103221533820033, 0.004820587113499641, 0.017674623057246208, 0.033219773322343826, -0.008079400286078453, 0.006038190331310034, -0.022236201912164688, 0.021077798679471016, -0.041143063455820084, 0.01400095783174038, -0.01943226158618927, -0.07470017671585083, -0.013918253593146801, -0.0484987311065197, 0.014453936368227005, -0.046270642429590225, -0.040542494505643845, 0.0009530349052511156, -0.011033637449145317, 0.0288991741836071, -0.020551159977912903, 0.007450525648891926, 0.07448555529117584, 0.0012305636191740632, 0.06194360554218292, -0.03057747520506382, -0.025799747556447983, -0.0206142645329237, -0.015914734452962875, -0.012233829125761986, 0.025355052202939987, 0.04611332342028618, 0.008445783518254757, -0.012807692401111126, -0.00039887873572297394, -0.071524478495121, 0.014156787656247616, 0.045024625957012177, 0.01286517083644867, -0.0035007379483431578, 0.03245505690574646, 0.04148152843117714, -0.03388558700680733, -0.045247457921504974, -0.0004957998171448708, 0.06564440578222275, 0.0012235846370458603, -0.1012735441327095, -0.033462245017290115, -0.002487019868567586, 0.01012384332716465, -0.032645393162965775, 0.007887774147093296, 0.019490107893943787, -0.019473910331726074, -0.032224588096141815, -0.02510884590446949, -0.04298008605837822, -0.05245182290673256, 0.005896999035030603, -0.007675839122384787, -0.0070358323864638805, -0.04728945717215538, 0.00008255374268628657, 0.023804979398846626, -0.0207237396389246, -0.03235122561454773, 0.002283118199557066, 0.0020974348299205303, -0.01659698225557804, -0.04090586677193642, 0.01570274867117405, 0.009704519994556904, 0.016761327162384987, -0.02920578233897686, -0.01445857435464859, -0.028439052402973175, 0.011796175502240658, 0.012136267498135567, -0.04193912073969841, 0.03489028289914131, 0.010975274257361889, -0.009870406240224838, 0.06663207709789276, -0.01667701080441475, -0.01817295327782631, 0.053755395114421844, 0.06388401240110397, 0.01147095300257206, 0.08633726090192795, -0.013221531175076962, -0.051957033574581146, 0.045876555144786835, 0.028857864439487457, -0.0355207584798336, -0.02910470776259899, -0.003899297909811139, -0.06099913641810417, -0.022735850885510445, -0.01766223832964897, 0.0421038419008255, -0.03854578360915184, -0.03550904989242554, 0.02144133858382702, -0.07110454887151718, 0.014962445013225079, 0.005300138611346483 ]
<p>Is it possible to derive an uncertainty relation (Karolyhazy Uncertainty: <a href="http://dx.doi.org/10.1007/BF02717926" rel="nofollow">http://dx.doi.org/10.1007/BF02717926</a>) with photons? I brainstormed a bit to get the following:</p> <p>$$ \Delta x_0 \Delta p_0 = \frac{\hbar}2,$$ </p> <p>and then, </p> <p>$$\Delta k_0=\frac{1}{2\Delta x_0}.$$</p> <p>I need to derive a relation such that </p> <p>$$\Delta x = (c)^a (\Delta x_0)^{1/3},$$ </p> <p>where $c$ is a constant and $a$ is a power term. The other symbols retain their usual meaning. How must I go about this, if it is possible? </p>
g5393
[ -0.0065568373538553715, -0.012703566811978817, -0.019592486321926117, 0.018816497176885605, 0.008253214880824089, -0.003044549375772476, -0.03379910811781883, 0.028159644454717636, -0.02072661928832531, -0.02815788984298706, 0.003758648643270135, 0.024686070159077644, -0.031035304069519043, -0.013207773678004742, 0.009417696855962276, -0.007638629991561174, 0.026736702769994736, 0.028205448761582375, 0.03675202652812004, 0.003129181917756796, -0.015041079372167587, -0.0014331407146528363, -0.02398095838725567, -0.04168049991130829, 0.0452369786798954, -0.07065527141094208, 0.014619339257478714, -0.036984752863645554, -0.05142848566174507, -0.058866824954748154, 0.02985818311572075, -0.020398719236254692, 0.05360083281993866, 0.010576424188911915, -0.005117270164191723, -0.05013829097151756, 0.045713454484939575, 0.027393465861678123, -0.004063133616000414, 0.016790959984064102, -0.056403785943984985, 0.03644206002354622, 0.0401909165084362, 0.005586565937846899, -0.009574421681463718, 0.019268693402409554, 0.009626095183193684, 0.06332213431596756, -0.009937971830368042, -0.07169438898563385, 0.04198633134365082, 0.013704268261790276, 0.026290101930499077, 0.01775735802948475, 0.03333507105708122, 0.05372675880789757, 0.11807017028331757, -0.0424395427107811, 0.02633211575448513, 0.05059019848704338, -0.023086141794919968, -0.019517160952091217, 0.00485850777477026, 0.004980475641787052, 0.051181089133024216, -0.014642573893070221, -0.06175326928496361, -0.04297515004873276, -0.07977858930826187, -0.027766166254878044, 0.03904145583510399, -0.015529051423072815, 0.02891731821000576, -0.005267379805445671, -0.038494598120450974, -0.009034784510731697, 0.012625585310161114, -0.02427549660205841, 0.04147005453705788, 0.022556854411959648, 0.020150350406765938, -0.01398999523371458, 0.08313890546560287, 0.025425177067518234, -0.005327168852090836, 0.02159738726913929, -0.015303097665309906, -0.01208936795592308, 0.0387568324804306, -0.003148352261632681, 0.020831067115068436, -0.01127542182803154, -0.00877868290990591, 0.03451874479651451, 0.05177305266261101, 0.005395210348069668, -0.021990425884723663, 0.04241032898426056, 0.011767871677875519, -0.033934302628040314, 0.020922638475894928, 0.061418261379003525, 0.0595986545085907, 0.016560619696974754, -0.044188328087329865, -0.01725158281624317, -0.00037654649349860847, -0.03209163621068001, 0.016836507245898247, 0.019474750384688377, -0.04192867502570152, 0.01975269988179207, -0.04981222003698349, -0.08242767304182053, 0.003932407591491938, -0.03762681782245636, 0.013037649914622307, 0.028650306165218353, 0.02270212210714817, -0.0040189772844314575, 0.06294779479503632, -0.009010682813823223, 0.05621424317359924, 0.06718938052654266, -0.0159932691603899, 0.05948041006922722, 0.01125132292509079, 0.008043483830988407, 0.11268505454063416, 0.0009377409587614238, 0.030437801033258438, 0.02800096943974495, 0.01558410283178091, 0.07861398905515671, -0.023083709180355072, 0.023880187422037125, 0.026144813746213913, -0.023036034777760506, 0.05917101725935936, 0.020794248208403587, 0.0013916650786995888, -0.034561123698949814, -0.01950667053461075, -0.08195289224386215, -0.015417354181408882, -0.023923354223370552, 0.016228539869189262, -0.03660578653216362, 0.02728634513914585, -0.025219110772013664, 0.0475817508995533, 0.04245545342564583, -0.0331878624856472, 0.00891940202564001, 0.040735915303230286, 0.017237620428204536, 0.052095454186201096, 0.017899801954627037, -0.08236382156610489, -0.00465368153527379, 0.034349922090768814, 0.030795078724622726, 0.06249852478504181, -0.04738783836364746, 0.02374882437288761, -0.053958188742399216, 0.04727688431739807, -0.04263615235686302, -0.06138603016734123, -0.03486090898513794, -0.026930851861834526, 0.0021178005263209343, -0.002463509561493993, -0.05485478788614273, 0.04253743961453438, 0.04418129846453667, -0.013217037543654442, 0.04015560820698738, 0.005665524397045374, 0.013157684355974197, -0.050658803433179855, 0.043804340064525604, -0.00978491734713316, -0.023649096488952637, -0.017276575788855553, 0.06264090538024902, 0.03260798752307892, -0.007932214066386223, -0.010634288191795349, -0.015471938997507095, -0.009976753033697605, -0.049637772142887115, -0.05546509101986885, -0.020064838230609894, -0.009169045835733414, 0.03115127421915531, 0.048237208276987076, -0.05952240899205208, 0.02171638049185276, 0.03613046929240227, 0.01973363384604454, 0.060548800975084305, -0.021921133622527122, 0.0118258660659194, 0.05660020932555199, -0.00244735786691308, -0.0003944763448089361, -0.04080594331026077, -0.010348135605454445, -0.015288634225726128, -0.0032236590050160885, -0.05027147755026817, 0.004600198939442635, 0.045418307185173035, 0.0302764642983675, -0.08573443442583084, 0.033601824194192886, -0.01844371296465397, 0.018622644245624542, -0.005264748819172382, -0.06392859667539597, 0.03037092834711075, 0.019285034388303757, 0.02747790887951851, -0.05724775418639183, 0.04506421461701393, -0.006187671795487404, 0.016307897865772247, -0.02551775611937046, 0.005911795422434807, -0.05673152953386307, -0.05320592597126961, 0.023573365062475204, 0.06063816323876381, 0.038354162126779556, 0.06141296774148941, -0.012598727829754353, 0.010971365496516228, 0.007598157972097397, 0.036722004413604736, -0.02354244329035282, 0.011587809771299362, -0.03829452767968178, 0.057707998901605606, -0.051672790199518204, -0.028810974210500717, 0.07668228447437286, 0.009584705345332623, -0.017838802188634872, 0.022917499765753746, -0.007963350042700768, -0.012360602617263794, 0.06852378696203232, -0.015480220317840576, -0.01317029632627964, -0.0719793438911438, -0.004608744289726019, 0.0019798988942056894, 0.038634344935417175, 0.03070269711315632, 0.046541422605514526, -0.09751275181770325, -0.011027307249605656, 0.0057516321539878845, -0.00017294115968979895, 0.004384735133498907, -0.030161956325173378, 0.0018976232968270779, 0.05244484171271324, 0.00968554150313139, -0.00960354134440422, -0.03192281350493431, 0.06573401391506195, 0.010867983102798462, -0.02715403027832508, -0.045908521860837936, -0.005546567961573601, -0.009896593168377876, 0.040751732885837555, 0.0352616012096405, 0.035739049315452576, -0.0005634181434288621, -0.00035951368045061827, 0.003596806898713112, -0.01934075355529785, -0.015544607304036617, 0.020063264295458794, 0.0981307402253151, 0.008443551138043404, -0.01036046165972948, -0.0021986200008541346, 0.022896658629179, -0.024238167330622673, 0.0006430327193811536, -0.05191001296043396, -0.010064709931612015, 0.03303489834070206, -0.03554894030094147, 0.03407924249768257, 0.057989370077848434, 0.010289609432220459, 0.03786357492208481, -0.04625217244029045, -0.003881447948515415, 0.004108313471078873, 0.005132853053510189, -0.04783038794994354, -0.016903527081012726, 0.06333538144826889, 0.0031264778226614, -0.0007801592000760138, 0.036457519978284836, 0.020650744438171387, -0.00429316284134984, -0.010438373312354088, 0.01620825007557869, -0.012769904918968678, 0.027170466259121895, -0.01814652793109417, -0.018907679244875908, -0.04413433000445366, -0.07492943853139877, -0.026416080072522163, -0.0017472051549702883, 0.03875225409865379, 0.01703452318906784, -0.06408148258924484, -0.011675200425088406, -0.050050459802150726, 0.009667880833148956, -0.017085378989577293, -0.09252441674470901, -0.002036368940025568, -0.03561904653906822, -0.048610419034957886, -0.038522522896528244, -0.000817637424916029, -0.0064860074780881405, 0.0016261801356449723, 0.0029934493359178305, -0.015627413988113403, -0.02240576595067978, -0.03511647507548332, 0.03888030722737312, 0.010706196539103985, -0.054304905235767365, -0.05595662072300911, 0.02287069708108902, 0.027239488437771797, -0.06655498594045639, -0.0016059039626270533, -0.014546825550496578, 0.0339631624519825, 0.010274953208863735, 0.009824424982070923, 0.022836359217762947, 0.004637292120605707, 0.00043350912164896727, 0.013887320645153522, 0.011142690666019917, -0.05011606961488724, -0.018670158460736275, 0.02853221446275711, -0.021283376961946487, -0.0038295357953757048, 0.03976763039827347, 0.01030668057501316, 0.09422381967306137, -0.02409548871219158, 0.011607933789491653, 0.0073498752899467945, -0.010047580115497112, 0.0007353289984166622, 0.021788019686937332, -0.018798720091581345, -0.0772382989525795, 0.02855842001736164, -0.029666386544704437, -0.05752526968717575, 0.04484414681792259, -0.019148051738739014, 0.06167900934815407, 0.045580875128507614, 0.06020621210336685, 0.06148257479071617, 0.027269182726740837, 0.005926673766225576, 0.01276462897658348, 0.01779203489422798, -0.04477011784911156, -0.003619575407356024, -0.03955477848649025, -0.05251076817512512, 0.03380999714136124, -0.008699514903128147, -0.030373167246580124, 0.014956955797970295, -0.025912128388881683, -0.04167656600475311, -0.0317816324532032, -0.030405763536691666, -0.022302547469735146, 0.05674261227250099, 0.048386234790086746, 0.005241045728325844, 0.002983511658385396, 0.023126179352402687, -0.04976804554462433, 0.05641534551978111, -0.03651554509997368, 0.003379456466063857, -0.007119514513760805, 0.034873850643634796, -0.046690523624420166, -0.026071958243846893, 0.006932294461876154, 0.013946853578090668, -0.06429734081029892, 0.025363855063915253, 0.03490008786320686, 0.012796302326023579, 0.024538908153772354, 0.03672926127910614, -0.016620313748717308, 0.041968781501054764, -0.05302722752094269, 0.0551232248544693, -0.021620968356728554, 0.03300124779343605, 0.009684113785624504, 0.013029643334448338, 0.031079577282071114, 0.018480882048606873, 0.006591626442968845, -0.03400365635752678, 0.024858523160219193, -0.07988941669464111, -0.020535774528980255, -0.0029071590397506952, 0.015345551073551178, 0.03447815775871277, 0.03410346806049347, 0.03119952604174614, -0.05241869390010834, -0.04183544963598251, 0.06314671039581299, -0.012528852559626102, -0.007827948778867722, 0.04518912732601166, 0.03398369625210762, -0.0726424977183342, -0.0018062819726765156, -0.05187993496656418, -0.06193770840764046, 0.030001934617757797, -0.009345097467303276, -0.029436716809868813, -0.006383321713656187, 0.037513311952352524, -0.017715688794851303, 0.000263310968875885, -0.022087248042225838, 0.029555410146713257, -0.0408981628715992, 0.055320411920547485, -0.014487658627331257, -0.12195032835006714, 0.005908628925681114, -0.048734329640865326, -0.03376566618680954, -0.020798223093152046, 0.01435448694974184, 0.0462423674762249, 0.00031725133885629475, -0.03529929742217064, -0.03185887634754181, 0.0014039288507774472, 0.006854252424091101, -0.05672910809516907, -0.009932602755725384, -0.004639767576009035, 0.0114304693415761, -0.043651267886161804, 0.032077573239803314, 0.0024272382725030184, 0.01644170470535755, 0.025097979232668877, -0.024654271081089973, 0.013804848305881023, 0.002548114862293005, 0.017713384702801704, -0.05398119240999222, 0.032220058143138885, -0.020249897614121437, -0.05111151933670044, -0.012194653041660786, 0.012543555349111557, -0.01664360798895359, 0.03816433623433113, 0.021076148375868797, -0.0460268072783947, 0.023128772154450417, -0.017059165984392166, 0.01779131032526493, 0.010110526345670223, 0.03985220566391945, 0.026707706972956657, 0.021493392065167427, 0.03687267377972603, -0.001430438132956624, -0.03309548273682594, -0.016709862276911736, -0.011591474525630474, 0.016276126727461815, -0.022552311420440674, 0.04302515089511871, -0.056790418922901154, 0.0071987584233284, -0.036680977791547775, -0.049290981143713, 0.0532204732298851, 0.008607493713498116, 0.09413779526948929, -0.01640426181256771, 0.011398417875170708, 0.013841044157743454, -0.034271884709596634, -0.041911207139492035, 0.043813567608594894, -0.08136138319969177, 0.03293276205658913, 0.034379325807094574, -0.0021686165127903223, -0.0680147334933281, 0.0023045483976602554, -0.045697420835494995, 0.002771935425698757, 0.013823114335536957, 0.010272805579006672, -0.014986362308263779, -0.014787119813263416, 0.02722218818962574, -0.010650156065821648, 0.038860488682985306, 0.011580733582377434, -0.0035365186631679535, 0.05756952613592148, 0.01349512580782175, -0.006608432158827782, 0.002252402948215604, 0.04933643341064453, -0.04118195176124573, -0.026207515969872475, 0.01165465172380209, 0.04214916005730629, 0.014712587930262089, 0.014831909909844398, 0.01020263135433197, -0.006009256932884455, 0.032897867262363434, -0.025847239419817924, -0.004882351029664278, 0.035321030765771866, 0.02637799270451069, -0.035452306270599365, -0.015753107145428658, 0.0025747145991772413, -0.012528379447758198, -0.004870816133916378, 0.10481724888086319, 0.03536642715334892, 0.06702515482902527, -0.057331010699272156, 0.006031866651028395, 0.0012455465039238334, -0.022084727883338928, -0.016383463516831398, -0.02476336993277073, -0.012033142149448395, -0.005392113700509071, -0.03398755192756653, 0.03705272078514099, 0.023148924112319946, -0.06484310328960419, -0.05836961045861244, 0.008866049349308014, 0.026057176291942596, 0.006827722303569317, 0.006105777341872454, -0.006634271703660488, -0.022283300757408142, -0.021134011447429657, -0.02684978023171425, -0.008716525509953499, -0.03675062954425812, -0.0032452959567308426, 0.01962713710963726, -0.00047942457604222, -0.0046153562143445015, -0.014394252561032772, 0.009448859840631485, 0.03987529128789902, 0.03815174475312233, 0.03257349506020546, 0.00037282489938661456, 0.04361527040600777, -0.0269764494150877, 0.030496489256620407, -0.0029578020330518484, 0.0064137461595237255, -0.021346183493733406, -0.027617791667580605, 0.023355180397629738, 0.021948030218482018, 0.003675755811855197, -0.0349460244178772, 0.04447539150714874, 0.07104070484638214, -0.06329610198736191, 0.009412605315446854, 0.007214316166937351, 0.01147245429456234, -0.023306449875235558, 0.06118301674723625, 0.0684405118227005, 0.036272499710321426, -0.03141092509031296, -0.015747113153338432, 0.013791391626000404, 0.03311925753951073, -0.0067482804879546165, -0.01895993761718273, 0.049234747886657715, 0.055871132761240005, 0.002200802555307746, 0.053603239357471466, -0.07510366290807724, 0.05428449064493179, 0.01298608910292387, 0.04658191651105881, 0.007963758893311024, -0.024405701085925102, 0.023712782189249992, -0.004596134647727013, -0.036227062344551086, -0.008528596721589565, 0.03041326068341732, -0.05234108120203018, -0.045729730278253555, 0.02676556445658207, 0.007829377427697182, -0.0076009491458535194, -0.02162068523466587, 0.018518364056944847, 0.01951773464679718, 0.006113896612077951, 0.007613453082740307, -0.016376756131649017, -0.05358704552054405, -0.055413100868463516, 0.0034252305049449205, -0.05926891043782234, -0.010059131309390068, -0.0024894308298826218, -0.02007201313972473, 0.05009195953607559, 0.0039118314161896706, -0.05715879797935486, -0.0028917768504470587, -0.03611132502555847, 0.02300235815346241, -0.02604987658560276, 0.0057962131686508656, -0.013846219517290592, -0.010751668363809586, -0.0016234845388680696, 0.011600679717957973, 0.07396849989891052, -0.04975631460547447, 0.01791112683713436, -0.034941352903842926, -0.01733739674091339, -0.00968595128506422, -0.03268584981560707, -0.02854212373495102, 0.07937656342983246, 0.02798916958272457, -0.015615458600223064, 0.021110333502292633, 0.0008290415280498564, -0.07574746012687683, -0.08938983827829361, 0.062066201120615005, -0.042810019105672836, -0.01643299125134945, -0.013120424933731556, 0.012116583064198494, 0.007379020098596811, 0.016272304579615593, -0.012530002743005753, -0.012207222171127796, -0.017259743064641953, -0.01263431180268526, -0.03567852824926376, -0.0413040928542614, -0.011965201236307621, -0.06555753201246262, -0.028898879885673523, 0.0010580183006823063, -0.00006295319326454774, 0.0680672749876976, -0.028176873922348022, -0.08189447224140167, -0.05398639291524887, -0.0032492117024958134, -0.005438465625047684, 0.02231009677052498, -0.005386559292674065, -0.028781156986951828, -0.010816343128681183, -0.0020853665191680193, -0.07490480691194534, -0.031774815171957016, -0.018375927582383156, -0.03856914862990379, -0.045668523758649826, -0.06029907241463661, -0.02796332724392414, -0.028577055782079697, -0.005376147106289864, 0.004501925315707922, 0.04163806885480881, -0.06505171209573746, 0.050779253244400024, -0.008011061698198318, 0.04614828899502754, 0.003405455034226179, 0.016882261261343956, 0.01852424442768097, -0.0024863150902092457, -0.04198017716407776, -0.05835932120680809, 0.023739950731396675, -0.0368015430867672, 0.048249565064907074, -0.028967708349227905, -0.03761455789208412, 0.057709701359272, 0.05250820145010948, -0.019734729081392288, -0.07755820453166962, 0.06872986257076263, -0.003906627185642719, 0.06221940740942955, 0.08159133046865463, -0.021004702895879745, 0.038268644362688065, 0.015653859823942184, 0.00993648823350668, -0.016763297840952873, 0.010999216698110104, -0.03667319938540459, -0.08086863160133362, 0.084110789000988, -0.046880368143320084, -0.035192303359508514, -0.0425003282725811, 0.018524745479226112 ]
<p>It is well known that if you blow horizontally on a bottle top it creates a sound. Pouring water to the bottle changes the pitch.</p> <p>I have been doing experiments on the relation between the sound's main frequency (or rather the corresponding wavelength) and the vertical distance between the bottle top and the water level.</p> <p>My (poor) theoretical thoughts were that by blowing on the top I create a standing wave exactly between the bottle top and the water surface, therefore the wavelength should be equal to the height of the air column.</p> <p>Apparently, I was wrong, but not completely -- it's not $y=x$, but rather a linear relation $y=ax+b$. I have been conducting several experiments with different bottles, and the results are:</p> <p>A 18cm high bottle gave me $a=5.5$ and $b=26.65$. A 21.7cm bottle gave me $a=7.94$ and $b=14.54$. A tall 32.5cm bottle resulted in $a=7.1$ and $b=34.21$. But my biggest surprise was to find a negative $b$, with a glass 19.3cm bottle (the rest were plastic), and $a=9.16$ and $b=-22.43$.</p> <p>Is there a plausible explanation for this phenomenon?</p> <p>(I didn't consider the actual shape of the bottle as I assumed a vertical standing wave will emerge. Most of the bottles are pretty constant in shape, except for the glass bottle which is closer to a cone. Looking at the signal itself one can clearly see a high energy peak at the pitch, and smaller peaks at the pitch's multiples. I noticed that the slopes are close to natural numbers or half thereof.)</p>
g5394
[ 0.023919610306620598, -0.03932264819741249, -0.0009603462531231344, 0.0006082738982513547, 0.06500348448753357, 0.054235320538282394, 0.010192928835749626, 0.026304909959435463, -0.03357518091797829, -0.029942139983177185, 0.013715441338717937, 0.02469341829419136, 0.006808331236243248, -0.005793729331344366, -0.0025546483229845762, -0.014283224008977413, -0.024355968460440636, -0.06907182186841965, -0.008482318371534348, -0.021106475964188576, -0.07101881504058838, -0.06003652140498161, -0.01970616728067398, -0.05241427943110466, -0.06425901502370834, -0.02516394853591919, 0.030943069607019424, 0.020048771053552628, 0.009726086631417274, 0.0341082438826561, -0.05123205855488777, 0.06613684445619583, 0.06214037910103798, 0.046678896993398666, -0.06350019574165344, 0.013563517481088638, 0.016086125746369362, 0.034872785210609436, -0.013630988076329231, 0.008939682506024837, -0.013165168464183807, 0.051133789122104645, -0.032471008598804474, 0.02708325907588005, -0.002274720696732402, -0.01479427982121706, -0.025025809183716774, 0.05637209862470627, -0.0436038114130497, -0.04353819042444229, 0.02318132109940052, -0.038791630417108536, -0.013022404164075851, 0.07209967821836472, 0.01186725590378046, 0.05209682881832123, 0.015463669784367085, 0.026032734662294388, 0.04419754073023796, 0.029955744743347168, -0.006204967852681875, 0.022797562181949615, -0.0059051415883004665, 0.03266552835702896, 0.013380751013755798, -0.04641501605510712, -0.019316693767905235, -0.02797890640795231, -0.01492686290293932, -0.04032459855079651, 0.005036573391407728, -0.08159735053777695, 0.04254063218832016, -0.0061451406218111515, -0.0844348892569542, 0.06427356600761414, -0.025540219619870186, -0.0016774352407082915, -0.004629825241863728, 0.018634377047419548, 0.07616649568080902, 0.03071064129471779, 0.026590624824166298, 0.0004900077474303544, 0.05617870017886162, -0.0015569786773994565, 0.02665419690310955, 0.0455775111913681, -0.011890511959791183, 0.000292065495159477, 0.004243627190589905, -0.06464996933937073, 0.02577056549489498, -0.00021603294590022415, -0.0034471459221094847, -0.03624013811349869, -0.015907371416687965, 0.05502045527100563, 0.03289380297064781, 0.008821521885693073, -0.00762577261775732, 0.049116287380456924, 0.029752444475889206, 0.02282261662185192, -0.02857973426580429, 0.021627584472298622, 0.029894845560193062, -0.032096631824970245, -0.02615228109061718, -0.050460051745176315, -0.026186242699623108, -0.03186367452144623, -0.001267184386961162, -0.005440851207822561, -0.0061440481804311275, -0.03753140568733215, 0.03312448412179947, 0.01942591741681099, 0.013178759254515171, 0.050864703953266144, 0.03143445774912834, 0.02833237126469612, 0.02069755271077156, 0.038947101682424545, -0.05252451077103615, -0.02137693203985691, 0.0037829498760402203, -0.02939213439822197, 0.041866485029459, -0.003619368653744459, 0.057482559233903885, -0.0238894522190094, -0.05693169683218002, -0.02674899436533451, 0.07861405611038208, 0.01918013021349907, -0.000611835450399667, 0.022932693362236023, 0.05113182216882706, -0.029015984386205673, 0.014204578474164009, -0.03708208352327347, 0.0926569327712059, -0.04312659427523613, -0.021554410457611084, -0.009610946290194988, 0.02684769406914711, -0.04361362010240555, 0.02994086779654026, -0.052651796489953995, -0.01717308722436428, 0.038544148206710815, 0.030330607667565346, -0.0055449726060032845, 0.00776138948276639, 0.052775789052248, 0.0018446744652464986, 0.03093576990067959, 0.028293119743466377, 0.04076189547777176, 0.014015691354870796, -0.0558297373354435, 0.002190240193158388, -0.00508139980956912, -0.09086181223392487, -0.045965999364852905, 0.004363668616861105, -0.020772360265254974, -0.028211502358317375, 0.023439140990376472, -0.0967157706618309, 0.007025516591966152, -0.01476546935737133, 0.021187329664826393, 0.023544905707240105, 0.019337596371769905, 0.06486022472381592, -0.04483964666724205, 0.008347757160663605, 0.04217620939016342, -0.025396481156349182, -0.012439335696399212, -0.054787322878837585, -0.028013786301016808, 0.07462824136018753, 0.007533975411206484, 0.018450871109962463, 0.015348277986049652, -0.0618533194065094, -0.006966038141399622, -0.06013127416372299, -0.0071671041660010815, -0.005077071022242308, -0.0037337346002459526, 0.013923868536949158, -0.045114900916814804, 0.018135281279683113, -0.0044769239611923695, -0.042591676115989685, 0.06757868081331253, -0.03425569459795952, 0.014901434071362019, 0.04500151798129082, -0.0016647978918626904, -0.0031862894538789988, 0.07825551927089691, -0.0022908614482730627, 0.0037777177058160305, -0.024289339780807495, 0.0334215871989727, -0.07136883586645126, 0.017458349466323853, 0.01467449963092804, -0.060980454087257385, 0.025869784876704216, 0.00026953514316119254, -0.02848963811993599, 0.008962304331362247, -0.0403071865439415, 0.050112806260585785, -0.012079811654984951, 0.022014712914824486, -0.0080634830519557, 0.046851370483636856, 0.012569204904139042, -0.018603932112455368, 0.01889662817120552, 0.004352566320449114, -0.0618487149477005, -0.02451077289879322, 0.03231693059206009, 0.014805400744080544, 0.03141438215970993, -0.01714148186147213, -0.0032058057840913534, 0.02575879916548729, 0.01481640711426735, -0.0128792654722929, 0.018729953095316887, -0.015462496317923069, -0.015935340896248817, -0.07428757846355438, -0.04717407375574112, 0.01415843516588211, 0.03319590538740158, 0.04732391983270645, 0.028869470581412315, -0.007283139042556286, -0.03508970886468887, 0.01901545375585556, 0.06160832941532135, -0.022761821746826172, -0.0028373305685818195, 0.05873608961701393, -0.0051496331579983234, -0.008200772106647491, -0.04715757817029953, 0.05512688308954239, -0.04591907560825348, -0.09431565552949905, -0.030289310961961746, -0.056517455726861954, 0.041473113000392914, -0.05923359841108322, -0.006558879744261503, 0.006256481632590294, -0.023664578795433044, 0.03279535099864006, -0.043198201805353165, -0.005724802613258362, 0.002582387300208211, -0.016346869990229607, 0.0783175602555275, -0.013297556899487972, -0.056663673371076584, 0.013748111203312874, 0.013850048184394836, 0.03864285722374916, -0.02611672878265381, 0.00675609614700079, -0.02612670138478279, -0.02532629854977131, -0.06970087438821793, -0.014684020541608334, 0.044122371822595596, 0.01015009731054306, -0.012241180986166, -0.00008500905096298084, 0.00013824398047290742, -0.009706596843898296, 0.008460037410259247, 0.03051074966788292, 0.01734277606010437, 0.04289504885673523, 0.002690971130505204, 0.041622359305620193, 0.0103988666087389, -0.021893326193094254, -0.012805777601897717, 0.0010260270209982991, -0.0004531568265520036, -0.013256764970719814, 0.002087104134261608, -0.012467832304537296, -0.023199517279863358, 0.030163925141096115, -0.03847863897681236, 0.0011359916534274817, -0.027195245027542114, 0.04982583969831467, -0.03574014827609062, -0.0022493177093565464, -0.031883154064416885, 0.001139310421422124, -0.04950220137834549, 0.0023504910059273243, -0.0019165388075634837, 0.026535682380199432, -0.049789395183324814, 0.026135282590985298, -0.013270369730889797, -0.05498306080698967, -0.03946036472916603, 0.0008122638100758195, 0.04110289737582207, -0.027600105851888657, -0.00018869785708375275, 0.043599262833595276, -0.030139096081256866, -0.05743679404258728, 0.045058976858854294, 0.012252992950379848, 0.020352808758616447, -0.030079951509833336, 0.03840992599725723, 0.003413291648030281, 0.028100060299038887, 0.03262133151292801, 0.03464335948228836, 0.07222548872232437, -0.0026223405729979277, -0.00849680881947279, -0.001523188198916614, -0.05036047101020813, 0.007607170380651951, 0.013623103499412537, -0.03411909192800522, 0.057630669325590134, -0.01904541812837124, -0.02316110022366047, 0.013431157916784286, -0.06468125432729721, -0.013974691741168499, -0.0003872574307024479, -0.008778641000390053, 0.056614670902490616, 0.06790054589509964, -0.006939769256860018, 0.014174277894198895, -0.028641991317272186, -0.023568306118249893, -0.0371275432407856, 0.03963311016559601, 0.05320462957024574, 0.021681921556591988, -0.028914572671055794, -0.03971103951334953, 0.00870583113282919, -0.022918354719877243, 0.030594874173402786, -0.026113661006093025, -0.009191464632749557, -0.014495561830699444, -0.04127173125743866, -0.013624479994177818, 0.012810034677386284, 0.018012572079896927, -0.01805233024060726, -0.02875005640089512, 0.03778672218322754, 0.08376217633485794, 0.017570799216628075, 0.03028201125562191, 0.0028095985762774944, -0.038510650396347046, -0.02669503353536129, -0.11789117753505707, -0.006886174436658621, 0.021252254024147987, -0.013921338133513927, -0.07360377907752991, -0.050178591161966324, 0.01184706762433052, 0.004299003165215254, -0.0257019754499197, 0.0012327367439866066, 0.03152485936880112, -0.013785467483103275, -0.04867084324359894, 0.059403322637081146, 0.023365890607237816, -0.03826327994465828, -0.0235859714448452, -0.006574355065822601, -0.03370968624949455, -0.0030815519858151674, 0.0718662366271019, -0.0071974159218370914, -0.0386185348033905, -0.01088723260909319, 0.04026991128921509, -0.007421556394547224, -0.06011497974395752, -0.0958801656961441, -0.020685989409685135, 0.03782179579138756, 0.05391676723957062, 0.038343317806720734, 0.052301011979579926, 0.06363289058208466, 0.01650012657046318, 0.07429572194814682, -0.018931735306978226, -0.02751946449279785, 0.023062491789460182, 0.018064672127366066, 0.016191981732845306, -0.005828594323247671, 0.019021794199943542, 0.0019301272695884109, -0.020185580477118492, 0.01455109566450119, -0.007258334197103977, -0.03280814737081528, 0.03305802494287491, 0.05024295672774315, -0.026053374633193016, 0.009429396130144596, 0.014721346087753773, -0.024269087240099907, 0.05749299377202988, -0.07222732901573181, -0.018019603565335274, 0.00742286816239357, 0.03430667147040367, 0.01952369324862957, -0.025793734937906265, -0.010627330280840397, -0.027339160442352295, -0.02248859964311123, -0.01684710942208767, 0.06631253659725189, 0.017215723171830177, -0.03909365087747574, 0.005572454538196325, -0.014189379289746284, -0.0041806683875620365, -0.01975720003247261, 0.028853606432676315, -0.031224828213453293, -0.011755832470953465, -0.03227359801530838, -0.02647579275071621, -0.023115763440728188, 0.08296319097280502, 0.00401332275941968, 0.007705762051045895, -0.07209394127130508, -0.04138018935918808, 0.05065177381038666, 0.005297084338963032, -0.010387041606009007, 0.03687214106321335, 0.03951922431588173, -0.03871389850974083, 0.0192927997559309, -0.031460005789995193, -0.014633730985224247, 0.0027162993792444468, -0.04567909240722656, 0.024212073534727097, -0.0361628532409668, 0.019788438454270363, 0.0012280838564038277, -0.05028108134865761, 0.02596106566488743, -0.041065216064453125, 0.016165507957339287, 0.008564913645386696, -0.013955676928162575, 0.04513060301542282, 0.00261168391443789, -0.06842726469039917, -0.01838783361017704, -0.03368408605456352, -0.061463482677936554, -0.01173863559961319, 0.007821382954716682, -0.009904617443680763, -0.010452107526361942, -0.08205457776784897, -0.01881515234708786, -0.0002428727748338133, 0.017188575118780136, 0.015751734375953674, 0.03329121321439743, 0.03002244420349598, 0.052448295056819916, 0.05906108766794205, 0.07133844494819641, 0.07395561039447784, -0.06062089279294014, -0.004955087788403034, 0.06050464138388634, 0.0023816553875803947, -0.05818246677517891, -0.010392623022198677, 0.02145266905426979, -0.029295921325683594, 0.06465441733598709, 0.02647409401834011, 0.0014209420187398791, -0.03045692853629589, -0.04275408759713173, -0.017957046627998352, 0.05108962953090668, -0.026032034307718277, -0.011205428279936314, 0.03632194921374321, -0.028676379472017288, -0.0007019333424977958, 0.006628506816923618, 0.015805566683411598, -0.01966354437172413, 0.0426892526447773, -0.04304578900337219, 0.05596880987286568, 0.02731061913073063, 0.021415987983345985, 0.04196453094482422, -0.005313756410032511, -0.013332127593457699, -0.006228729151189327, 0.029033910483121872, 0.011164943687617779, -0.004987786058336496, 0.023037662729620934, -0.00040589095442555845, 0.03757183253765106, 0.05880317464470863, 0.010876523330807686, 0.05138478800654411, 0.018332360312342644, 0.08532469719648361, 0.04790449142456055, -0.01001024805009365, -0.09101910144090652, -0.050803784281015396, 0.02070123702287674, -0.06109188124537468, -0.003978962078690529, 0.0470939576625824, 0.010477211326360703, 0.07681472599506378, 0.023085614666342735, -0.009015625342726707, 0.03276803717017174, 0.05244148150086403, 0.036593593657016754, 0.022336190566420555, -0.01900860294699669, -0.00675441138446331, -0.020002588629722595, -0.024642420932650566, 0.03371027484536171, -0.008274578489363194, -0.011537408456206322, 0.03285667672753334, 0.006169614382088184, 0.026491206139326096, 0.014722537249326706, 0.006631721742451191, -0.0035043121315538883, -0.009833353571593761, 0.01133960485458374, -0.047884054481983185, -0.0444636233150959, -0.04603172466158867, -0.022221611812710762, -0.08483366668224335, 0.019794413819909096, -0.08470772206783295, -0.03488108143210411, 0.021587729454040527, 0.013754842802882195, -0.0544317327439785, -0.007952764630317688, -0.016885971650481224, -0.05981026589870453, -0.022705931216478348, 0.023166684433817863, 0.08118303120136261, 0.039875518530607224, -0.046210769563913345, -0.029009340330958366, -0.0024697575718164444, -0.0046312082558870316, 0.045654308050870895, 0.015312286093831062, -0.007654417771846056, -0.045437633991241455, 0.0725148543715477, 0.05979707092046738, -0.03697977587580681, -0.05209309607744217, -0.03677754104137421, 0.05702318623661995, 0.004028502386063337, 0.062353044748306274, -0.004854538477957249, -0.005741726141422987, -0.008603094145655632, -0.003171775955706835, -0.05252569168806076, 0.07097231596708298, -0.022195154801011086, -0.00963221862912178, -0.02048516646027565, -0.03372100368142128, 0.012915268540382385, 0.04814755916595459, 0.03090103529393673, -0.015153679065406322, 0.0025540676433593035, -0.0030378508381545544, 0.004899938590824604, -0.03661860153079033, 0.01517083216458559, 0.03739503398537636, 0.016631169244647026, 0.009542673826217651, -0.000251762627158314, 0.010073475539684296, 0.04773150756955147, 0.00653927493840456, -0.018197879195213318, 0.022091785445809364, 0.0001792827679309994, -0.033314552158117294, -0.016349518671631813, -0.014463785104453564, -0.05140011012554169, -0.04398076608777046, 0.04105972871184349, 0.007309828419238329, 0.03553939610719681, -0.005944985430687666, -0.02527964673936367, -0.0022750606294721365, -0.05831918492913246, 0.02889605425298214, -0.05196415260434151, -0.008051366545259953, 0.022311542183160782, -0.053230736404657364, 0.0329768992960453, -0.02951044775545597, -0.059167928993701935, 0.017784029245376587, 0.003793631214648485, 0.010806996375322342, -0.030190443620085716, -0.01669195108115673, -0.035456158220767975, -0.03019144758582115, 0.040123119950294495, -0.04873068258166313, 0.039664607495069504, 0.0004896180471405387, 0.01121609564870596, -0.029649337753653526, -0.017167456448078156, -0.009286643005907536, -0.03848208114504814, -0.009877468459308147, -0.02912231534719467, -0.06334734708070755, 0.022779133170843124, 0.03285249322652817, -0.04181589558720589, 0.011953086592257023, -0.007608355022966862, 0.04074878245592117, 0.0033662673085927963, -0.030166134238243103, 0.024110978469252586, 0.056442152708768845, 0.005488515365868807, -0.017500516027212143, 0.05742500722408295, 0.034744810312986374, 0.01930094324052334, -0.06512153148651123, -0.01939157210290432, 0.03327973186969757, 0.002180017065256834, 0.007185552269220352, 0.024568887427449226, -0.030521785840392113, -0.04145802557468414, -0.038317445665597916, -0.00016639370005577803, 0.01826985366642475, -0.0071336738765239716, 0.02183619514107704, -0.019921140745282173, -0.02218981646001339, 0.019123466685414314, -0.08747820556163788, 0.011631783097982407, -0.10374212265014648, 0.02283976413309574, 0.07905862480401993, -0.012226428836584091, -0.02564390003681183, -0.026137614622712135, 0.023778103291988373, 0.02699883282184601, -0.0026653287932276726, 0.026914747431874275, -0.05920007824897766, 0.008502104319632053, -0.005266140215098858, 0.001475993194617331, 0.005126494448632002, -0.023964282125234604, 0.04516526311635971, 0.07469292730093002, 0.01885054260492325, -0.03565298765897751, 0.037650685757398605, 0.08586429804563522, 0.010159846395254135, -0.008363400585949421, -0.025214578956365585, -0.07102777808904648, 0.010533624328672886, 0.01951105333864689, 0.04167237877845764, -0.06461804360151291, -0.007661269512027502, 0.06201582029461861, 0.037906866520643234, 0.050262704491615295, 0.03443964570760727, -0.032480768859386444, 0.023168915882706642, 0.07893949002027512, 0.00898512452840805, -0.08603785932064056, -0.03866580128669739, -0.023047244176268578, 0.002970830537378788, -0.01794389635324478, 0.006167723797261715, 0.04204737767577171, -0.02918316423892975, 0.0227927528321743 ]
<p>Many times in physics when we analyze a physical system mathematicly we get divergences, but when those divergences has no dependence on any actual physical quantity of interest we tend to disregard those "infinity Constants". </p> <p>An example where such a thing happens is in the derivation of the Casimir force for two metal plates we get $\zeta(-3)$ which contains infinities.</p> <p>One can provide many more examples where we make this analytical approach.</p> <p>My question is why those infinities are treated this way, is there a deep mathematical reason why we do it?</p>
g190
[ 0.07144636660814285, 0.02961929328739643, 0.012269893661141396, -0.09062368422746658, 0.0754905417561531, 0.0069914706982672215, 0.02921406179666519, 0.026695841923356056, -0.04758056253194809, -0.01591399870812893, -0.057831089943647385, -0.010276976972818375, -0.044302769005298615, 0.038749951869249344, 0.0332866869866848, -0.05500882863998413, 0.01047477126121521, 0.0014540217816829681, 0.012949713505804539, 0.042219746857881546, -0.027289345860481262, 0.03513872250914574, -0.00204369961284101, -0.032810062170028687, -0.011763094924390316, 0.0012371174525469542, 0.04960593208670616, -0.02135326713323593, 0.03970085456967354, -0.010684737004339695, 0.026249803602695465, 0.02785670757293701, 0.03578970953822136, -0.013916426338255405, 0.040767814964056015, -0.0033983630128204823, 0.059455230832099915, 0.050047796219587326, 0.04335687309503555, -0.0370430126786232, -0.018289858475327492, 0.011915178038179874, 0.019697505980730057, 0.02690833993256092, -0.030506983399391174, -0.055309560149908066, -0.020744681358337402, 0.007115992717444897, 0.008031721226871014, -0.030031869187951088, 0.01167108491063118, 0.02038983441889286, 0.0682709664106369, -0.003568818559870124, 0.01517925038933754, -0.028556587174534798, 0.06727161258459091, -0.06646370887756348, 0.10608801990747452, 0.030600331723690033, -0.005104157608002424, 0.0013455129228532314, 0.016671281307935715, 0.02654311992228031, 0.05835932493209839, -0.04224620759487152, -0.05383572354912758, -0.04820917546749115, -0.03112407959997654, 0.013117719441652298, -0.022915435954928398, -0.03988561034202576, -0.024261431768536568, -0.06179596111178398, -0.08242952078580856, 0.04251201078295708, 0.0440945141017437, 0.0008392771705985069, -0.027682553976774216, 0.010235588997602463, -0.08950119465589523, -0.015878772363066673, 0.04736045375466347, 0.005347405094653368, 0.07067659497261047, 0.007521680556237698, 0.0285815242677927, -0.01401787530630827, -0.034128423780202866, -0.009930555708706379, -0.0022232336923480034, 0.0329887755215168, -0.0049336557276546955, -0.014530610293149948, -0.024734575301408768, -0.038358595222234726, 0.03395980969071388, 0.05249328911304474, 0.012848036363720894, 0.03334132954478264, 0.03769814223051071, 0.04815281927585602, -0.003689930774271488, -0.005288485437631607, 0.01648223027586937, -0.05527457594871521, 0.05233249440789223, -0.0029717946890741587, 0.02200101502239704, -0.019152816385030746, -0.07709214836359024, 0.025359081104397774, -0.030737074092030525, -0.045526135712862015, -0.0023997589014470577, 0.027426283806562424, 0.001918909838423133, 0.029892554506659508, -0.02520240843296051, 0.04341064393520355, -0.018457304686307907, -0.05849462002515793, 0.041864972561597824, 0.008260414935648441, -0.03835432231426239, -0.015083513222634792, -0.0017153191147372127, 0.02769722230732441, 0.03405044227838516, -0.08589053899049759, 0.05350688844919205, -0.0028518245089799166, 0.01898025907576084, -0.007666842546314001, -0.04165703430771828, 0.01346781849861145, -0.019808612763881683, -0.027803530916571617, 0.0011398198548704386, 0.06734228134155273, -0.022141175344586372, -0.08338481932878494, -0.017999067902565002, -0.037175048142671585, -0.007660415023565292, 0.0267734844237566, -0.056616976857185364, -0.019099416211247444, 0.015317952260375023, -0.022953443229198456, -0.019925791770219803, 0.07861476391553879, 0.038401924073696136, -0.02264976315200329, 0.030577221885323524, 0.03215336054563522, 0.06677868217229843, -0.029073182493448257, -0.02724945731461048, -0.004683761391788721, 0.06864450126886368, 0.014492470771074295, 0.009853535331785679, -0.01827639527618885, -0.03938158228993416, 0.03622588887810707, -0.021725473925471306, -0.02273452840745449, 0.00630434975028038, -0.048858825117349625, -0.052827075123786926, -0.0010149788577109575, -0.01391526497900486, 0.005003847181797028, 0.06109796464443207, 0.04506690800189972, 0.012149715796113014, -0.029943926259875298, 0.012927975505590439, -0.0018446313915774226, -0.023354407399892807, -0.0043272459879517555, 0.016235100105404854, 0.011836794205009937, -0.019514361396431923, 0.016187436878681183, -0.02073965035378933, 0.0032659058924764395, -0.03131308779120445, 0.01069942768663168, 0.012353223748505116, -0.02874242514371872, 0.021663695573806763, 0.03295299410820007, -0.032887134701013565, 0.042945243418216705, 0.0446227490901947, 0.0010902696521952748, -0.03597502410411835, 0.0052494630217552185, 0.0113393384963274, 0.07770376652479172, 0.03176583722233772, 0.0221018698066473, 0.0010365573689341545, -0.01632031798362732, -0.04503489285707474, -0.017963694408535957, -0.008479095064103603, -0.03696683794260025, 0.007885865867137909, -0.03886064887046814, -0.004628011956810951, -0.015444310382008553, -0.0035725401248782873, -0.06439651548862457, -0.0012431757058948278, 0.00401371018961072, -0.007372924592345953, 0.07970788329839706, -0.011061666533350945, -0.03613199666142464, 0.0549888014793396, 0.04650985822081566, -0.08587218821048737, -0.002532548038288951, -0.03576009348034859, -0.08111664652824402, 0.02680867165327072, -0.044389937072992325, -0.06590691208839417, -0.09771590679883957, 0.03234267607331276, 0.03089495375752449, 0.018179526552557945, -0.004065915010869503, -0.0131031209602952, 0.01718989759683609, 0.041256919503211975, 0.008440107107162476, 0.04281461611390114, -0.0328022725880146, -0.04894325137138367, 0.005117789376527071, -0.01379974465817213, -0.0421566367149353, -0.044220805168151855, -0.004745522513985634, -0.023596102371811867, -0.01609882526099682, 0.008401473984122276, 0.0041905115358531475, -0.024005049839615822, 0.01389692910015583, 0.0005471869953908026, -0.01905662938952446, 0.004862558096647263, 0.038759950548410416, 0.005079450085759163, -0.04907888546586037, -0.021558137610554695, -0.013994374312460423, 0.033031586557626724, -0.019427912309765816, -0.016752956435084343, 0.042298588901758194, -0.028740720823407173, 0.008750234730541706, 0.02409401163458824, -0.0029043464455753565, -0.010898428969085217, -0.009982524439692497, 0.042212143540382385, 0.03804713487625122, -0.0006009883945807815, 0.013267800211906433, -0.01592440716922283, 0.0008357473998330534, 0.03198561072349548, -0.05454496666789055, -0.06582441180944443, 0.004146733321249485, -0.030242089182138443, 0.04015045240521431, 0.037762872874736786, 0.009740547277033329, -0.007843266241252422, -0.0026658866554498672, 0.00828719325363636, -0.003929540980607271, -0.000989803927950561, -0.026266098022460938, 0.0435718297958374, -0.0524321123957634, -0.012711916118860245, 0.06337227672338486, 0.037596624344587326, -0.049811214208602905, -0.02333410456776619, 0.05131406709551811, 0.060634251683950424, 0.0031020427122712135, -0.015871470794081688, 0.01882609911262989, -0.007493253331631422, 0.039989326149225235, 0.02147546410560608, -0.003355093067511916, -0.03404765576124191, -0.029444705694913864, -0.008644076995551586, 0.036000922322273254, 0.055830009281635284, 0.022929035127162933, -0.03172304853796959, 0.08876015245914459, 0.032606206834316254, -0.06542550027370453, -0.008807111531496048, -0.04627744108438492, -0.02502410300076008, -0.008521666750311852, 0.06108970195055008, -0.002803283277899027, 0.011849403381347656, 0.05925246328115463, -0.08444583415985107, -0.020280735567212105, -0.016513030976057053, 0.018875405192375183, -0.05109217390418053, -0.07869922369718552, 0.03111264482140541, -0.0019259594846516848, -0.08744768798351288, -0.08933853358030319, -0.05767982080578804, 0.0158767681568861, 0.0376470610499382, 0.021794529631733894, -0.07408332079648972, -0.042605530470609665, 0.0010998911457136273, 0.04721643775701523, -0.02107052691280842, 0.07511807978153229, 0.04630608111619949, 0.06231305003166199, 0.02937687374651432, -0.006410166621208191, 0.041190773248672485, -0.009745518676936626, 0.04920690879225731, -0.013953877612948418, 0.014160904102027416, 0.03234419226646423, 0.026212193071842194, 0.02864994667470455, -0.02246231772005558, -0.05110787972807884, 0.017076268792152405, -0.02310873754322529, 0.003970084711909294, -0.014844886027276516, 0.04018625617027283, 0.031231770291924477, -0.020923029631376266, 0.03404311463236809, -0.0019138631178066134, -0.06260925531387329, 0.0102694658562541, -0.009968018159270287, -0.0034924354404211044, 0.0015025116736069322, 0.0399976521730423, -0.09216197580099106, 0.04813380911946297, 0.036519166082143784, -0.021497638896107674, -0.03772304579615593, 0.07944928109645844, 0.028733400627970695, -0.018512142822146416, 0.025773102417588234, 0.016726911067962646, 0.04020922631025314, -0.01821696199476719, 0.030623557046055794, -0.04741155356168747, -0.01831376738846302, 0.03313874825835228, -0.004912940785288811, -0.021028291434049606, 0.0016506992978975177, -0.0017412416636943817, -0.08539362251758575, 0.01524448674172163, -0.06325657665729523, 0.056007806211709976, 0.03014007955789566, -0.010160648263990879, -0.033938419073820114, -0.03082338348031044, 0.04659697413444519, -0.004360591061413288, 0.03328805789351463, 0.05868599936366081, -0.06795494258403778, 0.05584745481610298, -0.04771161451935768, 0.02048775553703308, -0.02792579121887684, 0.023060085251927376, -0.04686053469777107, 0.044914811849594116, -0.02677890658378601, 0.0013344958424568176, 0.01503275241702795, 0.05941474810242653, -0.004631289280951023, -0.03957117348909378, 0.021635668352246284, -0.029497915878891945, 0.006749861408025026, 0.04393903911113739, 0.03291900083422661, -0.009291266091167927, 0.02510739304125309, 0.009608644060790539, -0.03304096311330795, -0.0034337176475673914, 0.02199854515492916, -0.008722641505300999, -0.013038288801908493, -0.0545974038541317, -0.00005805363252875395, -0.06319201737642288, 0.07564064115285873, -0.01904202252626419, 0.059849370270967484, 0.05179567262530327, 0.02661619521677494, 0.014769401401281357, 0.03027917817234993, 0.02606416866183281, 0.02525314874947071, -0.028670908883213997, -0.014457358978688717, -0.004664186853915453, -0.005536738783121109, -0.042712196707725525, -0.022923298180103302, -0.049240779131650925, -0.04433359578251839, -0.02629648521542549, -0.020704174414277077, -0.05555232986807823, 0.04297991842031479, 0.0025574909523129463, 0.02682454138994217, 0.015721220523118973, -0.04098401963710785, -0.07165724784135818, 0.005764254368841648, -0.013876369222998619, 0.03800271824002266, -0.015379885211586952, 0.025881359353661537, -0.08323388546705246, 0.027838215231895447, 0.0004583225818350911, 0.07320992648601532, 0.028563423082232475, 0.007833012379705906, -0.011087615974247456, -0.04307899624109268, 0.01004869770258665, 0.028796078637242317, -0.015058102086186409, -0.0757080689072609, -0.057862330228090286, 0.01935151405632496, 0.01745639182627201, 0.030220119282603264, -0.029034096747636795, -0.012670992873609066, -0.030094968155026436, -0.04790811240673065, 0.016263725236058235, -0.011238287203013897, 0.033147938549518585, 0.023014197126030922, 0.04354136437177658, -0.008256364613771439, -0.06734705716371536, -0.011872263625264168, 0.015365468338131905, -0.039528001099824905, -0.0035785995423793793, -0.044128190726041794, -0.046353984624147415, -0.023303886875510216, -0.022074932232499123, -0.059545643627643585, 0.022701965644955635, 0.04560375586152077, 0.10774343460798264, -0.01660454273223877, 0.030059194192290306, -0.03219118341803551, 0.01693311333656311, 0.059482187032699585, 0.05592473968863487, -0.01120653748512268, 0.03730197623372078, 0.008545484393835068, -0.013029932975769043, -0.032790716737508774, -0.009892219677567482, -0.0814356878399849, 0.05509187653660774, 0.0020514721982181072, 0.01849711872637272, -0.02215201035141945, 0.017821913585066795, 0.05515303835272789, -0.01770239882171154, -0.055971838533878326, -0.046201638877391815, 0.01688074693083763, 0.06153804063796997, -0.010921218432486057, 0.0020931116305291653, -0.011972171254456043, -0.01510333176702261, 0.04675914719700813, 0.010624541901051998, -0.0004171850741840899, -0.032114434987306595, 0.0037537890020757914, 0.04225624352693558, 0.008924111723899841, 0.02981114387512207, 0.0655050203204155, -0.023453831672668457, 0.0006692399620078504, -0.020799756050109863, 0.006940539926290512, 0.05778804048895836, -0.05815272405743599, -0.044651445001363754, 0.03536001220345497, 0.030754070729017258, -0.008485850878059864, -0.008179252967238426, 0.03640589118003845, 0.014732759445905685, 0.060302797704935074, -0.05335657671093941, 0.011278253048658371, -0.004112678579986095, -0.007059792522341013, 0.03840693086385727, -0.006873356178402901, 0.01277197152376175, -0.07903434336185455, 0.018888739868998528, -0.016572635620832443, 0.033839814364910126, 0.014833890832960606, 0.028911398723721504, 0.023178288713097572, 0.03486026078462601, 0.0264121200889349, 0.03709534555673599, 0.02647455781698227, -0.03330153971910477, -0.037704285234212875, -0.008190897293388844, -0.04176684468984604, 0.0015048999339342117, 0.028591090813279152, 0.01317271776497364, -0.021012604236602783, -0.000912143790628761, 0.05717872455716133, 0.006849569734185934, -0.007331873755902052, -0.013393194414675236, -0.05180470272898674, -0.026951288804411888, -0.033041853457689285, 0.042989473789930344, -0.025060337036848068, -0.0030925225000828505, 0.006283797789365053, 0.02616744488477707, -0.01768006943166256, -0.013040194287896156, -0.01314843911677599, 0.01126242894679308, -0.013876491226255894, 0.029717644676566124, -0.02831953950226307, 0.024487372487783432, 0.01519023161381483, -0.024443455040454865, -0.01617938093841076, -0.01711895689368248, 0.01175524853169918, 0.026719368994235992, -0.007598646450787783, -0.00982851441949606, -0.0010064293164759874, -0.007816798985004425, 0.01012312714010477, 0.00829413253813982, 0.008496133610606194, -0.040958795696496964, 0.00510655390098691, 0.030837420374155045, -0.08347275108098984, 0.031887080520391464, 0.0026750604156404734, 0.025306185707449913, -0.0026936696376651525, -0.06221788749098778, 0.07009491324424744, 0.05259450152516365, 0.009114638902246952, 0.003474750556051731, 0.035093922168016434, -0.0000692032917868346, 0.05135134235024452, -0.02824222482740879, 0.0705329179763794, -0.006686657201498747, -0.029617058113217354, 0.05643969029188156, 0.03354089334607124, -0.026643138378858566, 0.05211170017719269, 0.03127116709947586, 0.016809487715363503, -0.00729020033031702, 0.04765336215496063, -0.0016314102103933692, 0.025612179189920425, -0.05698776990175247, 0.023117778822779655, 0.012019381858408451, -0.010383124463260174, -0.01644725911319256, 0.023320185020565987, -0.02780696004629135, -0.023922020569443703, -0.020346445962786674, -0.03135773539543152, 0.02297564595937729, -0.02334083616733551, -0.0332544706761837, 0.05333478003740311, 0.027924779802560806, 0.0003534466668497771, -0.012441610917448997, 0.05362046882510185, -0.0011460748501121998, -0.06727425754070282, -0.017013629898428917, 0.02513962611556053, 0.024751247838139534, -0.03668149560689926, 0.004774940200150013, -0.004189914558082819, 0.006947209592908621, 0.020910492166876793, -0.0032139490358531475, -0.0006795066292397678, -0.019749660044908524, -0.0038751992397010326, -0.012174779549241066, 0.0089510353282094, 0.010623880662024021, -0.0808010846376419, -0.03417421132326126, 0.06513015180826187, -0.012946618720889091, -0.046988293528556824, -0.028818270191550255, -0.022925101220607758, -0.00816379114985466, -0.004708465654402971, 0.05532580614089966, -0.004018520470708609, 0.04086795821785927, -0.008233883418142796, 0.004609944298863411, 0.0604679100215435, 0.0012849996564909816, 0.007829384878277779, -0.012106413021683693, -0.012769613415002823, 0.021951857954263687, -0.039178770035505295, 0.03642396628856659, 0.018001455813646317, 0.015361636877059937, -0.022678006440401077, 0.03221771866083145, -0.007427138742059469, -0.005689387675374746, 0.018274545669555664, -0.037715088576078415, -0.028089351952075958, 0.046212755143642426, -0.015151155181229115, -0.0330188013613224, -0.010438641533255577, 0.0444009006023407, -0.002313292119652033, 0.0073176962323486805, -0.009403897449374199, 0.006929920520633459, -0.08841488510370255, -0.06446412205696106, 0.001074664294719696, -0.052535660564899445, -0.03564077243208885, -0.059213705360889435, 0.023840343579649925, -0.035819195210933685, 0.009857459925115108, -0.032537296414375305, 0.07811883836984634, -0.06104857847094536, -0.0077582155354321, 0.032242484390735626, -0.0072362544015049934, -0.01694660261273384, 0.019030822440981865, 0.03856932744383812, -0.0433226116001606, 0.004824711941182613, -0.07423025369644165, -0.03527241572737694, 0.0015903132734820247, -0.02020956762135029, -0.0006924706976860762, 0.03912913426756859, 0.028754577040672302, -0.07766470313072205, 0.054528772830963135, -0.016078375279903412, 0.04391231760382652, 0.04024539515376091, -0.0032872953452169895, 0.03389148786664009, 0.019992228597402573, 0.048900242894887924, 0.03227200359106064, -0.024772897362709045, -0.010399449616670609, -0.06007718667387962, 0.05705853924155235, -0.016218816861510277, -0.06565925478935242, -0.06932120770215988, -0.012573779560625553 ]
<p>I was looking up for how polarisers work, I understood mostly everything except the part that explains that the polariser filters everything except light that is in a certain orientation.</p> <p>Here are my questions. How do waves have different orientation except being either vertical or horizantal? What determines the orientation and how does that affect in absorption of the wave?</p>
g5395
[ -0.015408577397465706, -0.01497340016067028, 0.0007079823990352452, 0.04638594388961792, 0.07476221024990082, 0.03270931914448738, 0.00564847094938159, 0.042782511562108994, 0.0119603481143713, -0.03279194235801697, -0.01983470283448696, -0.02310822531580925, -0.030897710472345352, 0.0042996760457754135, 0.056172482669353485, -0.01757020689547062, 0.0076199485920369625, 0.009832487441599369, 0.014546597376465797, -0.0030973718967288733, -0.019895097240805626, 0.03342324122786522, -0.016220182180404663, -0.054484475404024124, -0.04303658753633499, 0.019603857770562172, -0.011683906428515911, -0.05017085373401642, 0.04082502797245979, -0.05649815872311592, 0.042391009628772736, -0.024455787613987923, -0.016967127099633217, -0.025344837456941605, 0.004741600714623928, -0.029336145147681236, -0.0060133421793580055, 0.01372286956757307, 0.019153781235218048, 0.058113984763622284, -0.039973821491003036, 0.023452438414096832, -0.010384068824350834, -0.04650590568780899, -0.003556283423677087, -0.0402858629822731, 0.0052057113498449326, -0.04512259364128113, 0.0026457132771611214, -0.023760097101330757, -0.004603762645274401, -0.029544174671173096, 0.019932935014367104, 0.018522368744015694, 0.027175242081284523, 0.060287948697805405, -0.010637807659804821, 0.029700137674808502, 0.08384869247674942, -0.0038266752380877733, -0.04002349078655243, 0.018779678270220757, -0.009432711638510227, 0.06248871982097626, -0.023694109171628952, -0.08106708526611328, -0.04646521434187889, -0.06116662546992302, 0.004730381071567535, 0.07354442775249481, 0.018103836104273796, -0.020148931071162224, -0.016567857936024666, -0.06328583508729935, -0.008836297318339348, 0.009690036997199059, 0.0022916488815099, -0.0020774167496711016, 0.03187619522213936, 0.03553769364953041, 0.02245219610631466, -0.0082248505204916, -0.0035985982976853848, -0.001729629235342145, 0.07076316326856613, -0.01377591211348772, 0.03235494717955589, -0.011000655591487885, -0.04457777366042137, -0.0642876848578453, 0.006412208545953035, -0.01188796479254961, 0.06588436663150787, 0.06565879285335541, -0.030509300529956818, 0.010610529221594334, -0.02763492614030838, 0.007345995865762234, -0.02534586936235428, 0.03926784545183182, -0.03160793334245682, -0.008590837009251118, 0.021205054596066475, 0.027235480025410652, 0.02296353317797184, 0.015354053117334843, 0.03868699073791504, -0.007866778410971165, -0.023706115782260895, 0.03121066465973854, -0.06222366541624069, -0.05230456218123436, -0.05168161913752556, -0.08537036180496216, -0.05269727110862732, -0.00020880716328974813, 0.05515532195568085, 0.005183883477002382, 0.040808189660310745, 0.00008747435640543699, 0.07098449766635895, 0.08975842595100403, -0.01684914156794548, 0.04143759235739708, 0.0376664437353611, 0.028369281440973282, 0.010020293295383453, -0.02211202122271061, 0.00783976074308157, 0.00433563906699419, 0.07965944707393646, 0.005760073661804199, -0.018426060676574707, -0.014776680618524551, 0.021013151854276657, 0.001268586958758533, 0.02481490932404995, -0.02444886602461338, 0.027055976912379265, -0.008970305323600769, 0.03548993915319443, -0.0008145446190610528, 0.003768383292481303, -0.05005752667784691, 0.02042914554476738, -0.04261711612343788, 0.014478631317615509, 0.00032302842009812593, 0.03271881118416786, -0.006734306458383799, 0.011779721826314926, 0.0459347665309906, 0.022365570068359375, 0.052909690886735916, 0.04604388028383255, -0.06541778892278671, 0.03322094306349754, -0.009864117950201035, 0.017694629728794098, 0.017511995509266853, 0.04436458647251129, 0.0017271025571972132, -0.023141760379076004, 0.05889832228422165, -0.07621826976537704, -0.03532145172357559, 0.041249651461839676, -0.07762417942285538, 0.005976349115371704, 0.00245296279899776, -0.013389894738793373, 0.07168662548065186, 0.009588274173438549, 0.03435102105140686, 0.04642147570848465, 0.10608218610286713, -0.014773841015994549, 0.00544523261487484, 0.02784966304898262, 0.04323103278875351, -0.06993237137794495, 0.0017387991538271308, -0.004016332793980837, -0.03101593255996704, -0.006696400698274374, -0.041874248534440994, 0.017675084993243217, -0.0014560379786416888, -0.10447714477777481, 0.02790134772658348, 0.022867238149046898, -0.01588095724582672, -0.006393120624125004, -0.03549261763691902, -0.062394145876169205, -0.017236648127436638, -0.025624725967645645, 0.010837568901479244, -0.027199774980545044, 0.044582173228263855, -0.024724192917346954, -0.011796455830335617, 0.0438566729426384, 0.022053096443414688, 0.06758999079465866, 0.0021253915037959814, 0.028044018894433975, -0.0201166532933712, -0.013842388987541199, 0.012233179993927479, -0.017296675592660904, -0.024052685126662254, 0.06871487200260162, -0.057978495955467224, -0.024706969037652016, 0.08475259691476822, -0.011683208867907524, 0.06353993713855743, -0.013812115415930748, -0.028357306495308876, 0.032159242779016495, -0.00045870867324993014, -0.010929989628493786, 0.03292342275381088, -0.0430462509393692, -0.00916009396314621, -0.04342854768037796, 0.008181845769286156, 0.045367397367954254, 0.0338624082505703, -0.017712309956550598, 0.004575266968458891, 0.03523634374141693, 0.020655842497944832, 0.0362587533891201, 0.006132455542683601, -0.02638251520693302, -0.0011085602454841137, 0.004561907146126032, -0.04255622997879982, -0.05321194604039192, 0.0538518950343132, 0.014642016030848026, 0.012485306710004807, 0.033186253160238266, -0.0704805925488472, 0.04406356438994408, 0.029183581471443176, -0.041851937770843506, 0.016989674419164658, 0.034838031977415085, 0.002162129618227482, -0.024186888709664345, 0.018558859825134277, -0.04491155967116356, -0.05860454589128494, -0.04965083301067352, -0.0001541770761832595, -0.04100196436047554, -0.009998884983360767, 0.03104417957365513, 0.028910333290696144, 0.034020327031612396, -0.006096688564866781, -0.0445014126598835, -0.026827571913599968, 0.03150942921638489, 0.022047946229577065, 0.04138699173927307, -0.018489912152290344, 0.007644350174814463, 0.054971855133771896, 0.002752716187387705, 0.008611936122179031, -0.021003495901823044, -0.02046646922826767, -0.00030954802059568465, -0.01708045043051243, -0.008618895895779133, -0.04930739104747772, 0.018682660534977913, 0.05319446697831154, -0.045935165137052536, -0.008015058934688568, 0.021794503554701805, -0.00040265326970256865, 0.011148556135594845, 0.008277867920696735, -0.037717197090387344, -0.02832040935754776, -0.03770323470234871, -0.010703206062316895, 0.010209749452769756, -0.05280454084277153, 0.021162813529372215, -0.00885811448097229, 0.05435847118496895, -0.08876115083694458, -0.06133647635579109, 0.06582172214984894, 0.0037643667310476303, 0.012056807987391949, 0.057722654193639755, -0.03714432194828987, 0.021190131083130836, -0.00749850831925869, -0.04694504290819168, -0.04905519634485245, -0.025025462731719017, 0.05844472721219063, -0.03507881239056587, 0.021445320919156075, -0.03937971219420433, 0.026923740282654762, 0.020599106326699257, -0.0011618518037721515, -0.028300119563937187, -0.05432090163230896, -0.009605340659618378, 0.02157917246222496, -0.07262036949396133, 0.0008310821722261608, -0.02790887840092182, 0.026110053062438965, 0.005350741092115641, -0.02816466987133026, 0.048193126916885376, 0.0022774911485612392, -0.030582208186388016, -0.018176579847931862, 0.03141278773546219, -0.02916106767952442, -0.055615007877349854, 0.004023288376629353, 0.026150917634367943, 0.008102414198219776, -0.021852247416973114, 0.014992914162576199, -0.008242812938988209, -0.037138402462005615, 0.04044349119067192, -0.013031559064984322, -0.053679630160331726, 0.005867558531463146, -0.02146124467253685, 0.011387350037693977, -0.024111101403832436, -0.03391240909695625, -0.008814574219286442, 0.01116280909627676, -0.01687847264111042, 0.020732399076223373, -0.019396649673581123, 0.0008034111233428121, -0.011062797158956528, 0.005726834759116173, -0.018223727121949196, 0.044466275721788406, -0.01923495903611183, 0.010131231509149075, -0.027321234345436096, 0.04407208040356636, 0.027510572224855423, -0.03308707848191261, -0.03453120216727257, 0.027868779376149178, 0.052902646362781525, -0.06385499984025955, -0.029350969940423965, 0.011811583302915096, 0.026427187025547028, -0.031739283353090286, -0.03157034516334534, -0.006115297321230173, -0.028024086728692055, -0.021112848073244095, 0.0057734898291528225, 0.0856296643614769, 0.0031048187520354986, -0.020852545276284218, -0.028969960287213326, -0.0006349423783831298, 0.06687427312135696, 0.023410718888044357, 0.034177884459495544, 0.03862606734037399, -0.007377275265753269, 0.04910215735435486, -0.010140104219317436, -0.012807623483240604, 0.005524225067347288, -0.0072642480954527855, -0.00785769522190094, -0.04951515048742294, 0.02585436776280403, -0.058867741376161575, 0.019228648394346237, -0.024125102907419205, -0.03146950900554657, 0.0026274602860212326, 0.04488948732614517, 0.026149151846766472, 0.05994132533669472, -0.007902375422418118, -0.009866833686828613, 0.046176157891750336, -0.02054387889802456, -0.03835664317011833, -0.06087323650717735, -0.018521498888731003, -0.01539637427777052, 0.06804946810007095, -0.030594540759921074, -0.07205423712730408, 0.03593022748827934, 0.04565625637769699, 0.04348240792751312, 0.051288850605487823, 0.010378689505159855, -0.019835060462355614, 0.07616246491670609, 0.06613299995660782, -0.03569753095507622, -0.008445878513157368, -0.02114933170378208, 0.07678019255399704, 0.03555263578891754, -0.031170042231678963, -0.010830346494913101, -0.012682154774665833, 0.04968918859958649, -0.055751051753759384, 0.01659177802503109, -0.004315135069191456, -0.0017130562337115407, -0.013891695067286491, -0.04252893477678299, 0.013492710888385773, 0.014154434204101562, -0.03706740215420723, 0.041406795382499695, 0.004098502453416586, -0.05324224382638931, -0.04959770292043686, -0.014586671255528927, -0.040549930185079575, -0.043997619301080704, 0.0006737372023053467, -0.003798231715336442, -0.01178852841258049, -0.025037657469511032, 0.03373973071575165, -0.04126795008778572, -0.07156103849411011, 0.01282875332981348, 0.05348518118262291, -0.019336743280291557, 0.01491501834243536, 0.011426806449890137, -0.026878857985138893, -0.09982061386108398, -0.05540172755718231, 0.032275356352329254, -0.028712335973978043, -0.010977407917380333, -0.0692519024014473, 0.014267791993916035, -0.01720181666314602, -0.057713206857442856, 0.05077095702290535, -0.02019510231912136, -0.006624838337302208, -0.018499983474612236, 0.002542853355407715, 0.014146095141768456, -0.014919977635145187, -0.005769956391304731, -0.05069046467542648, -0.0521315336227417, -0.0585547611117363, 0.006731401663273573, 0.01403131615370512, 0.022355221211910248, 0.015356733463704586, -0.023574238643050194, -0.008325462229549885, -0.024013178423047066, 0.02268749661743641, -0.03217276558279991, -0.06619558483362198, -0.0002563299785833806, 0.035886216908693314, -0.04213839769363403, -0.014274755492806435, -0.01237651240080595, -0.007052376866340637, 0.014519739896059036, 0.020351437851786613, 0.035489220172166824, -0.030525168403983116, -0.0041732522659003735, -0.014213910326361656, -0.03621843084692955, 0.002980718621984124, -0.04047529399394989, 0.0033449295442551374, 0.02212418243288994, -0.01144448108971119, 0.003161280881613493, 0.060755934566259384, 0.010324584320187569, -0.02954256162047386, -0.04529295861721039, 0.06660200655460358, 0.013071348890662193, -0.04680594429373741, 0.0015956058632582426, 0.07002179324626923, -0.018506065011024475, 0.052477627992630005, -0.09075164794921875, 0.0026366538368165493, -0.03329415246844292, -0.005017355550080538, -0.012233785353600979, 0.006781410425901413, -0.05979423224925995, -0.0034720953553915024, 0.06327840685844421, -0.02971128560602665, 0.019821686670184135, 0.04559536278247833, 0.02623852901160717, 0.07330382615327835, 0.025782354176044464, -0.05963105708360672, 0.0322871096432209, -0.024490268900990486, 0.028123093768954277, -0.0021329878363758326, -0.020927274599671364, 0.0341356061398983, 0.010208134539425373, 0.0782899335026741, 0.002215573564171791, 0.06245842203497887, 0.0034809578210115433, 0.030681461095809937, 0.020785212516784668, 0.02613815851509571, -0.07524599879980087, 0.013691863976418972, 0.053829584270715714, -0.02484603226184845, -0.02555682882666588, 0.02991577982902527, -0.03502673655748367, -0.042866338044404984, -0.002137807197868824, -0.05286375805735588, 0.08951843529939651, 0.025896035134792328, -0.03585520759224892, -0.10278927534818649, 0.007641725707799196, -0.0369739904999733, 0.03463425487279892, 0.03786919638514519, 0.0419696606695652, 0.02903689816594124, -0.0006247361307032406, -0.032885897904634476, -0.07090030610561371, 0.04599429666996002, 0.05167850852012634, -0.009200667031109333, 0.022542059421539307, -0.025140993297100067, -0.009579201228916645, 0.05526641011238098, 0.056950684636831284, -0.028905028477311134, -0.019447727128863335, -0.03135933727025986, -0.012190008535981178, -0.010263274423778057, -0.016185110434889793, -0.02429855987429619, 0.02395051158964634, -0.037740811705589294, -0.019597668200731277, -0.02038409560918808, -0.003454115241765976, -0.03303661197423935, 0.0219498872756958, -0.02923714742064476, 0.028671305626630783, 0.05921247601509094, 0.00026083391276188195, -0.04903317987918854, 0.004334087483584881, 0.009753982536494732, 0.040992509573698044, -0.020957695320248604, 0.029062088578939438, 0.002858104882761836, -0.009527573361992836, -0.03402361646294594, 0.031400199979543686, -0.01069458108395338, 0.005481933243572712, 0.004512626677751541, -0.006969849579036236, -0.015409865416586399, -0.018282046541571617, 0.002949208952486515, -0.04621970281004906, 0.016117462888360023, 0.08547016233205795, 0.0298016220331192, -0.022034665569663048, -0.023515064269304276, -0.002041541738435626, 0.039343055337667465, 0.004964076913893223, 0.02900998666882515, -0.004038133192807436, -0.029800062999129295, 0.021734902635216713, 0.03206164017319679, 0.028758978471159935, 0.029188213869929314, 0.05422079190611839, 0.04463664069771767, 0.07281613349914551, 0.008078529499471188, -0.0363638699054718, 0.006463769823312759, 0.04656660184264183, 0.05833651125431061, 0.04485723003745079, 0.014963570982217789, 0.02880578301846981, 0.046904582530260086, -0.011542006395757198, 0.06820511072874069, -0.05510391294956207, -0.0662212073802948, 0.014098099432885647, -0.011567799374461174, -0.05059454217553139, -0.05889897793531418, 0.023334572091698647, 0.05925372987985611, -0.015829524025321007, 0.06170087307691574, 0.002914158394560218, 0.01340046152472496, -0.04784959927201271, 0.0044478243216872215, -0.01994466409087181, -0.012657430954277515, -0.004623685032129288, 0.037694744765758514, -0.009204709902405739, 0.00016883468197192997, -0.018228240311145782, -0.019283482804894447, -0.02491621859371662, 0.03731418401002884, -0.05616532266139984, -0.06203986331820488, 0.021689701825380325, -0.03065217100083828, 0.016957858577370644, -0.025830445811152458, -0.09086783975362778, -0.02015143819153309, 0.002983184764161706, -0.00048144871834665537, 0.0022488743998110294, 0.049677588045597076, -0.017674067988991737, -0.016861092299222946, 0.0355822816491127, 0.004577350337058306, -0.04792579263448715, 0.019204450771212578, 0.03908281400799751, 0.005403049290180206, -0.02527596242725849, -0.018235638737678528, 0.02929643727838993, -0.013859582133591175, 0.008447900414466858, -0.04658982530236244, 0.010738305747509003, 0.07180999964475632, -0.04553385451436043, -0.01952783390879631, 0.020180465653538704, -0.01898225210607052, 0.06526941061019897, -0.015558873303234577, 0.08995414525270462, -0.07335381954908371, 0.006681147031486034, -0.028589537367224693, 0.028336752206087112, 0.049565937370061874, 0.03020104579627514, 0.009523427113890648, 0.023401277139782906, -0.038121942430734634, 0.02430090121924877, -0.01936371996998787, -0.08665002137422562, 0.015225841663777828, -0.05865680053830147, -0.042827386409044266, 0.004479876719415188, 0.02262950874865055, 0.043049152940511703, -0.05109032243490219, 0.008854761719703674, 0.03558281064033508, 0.002934996737167239, 0.027753885835409164, 0.051214322447776794, 0.03501727059483528, 0.014668401330709457, 0.0592680387198925, -0.053759537637233734, 0.005038578063249588, -0.01010514609515667, 0.07005704194307327, -0.0011939193354919553, -0.05306505784392357, 0.014724607579410076, -0.01099433284252882, 0.04382620379328728, -0.011319559067487717, -0.021666623651981354, -0.026399094611406326, -0.021150872111320496, -0.03277266398072243, -0.027150694280862808, 0.026684492826461792, -0.03205927088856697, -0.031686943024396896, 0.018826717510819435, 0.07161597907543182, 0.00464216060936451, 0.020082248374819756, -0.024438941851258278, -0.07665975391864777, 0.013270735740661621, 0.025639092549681664, 0.04672430828213692, -0.0033080289140343666, 0.026025181636214256, 0.03147971257567406, 0.01525148656219244, -0.02590416558086872, -0.0314713679254055, 0.017096711322665215, -0.04989474266767502, -0.02542361430823803 ]
<p>Mathematician here with a speculative physical question -- feel free to boot me if the level isn't right.</p> <p>Suppose one finds, or builds, a constellation of several black holes arranged in a circle. (To get a stable arrangement, presumably one could put a bunch of small positively charged black holes at equal angles around a central positively charged object, or alternatively suspend uncharged black holes gravitationally in a circle surrounded by a quickly rotating ring of heavy matter). Suppose moreover that the event horizons of neighboring holes overlap -- or if there's some reason this is theoretically impossible, suppose they're really, really close to being tangent, while leaving room for light and matter to pass through the middle of this ring. (Is this possible?)</p> <p>My question is whether a trajectory from point A to point B that goes through the middle of the ring is causally related to one that does not. For example say a space explorer measures the spin of an electron, writes down the result and puts it in a box which he leaves at some fixed point in space (we've chosen a reference frame), then goes in a loop through the middle of the ring of black holes and comes back. When he comes back and opens the box again, will the recorded result be the same?</p> <p>I got this question after someone told me about quantum decoherence, and I was curious whether the world can change significantly if you go around a loop that either cannot be contracted or cannot be contracted without at some point becoming ridiculously long (where it's up to you to decide the value of "ridiculously").</p>
g5396
[ -0.0033285007812082767, 0.01537630707025528, 0.009036369621753693, -0.012194071896374226, 0.018289804458618164, -0.023753322660923004, 0.07317012548446655, -0.02221977896988392, -0.01724492572247982, -0.009884355589747429, 0.008589579723775387, 0.006756745744496584, 0.019348278641700745, -0.02918635867536068, -0.02740180678665638, -0.006162690464407206, 0.04310305416584015, 0.0026037825737148523, 0.01056801900267601, -0.01044794637709856, 0.024811850860714912, -0.012605521827936172, 0.03189767897129059, 0.0008779915515333414, -0.07395292073488235, -0.01928727515041828, 0.041385065764188766, -0.030618607997894287, -0.06139039620757103, -0.000787355296779424, 0.001860280055552721, -0.024199577048420906, 0.019030386582016945, -0.04046871140599251, -0.02997857704758644, -0.03279706835746765, -0.0256650410592556, 0.029997337609529495, 0.007719219662249088, 0.041832927614450455, 0.03376898169517517, -0.04716901853680611, -0.015643734484910965, -0.019861746579408646, 0.012896989472210407, 0.017354240640997887, 0.04138156771659851, 0.030473368242383003, 0.06622512638568878, -0.00645665917545557, -0.06391790509223938, 0.03876987844705582, 0.0009914091788232327, 0.03413764014840126, 0.00852897297590971, 0.10069829970598221, 0.038596972823143005, 0.018762994557619095, 0.044928357005119324, 0.024495137855410576, -0.044631365686655045, 0.00529470294713974, 0.017496338114142418, 0.023935941979289055, 0.02849486656486988, 0.015283987857401371, -0.05002465471625328, -0.008955449797213078, -0.08043194562196732, 0.004254693631082773, 0.018098797649145126, -0.02081960439682007, -0.020861906930804253, -0.015717841684818268, 0.001207234337925911, 0.08484296500682831, -0.02541760541498661, 0.0162057988345623, 0.002851673401892185, -0.0033186161890625954, -0.09274414926767349, -0.028487276285886765, -0.020732060074806213, 0.05096358433365822, 0.07027607411146164, 0.014526758342981339, -0.004731179215013981, -0.022839253768324852, -0.05738760158419609, 0.06606593728065491, 0.0559973381459713, -0.0543612539768219, 0.048072680830955505, 0.004058169666677713, -0.030569281429052353, 0.0404515340924263, -0.005134412553161383, 0.05763799324631691, 0.009326398372650146, -0.0049283760599792, -0.09172976762056351, 0.00824756734073162, -0.04768388345837593, 0.015895923599600792, -0.0046944753266870975, -0.005137979052960873, -0.021463993936777115, 0.06922388821840286, 0.028177235275506973, 0.010497109964489937, -0.017055312171578407, -0.1197681650519371, -0.010587460361421108, -0.010442779399454594, -0.013726969249546528, -0.004046278074383736, 0.06648756563663483, 0.029467135667800903, 0.011270599439740181, 0.056896574795246124, 0.009151318110525608, -0.016380347311496735, 0.013427740894258022, 0.07410281151533127, -0.0223098024725914, 0.04233852028846741, -0.029445011168718338, -0.01320650801062584, 0.04796135798096657, 0.02821960672736168, -0.013470125384628773, -0.03783672675490379, 0.023010438308119774, 0.09422081708908081, -0.059128858149051666, -0.037064891308546066, 0.03222740441560745, 0.017555832862854004, -0.011136536486446857, -0.0014083015266805887, 0.019716188311576843, -0.09624851495027542, 0.013694584369659424, -0.005391023587435484, -0.038298361003398895, 0.040214475244283676, -0.00657129380851984, -0.06080854684114456, 0.0552966445684433, 0.02084335871040821, -0.012581240385770798, 0.06895783543586731, -0.059256602078676224, -0.045692507177591324, 0.0011009674053639174, 0.020996280014514923, -0.0025631736498326063, 0.016180066391825676, 0.028034672141075134, -0.02009638398885727, 0.06543243676424026, -0.004662160761654377, -0.026812070980668068, 0.010457602329552174, -0.04750504717230797, -0.0017179461428895593, -0.01890656352043152, -0.012389593757689, 0.011159081943333149, -0.04893387854099274, -0.019725272431969643, 0.03232277184724808, 0.0008019963279366493, 0.016640061512589455, 0.018619965761899948, 0.05044102668762207, 0.015394655987620354, 0.003804640145972371, 0.015241670422255993, -0.0006868019117973745, -0.018520653247833252, 0.065340057015419, -0.02916855737566948, -0.023267202079296112, 0.05365687236189842, 0.011326550506055355, 0.03573242947459221, 0.006220053881406784, -0.013217422179877758, -0.04485948011279106, 0.04180385172367096, -0.029224136844277382, -0.012149752117693424, 0.0660569816827774, -0.03953966870903969, -0.04076581075787544, 0.03495652601122856, -0.0007127407588995993, -0.013536322861909866, 0.013941491022706032, 0.03507288545370102, 0.0028988404665142298, -0.015678465366363525, 0.028089357540011406, -0.0011500695254653692, 0.018347522243857384, 0.0034457093570381403, 0.0057412548922002316, 0.008846890181303024, 0.03781920298933983, 0.03876243159174919, -0.0032513702753931284, -0.003773340955376625, 0.027128225192427635, -0.09347820281982422, -0.015873748809099197, 0.018049193546175957, 0.03812655434012413, 0.023149661719799042, 0.005652281921356916, -0.03267291560769081, -0.020143015310168266, 0.03476380556821823, -0.060876812785863876, 0.028101442381739616, -0.03514498472213745, -0.025438638404011726, -0.05274345725774765, 0.008883100003004074, 0.04819377511739731, -0.04261200875043869, 0.011691280640661716, -0.006968701723963022, -0.03274296969175339, 0.08320302516222, 0.026973413303494453, 0.03353476896882057, -0.03221210837364197, -0.008938934653997421, -0.0003055206616409123, 0.04306166246533394, -0.003861253149807453, -0.025107387453317642, -0.021252619102597237, 0.06332431733608246, -0.07908503711223602, -0.0009669067803770304, -0.017597822472453117, -0.005271220579743385, 0.03979992866516113, -0.007497641257941723, -0.06016597896814346, -0.012344250455498695, 0.02740509621798992, -0.020250948145985603, 0.007153451442718506, -0.013075101189315319, 0.0292337778955698, -0.060961559414863586, -0.010487479157745838, 0.014915278181433678, -0.037818461656570435, 0.008676357567310333, 0.008157470263540745, -0.04185290262103081, -0.030217107385396957, -0.015176448971033096, -0.05853576958179474, -0.050254251807928085, 0.025460951030254364, -0.06604348868131638, 0.002535588340833783, 0.06962767988443375, 0.05604391545057297, 0.0205084178596735, 0.04009397700428963, -0.038368433713912964, -0.005276978015899658, 0.007391235791146755, 0.01693795435130596, -0.00035343202762305737, 0.010351408272981644, -0.040486495941877365, 0.032493844628334045, 0.03593064844608307, -0.04287749528884888, 0.0009156211162917316, 0.060556646436452866, -0.011788515374064445, 0.026461288332939148, 0.007026908919215202, 0.04746158421039581, 0.08417753875255585, 0.07678411900997162, 0.019126348197460175, 0.034508731216192245, -0.004733564332127571, 0.007926244288682938, 0.003982795402407646, 0.010606150142848492, 0.0045210435055196285, 0.01333201490342617, -0.03771022707223892, 0.02796395681798458, 0.025125350803136826, 0.03793029114603996, -0.04625030606985092, 0.020917193964123726, 0.039867956191301346, -0.02355888858437538, -0.008428147993981838, 0.0016382879111915827, -0.03370293974876404, 0.020253615453839302, 0.0193839892745018, -0.009181085042655468, 0.013708018697798252, 0.03612907975912094, 0.0057923500426113605, 0.020847953855991364, -0.014585883356630802, 0.02257048711180687, -0.014465299434959888, -0.038701605051755905, 0.09406837075948715, 0.04015990346670151, -0.03878801688551903, -0.08927872031927109, -0.07028929144144058, -0.011443942785263062, -0.050020746886730194, -0.024142244830727577, 0.01334427110850811, 0.041225701570510864, -0.019355634227395058, -0.04053041338920593, -0.03307540342211723, -0.00984981469810009, 0.04957342892885208, 0.030431091785430908, 0.0040587009862065315, -0.014913947321474552, -0.012032309547066689, -0.022685706615447998, 0.03000853955745697, 0.017050616443157196, 0.02284643054008484, -0.0038151354528963566, 0.019439352676272392, -0.016992483288049698, 0.03596232458949089, -0.06314750015735626, -0.012464658357203007, -0.025474075227975845, 0.018062999472022057, 0.032974712550640106, -0.014316587708890438, -0.006873228121548891, 0.0004673647345043719, -0.036613255739212036, -0.050491344183683395, -0.016779141500592232, -0.004614972043782473, -0.05952383577823639, -0.003915587905794382, 0.008179418742656708, 0.052012305706739426, 0.020096030086278915, 0.04232167452573776, -0.0011248169466853142, 0.012250502593815327, 0.03407463803887367, -0.009546903893351555, -0.025213191285729408, 0.04648702219128609, -0.0443820096552372, 0.033848829567432404, 0.0007378236041404307, -0.022368669509887695, 0.057059720158576965, -0.02007734403014183, 0.09296815097332001, 0.05380449816584587, -0.037610553205013275, -0.006395560689270496, 0.03398270905017853, 0.0027613304555416107, -0.05842229723930359, -0.03045244887471199, -0.007826374843716621, -0.004790511913597584, -0.018758714199066162, 0.006968451663851738, -0.06282731890678406, 0.03706996515393257, -0.019461151212453842, -0.033124007284641266, -0.045620162039995193, 0.024901708588004112, 0.004165473394095898, 0.0954032689332962, 0.0034891385585069656, -0.01766299642622471, -0.009546371176838875, 0.04739895462989807, -0.012050674296915531, -0.007307724561542273, 0.03373132646083832, -0.04048671945929527, -0.04440705105662346, 0.05501808226108551, -0.01859293505549431, -0.012326778843998909, -0.03678111359477043, 0.07848836481571198, -0.008978652767837048, 0.011639597825706005, 0.029905473813414574, -0.020657476037740707, -0.025189640000462532, -0.0395466573536396, 0.03870037943124771, 0.02864057384431362, 0.026801230385899544, -0.006797236856073141, 0.03986824303865433, -0.029615439474582672, -0.04577085003256798, -0.0009498028666712344, 0.02797524258494377, -0.00039153307443484664, 0.05614380165934563, 0.005083847790956497, -0.0018257019110023975, -0.05229474976658821, 0.008500153198838234, -0.060281142592430115, 0.022342326119542122, 0.02243800088763237, 0.03506208583712578, 0.06352820247411728, -0.007586758118122816, -0.014278573915362358, -0.06098471209406853, -0.05208704620599747, 0.010409435257315636, -0.06754612177610397, 0.006419910583645105, -0.022420033812522888, -0.05548723787069321, -0.04196830466389656, -0.025647999718785286, -0.005121347960084677, -0.059124771505594254, -0.0368296280503273, -0.055472031235694885, -0.015329418703913689, 0.04202224314212799, -0.030153758823871613, 0.0036492713261395693, -0.04809347167611122, -0.017902908846735954, -0.007463783025741577, 0.03454074263572693, -0.019405370578169823, -0.022721413522958755, -0.04404580965638161, -0.049690186977386475, -0.05633002519607544, 0.04114699736237526, -0.05307351052761078, 0.06584317237138748, 0.010823597200214863, 0.029925372451543808, -0.02043490670621395, -0.04201200604438782, -0.03956322371959686, 0.012345949187874794, -0.019633639603853226, -0.05033606290817261, -0.007516036741435528, 0.006870395038276911, 0.00976477563381195, 0.0024215453304350376, 0.015680551528930664, 0.03722064569592476, -0.002410315442830324, -0.026909437030553818, -0.013762179762125015, 0.022761991247534752, 0.016914593055844307, -0.04538124054670334, 0.03953113406896591, 0.0028027095831930637, 0.03428533673286438, -0.07490885257720947, 0.03520626574754715, 0.014018572866916656, 0.012296058237552643, -0.002474240493029356, -0.012132460251450539, 0.03706958517432213, 0.023371431976556778, 0.044402237981557846, -0.0469181053340435, 0.03715125098824501, 0.008311719633638859, -0.001015871181152761, -0.006905124988406897, 0.0690673440694809, -0.0631789043545723, 0.04707808420062065, -0.04886958748102188, 0.0045837475918233395, 0.031307581812143326, -0.029867714270949364, -0.013095916248857975, -0.006430667359381914, 0.014246328733861446, 0.014987597241997719, 0.02114342525601387, -0.0011014051269739866, -0.028053639456629753, 0.028409531340003014, 0.081491619348526, -0.00497584929689765, -0.021584825590252876, 0.005525132175534964, 0.034412652254104614, 0.06625327467918396, 0.03915583714842796, -0.0018538907170295715, 0.03734744340181351, -0.004787886049598455, -0.015922706574201584, -0.04430459812283516, 0.0037989525590091944, -0.028023064136505127, 0.09059461951255798, 0.026370413601398468, -0.02843194082379341, -0.05346363037824631, 0.047624461352825165, 0.07206947356462479, -0.009129802696406841, -0.02746269293129444, -0.05094804987311363, 0.031577493995428085, -0.005705428309738636, -0.04193950816988945, -0.06643252819776535, 0.04260865971446037, -0.014888420701026917, 0.020605403929948807, -0.04807254299521446, 0.05500686913728714, -0.01718221977353096, -0.02734426222741604, -0.015337103046476841, -0.047615788877010345, 0.022314509376883507, -0.0224064402282238, 0.015620659105479717, 0.02154488116502762, -0.0070015257224440575, -0.016131553798913956, -0.04078829288482666, -0.04004031419754028, 0.0409681499004364, 0.03548511490225792, 0.005693636368960142, -0.007067155558615923, -0.06651018559932709, 0.050326161086559296, 0.0027703498490154743, -0.014072326011955738, -0.03085816465318203, 0.0018058744026347995, -0.01044685859233141, -0.0031177529599517584, 0.0036828243173658848, -0.0028090982232242823, 0.1016763299703598, -0.041136808693408966, 0.010350263677537441, 0.04848654195666313, -0.03255195915699005, 0.08673051744699478, -0.0003411211946513504, -0.020819805562496185, -0.029520899057388306, 0.022945405915379524, 0.008410261012613773, -0.015449365600943565, -0.0673709437251091, 0.012080256827175617, -0.003870416898280382, -0.049251869320869446, -0.054495979100465775, 0.004917331039905548, 0.005893074441701174, -0.02911200001835823, 0.020959828048944473, -0.020680077373981476, -0.015151134692132473, 0.04353867098689079, -0.03130427375435829, -0.037193384021520615, 0.03073946386575699, 0.020354796200990677, 0.02908029407262802, 0.03042934089899063, 0.036122843623161316, 0.04666775465011597, -0.05716947466135025, 0.029824864119291306, -0.009859607554972172, -0.08237089961767197, 0.018685169517993927, -0.03133290633559227, 0.02044084668159485, 0.029167531058192253, -0.09178341180086136, 0.01769261434674263, -0.015043755993247032, 0.049178216606378555, 0.024131495505571365, 0.013796370476484299, 0.022643014788627625, 0.05559549108147621, 0.030310355126857758, 0.016635240986943245, -0.03719810023903847, 0.031140781939029694, 0.027473358437418938, 0.02763483114540577, -0.07633548229932785, 0.04417969658970833, 0.006456310860812664, -0.019784685224294662, 0.03775671124458313, -0.03314957022666931, -0.0010007192613556981, 0.05293496325612068, -0.017704537138342857, -0.0536859855055809, 0.06207903474569321, -0.010386507026851177, -0.04796246439218521, 0.06358060985803604, 0.005441548768430948, -0.044916994869709015, -0.07202953100204468, 0.03692822530865669, -0.052539024502038956, -0.017270872369408607, -0.020719273015856743, 0.0347370021045208, -0.03875517472624779, -0.051256824284791946, -0.037187572568655014, 0.01746571809053421, -0.022934401407837868, -0.009499110281467438, -0.018386054784059525, 0.01358170248568058, 0.01794557459652424, -0.01631123013794422, -0.05371468514204025, -0.043336741626262665, 0.021430715918540955, -0.03284330293536186, -0.07472275197505951, 0.016475079581141472, 0.0011606259504333138, -0.04936259984970093, 0.04906897619366646, 0.024310903623700142, 0.03551692143082619, 0.06864947825670242, 0.054044339805841446, 0.00901202205568552, 0.016942806541919708, 0.05849672108888626, -0.044331423938274384, 0.061835721135139465, -0.01574709080159664, 0.0301956869661808, -0.03003799542784691, -0.047595929354429245, 0.020396051928400993, 0.03656097501516342, 0.018653903156518936, -0.009717821143567562, 0.010479339398443699, 0.023208418861031532, 0.02925899438560009, 0.026436880230903625, 0.0009862047154456377, -0.050031546503305435, -0.01255633682012558, 0.01658038981258869, -0.006029522977769375, -0.005519833881407976, 0.04156675934791565, 0.03770606592297554, -0.03450542688369751, 0.008158680982887745, -0.05783212557435036, -0.014812067151069641, 0.007410096470266581, 0.04393389821052551, -0.06706417351961136, -0.008779830299317837, -0.07957223057746887, -0.05286416783928871, 0.0047930446453392506, 0.008564469404518604, 0.02852500043809414, 0.03370000049471855, -0.09239713102579117, 0.012689702212810516, -0.02452206052839756, -0.02326786145567894, 0.01753629930317402, -0.0314670130610466, -0.011176074855029583, -0.046509746462106705, -0.008454916998744011, -0.008324733003973961, 0.005281363148242235, 0.009502027183771133, -0.07048629969358444, 0.012816768139600754, 0.013549712486565113, -0.007258398924022913, -0.053203046321868896, -0.015164772979915142, -0.0086299953982234, -0.010990831069648266, -0.004672175273299217, -0.05623291805386543, -0.0006264029070734978, -0.054211802780628204, -0.001894150162115693, 0.037076614797115326, 0.009148933924734592, 0.028867516666650772, 0.03358669951558113, 0.009700886905193329, -0.011428258381783962, -0.009408258832991123, 0.012865941971540451, 0.03131746128201485, 0.04423688352108002, -0.014142240397632122, -0.045156329870224, -0.014102526940405369, -0.014810402877628803, 0.0301191508769989, -0.010424141772091389, -0.0015372782945632935, -0.01673295721411705, -0.018692471086978912, -0.05588192492723465, -0.0365903303027153, 0.020561542361974716, 0.07722373306751251 ]
<p>Assume a small square block $m$ is sitting on a larger wedge-shaped block of mass $M$ at an upper angle $\theta$ such that the little block will slide on the big block if both are started from rest and no other forces are present. The large block is sitting on a frictionless table. The coefficient of static friction between the large and small blocks is µs. With what range of force $F$ can you push on the large block to the right such that the small block will remain motionless with respect to the large block and neither slide up nor down? </p> <p>This question really is not too complicated without friction acting upon the small block (<a href="http://physics.stackexchange.com/questions/35978/preventing-a-block-from-sliding-on-a-frictionless-inclined-plane">Preventing a block from sliding on a frictionless inclined plane</a>) </p> <p>But what happens when we add friction to the system? Why is it considered static, if at rest, the mass would slide down the plane? </p>
g5397
[ 0.044441211968660355, 0.022264020517468452, 0.02000271901488304, 0.008459644392132759, -0.0005170099320821464, 0.006864675786346197, 0.05180254578590393, 0.014977816492319107, -0.03514312952756882, -0.05870145559310913, -0.015613818541169167, -0.04016389325261116, -0.024906806647777557, -0.0019329488277435303, 0.019242407754063606, 0.10755013674497604, 0.0678989365696907, -0.0044335355050861835, 0.02136114239692688, 0.02068443037569523, -0.02205015905201435, 0.024674823507666588, -0.01862061396241188, -0.0002641882165335119, 0.019213156774640083, -0.020810022950172424, 0.07111938297748566, -0.006120511796325445, 0.02507525123655796, 0.005045752041041851, 0.001040165196172893, -0.00519968057051301, 0.024841776117682457, 0.0029524313285946846, 0.019830090925097466, 0.03218560293316841, 0.06195593252778053, -0.030243700370192528, 0.030321456491947174, -0.023723270744085312, -0.03310076892375946, -0.04879484325647354, -0.0015280728694051504, -0.020947733893990517, 0.006417202763259411, 0.013512147590517998, -0.0119668273255229, -0.010665074922144413, -0.01848176121711731, 0.014219658449292183, -0.002554600825533271, -0.009084894321858883, 0.018937354907393456, 0.007874567061662674, -0.05789598822593689, 0.01512027345597744, 0.04023892804980278, -0.013902796432375908, 0.04417632147669792, 0.09971281886100769, -0.05559338629245758, -0.02851676195859909, 0.026314925402402878, -0.027429234236478806, 0.014947295188903809, -0.012574429623782635, -0.01588113233447075, 0.01181259285658598, 0.0018758421065285802, 0.02440849505364895, -0.017097966745495796, -0.028891196474432945, 0.04065496101975441, -0.05229303240776062, -0.055093128234148026, 0.0234872754663229, 0.049161069095134735, 0.010650736279785633, 0.018464192748069763, -0.029507599771022797, -0.0329473651945591, 0.02785990573465824, 0.051891785115003586, 0.0029901182278990746, 0.06481410562992096, -0.0060826558619737625, 0.0018478422425687313, -0.022235633805394173, -0.051830075681209564, 0.051306407898664474, -0.0029725655913352966, -0.011349564418196678, 0.04054749757051468, 0.027670836076140404, 0.03100808896124363, 0.001530778594315052, -0.005191455595195293, 0.0595584474503994, -0.033652037382125854, 0.036288078874349594, -0.021349001675844193, -0.008265949785709381, 0.025866156443953514, -0.006617011968046427, 0.03621257469058037, -0.03915959224104881, -0.0021418200340121984, 0.03767525777220726, 0.011613305658102036, 0.007075492758303881, 0.030689969658851624, 0.01290347333997488, -0.09847181290388107, -0.06949768215417862, -0.013974647969007492, -0.03282088413834572, 0.08748166263103485, 0.031503453850746155, -0.028417369350790977, 0.03439999371767044, -0.03331197425723076, 0.012838130816817284, 0.0006683877436444163, 0.04777603968977928, 0.009918642230331898, 0.015630358830094337, 0.016151463612914085, 0.04786926135420799, -0.0058201211504638195, -0.01155558880418539, -0.015731755644083023, 0.028315767645835876, -0.025132590904831886, -0.0260133258998394, 0.017618872225284576, 0.040954988449811935, -0.047455091029405594, -0.03960198536515236, 0.014469942077994347, -0.011317417956888676, 0.008964204229414463, 0.048534147441387177, -0.020167971029877663, -0.008423492312431335, -0.05897969380021095, 0.016066988930106163, -0.009931353852152824, 0.04384066164493561, 0.0477011539041996, 0.034091927111148834, -0.01279191393405199, 0.03622671216726303, 0.021566180512309074, -0.0584147609770298, 0.0477164201438427, -0.008881879039108753, 0.05776798352599144, 0.0058468785136938095, 0.02207697182893753, -0.006133832037448883, 0.026221515610814095, -0.022705750539898872, 0.045261844992637634, -0.015541407279670238, -0.08820085227489471, -0.010951640084385872, -0.07218170911073685, -0.05671665444970131, 0.0179484561085701, -0.01146212499588728, -0.038858622312545776, 0.027217524126172066, 0.008806328289210796, 0.07571253925561905, -0.014384527690708637, 0.00253778207115829, 0.05309195816516876, 0.003152342513203621, 0.07325655966997147, 0.0007706040050834417, -0.006291423924267292, 0.01600649021565914, 0.03629312664270401, 0.043541017919778824, -0.06024147942662239, -0.03215658664703369, 0.00962318666279316, 0.018651597201824188, 0.031112948432564735, -0.009892880916595459, -0.04380197450518608, -0.06395074725151062, -0.02180456928908825, 0.04059318080544472, -0.014976037666201591, 0.026086531579494476, 0.03245198354125023, -0.03922395035624504, 0.013627266511321068, -0.038172490894794464, -0.003959870897233486, 0.031950268894433975, 0.014089283533394337, -0.012172503396868706, -0.01577625796198845, 0.05202093347907066, -0.0027933435048907995, -0.006606668699532747, 0.018369654193520546, -0.025917619466781616, 0.05099615827202797, 0.047124236822128296, -0.033290281891822815, 0.00834397692233324, 0.008912164717912674, -0.0374998115003109, -0.009579871781170368, -0.0016541153891012073, 0.0083968760445714, 0.023013358935713768, -0.02411682717502117, -0.06420683115720749, -0.044160109013319016, 0.008628014475107193, 0.008530027233064175, -0.030407726764678955, -0.03255227580666542, -0.028924303129315376, -0.02306539937853813, 0.05570278316736221, -0.0724974200129509, -0.03840529918670654, -0.005848338827490807, -0.01771453581750393, 0.01145513728260994, 0.03429615497589111, 0.01477834302932024, 0.0403565876185894, 0.01619279384613037, -0.00748069491237402, 0.014969781041145325, -0.029082942754030228, -0.035036686807870865, -0.0405990369617939, 0.015075134113430977, -0.04981880262494087, -0.005924665369093418, 0.023129621520638466, 0.02670055627822876, 0.020075516775250435, -0.01647278666496277, -0.017026089131832123, -0.048305682837963104, 0.02503334917128086, -0.01816144771873951, 0.01695355959236622, -0.07175973802804947, -0.012399275787174702, -0.008326730690896511, -0.08418958634138107, -0.02885272353887558, -0.03045640140771866, -0.047623708844184875, 0.06916492432355881, -0.0501900240778923, 0.011313154362142086, -0.07884638011455536, 0.007300323806703091, 0.05619841441512108, 0.043484147638082504, 0.0250406451523304, 0.03733666613698006, 0.017090825363993645, 0.08276432752609253, -0.0016963115194812417, -0.0333867073059082, 0.004504689946770668, -0.024670111015439034, -0.04521239921450615, 0.00969845149666071, -0.0060339332558214664, 0.017332106828689575, -0.029885293915867805, 0.04265948385000229, 0.008802928030490875, -0.009470083750784397, 0.01256954949349165, -0.03832155838608742, -0.043784018605947495, -0.04108843207359314, -0.06357931345701218, 0.03716183453798294, 0.0908304750919342, 0.05544063076376915, 0.02912384830415249, 0.04690100997686386, -0.04813966900110245, -0.06622038781642914, -0.03738454729318619, 0.07737915962934494, -0.011251422576606274, -0.04118718206882477, -0.013543962500989437, -0.02132740058004856, -0.03807813674211502, 0.002490170067176223, -0.005261082202196121, -0.051231205463409424, -0.03783085197210312, 0.026383722200989723, -0.011962605640292168, 0.06680893152952194, -0.01292969100177288, -0.02376733534038067, -0.06920283287763596, 0.005561483092606068, 0.024170046672225, 0.03127856180071831, 0.006136555224657059, 0.016945701092481613, -0.038145262748003006, -0.018074901774525642, -0.00886080227792263, -0.013195806182920933, 0.04423806071281433, 0.019029786810278893, -0.04213107004761696, 0.05861144885420799, -0.052831899374723434, -0.010306931100785732, 0.048463672399520874, 0.034805603325366974, -0.024581052362918854, -0.038246359676122665, -0.017642026767134666, 0.000700558943208307, 0.047997456043958664, 0.009582970291376114, 0.027794595807790756, 0.044768381863832474, -0.037408530712127686, -0.03010367788374424, -0.024427300319075584, -0.022731000557541847, -0.04033863916993141, 0.048710163682699203, 0.0006955703138373792, -0.030494224280118942, 0.006499603856354952, -0.025491615757346153, 0.07058140635490417, -0.06362690776586533, -0.0027559595182538033, 0.020699406042695045, 0.026505282148718834, 0.02407425455749035, -0.04999397322535515, 0.013635911978781223, -0.059533536434173584, -0.05183231085538864, 0.010832993313670158, -0.044225387275218964, 0.043130598962306976, 0.02311939001083374, 0.036975108087062836, -0.003163652727380395, -0.053912676870822906, 0.00014786282554268837, -0.007053993176668882, -0.005386885721236467, -0.0003241146623622626, -0.03291734680533409, -0.03693639487028122, -0.048810139298439026, 0.027745623141527176, -0.021373312920331955, 0.0390203595161438, 0.028456849977374077, -0.019083350896835327, 0.022236937656998634, 0.011178536340594292, 0.02827727049589157, -0.04147707298398018, -0.004659498110413551, -0.022017212584614754, 0.046837177127599716, -0.03493807837367058, 0.032850779592990875, 0.04898178204894066, -0.00948404986411333, 0.01985737308859825, -0.02025688998401165, 0.00888666883111, 0.05807213485240936, -0.013404561206698418, 0.023523373529314995, -0.002323875203728676, -0.029853524640202522, 0.035320401191711426, -0.02794848382472992, 0.04983459413051605, 0.032816510647535324, -0.07165879011154175, 0.05519789457321167, 0.03591855242848396, 0.06505311280488968, 0.04874420911073685, 0.0015117492293938994, 0.01514002587646246, -0.04562715068459511, 0.04266095906496048, -0.09139318019151688, -0.07899365574121475, -0.002388271503150463, 0.026388777419924736, 0.012902611866593361, 0.011795024387538433, 0.05765553191304207, 0.0007125336560420692, 0.01633276604115963, -0.06910926848649979, 0.06916493922472, -0.030905939638614655, -0.0051142130978405476, 0.005280208308249712, -0.053776584565639496, -0.03222740814089775, -0.0005550840287469327, -0.02121852897107601, 0.006569341756403446, -0.033948250114917755, 0.027369314804673195, -0.023261260241270065, -0.010416104458272457, -0.021909920498728752, 0.018628763034939766, 0.0014011774910613894, -0.02681180089712143, -0.0353936031460762, 0.029294582083821297, -0.028472065925598145, 0.052409764379262924, 0.05581296980381012, 0.0062896739691495895, -0.033929020166397095, 0.05192141607403755, 0.016332635655999184, 0.014129121787846088, 0.06440157443284988, 0.014305983670055866, 0.008257503621280193, -0.04288580268621445, -0.032997000962495804, -0.034371014684438705, -0.04094914346933365, 0.02055996097624302, -0.024532269686460495, 0.03582703322172165, -0.04674952104687691, 0.002276438055559993, 0.03618088364601135, -0.05844378471374512, -0.025274131447076797, -0.016092104837298393, -0.014670220203697681, 0.014909373596310616, -0.01904142275452614, 0.03682270273566246, -0.0580628402531147, 0.04083488509058952, 0.017681078985333443, -0.01468763966113329, -0.00047427613753825426, 0.06233195960521698, -0.00733097642660141, 0.02472843788564205, 0.0391075573861599, 0.029155442491173744, 0.07637069374322891, -0.042489029467105865, -0.02120296098291874, 0.027929769828915596, 0.041891857981681824, -0.022396929562091827, 0.015847880393266678, -0.07586081326007843, -0.03650258854031563, -0.0073354956693947315, 0.002323733875527978, 0.023594621568918228, 0.04418737441301346, 0.008567786775529385, -0.053451091051101685, 0.0048599825240671635, -0.027802515774965286, 0.04137749969959259, -0.054044369608163834, -0.039786260575056076, 0.01610114797949791, 0.006814385764300823, 0.005093815736472607, 0.01174937654286623, 0.09214024990797043, 0.0006023596506565809, -0.03040762059390545, -0.04177461192011833, 0.05380987003445625, -0.09231992810964584, -0.0022226113360375166, 0.04875806346535683, -0.05657391622662544, -0.007305920589715242, 0.04794241487979889, 0.06394144892692566, -0.03788507729768753, 0.006759935524314642, 0.007717920001596212, -0.0018388871103525162, -0.05715443566441536, 0.018083103001117706, 0.0019641921389847994, -0.01091380137950182, -0.005838009528815746, -0.014737049117684364, -0.007218067534267902, 0.007919324561953545, -0.013868001289665699, -0.011197282932698727, -0.09534231573343277, 0.057971492409706116, 0.004181409254670143, 0.004745004698634148, 0.007714264560490847, 0.004592699930071831, 0.011434420943260193, -0.004322388209402561, -0.009585616178810596, -0.0551469661295414, 0.007185916882008314, -0.055516257882118225, -0.045441772788763046, -0.06353947520256042, 0.04391804337501526, 0.05022798851132393, -0.010803411714732647, 0.004273178055882454, -0.02457658387720585, 0.02516934648156166, 0.04219316318631172, -0.006497201044112444, -0.03890393301844597, 0.09393205493688583, -0.058214832097291946, 0.06291244179010391, -0.03091128170490265, -0.0032904797699302435, 0.011293803341686726, 0.01688852161169052, 0.042938608676195145, -0.05906867980957031, 0.023673243820667267, -0.03400880843400955, -0.0023253418039530516, -0.009663962759077549, 0.01791447401046753, -0.037400923669338226, 0.03032032772898674, 0.009908533655107021, 0.02495097555220127, -0.0005214955890551209, -0.009227391332387924, 0.020668838173151016, 0.005532177165150642, 0.05730726942420006, 0.0698905885219574, 0.012533402070403099, -0.08771712332963943, -0.0014376867329701781, 0.0022942256182432175, 0.08224322646856308, -0.016672199591994286, 0.026081407442688942, 0.0010470016859471798, -0.006733976770192385, 0.031017255038022995, 0.006630490999668837, -0.10061921924352646, -0.02084486372768879, 0.05792165920138359, 0.0005122672882862389, -0.060909222811460495, 0.02284022606909275, -0.046141352504491806, 0.10097458958625793, 0.004653878975659609, -0.019826781004667282, -0.02826610580086708, 0.03079073503613472, 0.008444922976195812, 0.022588564082980156, -0.0023368329275399446, 0.040259964764118195, 0.10238077491521835, -0.030637633055448532, -0.009538225829601288, 0.03859036788344383, -0.0077942912466824055, -0.012797259725630283, 0.04732880741357803, -0.011462485417723656, -0.048354730010032654, 0.025914717465639114, 0.00036373993498273194, -0.030893336981534958, -0.004158095922321081, -0.015422709286212921, -0.008964219130575657, -0.045747268944978714, -0.06159413605928421, -0.09907478094100952, -0.03575883433222771, -0.0152561254799366, -0.013086418621242046, -0.0825154259800911, -0.020743144676089287, -0.03627685829997063, -0.013381054624915123, -0.005183028988540173, 0.03306280076503754, 0.021479010581970215, 0.05047779157757759, -0.02444116398692131, -0.01160226296633482, -0.03456892445683479, -0.022766822949051857, 0.034381698817014694, -0.08944450318813324, 0.012429202906787395, 0.01322504784911871, 0.049157168716192245, -0.0000010029791610577377, 0.05861689895391464, -0.021854165941476822, 0.02157670445740223, -0.01966322585940361, -0.030737217515707016, 0.019817132502794266, -0.013594754971563816, -0.03839023411273956, -0.027291245758533478, 0.01478904951363802, -0.00471767783164978, -0.06790579110383987, 0.016003312543034554, -0.024247534573078156, -0.014305737800896168, 0.024732474237680435, -0.013028247281908989, 0.0206645205616951, 0.017458679154515266, -0.00668680015951395, 0.026944441720843315, 0.00989015493541956, 0.010508432984352112, -0.047404125332832336, 0.033971454948186874, -0.03668583929538727, 0.02253837138414383, -0.0029077872168272734, 0.00947300810366869, -0.011299294419586658, -0.07375115156173706, -0.0177170243114233, 0.02982291765511036, 0.03140728920698166, 0.026936639100313187, 0.013096991926431656, -0.03229335695505142, 0.07386104762554169, 0.0225457102060318, 0.04345647618174553, -0.0007215521181933582, 0.03234236314892769, 0.008887339383363724, -0.011881548911333084, 0.027873001992702484, 0.05930008366703987, 0.030120523646473885, -0.02607174590229988, -0.036448583006858826, 0.028735371306538582, 0.013423101976513863, -0.04324609413743019, 0.016045328229665756, -0.012728986330330372, -0.014225197024643421, -0.036670982837677, 0.005366288125514984, -0.07436823844909668, -0.06169823557138443, -0.022502819076180458, -0.011496687307953835, -0.050792064517736435, -0.0212579183280468, 0.027154583483934402, 0.042254433035850525, 0.024516941979527473, -0.0017793780425563455, -0.04608975723385811, -0.04687696322798729, 0.04126029461622238, 0.07318393141031265, 0.018625838682055473, -0.017004510387778282, 0.023221079260110855, 0.04596796631813049, -0.017669394612312317, 0.0007020561606623232, 0.0015299272490665317, -0.025922372937202454, -0.02010917291045189, -0.016843682155013084, -0.023630362004041672, -0.09907558560371399, -0.027680031955242157, -0.040709324181079865, 0.013309602625668049, -0.058897215873003006, 0.03355500474572182, -0.024140020832419395, 0.0005079608527012169, -0.009442713111639023, 0.05047426372766495, 0.01778005063533783, -0.02755751647055149, -0.003461551619693637, 0.04932234063744545, 0.006438949145376682, -0.03427894786000252, 0.024841981008648872, -0.015421591699123383, -0.014548399485647678, -0.006581149064004421, 0.03288000822067261, 0.04999852925539017, 0.03969128802418709, 0.010316586121916771, 0.00548213254660368, 0.026489688083529472, -0.009481489658355713, 0.021295621991157532, 0.021543556824326515, -0.024931058287620544, -0.02509782463312149, 0.04505356773734093, 0.00014989763440098614, -0.04121854901313782, -0.00037916534347459674, 0.01454742532223463, -0.007326861843466759, -0.0037268935702741146, 0.013963677920401096, 0.003183038905262947, -0.022196752950549126, 0.017119409516453743, -0.09939064085483551, 0.027337275445461273, 0.0024522957392036915 ]
<p>What is the value of $g$ at the centre of the Earth? Is it zero or infinity? My attempt: I know it's zero but applying law made me on fused.</p>
g50
[ 0.004624827764928341, 0.026613697409629822, -0.004544204566627741, -0.05922127142548561, 0.0679333433508873, 0.049665167927742004, 0.021423982456326485, 0.05636104196310043, -0.0367395356297493, -0.03371318429708481, -0.03351913392543793, 0.01322303805500269, -0.020992590114474297, -0.015199513174593449, 0.057233452796936035, -0.027962980791926384, 0.05718307942152023, 0.05030867084860802, 0.011221110820770264, 0.018616842105984688, -0.029573209583759308, -0.07962752133607864, -0.0021395920775830746, -0.049387093633413315, 0.04317652806639671, -0.04091949015855789, 0.06427723914384842, 0.05881015211343765, -0.054290708154439926, -0.02978886477649212, 0.00936981663107872, 0.014015091583132744, 0.02211109735071659, -0.06192144379019737, -0.02494540438055992, 0.022761212661862373, -0.00313490629196167, 0.015655774623155594, 0.04657304659485817, -0.009547669440507889, 0.012290393002331257, -0.026788776740431786, -0.006001558154821396, 0.018630793318152428, -0.04074893519282341, 0.03604862838983536, -0.000052789924666285515, 0.019058123230934143, 0.030493414029479027, 0.002068137051537633, -0.04108211025595665, 0.027399739250540733, 0.07650044560432434, -0.06872217357158661, 0.004806330427527428, -0.0008631831151433289, -0.02313178963959217, -0.014611230231821537, 0.003867136314511299, 0.06049664691090584, 0.013133424334228039, -0.0005971421487629414, 0.04184066504240036, -0.001966299256309867, 0.04234578087925911, -0.013762025162577629, -0.024822933599352837, 0.039404209703207016, -0.014226730912923813, 0.024640176445245743, 0.037217289209365845, -0.043070390820503235, 0.014210933819413185, -0.0033783921971917152, -0.03933453559875488, -0.019780242815613747, 0.022129623219370842, 0.05594955384731293, 0.029075991362333298, -0.0003409053315408528, 0.021360943093895912, -0.01651093177497387, 0.005944765638560057, -0.028390413150191307, -0.01047128438949585, -0.018688593059778214, 0.02422414906322956, 0.02327161654829979, -0.055079229176044464, 0.010459435172379017, 0.04426351189613342, 0.021621350198984146, 0.02767390012741089, -0.02978713996708393, 0.009784757159650326, -0.02172345109283924, 0.037387266755104065, 0.03226112574338913, -0.0011934234062209725, 0.037813249975442886, -0.050081830471754074, 0.0004735952243208885, 0.011513191275298595, -0.003227192908525467, 0.01485464721918106, 0.023526985198259354, 0.021732429042458534, -0.005951952654868364, 0.00945077370852232, -0.043007850646972656, -0.00367159117013216, 0.029621191322803497, -0.02238311618566513, -0.04815787822008133, -0.014158517122268677, 0.0012529311934486032, 0.06338418275117874, -0.019900452345609665, 0.012462219223380089, 0.0070841326378285885, 0.0699651837348938, 0.010988296940922737, 0.022279614582657814, 0.06301304697990417, -0.04591905698180199, -0.036789797246456146, 0.02427108772099018, -0.008844888769090176, 0.04263937845826149, -0.017975205555558205, -0.06866094470024109, -0.021198440343141556, -0.03282880783081055, -0.036560554057359695, -0.026442933827638626, 0.017586667090654373, 0.01234620064496994, -0.014458402059972286, -0.07288910448551178, 0.0030668010003864765, -0.09375402331352234, -0.0317351333796978, 0.05379744991660118, -0.013249851763248444, -0.002005130285397172, 0.005215857177972794, 0.011496572755277157, 0.019602095708251, 0.05276869982481003, -0.007520277518779039, -0.0016669736942276359, 0.05120474845170975, 0.04092825949192047, -0.015195759013295174, 0.04658516123890877, -0.07556603848934174, 0.09938689321279526, -0.014666402712464333, -0.059793245047330856, -0.040784358978271484, 0.0018339295638725162, 0.011082949116826057, 0.029298389330506325, -0.005452634301036596, -0.0371612049639225, 0.018835192546248436, -0.0010321771260350943, -0.0631905049085617, 0.024601025506854057, 0.02122034691274166, -0.037525106221437454, 0.031626105308532715, 0.01209635753184557, 0.013633769936859608, -0.013243291527032852, 0.027655690908432007, 0.014067414216697216, -0.01569540984928608, 0.03166158124804497, -0.013897528871893883, 0.01312275230884552, -0.011729600839316845, 0.024346929043531418, 0.006308669690042734, -0.0026238872669637203, 0.037061333656311035, -0.0011994054075330496, -0.009301972575485706, -0.013289818540215492, 0.02082795277237892, -0.04588978737592697, -0.022989988327026367, -0.027675434947013855, 0.03353133797645569, 0.03722788766026497, 0.006577757652848959, -0.02476957067847252, -0.03364897146821022, -0.06419164687395096, 0.05413734167814255, -0.021725883707404137, 0.045926060527563095, 0.016087453812360764, 0.006663469132035971, -0.031388867646455765, -0.0013216957449913025, 0.017298530787229538, 0.0016678632237017155, 0.012057066895067692, -0.0032615100499242544, 0.015739159658551216, -0.048695508390665054, 0.009296593256294727, 0.0619388222694397, -0.03411416336894035, -0.026594115421175957, -0.004487859550863504, 0.06902565807104111, 0.018424684181809425, 0.017941778525710106, -0.0009060266893357038, 0.06117254123091698, 0.0349758006632328, 0.021598104387521744, 0.09575054794549942, -0.027904292568564415, -0.009065642952919006, -0.01281230989843607, 0.03727097436785698, -0.022079041227698326, -0.013177773915231228, -0.005626361817121506, -0.01585443876683712, -0.015268390066921711, 0.02339714765548706, 0.05748630315065384, -0.04495865851640701, -0.06467548757791519, -0.006484129466116428, 0.044270072132349014, -0.05145418271422386, 0.013054823502898216, -0.053225256502628326, -0.04817759245634079, 0.034262415021657944, -0.0012808472383767366, 0.027108067646622658, 0.05991516634821892, 0.0207025445997715, 0.010842357762157917, 0.0026010582223534584, 0.006589358206838369, -0.0032118207309395075, 0.07381471991539001, 0.02535785175859928, 0.05363253876566887, -0.043080367147922516, -0.017540166154503822, -0.029558932408690453, -0.022825876250863075, -0.013373826630413532, -0.06566128879785538, 0.0049119750037789345, 0.021801166236400604, -0.08822444826364517, 0.002051060553640127, -0.026469947770237923, -0.01999284140765667, 0.011243472807109356, 0.001669892924837768, -0.02428574673831463, 0.03941163793206215, 0.0016224711434915662, 0.03942222148180008, -0.05062223970890045, -0.0011205208720639348, -0.016668297350406647, -0.03233170509338379, 0.04178265854716301, -0.01200274471193552, -0.0006862061563879251, 0.019875304773449898, 0.013767163269221783, 0.03261279687285423, -0.014200138859450817, -0.016595792025327682, -0.012692735530436039, 0.08736897259950638, 0.03240601718425751, 0.003632605541497469, 0.0008325783419422805, -0.005431320983916521, 0.08102227002382278, 0.016509730368852615, -0.028811246156692505, 0.04702131822705269, 0.040771160274744034, 0.0021426232997328043, 0.009739064611494541, 0.04676777496933937, 0.060934849083423615, -0.03181568905711174, -0.016345445066690445, -0.0018970154924318194, -0.05407557263970375, -0.014566431753337383, 0.06774798780679703, -0.051072001457214355, 0.01859458163380623, 0.0157920029014349, 0.0030197908636182547, 0.05447837710380554, 0.010412784293293953, -0.05103152617812157, 0.033902186900377274, -0.016584977507591248, -0.05050100013613701, -0.0002330144343432039, 0.030209941789507866, 0.0020246775820851326, -0.05019470676779747, -0.05583332106471062, 0.004504116252064705, -0.014228587038815022, -0.002734760520979762, 0.05619163066148758, -0.07524066418409348, -0.016518734395503998, -0.0010703862644731998, 0.010024112649261951, -0.05448630824685097, 0.015887215733528137, -0.07381621748209, 0.02644847333431244, 0.028240256011486053, -0.012579727917909622, 0.023271098732948303, -0.02816406637430191, 0.028786398470401764, 0.09967958927154541, -0.08206155896186829, 0.010675264522433281, 0.026485826820135117, -0.02083076909184456, 0.050853922963142395, -0.025620002299547195, -0.045900195837020874, -0.0031876820139586926, -0.006524195894598961, -0.015197579748928547, 0.000720721494872123, -0.019234387204051018, -0.02555786445736885, -0.042270269244909286, -0.016957223415374756, 0.020983874797821045, -0.002245893469080329, 0.017800625413656235, -0.0503363274037838, -0.034568510949611664, -0.01854494772851467, 0.0074151321314275265, 0.019974995404481888, 0.03546133637428284, 0.030283598229289055, -0.003642168128862977, -0.034320421516895294, 0.018886748701334, 0.00627491157501936, -0.0014916765503585339, 0.033728793263435364, -0.025010067969560623, 0.019454220309853554, 0.024908218532800674, 0.0010938547784462571, -0.06395010650157928, -0.01478631142526865, -0.045867811888456345, 0.009033969603478909, 0.054006628692150116, 0.024148572236299515, -0.03428938239812851, 0.015381951816380024, 0.008649587631225586, -0.04727375879883766, -0.01844959333539009, 0.04033387824892998, -0.06068476662039757, 0.045304059982299805, 0.004701466765254736, 0.06884116679430008, -0.01112737599760294, 0.05561228096485138, -0.018016459420323372, 0.007427615113556385, -0.014645146206021309, -0.04929838329553604, -0.006148796994239092, -0.04570065811276436, -0.003499082988128066, 0.03541421517729759, -0.03188640624284744, 0.04059166461229324, -0.0317707397043705, 0.019702164456248283, 0.006331858690828085, 0.04788167029619217, -0.022520067170262337, 0.0600932277739048, -0.06744229048490524, 0.0021600788459181786, 0.047846972942352295, 0.0191788449883461, -0.03764384984970093, 0.14030146598815918, 0.010112684220075607, 0.026236768811941147, -0.0627606064081192, -0.024032875895500183, -0.03517308831214905, 0.06174369528889656, 0.038068003952503204, -0.027685530483722687, -0.10235936939716339, -0.03464226424694061, 0.005779503844678402, -0.013226722367107868, 0.016995972022414207, 0.0030251406133174896, 0.007132051512598991, 0.02933506853878498, 0.0060407985001802444, -0.031313177198171616, 0.01671532168984413, -0.10555602610111237, 0.061429187655448914, -0.010361813940107822, 0.018373336642980576, -0.010983556509017944, 0.03302238509058952, 0.07651271671056747, 0.049756381660699844, 0.004512073006480932, 0.05513563007116318, -0.035813141614198685, 0.014416537247598171, 0.007531844079494476, -0.05366227775812149, 0.007782739121466875, -0.04447729140520096, -0.0010630980832502246, -0.044065382331609726, -0.05515469238162041, -0.017897266894578934, -0.0012948047369718552, 0.027036229148507118, -0.018919620662927628, 0.0688713788986206, -0.04893983528017998, -0.03147650137543678, -0.07387464493513107, -0.046331267803907394, -0.05633797496557236, -0.01115227397531271, 0.11329801380634308, -0.016001908108592033, -0.03382968530058861, 0.04417342320084572, 0.005616243463009596, 0.0025192939210683107, 0.039550311863422394, -0.007219374179840088, 0.03197097033262253, -0.0504927895963192, -0.04879302158951759, 0.03866683691740036, 0.010015229694545269, 0.007482532411813736, 0.02056414633989334, -0.06410927325487137, -0.045845016837120056, 0.027432208880782127, -0.00695825694128871, -0.04012839123606682, 0.015005310997366905, 0.02868436835706234, -0.009124264121055603, -0.022228244692087173, 0.006505573634058237, -0.041729871183633804, 0.037032272666692734, -0.05473581328988075, 0.04642845690250397, -0.017950771376490593, 0.03756679594516754, -0.009826945140957832, -0.047443270683288574, -0.029836276546120644, 0.04607829824090004, -0.0013262606225907803, -0.026149675250053406, 0.07443077117204666, -0.05723278596997261, 0.04481779411435127, -0.031032411381602287, 0.00027470229542814195, 0.02191608026623726, -0.010650808922946453, 0.00701084453612566, 0.024082543328404427, 0.03613847866654396, 0.001706305076368153, 0.022322997450828552, 0.003922260366380215, 0.010802687145769596, -0.007802839856594801, -0.06328065693378448, -0.009506208822131157, 0.0028942120261490345, 0.06485118716955185, -0.0006774436915293336, -0.005978032015264034, -0.016996823251247406, -0.010783222503960133, -0.015149205923080444, 0.009658392518758774, -0.019000764936208725, -0.015505057759582996, 0.021030373871326447, -0.010889698751270771, 0.02009643241763115, -0.0027570179663598537, 0.03668868541717529, -0.06005200743675232, 0.012975834310054779, -0.006464860402047634, 0.01516858208924532, 0.04644455015659332, 0.06764506548643112, -0.04776565358042717, 0.00300589925609529, 0.018991123884916306, -0.03726884722709656, 0.006779158022254705, -0.038341131061315536, 0.04348163679242134, -0.10483292490243912, 0.008199638687074184, 0.03122551739215851, -0.0329914391040802, -0.01961129531264305, -0.02341223508119583, 0.03192681446671486, -0.002913866890594363, 0.07216011732816696, 0.0215939749032259, -0.018308674916625023, 0.03532329946756363, 0.008987446315586567, -0.011178211309015751, 0.003716853214427829, 0.0004605217545758933, -0.04653673991560936, 0.051015086472034454, 0.014832868240773678, -0.09512700885534286, -0.0004099724756088108, -0.043247874826192856, 0.028370432555675507, -0.034508783370256424, -0.02391226775944233, 0.013693413697183132, -0.018013376742601395, 0.04086444526910782, 0.03654170036315918, -0.03494017571210861, -0.00353383831679821, -0.014592482708394527, -0.014292058534920216, 0.025643005967140198, -0.012153205461800098, 0.02014370635151863, 0.069340780377388, -0.02898668870329857, 0.015827573835849762, 0.06263373792171478, -0.054852552711963654, -0.018322207033634186, -0.00001868017170636449, -0.0022265117149800062, -0.010022440925240517, 0.00127976736985147, -0.028075557202100754, 0.020921647548675537, 0.01675107330083847, -0.033731501549482346, 0.024656441062688828, 0.012684300541877747, 0.025115815922617912, -0.027353620156645775, -0.006314405705779791, 0.021590564399957657, 0.029919184744358063, 0.015570614486932755, 0.09276074916124344, -0.01260295882821083, -0.020228678360581398, -0.046381838619709015, -0.03618224710226059, -0.005579074844717979, 0.06182732805609703, 0.02168377861380577, -0.003468309063464403, -0.04417584091424942, 0.003237539902329445, -0.02540852501988411, 0.028527675196528435, -0.02551431581377983, 0.026022156700491905, 0.005713314283639193, 0.06561511009931564, 0.0256281066685915, -0.03638017922639847, 0.01739376410841942, 0.05447915568947792, 0.021377280354499817, -0.033929552882909775, 0.02702672965824604, 0.006802986841648817, -0.02187122404575348, -0.02188699133694172, 0.04729010909795761, -0.0263502337038517, -0.011581297032535076, 0.03001527488231659, 0.040710918605327606, -0.027533965185284615, 0.006371429655700922, 0.023191895335912704, 0.05957115814089775, -0.004236317239701748, -0.003182868706062436, 0.013043556362390518, 0.0003925227792933583, 0.01055313739925623, 0.07668471336364746, -0.02000858075916767, -0.09235016256570816, 0.003141070017591119, -0.004829969722777605, -0.0009469616343267262, 0.009404181502759457, -0.000292203709250316, 0.023563211783766747, -0.06731414049863815, 0.008439455181360245, -0.02050255611538887, -0.01187859196215868, 0.013682890683412552, -0.03268906846642494, -0.003919674549251795, -0.035243235528469086, -0.0038516416680067778, 0.018385224044322968, -0.0151054123416543, 0.041749171912670135, 0.06018712744116783, -0.008932343684136868, -0.03287344425916672, -0.032050251960754395, -0.04683879762887955, -0.025995392352342606, -0.08478564769029617, -0.037405505776405334, 0.0005882965051569045, 0.0459786094725132, -0.024593375623226166, 0.00436220970004797, -0.05555051192641258, 0.0414692759513855, 0.022007150575518608, 0.04393630474805832, -0.025422263890504837, -0.054294388741254807, -0.026833394542336464, -0.04722394049167633, 0.04707341641187668, 0.025566814467310905, -0.015510207042098045, -0.007525817956775427, -0.011320341378450394, 0.04499145969748497, 0.030873622745275497, -0.059065576642751694, 0.009401884861290455, -0.053566545248031616, -0.010225975885987282, 0.05058801546692848, 0.012006066739559174, -0.05624474212527275, 0.04908037930727005, -0.049362778663635254, -0.0781768336892128, -0.029670419171452522, 0.005774345714598894, 0.03091263584792614, 0.020292852073907852, 0.03090798854827881, -0.07280899584293365, 0.013415899127721786, -0.0001407892705174163, 0.009303114376962185, -0.00864169280976057, 0.004931717645376921, 0.06467360258102417, 0.09473420679569244, -0.01665257103741169, 0.008048785850405693, -0.00331099983304739, -0.03890009596943855, -0.01107405498623848, 0.01523648016154766, -0.03586253896355629, -0.07838373631238937, -0.07857301086187363, 0.03638692572712898, -0.043354250490665436, 0.003087766468524933, 0.02551722154021263, -0.01438662875443697, 0.009694195352494717, 0.02808721922338009, -0.03007570281624794, -0.0010200970573350787, -0.053888365626335144, -0.025420939549803734, 0.007593841291964054, -0.10733047127723694, 0.00017711843247525394, 0.02608967386186123, -0.014271288178861141, -0.06769995391368866, -0.04095068946480751, -0.02089129015803337, -0.004507892765104771, 0.044314946979284286, -0.0757555440068245, 0.05225050821900368, -0.01148331630975008, -0.0466916449368, -0.01231024693697691, -0.04030049592256546, 0.006978753954172134, 0.018635479733347893, 0.016179991886019707, -0.029043320566415787, 0.005740076769143343, -0.0008288174867630005, 0.004368919879198074, 0.03881562873721123, -0.006517293397337198, -0.010497363284230232, 0.03499438241124153, 0.029399113729596138, 0.02427292987704277, -0.018023747950792313, 0.0036064705345779657, -0.00028259135433472693 ]
<p>Folks, I have a naive question regarding the subject of dark energy and an accelerating universe:</p> <p>From what I understand/read, it seems that the further we look out into deep space, the faster the objects are moving away from us - in all directions. </p> <p>Is this basically what is meant by "accelerating universe"?</p> <p>Because it seems that this situation is exactly what we should expect to see (according to Big Bang theory). The further out we peer into space, the further back in time we are "seeing", so wouldn't we expect to see higher rates of acceleration/expansion the further back in time we peer?</p>
g336
[ 0.047015994787216187, 0.08646269887685776, 0.019093628972768784, -0.012912257574498653, -0.014402734115719795, 0.015154416672885418, 0.0008326153620146215, 0.04384457319974899, -0.060069795697927475, -0.07394155859947205, 0.09062132984399796, 0.06775254756212234, 0.03033534251153469, -0.0013127622660249472, 0.027301179245114326, -0.04152892157435417, 0.013960421085357666, -0.026425860822200775, -0.006135918200016022, -0.045605894178152084, -0.03133561834692955, -0.021309705451130867, -0.0018224162049591541, -0.03634866327047348, -0.022770319133996964, -0.019622966647148132, 0.01614372991025448, -0.052194032818078995, 0.02364104799926281, 0.013308409601449966, 0.060775287449359894, -0.006056597921997309, 0.014959556981921196, -0.004644639790058136, 0.027871297672390938, -0.010098290629684925, 0.023865360766649246, 0.007731718011200428, 0.04846187308430672, -0.05379627272486687, -0.02152234874665737, -0.002735183108597994, -0.020525207743048668, 0.0038735712878406048, 0.06007891893386841, 0.031473979353904724, -0.055319178849458694, -0.012931017205119133, 0.05072185769677162, -0.07057004421949387, -0.02543923445045948, 0.006479200441390276, 0.009469669312238693, 0.031189993023872375, -0.020010927692055702, 0.006961481645703316, -0.03170613572001457, -0.05210218206048012, 0.08283673226833344, 0.03316708281636238, -0.02341480180621147, 0.009892384521663189, 0.06859350204467773, 0.004156255163252354, 0.05951116234064102, 0.024505887180566788, -0.016739776358008385, 0.01723429001867771, 0.03976782411336899, -0.001620891853235662, 0.035591766238212585, -0.021373003721237183, -0.0717460960149765, -0.04978588595986366, 0.0028175648767501116, -0.011870729736983776, 0.027672963216900826, -0.05725526064634323, -0.0025823968462646008, -0.000460679002571851, -0.04805900901556015, -0.025110658258199692, -0.029610585421323776, 0.009408234618604183, 0.012993746437132359, -0.0023170383647084236, 0.0002037014637608081, 0.07744105905294418, 0.010488225147128105, 0.027411077171564102, 0.04466377943754196, 0.0064501771703362465, 0.040438346564769745, 0.01606595143675804, -0.022220613434910774, 0.015850482508540154, -0.04006899893283844, 0.08697246015071869, -0.0213692057877779, -0.021222911775112152, -0.07113991677761078, 0.024801697582006454, 0.058143239468336105, 0.011049174703657627, 0.024030540138483047, -0.04162491112947464, -0.0026424797251820564, -0.04541773349046707, 0.02030208893120289, -0.01337988767772913, -0.031183095648884773, -0.050329793244600296, 0.006362076383084059, -0.03857870399951935, -0.0399063304066658, -0.014785222709178925, 0.0394759327173233, 0.03708696737885475, -0.008193649351596832, 0.04312882944941521, 0.024042537435889244, 0.06220884993672371, -0.016506459563970566, 0.020176220685243607, -0.015919964760541916, -0.028409667313098907, -0.04517025873064995, -0.044523488730192184, 0.004802762530744076, 0.015533700585365295, 0.018980901688337326, 0.009961755946278572, 0.01768568903207779, 0.036930449306964874, -0.016410963609814644, 0.03227797523140907, -0.04001816362142563, -0.02052403800189495, 0.024491429328918457, 0.05047031119465828, 0.04219925403594971, -0.038708195090293884, 0.013565811328589916, -0.024034466594457626, -0.04192662611603737, 0.014165615662932396, -0.023043852299451828, -0.042808011174201965, 0.01820436120033264, 0.03426719084382057, -0.0019237133674323559, 0.08185482770204544, 0.0006093934061937034, -0.05771055072546005, 0.030452344566583633, 0.04965052753686905, -0.0023992762435227633, 0.01294028852134943, 0.012807488441467285, 0.03253219276666641, 0.02846311591565609, -0.0031738290563225746, -0.0016960864886641502, -0.009494666010141373, -0.06034185737371445, 0.00802616961300373, 0.04545935243368149, -0.06715415418148041, 0.0461307130753994, 0.050031401216983795, -0.03703105449676514, 0.00007047199324006215, 0.04083346948027611, -0.008564790710806847, -0.023558733984827995, 0.03497561067342758, 0.09244273602962494, -0.012707126326858997, -0.10797084122896194, 0.009339177049696445, -0.018144143745303154, -0.06931925565004349, -0.004967642016708851, -0.012369857169687748, 0.05029744654893875, -0.02060549706220627, -0.028964892029762268, 0.016943687573075294, 0.06393995881080627, 0.00327139045111835, 0.06244593858718872, -0.03274748846888542, 0.05222535505890846, 0.027645854279398918, -0.012365446425974369, -0.01200020033866167, -0.0014768914552405477, -0.036912981420755386, -0.038956381380558014, -0.03146294876933098, 0.00933844968676567, 0.025168318301439285, 0.04694482311606407, 0.02126135490834713, 0.04889609292149544, 0.01517554186284542, -0.021769655868411064, 0.029598189517855644, 0.056679677218198776, -0.021508606150746346, 0.03230120614171028, 0.0016155559569597244, -0.000490721722599119, 0.00817999430000782, -0.009031884372234344, 0.02287532389163971, -0.014043393544852734, 0.04356926307082176, 0.04191116243600845, 0.02783050201833248, -0.04714712128043175, -0.05263080820441246, 0.022548912093043327, -0.017938457429409027, 0.0011768410913646221, 0.00894541759043932, -0.023331157863140106, -0.05586926266551018, 0.0037948263343423605, 0.04873159900307655, -0.05634690448641777, 0.043605171144008636, 0.01634061336517334, 0.0015352705959230661, 0.08349164575338364, -0.035559915006160736, -0.03407454490661621, 0.011361812241375446, 0.006865578703582287, 0.030013028532266617, -0.0076834335923194885, -0.07222942262887955, -0.038157057017087936, -0.04213447496294975, 0.07607334107160568, -0.07502401620149612, 0.11142289638519287, -0.03813807666301727, -0.011344713158905506, -0.01784544624388218, 0.056728724390268326, -0.0374908484518528, -0.0020801613572984934, 0.0008532420033589005, 0.011478247120976448, -0.03969605639576912, -0.03542957082390785, 0.07881351560354233, -0.08155462890863419, -0.0697002112865448, 0.049456872045993805, 0.007249671034514904, 0.0009964890778064728, -0.030463987961411476, -0.020115939900279045, 0.0112836342304945, -0.02109772339463234, -0.003150197444483638, -0.03258436918258667, 0.007908322848379612, -0.012812770903110504, 0.0472700260579586, -0.028372496366500854, -0.043480489403009415, 0.03766145184636116, 0.048381876200437546, -0.004583169240504503, -0.048038460314273834, 0.03638994321227074, -0.01678348332643509, -0.04257762059569359, 0.0004279518034309149, -0.07089202851057053, -0.019989043474197388, 0.022709831595420837, -0.03768699988722801, -0.013515266589820385, -0.057599034160375595, 0.017388494685292244, -0.010509781539440155, 0.014568180777132511, -0.003767079673707485, 0.019533352926373482, 0.062224168330430984, 0.008214871399104595, 0.028814008459448814, -0.00007784004264976829, -0.0011345160892233253, -0.0012080854503437877, -0.030060647055506706, -0.0354214683175087, -0.08413650095462799, -0.0017665618797764182, -0.0164607185870409, -0.018314018845558167, 0.026735445484519005, -0.034782774746418, -0.010944856330752373, -0.0571579784154892, -0.04024370387196541, -0.012233306653797626, -0.03357730060815811, -0.018850766122341156, 0.04106554016470909, 0.01744779944419861, -0.004407912492752075, -0.0017997329123318195, 0.027259407564997673, 0.03125418722629547, -0.01624477654695511, 0.025133894756436348, -0.011600663885474205, -0.013601290993392467, 0.015987852588295937, 0.04937175661325455, 0.006044848822057247, -0.008031065575778484, -0.028022047132253647, -0.043888237327337265, 0.009942090138792992, 0.03804376721382141, -0.020217066630721092, -0.000386259809602052, 0.024127408862113953, -0.07355810701847076, 0.04499925300478935, -0.008886360563337803, 0.049221280962228775, 0.07605846226215363, 0.04097530245780945, 0.0007930469000712037, 0.0078025865368545055, -0.01882275752723217, 0.046164583414793015, 0.0163460411131382, 0.04749591276049614, 0.020976079627871513, -0.01247722189873457, -0.024196423590183258, -0.022334039211273193, 0.03976389020681381, -0.004873769357800484, 0.009357573464512825, -0.019665973260998726, -0.020288806408643723, -0.006493871100246906, -0.002245873212814331, 0.005116430576890707, 0.023832423612475395, -0.038933731615543365, 0.002854346064850688, 0.01569625549018383, 0.00864442065358162, 0.00434108218178153, -0.03711974620819092, -0.03384092450141907, -0.02682354860007763, -0.020357470959424973, -0.0027472209185361862, -0.03158189356327057, -0.012155388481914997, -0.026354659348726273, -0.03590726479887962, 0.037279170006513596, 0.020229700952768326, -0.05577928200364113, 0.04355444014072418, 0.02001051791012287, -0.009554781019687653, -0.007632814347743988, 0.04871247336268425, 0.0690859854221344, -0.004980647470802069, 0.06810074299573898, -0.005326488986611366, 0.037016574293375015, -0.045320022851228714, -0.06911887973546982, 0.017816517502069473, -0.014363712631165981, 0.07307755202054977, 0.0214247889816761, -0.0067612044513225555, -0.01869894377887249, 0.03725919499993324, -0.05279325321316719, 0.016286620870232582, 0.025159670040011406, 0.00790870189666748, 0.009157223626971245, -0.015658147633075714, -0.011558790691196918, 0.020859135314822197, 0.021376682445406914, -0.00019577569037210196, -0.013095312751829624, 0.03185677528381348, 0.005587488412857056, -0.03397618606686592, -0.023456500843167305, 0.013129610568284988, -0.018069911748170853, -0.06049599125981331, -0.03217197582125664, 0.018876628950238228, -0.005548006854951382, 0.06265077739953995, -0.06470008939504623, 0.002448089886456728, 0.013329016044735909, 0.024035178124904633, 0.013762593269348145, 0.0026746143121272326, -0.008631814271211624, -0.04982763156294823, 0.12673160433769226, -0.006299649830907583, -0.007718191482126713, -0.0725104883313179, 0.017642825841903687, 0.018505780026316643, 0.014159620739519596, 0.004907635971903801, 0.054332029074430466, -0.03954558074474335, 0.027635131031274796, 0.03085671365261078, 0.06700824201107025, 0.027232153341174126, -0.005307267419993877, 0.05236954987049103, 0.019628537818789482, 0.06574136763811111, 0.014366500079631805, 0.013402426615357399, 0.07728872448205948, -0.04425043240189552, -0.031905435025691986, -0.020223988220095634, 0.0021353831980377436, -0.028814760968089104, 0.08166812360286713, -0.000641843129415065, -0.02126528136432171, 0.01804262213408947, 0.008013907819986343, -0.02028283290565014, -0.01735096238553524, -0.0031092651188373566, 0.01030941866338253, -0.06679777055978775, 0.0607641339302063, -0.014978066086769104, -0.01611318066716194, 0.017302153632044792, -0.033766988664865494, 0.003252844326198101, -0.03419424593448639, -0.0772182047367096, 0.03360036388039589, -0.01617325469851494, -0.023885225877165794, -0.03229094296693802, -0.008383234962821007, -0.021285245195031166, 0.012221161276102066, -0.024928223341703415, -0.03287579491734505, -0.018885457888245583, -0.021263141185045242, -0.054477348923683167, -0.004026934504508972, 0.06491103768348694, -0.03577058017253876, -0.04444414749741554, 0.052440788596868515, -0.023216450586915016, -0.01152771431952715, -0.0010231250198557973, -0.004965378437191248, 0.012664137408137321, 0.00009141257760347798, 0.021938716992735863, 0.019089380279183388, -0.05447649955749512, 0.062132906168699265, 0.05065244063735008, -0.019386447966098785, -0.014317787252366543, -0.011345251463353634, -0.011309295892715454, -0.009297079406678677, -0.004395920783281326, -0.06904008239507675, -0.012596221640706062, 0.08575668931007385, 0.05021459609270096, -0.05702212080359459, 0.032549187541007996, 0.01068041194230318, 0.007851816713809967, 0.027348460629582405, 0.014728656969964504, 0.03086092881858349, 0.030058739706873894, -0.10973900556564331, -0.003350574290379882, 0.023575274273753166, 0.02729058638215065, -0.00983367022126913, -0.0009962539188563824, 0.018794171512126923, 0.031436074525117874, 0.025607634335756302, 0.0963955968618393, 0.053544823080301285, 0.01980942115187645, 0.04939134046435356, -0.012270576320588589, 0.021659858524799347, 0.03244255855679512, -0.01620887964963913, 0.0053574093617498875, -0.05026218667626381, 0.018657345324754715, 0.023378543555736542, -0.02584657445549965, -0.025767195969820023, 0.05619654059410095, -0.009952792897820473, -0.031115010380744934, 0.0002024913701461628, -0.022788304835557938, 0.04567950218915939, -0.02786751464009285, 0.02037157490849495, -0.030843663960695267, 0.004615245386958122, 0.02549906075000763, -0.07900085300207138, -0.017596719786524773, -0.04852323979139328, -0.016837116330862045, 0.020893407985568047, -0.05347191542387009, 0.07230457663536072, 0.043493084609508514, 0.0232993196696043, -0.04281749948859215, -0.07226276397705078, 0.016382688656449318, -0.010333736427128315, 0.020457610487937927, -0.036097969859838486, 0.00950653851032257, -0.04203101620078087, 0.03195369243621826, -0.04887302964925766, 0.053161486983299255, -0.04436727240681648, 0.03503936529159546, -0.001386179937981069, -0.04525455832481384, 0.04913046956062317, 0.0024688036646693945, -0.028934206813573837, -0.0020498100202530622, -0.0351136215031147, -0.06099646911025047, 0.012310885824263096, 0.014504685066640377, -0.008029839023947716, 0.05570979416370392, -0.022193890064954758, 0.039617184549570084, 0.022997410967946053, -0.02101084217429161, 0.015796132385730743, 0.048597224056720734, -0.022737106308341026, -0.0473334975540638, 0.026603642851114273, 0.04417112469673157, -0.017669200897216797, -0.08167169243097305, -0.017435571178793907, 0.00476154824718833, -0.03751538693904877, -0.05995714291930199, -0.017509283497929573, -0.03510751202702522, -0.012300570495426655, 0.04299556463956833, -0.006451422348618507, 0.07087665796279907, -0.017397450283169746, -0.03107580728828907, 0.017619650810956955, 0.05564742907881737, 0.015153482556343079, 0.0231198538094759, 0.004128527827560902, 0.010204482823610306, 0.06434769928455353, 0.010001982562243938, 0.033128611743450165, 0.008781014941632748, -0.03200847655534744, 0.02626892179250717, 0.029859814792871475, 0.04821758344769478, 0.026498394086956978, -0.004420122597366571, 0.03447188436985016, 0.022715222090482712, 0.02445155195891857, -0.07215292751789093, 0.006851287558674812, 0.018069494515657425, 0.06761808693408966, 0.007250412832945585, -0.022179488092660904, -0.05527292937040329, 0.036521896719932556, 0.019494423642754555, -0.014875765889883041, 0.011232483200728893, 0.045774802565574646, -0.023045526817440987, -0.03691698983311653, 0.014821055345237255, -0.004371154122054577, -0.010408221744000912, 0.007190256845206022, -0.02439822629094124, -0.033574752509593964, -0.013140711933374405, 0.028936397284269333, -0.0323750302195549, -0.062299299985170364, -0.0532076396048069, -0.09395821392536163, -0.003870318876579404, -0.04310739412903786, 0.002553339581936598, 0.000014508728781947866, -0.0017296253936365247, -0.03001255728304386, -0.02883864939212799, -0.04055902361869812, 0.033464428037405014, -0.017181504517793655, -0.08627161383628845, 0.004701849538832903, 0.007104570511728525, 0.010147188790142536, 0.007817024365067482, 0.008864374831318855, -0.021725179627537727, -0.008710326626896858, 0.03239927068352699, -0.007003990467637777, -0.07319635152816772, -0.013522363267838955, 0.009628308936953545, -0.013180562295019627, -0.0453418605029583, -0.025929559022188187, 0.008343650959432125, 0.049278318881988525, 0.015162235125899315, 0.03018958680331707, 0.0075749000534415245, 0.050722796469926834, -0.030826620757579803, 0.03771144524216652, -0.03636203333735466, -0.04578367993235588, -0.10724658519029617, -0.0314292348921299, -0.044303588569164276, -0.04019938409328461, 0.013126776553690434, -0.057821162045001984, 0.008979812264442444, 0.04550502449274063, -0.0025515721645206213, 0.058531299233436584, -0.025585725903511047, 0.024016229435801506, -0.04455351456999779, 0.03202193230390549, 0.01578238047659397, 0.0380016453564167, 0.010755855590105057, 0.0031466202344745398, 0.02327742986381054, -0.018475836142897606, -0.030729839578270912, 0.025727739557623863, 0.02855874039232731, -0.006615174002945423, 0.0029722999315708876, -0.003332537831738591, 0.009641620330512524, -0.017407458275556564, -0.011589589528739452, -0.015006612055003643, -0.009578666649758816, -0.022874606773257256, -0.01653357222676277, 0.005616318434476852, 0.012800232507288456, 0.01975783333182335, 0.017633091658353806, 0.022143380716443062, -0.030410228297114372, -0.001058303634636104, 0.013517200015485287, -0.023868972435593605, 0.02178177423775196, 0.015552503056824207, -0.003514649113640189, 0.029640767723321915, -0.04098745062947273, 0.053255051374435425, -0.00894836150109768, -0.0280383862555027, 0.00368245760910213, 0.016739295795559883, -0.0019879101309925318, -0.028374196961522102, -0.010630615055561066, 0.022150665521621704, -0.016655024141073227, -0.022389937192201614, 0.017330029979348183, -0.009507031179964542, 0.03356648236513138, 0.004915473982691765, 0.0536021925508976, -0.02731158584356308, -0.010975668206810951, 0.0178053081035614, 0.011566166765987873, -0.03918481990695, 0.01270852331072092, -0.025701168924570084, -0.1369362622499466, -0.001161050982773304, 0.042785536497831345, -0.008600828237831593, 0.009547453373670578, -0.04340481385588646, 0.04853863641619682, -0.07228484004735947, -0.08338482677936554, -0.014259313233196735 ]
<p>I'm working on a problem with celestial bodies and for my purpose days and AUs are more appropriate units than seconds and meters. So I tried to convert the constant of gravitation, $G$, like this:</p> <p>$$ k= \frac{\frac{\text{AU}^3}{\text{kg}\times \text{D}^2}}{\frac{\text{m}^3}{\text{kg}\times \text{s}^2}}=(\frac{\text{AU}}{\text{m}})^3(\frac{s}{D})^2=\frac{(1.496\times 10^{-11})^3}{(24\times 60\times 60)^2}=4.485\times 10^{-43} $$ $$ G=6.673\times10^{-11}\times k = 6.673\times10^{-11}\times4.485\times 10^{-43}=2.993\times 10^{-53} $$</p> <p>Now I want to do some calculations with this value. First of all, what is the orbital period of a circular orbit around the sun?</p> <p>$$ v_0=\sqrt{\frac{G M_\odot}{r}} $$ $$ t = \frac{2\pi r}{v_0} $$</p> <p>The initial velocity has been adapted so that the centripetal force equals the force of gravitation, so the orbit will be circular.</p> <p>For $r=1$ I expected that the orbital period would be a couple of hundred days, since it takes about 365 days for the earth to circle the sun and one AU is the distance between the sun and the earth. However, when I do the calculation I get that $t=8.14462\times 10^{11}$. What did I do wrong?</p>
g5398
[ 0.03418304771184921, 0.005305255297571421, 0.013804215006530285, -0.05675080046057701, 0.03597087040543556, 0.017834531143307686, 0.04757348448038101, -0.009526546113193035, 0.012529179453849792, 0.026724262163043022, 0.03101690299808979, 0.01785632222890854, 0.027864689007401466, -0.022191960364580154, 0.07730888575315475, -0.023000914603471756, 0.07111956179141998, -0.004155722446739674, 0.013642910867929459, 0.006731587927788496, 0.02448165789246559, -0.03805239126086235, -0.07299257814884186, -0.052493564784526825, 0.000855290680192411, -0.0011153926607221365, 0.03737692907452583, 0.053034041076898575, -0.029116278514266014, 0.025509508326649666, 0.016637347638607025, -0.0006476204143837094, 0.02452867478132248, -0.06130141392350197, 0.007339720614254475, 0.02375529520213604, 0.03028302825987339, 0.007985453121364117, 0.022323761135339737, -0.029505303129553795, 0.02628534659743309, -0.05970587953925133, -0.008866529911756516, 0.055085983127355576, 0.07635603100061417, -0.009934148751199245, -0.04644104093313217, -0.03239130228757858, 0.0075070359744131565, -0.00846512895077467, 0.028309237211942673, 0.07901310175657272, 0.029849233105778694, -0.04100233316421509, -0.020445138216018677, 0.06192374229431152, 0.06383319944143295, -0.04121408984065056, -0.028641702607274055, 0.02546779438853264, 0.018474990501999855, -0.030278533697128296, 0.01756846159696579, -0.02165975235402584, 0.022457709535956383, -0.009934845380485058, 0.029136698693037033, 0.016079677268862724, -0.02566896565258503, 0.023429088294506073, -0.005366670433431864, -0.014313171617686749, 0.026275627315044403, -0.04801522567868233, 0.0012887915363535285, 0.010782470926642418, 0.03977436572313309, 0.02507069520652294, 0.04923763498663902, 0.009405344724655151, -0.011654168367385864, 0.016813574358820915, -0.023177938535809517, -0.021450644358992577, 0.03897564113140106, -0.04715566337108612, -0.028136206790804863, 0.02457127347588539, -0.020977411419153214, -0.023394310846924782, -0.031967248767614365, -0.09066756069660187, 0.020101919770240784, 0.004246702883392572, 0.041349176317453384, -0.03508879616856575, -0.01627441681921482, 0.08937282115221024, 0.01549634151160717, -0.003214469878003001, -0.03485895320773125, 0.027364138513803482, 0.04490511864423752, -0.008350466378033161, -0.010630108416080475, -0.029540834948420525, 0.02028799243271351, 0.0356120727956295, -0.0014857248170301318, -0.0756777971982956, -0.06218862906098366, 0.0034383884631097317, 0.028490368276834488, -0.048773858696222305, -0.05030418559908867, -0.02319609932601452, 0.011606140062212944, -0.027443384751677513, 0.05129566788673401, -0.05267976224422455, -0.02438926510512829, 0.009298727847635746, 0.008133376017212868, 0.053944580256938934, -0.04077455773949623, -0.01894444040954113, 0.01346549578011036, -0.000184375632670708, 0.07348039001226425, 0.010787751525640488, -0.04330270364880562, -0.02122487872838974, -0.04555927962064743, 0.00912866834551096, 0.027323009446263313, 0.012075567618012428, 0.017927752807736397, -0.048161402344703674, -0.049045611172914505, 0.053716812282800674, 0.007597967516630888, -0.06531508266925812, 0.026382386684417725, -0.011437904089689255, -0.04878989979624748, 0.06456833332777023, -0.03370583802461624, -0.02973305992782116, 0.02591325342655182, 0.02353977970778942, 0.025972874835133553, 0.04652101546525955, 0.03328704833984375, -0.008708067238330841, 0.0172673761844635, -0.04337066039443016, -0.007261362858116627, 0.025307750329375267, -0.0029590988997370005, 0.004124609287828207, 0.09293258935213089, -0.015988754108548164, 0.026149168610572815, 0.019090628251433372, -0.04322988912463188, 0.0673585757613182, -0.047825831919908524, -0.04053681716322899, -0.022332342341542244, 0.003140433691442013, -0.03087749518454075, 0.0017143700970336795, -0.026909222826361656, 0.028726723045110703, -0.06613700091838837, 0.028485309332609177, 0.035989418625831604, -0.001912714447826147, -0.018856888636946678, 0.03488218039274216, 0.06215691566467285, -0.027511483058333397, 0.05033567175269127, -0.006009095814079046, -0.05900189280509949, 0.01839274726808071, 0.0244669821113348, -0.01885818876326084, -0.03305310383439064, 0.004993406590074301, -0.006634993944317102, -0.034734878689050674, 0.014820917509496212, 0.04386170580983162, -0.03499886766076088, 0.02191993221640587, 0.004320783074945211, -0.02749909646809101, -0.08207038789987564, 0.04530775174498558, -0.024055100977420807, 0.005280208308249712, 0.02517622336745262, 0.008820760063827038, 0.07282256335020065, 0.008018267340958118, 0.04405853897333145, 0.005984361283481121, 0.02705255337059498, 0.03794039040803909, 0.03230976313352585, 0.010628785006701946, -0.035030871629714966, 0.04669865965843201, -0.05216800048947334, 0.009857885539531708, 0.012994500808417797, 0.0140457171946764, 0.026668362319469452, 0.034311529248952866, -0.005073579028248787, 0.027593379840254784, 0.02831852249801159, -0.05501676723361015, -0.009034987539052963, -0.001278398442082107, 0.007532990537583828, 0.03112160786986351, 0.05085653066635132, 0.006296726409345865, -0.011164954863488674, 0.04066159203648567, -0.04641375690698624, 0.0014270447427406907, 0.05591079965233803, 0.040522169321775436, -0.011917607858777046, -0.02001272514462471, 0.0029593987856060266, 0.039409808814525604, 0.041039928793907166, -0.031135253608226776, -0.016829369589686394, -0.03874140605330467, 0.02547663263976574, -0.036954257637262344, 0.020588912069797516, 0.019673090428113937, -0.01463899202644825, 0.016398310661315918, 0.01600104756653309, 0.028369203209877014, -0.04786405339837074, 0.029063446447253227, 0.023494284600019455, 0.025381820276379585, -0.08183661103248596, 0.018484434112906456, -0.03760724514722824, 0.0066716233268380165, 0.010211052373051643, -0.036386311054229736, 0.03815717622637749, 0.023557282984256744, -0.04034491255879402, -0.05881214886903763, -0.043690040707588196, 0.02891865000128746, 0.02241235226392746, 0.01977113075554371, 0.01834678277373314, 0.029069051146507263, 0.026341306045651436, 0.08280237764120102, -0.008720871061086655, -0.06867018342018127, 0.012674267403781414, -0.03930307924747467, -0.020167730748653412, -0.0036926118191331625, -0.018982045352458954, -0.0006652356241829693, -0.038609933108091354, 0.05763891711831093, 0.022473912686109543, -0.013377801515161991, -0.0366566926240921, 0.08235440403223038, 0.01471670437604189, -0.04461802914738655, 0.010217179544270039, 0.015858614817261696, -0.012440470047295094, 0.048851378262043, 0.034740518778562546, 0.024419492110610008, 0.06605049967765808, -0.02529715746641159, -0.004335511941462755, 0.017788764089345932, 0.017818110063672066, -0.009344115853309631, -0.028021203354001045, 0.05667020007967949, -0.030256830155849457, 0.011124534532427788, -0.009167332202196121, -0.03478258103132248, -0.0510585717856884, -0.01264135167002678, 0.0007374209817498922, -0.0032157329842448235, 0.06756193190813065, -0.011533986777067184, -0.031958650797605515, -0.045654576271772385, -0.04401608183979988, -0.03563617914915085, -0.041460633277893066, 0.026459146291017532, -0.001705378876067698, -0.07218892127275467, -0.004220206756144762, 0.005863817874342203, 0.05252762883901596, 0.07228749245405197, -0.0936751589179039, -0.01633688248693943, 0.017785072326660156, -0.05149296298623085, -0.059521108865737915, 0.012329664081335068, -0.05512050911784172, -0.01379346288740635, -0.023172300308942795, 0.028421441093087196, -0.01166248694062233, 0.02010355331003666, 0.008575847372412682, 0.022591397166252136, -0.04912847280502319, 0.013590154238045216, -0.06206236407160759, 0.014474539086222649, 0.011546485126018524, -0.003122684545814991, 0.009611573070287704, -0.02715625800192356, -0.040500033646821976, 0.00899108499288559, 0.004047025460749865, 0.013779721222817898, 0.006690392270684242, -0.04679960384964943, -0.0509057492017746, 0.055091742426157, -0.02188265137374401, 0.06588738411664963, -0.039098724722862244, 0.008082665503025055, 0.06226992979645729, -0.032696403563022614, -0.021407973021268845, 0.06441383063793182, -0.004571422468870878, 0.002172227017581463, 0.020318828523159027, 0.011409318074584007, 0.043919097632169724, -0.022325189784169197, -0.008815489709377289, -0.017559783533215523, 0.048273272812366486, -0.03318560868501663, 0.10881111025810242, -0.061943601816892624, 0.029742108657956123, -0.043451834470033646, 0.001384939532727003, 0.04247012361884117, -0.0006712359609082341, -0.02221837267279625, -0.0061028762720525265, 0.003952250350266695, 0.02868659421801567, 0.030888894572854042, -0.011190714314579964, -0.045373376458883286, 0.020388107746839523, -0.08518638461828232, 0.04837373271584511, -0.0580231137573719, -0.005394705105572939, -0.02956179529428482, 0.04751662537455559, -0.016017569229006767, 0.0591832771897316, 0.035983260720968246, -0.022145841270685196, -0.005353344604372978, -0.008160892874002457, 0.01613231934607029, -0.004634913522750139, -0.004552990198135376, -0.06560186296701431, 0.04986456036567688, -0.016945386305451393, -0.0019899962935596704, -0.02793828397989273, 0.023542754352092743, -0.022283311933279037, 0.024538574740290642, 0.03555607795715332, -0.04673430696129799, 0.04998147487640381, 0.050856415182352066, 0.004713755566626787, 0.005222128704190254, -0.030355429276823997, -0.044169388711452484, -0.010176774114370346, 0.07849013805389404, 0.0068626790307462215, -0.03190765902400017, -0.004104682710021734, 0.03185868263244629, 0.03737263381481171, -0.02650607004761696, 0.04894673079252243, 0.008223003707826138, 0.06876581907272339, -0.0009490168304182589, -0.003258457174524665, -0.011020133271813393, -0.02871832624077797, 0.05550992116332054, 0.009180866181850433, 0.010027645155787468, 0.027826465666294098, -0.005384504329413176, 0.005353390704840422, 0.046210579574108124, -0.008540044538676739, 0.006388854701071978, -0.009457348845899105, 0.02319723553955555, -0.027289696037769318, -0.060213636606931686, 0.020784951746463776, -0.011420376598834991, -0.03851189464330673, -0.0007202048436738551, -0.010544057935476303, 0.023646747693419456, -0.01181825716048479, -0.024075724184513092, -0.02445903606712818, 0.01540975272655487, -0.03397320955991745, 0.053837403655052185, -0.11031836271286011, -0.01840294525027275, -0.0008039095555432141, 0.00789154414087534, 0.03266676887869835, -0.009228297509253025, -0.0090637831017375, 0.051123667508363724, 0.0015601268969476223, -0.01778583601117134, -0.01254318282008171, -0.004241884686052799, -0.004291168414056301, -0.041481297463178635, -0.030693015083670616, 0.016169307753443718, -0.0071538337506353855, 0.004679363686591387, 0.11223708838224411, 0.004760912619531155, 0.010628034360706806, -0.004057141486555338, -0.016319477930665016, 0.041896551847457886, 0.012414582073688507, 0.03588368743658066, 0.021396638825535774, -0.023056313395500183, 0.011777100153267384, 0.012278291396796703, -0.024551628157496452, -0.024187061935663223, 0.03703037276864052, -0.06623341888189316, 0.033633504062891006, 0.04015899449586868, 0.00048170264926739037, 0.0030397744849324226, 0.034782424569129944, -0.03015393391251564, -0.04113634675741196, 0.013414714485406876, -0.044498369097709656, 0.029679590836167336, 0.03753102943301201, 0.052570682018995285, 0.05822531878948212, 0.004969033412635326, 0.004012268502265215, 0.0775945708155632, 0.017813676968216896, -0.011283034458756447, -0.009933913126587868, -0.011146907694637775, -0.0034488444216549397, -0.031236041337251663, 0.00924233440309763, 0.0033963483292609453, 0.013876823708415031, 0.003849863540381193, 0.028247473761439323, 0.057853832840919495, 0.007286552339792252, -0.009052651934325695, 0.03702222555875778, -0.025112209841609, -0.0584867037832737, -0.028255591168999672, 0.049724988639354706, -0.03461907058954239, -0.015911279246211052, -0.031721025705337524, -0.006511753425002098, -0.028326310217380524, -0.019863756373524666, -0.02322765812277794, -0.018849322572350502, 0.007001717574894428, 0.07340994477272034, -0.10363899916410446, -0.025690991431474686, -0.01081477478146553, -0.0017772145802155137, 0.004975756164640188, -0.08164070546627045, 0.038485392928123474, -0.04305078834295273, 0.008905027061700821, 0.025378135964274406, 0.005661348812282085, -0.02595636621117592, 0.03745533153414726, 0.009420985355973244, -0.0606641061604023, -0.030439190566539764, 0.03583047538995743, -0.00010982198000419885, 0.007962112314999104, 0.00014976866077631712, -0.015281877480447292, 0.07684566080570221, 0.014062645845115185, 0.030151592567563057, 0.037612441927194595, -0.0010360246524214745, -0.027118200436234474, 0.011987807229161263, -0.020865267142653465, 0.048689957708120346, -0.010375740006566048, -0.001038672518916428, 0.021655187010765076, -0.02758179046213627, 0.020083066076040268, -0.019411535933613777, -0.008981714025139809, -0.006010258570313454, -0.04211501032114029, -0.03785960003733635, -0.03527206555008888, 0.004225198179483414, -0.005775631871074438, -0.012172358110547066, -0.025627247989177704, -0.059196144342422485, 0.059726882725954056, -0.01352828647941351, -0.04035600274801254, -0.03916853666305542, -0.049908172339200974, -0.03729381412267685, -0.008106017485260963, -0.06210051104426384, 0.004665161482989788, 0.01955603063106537, -0.02098081074655056, -0.01871243119239807, 0.00533645786345005, 0.047952279448509216, 0.02564241737127304, 0.054741811007261276, 0.016756143420934677, 0.037928640842437744, 0.002855214523151517, 0.045962318778038025, -0.0037005168851464987, -0.056206006556749344, 0.03876793757081032, 0.04453372582793236, -0.00014976107922848314, 0.06826514005661011, 0.01741134561598301, 0.00024275819305330515, 0.04099380970001221, -0.02208411879837513, -0.005084270145744085, 0.05352828651666641, 0.035868722945451736, -0.0034788826014846563, -0.03310004249215126, 0.013935196213424206, 0.05930345132946968, 0.05418216437101364, -0.007609937340021133, -0.00794016383588314, 0.07419412583112717, -0.06535545736551285, 0.030678488314151764, 0.00826838705688715, -0.0781671330332756, 0.012418868020176888, 0.0007265437743626535, -0.05638211593031883, -0.0017691311659291387, 0.02924593724310398, 0.017430225387215614, -0.054999470710754395, 0.059461839497089386, -0.02175251767039299, 0.0640515461564064, -0.0009742969996295869, -0.037161655724048615, -0.0030268768314272165, -0.004806319251656532, -0.06260401010513306, -0.020747849717736244, 0.00935742724686861, 0.022608380764722824, -0.014719998463988304, 0.028015537187457085, 0.0242728590965271, -0.05081584304571152, 0.015924815088510513, 0.027211785316467285, 0.05786946415901184, 0.01995648443698883, 0.0004041010688524693, 0.0001581102260388434, 0.027031010016798973, -0.05217311531305313, 0.029738646000623703, -0.013513384386897087, -0.008142434991896152, 0.05642709881067276, -0.02245781384408474, 0.007126945536583662, -0.023151881992816925, -0.05561789125204086, 0.03609991818666458, -0.11169061809778214, -0.027843762189149857, 0.038767095655202866, 0.011037968099117279, 0.017739180475473404, 0.031896695494651794, 0.07146372646093369, -0.01892641931772232, -0.039347898215055466, -0.0380580872297287, -0.0003038193972315639, -0.05209009721875191, 0.02708742953836918, -0.03438624367117882, 0.006451008375734091, -0.008175746537744999, 0.00022499945771414787, -0.001650526886805892, -0.02356499806046486, 0.04623615741729736, 0.032381586730480194, -0.00037453093682415783, 0.07779332250356674, 0.005253705196082592, -0.01593867875635624, 0.02505757287144661, -0.0749291405081749, -0.0015364820137619972, -0.007313910871744156, 0.07262124866247177, -0.006295898929238319, 0.031080102548003197, -0.04354039579629898, -0.04690127074718475, -0.03601115569472313, -0.006052312441170216, 0.042646151036024094, -0.07244816422462463, -0.007288050372153521, -0.036284189671278, 0.009937706403434277, 0.07847275584936142, -0.03432503342628479, -0.05827944353222847, 0.0033113632816821337, 0.04124276712536812, -0.02548707090318203, -0.029745448380708694, 0.0663055032491684, -0.03025776892900467, -0.06142132356762886, -0.04645848646759987, -0.0988907441496849, -0.01347392424941063, -0.07898817211389542, 0.001646010554395616, -0.010790354572236538, -0.029120327904820442, -0.07797517627477646, 0.03539169579744339, -0.04676990211009979, -0.012775370851159096, -0.03968818113207817, -0.028335776180028915, 0.007428740616887808, -0.007115740329027176, -0.0031329886987805367, -0.026627523824572563, -0.08039634674787521, -0.008966892957687378, 0.009890011511743069, -0.03469640389084816, -0.040344297885894775, -0.002973397960886359, 0.024843992665410042, -0.019467556849122047, -0.041587986052036285, -0.09187162667512894, 0.03450866788625717, 0.010327888652682304, -0.02811817079782486, -0.008696025237441063, 0.04468875750899315, -0.04773096367716789, -0.04081156104803085, -0.007531613111495972, -0.010748092085123062, -0.00552388234063983, -0.0378829687833786, -0.005724072456359863, -0.05618793144822121, -0.021573718637228012, 0.02125895768404007, -0.009871692396700382, 0.023146113380789757, 0.05033491551876068, -0.01539987325668335, -0.005723937414586544, 0.030923495069146156 ]
<p>There's some constant relating to electrons that also has the same value as the speed of light. What is it, what is the value, and how are they related?</p> <p>EDIT: Is it the fine-structure constant?? Are there any other similar constants? If you posted that answer before, you shoulda left it (to the person who deleted their answer)!</p>
g5399
[ 0.05117618665099144, -0.003701603040099144, 0.008165485225617886, -0.008248592726886272, 0.043094683438539505, -0.004305602051317692, 0.03851764649152756, -0.004866895731538534, -0.0011729828547686338, -0.014551457017660141, -0.003800023114308715, 0.05217627063393593, -0.010906200855970383, 0.00514390179887414, 0.011076468043029308, -0.02187260054051876, 0.06769315898418427, -0.01783442124724388, 0.01811811327934265, -0.006622818764299154, 0.010121986269950867, -0.027020737528800964, -0.0034580628853291273, -0.06664484739303589, 0.0507107637822628, 0.02469990961253643, -0.0004862832429353148, -0.0398537814617157, 0.016143372282385826, -0.017395224422216415, 0.05636128410696983, -0.055493079125881195, 0.05653705820441246, -0.03835007920861244, 0.025960087776184082, -0.036919932812452316, -0.02541038766503334, 0.004065359011292458, 0.045864272862672806, 0.014391831122338772, 0.004665077198296785, 0.006763802841305733, -0.0619366429746151, 0.04087075591087341, 0.05096285417675972, -0.01354486495256424, -0.018727118149399757, -0.021492974832654, -0.006524757016450167, 0.0011938216630369425, 0.0450604110956192, 0.07226404547691345, 0.0063933380879461765, -0.03438737615942955, 0.0766507089138031, -0.017924807965755463, 0.03684623911976814, -0.004140513949096203, 0.031037410721182823, 0.11102843284606934, 0.021617930382490158, -0.007002329453825951, 0.028232907876372337, -0.024856282398104668, 0.1064552292227745, 0.011230184696614742, 0.032365210354328156, -0.010380242019891739, -0.040115971118211746, 0.02897089719772339, -0.01316155306994915, -0.04715915769338608, -0.05159362405538559, -0.08460068702697754, 0.01279506366699934, -0.014807715080678463, 0.06996876746416092, -0.004494063090533018, 0.030701206997036934, -0.004202382639050484, -0.012628784403204918, -0.022065743803977966, 0.020922906696796417, 0.041003212332725525, -0.03178821876645088, -0.04891911894083023, -0.027348283678293228, 0.03728490322828293, -0.04567163437604904, -0.022751426324248314, 0.0248899906873703, -0.07342901825904846, 0.0037325930316001177, -0.027611318975687027, 0.01182966586202383, -0.002730840817093849, -0.0005748956464231014, 0.08041559159755707, -0.009854909032583237, 0.014644746668636799, -0.010451077483594418, -0.019089989364147186, 0.03443264216184616, 0.038672566413879395, 0.001257182564586401, -0.03874950483441353, -0.007001853082329035, -0.002204662188887596, 0.025470277294516563, -0.00247220229357481, -0.00825458113104105, -0.03529275208711624, -0.012295503169298172, -0.06772767752408981, -0.09403588622808456, -0.07843825966119766, 0.0838313177227974, -0.03175164386630058, -0.017171040177345276, 0.001824491424486041, 0.02031221240758896, -0.006780473981052637, 0.025956643745303154, 0.047406427562236786, -0.00875153485685587, 0.010710428468883038, 0.05171481892466545, -0.03555568307638168, -0.025257056578993797, -0.014663241803646088, 0.02290508523583412, -0.03496377542614937, -0.045900341123342514, 0.0549667663872242, -0.040885958820581436, 0.05426537245512009, -0.015895308926701546, 0.0012196109164506197, -0.00856383889913559, 0.023582372814416885, -0.059561580419540405, -0.028966594487428665, 0.033108361065387726, -0.02387910522520542, -0.037327349185943604, 0.011203795671463013, -0.0360037125647068, -0.018458224833011627, 0.03266496956348419, 0.04770958796143532, 0.039544153958559036, 0.05733558535575867, -0.022435635328292847, -0.06298601627349854, -0.031430914998054504, -0.04887685924768448, 0.07061861455440521, -0.0014865425182506442, 0.00875184591859579, 0.08064096421003342, 0.003956819884479046, -0.0012603700160980225, -0.032011907547712326, 0.02062602899968624, -0.015186157077550888, -0.01074950210750103, 0.049363140016794205, -0.030889103189110756, 0.002932404400780797, -0.023659104481339455, -0.006228368263691664, -0.024855591356754303, 0.026124006137251854, 0.012447361834347248, 0.046520914882421494, -0.03799121081829071, 0.015948563814163208, -0.01889406144618988, -0.013704918324947357, -0.025578875094652176, -0.01978006400167942, 0.022621238604187965, 0.04466526210308075, -0.01595289260149002, -0.05466960370540619, 0.028960322961211205, -0.025250637903809547, -0.04440437629818916, -0.06023760512471199, 0.007305653300136328, 0.004314860329031944, -0.041723232716321945, -0.03192558139562607, 0.06425181776285172, -0.02715251035988331, -0.045278746634721756, -0.07481064647436142, -0.040036432445049286, -0.029204420745372772, -0.030958332121372223, -0.02617807127535343, 0.058845680207014084, 0.003267798339948058, -0.018123311921954155, 0.048497043550014496, 0.05259878560900688, -0.019491197541356087, -0.0058859409764409065, 0.03040105663239956, 0.06745212525129318, 0.026202356442809105, 0.0038262205198407173, 0.00619072699919343, 0.04605080187320709, 0.000804476032499224, -0.05638596788048744, 0.0036886571906507015, 0.004579842556267977, 0.0007482101791538298, 0.04031502828001976, -0.007385612931102514, -0.02136298641562462, 0.028263777494430542, -0.05886692926287651, -0.010572172701358795, -0.05576002597808838, -0.020354388281702995, 0.022538835182785988, 0.03709883242845535, 0.019596628844738007, -0.035066548734903336, 0.05345742404460907, -0.07174382358789444, 0.04359310865402222, 0.036732543259859085, 0.05687185376882553, -0.013424928300082684, 0.019864331930875778, -0.04621907323598862, 0.01282937079668045, 0.00577965984120965, 0.016740038990974426, 0.004144857171922922, 0.02125873602926731, -0.01637665368616581, -0.014550497755408287, -0.016340941190719604, -0.05235341563820839, -0.029058288782835007, 0.0062723830342292786, -0.013343362137675285, -0.058348800987005234, -0.023480454459786415, 0.055550262331962585, 0.02862558700144291, -0.05586988106369972, -0.006664150860160589, 0.023051997646689415, -0.053573500365018845, -0.05363214388489723, 0.004916984587907791, 0.02126038260757923, 0.0037825878243893385, -0.03700634464621544, -0.012403076514601707, -0.038643598556518555, 0.038943469524383545, 0.05572226643562317, 0.004225168377161026, 0.0074579836800694466, -0.03119397908449173, 0.003736681304872036, -0.00037750619230791926, -0.01592324674129486, 0.012197954580187798, -0.023196367546916008, 0.035617630928754807, -0.06276778131723404, -0.007923475466668606, -0.053369853645563126, 0.026230348274111748, 0.000056336317356908694, -0.07354320585727692, -0.03137322515249252, 0.026789221912622452, -0.04304657503962517, 0.013675658032298088, 0.0217530969530344, -0.01847747340798378, 0.058554649353027344, -0.018945373594760895, 0.02449154667556286, -0.003313728142529726, 0.03112596459686756, 0.01493930071592331, 0.05944252759218216, 0.14452730119228363, -0.013412855565547943, -0.04553931578993797, 0.03277035802602768, 0.028271442279219627, 0.0031634101178497076, 0.024975236505270004, 0.010783080011606216, 0.012274982407689095, 0.016321884468197823, -0.07750733196735382, -0.03405841812491417, -0.051838625222444534, 0.05837366729974747, -0.00058239686768502, 0.00674683740362525, -0.01759399101138115, 0.05324842408299446, -0.04506547749042511, -0.031219739466905594, -0.0006714636692777276, 0.013338033109903336, 0.009647191502153873, -0.017948128283023834, -0.004520854912698269, -0.024928800761699677, 0.00783563032746315, -0.04747873917222023, -0.011050665751099586, 0.0034024855121970177, 0.005147112999111414, 0.01706499047577381, -0.03235454484820366, -0.015485037118196487, 0.03139941021800041, -0.014053956605494022, -0.020885907113552094, 0.05883565545082092, 0.00106179213616997, -0.012927955947816372, 0.01214240025728941, 0.039357323199510574, 0.050308361649513245, 0.03313137963414192, 0.006275408901274204, 0.03559328615665436, -0.07152970880270004, 0.03403405100107193, -0.0010097846388816833, -0.038043614476919174, -0.05203261598944664, -0.05280857905745506, 0.00014004392141941935, 0.00809974130243063, 0.05498156324028969, 0.04274160414934158, -0.023386292159557343, -0.03880692645907402, -0.05334339663386345, -0.026913873851299286, -0.03390409052371979, -0.005481758154928684, -0.0003318832896184176, -0.028028903529047966, 0.045839205384254456, -0.03927407041192055, 0.07604753971099854, 0.02291746251285076, -0.049170903861522675, -0.05432276800274849, -0.041378702968358994, 0.06361822038888931, 0.03647826611995697, -0.03174826502799988, -0.03778495639562607, 0.002661292441189289, 0.004988296423107386, 0.06672654300928116, -0.024398405104875565, -0.014820612967014313, -0.031183592975139618, -0.030279630795121193, -0.12036401778459549, 0.028207950294017792, 0.05571167543530464, 0.014262533746659756, 0.0035136903170496225, 0.01153160072863102, 0.03538479283452034, -0.01305757462978363, -0.026785362511873245, -0.011424672789871693, -0.00742611987516284, -0.08084595203399658, 0.01723654381930828, -0.025556525215506554, -0.05289161577820778, 0.030126817524433136, 0.03002099134027958, -0.019290661439299583, 0.028004828840494156, -0.06499367207288742, 0.03448593616485596, 0.03022897243499756, 0.010773919522762299, 0.017526868730783463, 0.032750558108091354, -0.021751292049884796, -0.022939832881093025, 0.01109704002737999, 0.040873970836400986, -0.03173986077308655, 0.049770936369895935, -0.009274611249566078, -0.0680820420384407, 0.05168407782912254, 0.03293979912996292, 0.006042313762009144, -0.02492489106953144, 0.05267170071601868, 0.027910221368074417, -0.014833585359156132, 0.03388397768139839, -0.004436654970049858, -0.002537060994654894, 0.04898595064878464, 0.06613442301750183, -0.02986755408346653, 0.021699870005249977, 0.007720709778368473, 0.05598146840929985, 0.04444398730993271, -0.027314098551869392, -0.04678787291049957, 0.02405647560954094, 0.060732487589120865, 0.03203410655260086, 0.04552007094025612, -0.02626071311533451, 0.06238209828734398, -0.018769092857837677, 0.015429912135004997, -0.01532759703695774, 0.02269427292048931, 0.048844605684280396, 0.0455537810921669, 0.08289401978254318, 0.03931919485330582, -0.013309464789927006, 0.044513411819934845, -0.05091966316103935, 0.0122882891446352, -0.009744745679199696, -0.03111354634165764, -0.012413672171533108, 0.00043116300366818905, -0.02614491991698742, -0.012219739146530628, -0.02050803042948246, -0.032583605498075485, -0.04725620523095131, -0.05973373353481293, 0.038544729351997375, -0.0012357281520962715, -0.028583429753780365, 0.016400782391428947, 0.03443855047225952, -0.035112906247377396, 0.07907282561063766, -0.017025725916028023, -0.06653096526861191, -0.0053951614536345005, -0.07234511524438858, -0.027547908946871758, 0.013030205853283405, -0.036925308406353, -0.003507814835757017, 0.023122288286685944, 0.05515933781862259, 0.017646046355366707, -0.008600246161222458, -0.0010103865060955286, -0.06930413097143173, -0.018061429262161255, -0.02419533021748066, -0.01137581467628479, 0.02138630859553814, -0.05775197967886925, -0.029427777975797653, -0.03335435315966606, -0.02869378589093685, 0.10491758584976196, 0.028102587908506393, -0.061319515109062195, -0.03420848026871681, 0.009673647582530975, 0.03360000252723694, 0.0353090725839138, -0.06799453496932983, -0.008737817406654358, 0.01996094174683094, 0.05860574543476105, 0.033474285155534744, 0.03755047544836998, -0.025117581710219383, 0.024153664708137512, -0.007749967742711306, 0.025933759286999702, -0.017423391342163086, 0.026871779933571815, 0.052340101450681686, 0.002854808233678341, -0.004034990910440683, 0.007729670498520136, 0.008557443507015705, 0.008555665612220764, 0.0014607318444177508, 0.016486814245581627, 0.0006094811251387, 0.046982746571302414, 0.018255485221743584, -0.03984007611870766, 0.02628292143344879, -0.03319857269525528, 0.01776830665767193, 0.061885636299848557, -0.025870900601148605, -0.001364528201520443, 0.007735041901469231, -0.01132948137819767, -0.04781998321413994, 0.03999236971139908, 0.03219261392951012, 0.05810851976275444, 0.03216306120157242, 0.004423799924552441, 0.050342075526714325, -0.05246762931346893, -0.009514661505818367, 0.018075529485940933, -0.015343351289629936, -0.017678067088127136, -0.010688924230635166, 0.036499205976724625, -0.003087166463956237, 0.012422136962413788, -0.02606283687055111, 0.09828762710094452, 0.011854699812829494, -0.01762746274471283, -0.014779203571379185, -0.012429841794073582, -0.029312094673514366, -0.0014584859600290656, -0.0015367313753813505, -0.015564020723104477, 0.004473917186260223, -0.05308115482330322, 0.024376116693019867, 0.04132944345474243, 0.04476870223879814, 0.007075675763189793, -0.029365135356783867, -0.030459679663181305, 0.01335483230650425, 0.03955315425992012, 0.0020565970335155725, 0.01706639677286148, 0.003479349659755826, -0.07499723136425018, 0.023341547697782516, -0.052488792687654495, 0.008178990334272385, 0.013470632955431938, 0.0006634560995735228, -0.018299004063010216, 0.018343593925237656, -0.03832639753818512, 0.009694295935332775, -0.007845327258110046, -0.015809418633580208, -0.03894990682601929, -0.09501887857913971, -0.048855673521757126, 0.07475796341896057, 0.00690833106637001, -0.005517326295375824, -0.02438834309577942, -0.04390862211585045, 0.032220497727394104, -0.026119502261281013, 0.007387722376734018, 0.03808904439210892, -0.034180521965026855, -0.022036081179976463, 0.006344603840261698, -0.09122350811958313, -0.00017315190052613616, 0.011928916908800602, -0.007367128971964121, 0.00474834069609642, -0.02635817974805832, -0.004548072349280119, 0.009580177254974842, 0.02387799695134163, -0.030686547979712486, 0.03941389545798302, 0.003368299687281251, 0.020382961258292198, 0.038126878440380096, -0.029961682856082916, -0.026620030403137207, -0.05038464441895485, 0.029712775722146034, -0.04384388029575348, 0.017483364790678024, 0.007385652977973223, 0.005104629788547754, -0.05024680122733116, -0.04500336945056915, -0.026205185800790787, 0.003980591427534819, -0.04022468626499176, 0.023932665586471558, -0.0178832970559597, -0.020249370485544205, -0.04716034606099129, -0.004667936824262142, 0.02479710429906845, 0.060933470726013184, -0.017304034903645515, 0.023751327767968178, 0.018418477848172188, -0.029259156435728073, -0.005018265917897224, 0.03364906460046768, 0.006455021910369396, 0.026055259630084038, 0.03781632333993912, -0.0003026300691999495, -0.016660749912261963, -0.014556956477463245, 0.013306806795299053, 0.01793641410768032, 0.05682063102722168, 0.006512967403978109, 0.03825260326266289, 0.037125442177057266, -0.033515140414237976, -0.013944382779300213, 0.008077168837189674, -0.0667550191283226, 0.018214672803878784, -0.019947456195950508, 0.04843458905816078, -0.016824597492814064, -0.03134294971823692, 0.06885606050491333, 0.04319051280617714, -0.048850107938051224, 0.002227397868409753, 0.04884616285562515, -0.008830376900732517, -0.012991456314921379, -0.01487808208912611, -0.012450751848518848, 0.02425273507833481, 0.009013312868773937, -0.029248764738440514, 0.03242548555135727, -0.06134527176618576, -0.08841878920793533, 0.014934035018086433, -0.027692798525094986, -0.02194110117852688, -0.04086030647158623, 0.02561205066740513, 0.015127448365092278, -0.0036482135765254498, 0.07961960881948471, -0.04469889774918556, 0.056285690516233444, -0.007163059897720814, -0.06880423426628113, 0.0075202384032309055, 0.027750933542847633, 0.026483897119760513, -0.02590532973408699, -0.03609379008412361, 0.008879178203642368, -0.012290751561522484, -0.044410474598407745, 0.04245581105351448, -0.03396151214838028, 0.0070912037044763565, -0.03411359712481499, 0.007811264600604773, -0.03597875311970711, 0.014900551177561283, -0.04377635195851326, 0.03246794268488884, -0.022236758843064308, -0.00607796385884285, 0.0012411826755851507, -0.027240753173828125, -0.04252198711037636, -0.019793502986431122, 0.019349725916981697, 0.026478590443730354, 0.039085645228624344, -0.013058777898550034, -0.021224437281489372, -0.011921676807105541, -0.0011474016355350614, 0.02127128839492798, -0.006498565431684256, 0.04454266279935837, -0.01750759594142437, 0.04866466671228409, 0.04225536063313484, 0.061733029782772064, 0.009777718223631382, -0.018470313400030136, 0.03525639325380325, -0.015520489774644375, -0.029387328773736954, 0.04254670441150665, -0.01933174952864647, 0.022211896255612373, -0.00295830937102437, -0.00895889662206173, -0.03204486146569252, -0.013691798783838749, 0.03569560870528221, 0.006600738037377596, 0.0440024770796299, -0.04088772088289261, 0.03810613974928856, -0.0509164035320282, 0.010329035110771656, 0.03015330247581005, 0.04778395593166351, -0.0004061235231347382, 0.0363425649702549, 0.003872840665280819, -0.04005172476172447, -0.01373650785535574, 0.05250140279531479, -0.007979663088917732, -0.028042715042829514, -0.031821493059396744, 0.017691416665911674, 0.08072652667760849, -0.06771282851696014, -0.04536077007651329, 0.005379117093980312, -0.0625627413392067, 0.0322246216237545, 0.04203451797366142, -0.03562743589282036, 0.0013063243823125958, -0.011514207348227501, 0.02256174571812153, 0.024455934762954712, -0.06329585611820221, -0.02909502387046814, 0.023015454411506653, 0.06788571178913116, -0.003485355293378234, -0.05031753331422806, -0.06549979746341705, 0.02741595171391964 ]
<p>I've been looking for a long time and I've not had a lot of luck. I've found sources that <strong>use</strong> fermions in 3d Euclidean space but I can't find any that explain the Wick rotation from Minkowski space. </p> <p>This <a href="http://arxiv.org/abs/hep-th/9608174" rel="nofollow">source</a> provides a nice explanation of the Wick rotation procedure for fermions in 4d. However it leaves the odd dimensional case as an open question.</p>
g5400
[ 0.005537215620279312, 0.000052101342589594424, 0.007260048296302557, -0.07623128592967987, -0.022097116336226463, 0.016149066388607025, -0.005980092100799084, 0.07507482171058655, 0.003034929046407342, -0.03833905607461929, -0.016736503690481186, -0.03991777449846268, 0.01668245904147625, -0.005199901759624481, -0.030617402866482735, 0.03586670011281967, 0.009919896721839905, 0.05695510655641556, 0.054585084319114685, 0.021320698782801628, 0.02011318877339363, -0.008271358907222748, 0.007089742925018072, -0.044349078088998795, -0.04862814024090767, -0.016191929578781128, 0.020242169499397278, -0.007160705514252186, -0.04104335233569145, -0.049658436328172684, 0.049638960510492325, -0.010052592493593693, 0.025740085169672966, -0.06678739190101624, -0.007281019352376461, 0.00392988882958889, 0.043404288589954376, 0.003633292391896248, 0.02170991152524948, -0.010718666017055511, -0.05650893226265907, -0.005158385261893272, 0.0028206119313836098, 0.02132507599890232, 0.028069039806723595, 0.016095414757728577, -0.06403008103370667, 0.05460214242339134, -0.048181451857089996, 0.027763908728957176, -0.0395231731235981, -0.010367928072810173, 0.010425047017633915, -0.009881434962153435, 0.021445980295538902, 0.05288435146212578, -0.01172112300992012, -0.02616352029144764, 0.0726848691701889, 0.014450283721089363, -0.036020711064338684, -0.023720473051071167, 0.021334832534193993, -0.0005471560871228576, 0.06547898799180984, 0.03425145149230957, -0.03842684626579285, 0.020638715475797653, 0.04208262637257576, -0.038398902863264084, 0.07392051070928574, -0.01292186975479126, 0.017458882182836533, -0.04752890020608902, 0.009121150709688663, 0.012756134383380413, -0.010144392028450966, -0.042717255651950836, -0.012182778678834438, -0.03775980696082115, -0.03897733613848686, -0.0246463343501091, -0.0083001172170043, -0.014790710993111134, 0.05700267106294632, 0.021102899685502052, 0.05174488574266434, 0.024225909262895584, 0.06699050962924957, -0.02756761573255062, 0.01673221029341221, 0.03182466700673103, 0.02349770814180374, 0.03498612716794014, -0.04359452798962593, -0.0424521341919899, -0.0056223440915346146, 0.051349665969610214, 0.020049428567290306, -0.04004814475774765, -0.016344448551535606, -0.011139881797134876, -0.012446648441255093, -0.004628587979823351, 0.01781344972550869, 0.036612119525671005, 0.02526337094604969, -0.00943401176482439, 0.036245014518499374, 0.01844983920454979, -0.055379193276166916, -0.018931902945041656, 0.007821737788617611, -0.006453169975429773, -0.005689867772161961, 0.024939745664596558, 0.01680045761168003, -0.048111412674188614, 0.04409780353307724, 0.07977733016014099, 0.018077146261930466, 0.026971854269504547, 0.019073909148573875, 0.06089523807168007, -0.031467337161302567, -0.02079385332763195, -0.0024765366688370705, -0.011009173467755318, -0.015420757234096527, 0.031216086819767952, 0.022580774500966072, -0.02340550161898136, 0.024519743397831917, 0.006998633500188589, 0.004533314611762762, 0.013464697636663914, 0.009873057715594769, -0.01515771821141243, -0.005638588685542345, 0.02506670542061329, 0.005685483105480671, -0.060391705483198166, -0.003589045023545623, -0.023334870114922523, 0.014601522125303745, -0.0011861836537718773, 0.045666735619306564, 0.012317083775997162, 0.015592738054692745, 0.06029365584254265, 0.05839364975690842, 0.08297992497682571, 0.008067939430475235, -0.04158685356378555, 0.0222722589969635, 0.010535118170082569, 0.03508676961064339, -0.021762046962976456, 0.002170202089473605, 0.025456402450799942, 0.024993084371089935, -0.006773947272449732, -0.07634337246417999, -0.008729877881705761, -0.043941475450992584, -0.011475649662315845, 0.021816523745656013, -0.06471168994903564, -0.05914972722530365, -0.09129505604505539, -0.10553126037120819, -0.0025571747682988644, 0.045162271708250046, -0.03104705736041069, -0.03506520017981529, 0.034889109432697296, -0.02869134023785591, -0.03611956164240837, 0.01882806047797203, 0.009328547865152359, 0.02770659327507019, -0.0023141836281865835, 0.04825238138437271, 0.028805632144212723, -0.006822510156780481, -0.006396278273314238, -0.044800203293561935, 0.009662087075412273, 0.061201062053442, -0.03306317329406738, 0.03931300342082977, -0.034299336373806, 0.04991324618458748, 0.03766632080078125, -0.01810108684003353, -0.009857235476374626, 0.007396628614515066, -0.0673564150929451, -0.06700823456048965, 0.06273842602968216, -0.07375232875347137, -0.04244178161025047, 0.026205269619822502, 0.008903611451387405, 0.002995458198711276, 0.020822318270802498, -0.020346295088529587, 0.029868366196751595, 0.05155380442738533, 0.013236097060143948, 0.0007350221276283264, 0.020408278331160545, -0.014842045493423939, 0.01477676723152399, -0.014289540238678455, -0.009647435508668423, -0.017425399273633957, 0.009677272289991379, -0.036520496010780334, 0.08211860060691833, -0.02347499504685402, -0.044706009328365326, -0.027948636561632156, -0.004379520658403635, 0.038875874131917953, -0.028484409675002098, -0.010586787946522236, 0.038455747067928314, 0.06820125132799149, 0.03735750913619995, -0.12218029052019119, -0.0006749840686097741, -0.07998161017894745, 0.02998279221355915, 0.001995484111830592, 0.036160197108983994, -0.020543431863188744, 0.040379125624895096, 0.03915179893374443, 0.06490088999271393, 0.013884512707591057, -0.015077268704771996, 0.009293006733059883, -0.005491185933351517, 0.024998314678668976, -0.03294609114527702, 0.07066306471824646, -0.036944154649972916, -0.012064957991242409, -0.005305016878992319, 0.0090180030092597, 0.024012837558984756, -0.02244667522609234, 0.008117695339024067, -0.05741105228662491, -0.010531611740589142, 0.021739816293120384, 0.015715017914772034, -0.10215626657009125, -0.09615367650985718, 0.04902740567922592, 0.017079921439290047, -0.02441929094493389, 0.030510682612657547, 0.03190702572464943, 0.03339819237589836, -0.017639780417084694, 0.030730493366718292, -0.02708599343895912, 0.05231650546193123, -0.07613017410039902, 0.052824947983026505, -0.040272872895002365, -0.005018664989620447, -0.07183820009231567, -0.05832384154200554, 0.0038369677495211363, 0.017421476542949677, -0.03173552453517914, 0.01972845569252968, -0.025885513052344322, 0.06411271542310715, -0.07039408385753632, -0.0017622222658246756, 0.054168134927749634, -0.0036086677573621273, 0.004917441867291927, 0.05839347466826439, -0.0552251823246479, 0.04769335687160492, -0.0006981092737987638, -0.0321648046374321, -0.008618726395070553, -0.003376926062628627, -0.007854272611439228, -0.04518083482980728, -0.0028947594109922647, 0.011742052622139454, 0.0070581259205937386, 0.040649134665727615, 0.009905925951898098, -0.011455215513706207, -0.0026742855552583933, 0.016920655965805054, 0.009179563261568546, -0.016017794609069824, -0.020202364772558212, -0.05738518387079239, -0.014798181131482124, 0.010283812880516052, 0.010570264421403408, -0.004649361129850149, -0.026449237018823624, 0.05065964534878731, -0.06262174993753433, -0.058955926448106766, -0.034356385469436646, 0.024110080674290657, 0.04745526239275932, -0.05655515193939209, -0.03222489729523659, 0.00048372670426033437, -0.017632097005844116, 0.010355237871408463, 0.08554061502218246, 0.020840588957071304, 0.008738795295357704, 0.025528544560074806, -0.009086957201361656, -0.0021574946586042643, -0.013372596353292465, 0.04993036389350891, -0.03276064246892929, -0.009208493866026402, -0.09253864735364914, -0.006807081867009401, -0.07583697885274887, -0.03483515977859497, 0.00625408673658967, -0.06361813098192215, 0.009296667762100697, -0.04588291421532631, -0.03683546185493469, -0.029922207817435265, 0.028214523568749428, 0.016573715955018997, 0.0064871348440647125, -0.010058240033686161, -0.017491335049271584, -0.013398963958024979, 0.003792643779888749, 0.05461536720395088, 0.026102205738425255, 0.009559075348079205, 0.009040210396051407, -0.013690362684428692, -0.023775970563292503, 0.015056140720844269, 0.030010458081960678, -0.00762468297034502, -0.015332939103245735, -0.007252614013850689, -0.019168633967638016, -0.04578154906630516, -0.049168121069669724, 0.023256927728652954, 0.046150341629981995, 0.03154918923974037, 0.00510460464283824, 0.014705008827149868, 0.01000658143311739, -0.04884332790970802, -0.02875864878296852, 0.020095927640795708, -0.0030043432489037514, -0.020555436611175537, 0.03374244272708893, 0.008918200619518757, -0.07029080390930176, -0.028443437069654465, 0.02920876443386078, 0.014195544645190239, 0.03464898467063904, 0.03852744773030281, -0.05005593225359917, 0.03900555148720741, -0.06261951476335526, 0.014895079657435417, -0.0677613765001297, 0.0035357996821403503, 0.039375580847263336, -0.005445647053420544, 0.01333425473421812, -0.04068451747298241, 0.011417580768465996, -0.02987694926559925, 0.07440020889043808, 0.05428532883524895, -0.03424116224050522, -0.025568481534719467, -0.03064263053238392, -0.0010673032375052571, 0.024007491767406464, -0.014400739222764969, -0.03823662921786308, 0.003332811640575528, -0.06422785669565201, -0.0126293720677495, 0.043193377554416656, 0.007397317327558994, 0.007248773705214262, 0.01838483102619648, 0.02185995690524578, -0.04270540550351143, 0.07186165452003479, -0.041794177144765854, 0.02590160444378853, 0.015738224610686302, -0.02356472611427307, -0.01698434352874756, -0.021205449476838112, 0.03895750269293785, 0.007108985912054777, 0.009752415120601654, 0.08034022152423859, 0.07870066165924072, 0.06524539738893509, 0.01118321530520916, -0.010298704728484154, -0.015572345815598965, 0.0252546239644289, 0.0015556741273030639, -0.02222518064081669, 0.040412139147520065, -0.04397333785891533, -0.028903992846608162, -0.01985418237745762, -0.05681385099887848, 0.06401187181472778, 0.018023310229182243, 0.03451069816946983, 0.005729271564632654, 0.0206952765583992, -0.011365916579961777, -0.04758019372820854, 0.02974831871688366, -0.06346385926008224, -0.010777229443192482, -0.03379446268081665, 0.02342216670513153, -0.018555374816060066, -0.006396883632987738, 0.02568608708679676, 0.03400268405675888, 0.059514932334423065, 0.047444865107536316, -0.008175036869943142, -0.012173603288829327, -0.010904115624725819, -0.055574458092451096, -0.08924976736307144, -0.045483775436878204, 0.015674026682972908, -0.024377968162298203, -0.010401025414466858, 0.028688354417681694, -0.03444167226552963, 0.0070555550046265125, -0.03670291602611542, 0.07239770144224167, 0.08137500286102295, 0.0020700269378721714, -0.01271733082830906, -0.008680835366249084, 0.0054773129522800446, 0.05890496447682381, 0.01081976480782032, -0.030417252331972122, -0.011014464311301708, -0.042395491153001785, 0.03895086795091629, -0.04954008758068085, 0.04356923699378967, 0.031168069690465927, 0.030328182503581047, 0.01160335447639227, -0.06481827795505524, 0.002663298277184367, -0.0037092838902026415, -0.024440448731184006, -0.039196815341711044, 0.035899221897125244, -0.017029445618391037, -0.04118385538458824, -0.03404746577143669, 0.05676794797182083, 0.05806320905685425, -0.06704968214035034, -0.024393610656261444, 0.012013166211545467, 0.0004217522800900042, -0.0418136864900589, 0.03986096382141113, 0.016314629465341568, -0.036123886704444885, 0.023321134969592094, 0.0673515796661377, -0.05398155003786087, 0.0003526612126734108, 0.010047448799014091, -0.0004641808627638966, -0.015106244012713432, 0.04662756621837616, 0.008140740916132927, 0.005904009100049734, 0.01237182691693306, -0.007950803264975548, 0.01719861663877964, 0.060787491500377655, -0.02537325955927372, -0.008613303303718567, 0.07992616295814514, -0.03033122979104519, 0.0004944481188431382, 0.0032128943130373955, 0.01878300867974758, -0.0389464795589447, 0.0226557906717062, -0.010993956588208675, 0.022024307399988174, 0.013042643666267395, 0.0067527019418776035, 0.02430633269250393, 0.03055538982152939, 0.0013605025596916676, -0.04521163925528526, 0.02608475461602211, 0.03929128125309944, 0.024029027670621872, 0.024354320019483566, -0.01878873072564602, -0.054141368716955185, -0.024577559903264046, 0.021376261487603188, -0.03918692097067833, -0.07565587759017944, 0.05014241114258766, -0.03150414302945137, 0.06218089535832405, -0.009262915700674057, -0.04220407083630562, 0.03595074266195297, 0.02948905900120735, -0.07440579682588577, -0.01876744255423546, 0.02345496602356434, -0.0482579804956913, -0.03410356491804123, -0.03341462090611458, -0.019612599164247513, -0.028865136206150055, -0.011196128092706203, 0.0031699074897915125, 0.01434884499758482, 0.010679293423891068, 0.03848174959421158, -0.007886737585067749, -0.01011442020535469, 0.0323670357465744, 0.021507319062948227, -0.009400048293173313, 0.01885969378054142, 0.015494399704039097, 0.03165293112397194, 0.05642661079764366, -0.012590923346579075, 0.03900943696498871, 0.03855740278959274, -0.012021886184811592, -0.03573909401893616, 0.00572546012699604, 0.04525407776236534, 0.09699317812919617, -0.04021015763282776, -0.04287837818264961, 0.006854868493974209, 0.02475608140230179, 0.04703725129365921, -0.010243001393973827, -0.014566998928785324, -0.008638666942715645, 0.022239694371819496, -0.024613291025161743, 0.018019456416368484, -0.049943290650844574, 0.02154281549155712, -0.03075745888054371, 0.008514524437487125, -0.007843722589313984, -0.04744239151477814, 0.048029519617557526, 0.010052352212369442, -0.022750210016965866, 0.03622965142130852, 0.01537191029638052, -0.024896778166294098, -0.03237632289528847, 0.018136436119675636, -0.03878798335790634, 0.038843005895614624, 0.03392685577273369, 0.010036980733275414, -0.03940437361598015, 0.03198583051562309, -0.016832251101732254, -0.031236618757247925, 0.03159305825829506, 0.03153185173869133, 0.03569245710968971, -0.030047399923205376, 0.06772718578577042, -0.022234836593270302, 0.018175767734646797, 0.00018741656094789505, 0.04050050675868988, 0.03587270900607109, -0.03364882245659828, -0.059155430644750595, 0.10047326236963272, 0.021579544991254807, 0.032156236469745636, -0.0586218386888504, 0.03881219029426575, 0.0881010890007019, -0.00034694591886363924, -0.0005878511583432555, -0.08895646780729294, 0.06634864956140518, -0.00760261807590723, 0.048915181308984756, -0.04732996225357056, -0.04663622006773949, 0.0009967780206352472, -0.014605334028601646, -0.08282002806663513, 0.01824321411550045, -0.055182043462991714, 0.04542768374085426, -0.0012268139980733395, -0.028503887355327606, -0.009181595407426357, -0.005546592641621828, -0.011422784999012947, -0.00013612775364890695, -0.050783298909664154, -0.018894638866186142, 0.0011144648306071758, 0.032663363963365555, -0.018637394532561302, -0.046842753887176514, -0.0010035280138254166, 0.014776650816202164, -0.016286181285977364, -0.010376961901783943, -0.01314326748251915, 0.008199243806302547, -0.035821087658405304, 0.04549187421798706, 0.04514218494296074, 0.03361226245760918, -0.025956129655241966, 0.01281924918293953, -0.028302377089858055, 0.01762741059064865, -0.009642055258154869, -0.051826316863298416, -0.017159530892968178, 0.027125772088766098, -0.01920393668115139, 0.005248300731182098, -0.05053596943616867, 0.050304535776376724, -0.05499692261219025, 0.006212206091731787, -0.002460523508489132, 0.030447088181972504, 0.013927921652793884, 0.00489030173048377, 0.006225300952792168, 0.003832319052889943, 0.08376438170671463, 0.05112708732485771, -0.03278009220957756, -0.05665021017193794, -0.010121215134859085, 0.01825760118663311, 0.05114154517650604, -0.028675073757767677, -0.0358738973736763, 0.050464507192373276, 0.02013840153813362, -0.06247374042868614, -0.017327383160591125, -0.007199268788099289, 0.040306974202394485, -0.042624812573194504, -0.026279328390955925, -0.02190381847321987, 0.02695484645664692, 0.011581267230212688, 0.051651980727910995, -0.006585702765733004, -0.006249492987990379, 0.022598549723625183, -0.006027508992701769, 0.038485728204250336, -0.009780507534742355, 0.008757933974266052, 0.04527832195162773, 0.017840560525655746, -0.054230496287345886, -0.0027709132991731167, -0.05626785755157471, -0.03164485841989517, -0.0071370042860507965, -0.03556477278470993, -0.01784905605018139, -0.008415267802774906, 0.03257467970252037, 0.03669391945004463, 0.009572603739798069, -0.0064394851215183735, 0.0016765991458669305, 0.019245553761720657, 0.01792161539196968, -0.00044118394725956023, -0.09853304177522659, -0.018518364056944847, 0.03551967814564705, 0.012164131738245487, 0.08893734961748123, -0.022383686155080795, 0.011231460608541965, -0.0752757266163826, -0.014947118237614632, -0.0576816163957119, 0.001226733555085957, 0.019239645451307297, -0.01290877815335989, -0.03776325657963753, -0.03309079259634018, 0.020849883556365967, -0.018084095790982246, 0.0076533048413693905, 0.009863501414656639, -0.03860432654619217, 0.012424001470208168, -0.01686512492597103, 0.005534194875508547, 0.017090508714318275, 0.03923414275050163, -0.01957511343061924, 0.05124165490269661, 0.05068454518914223, 0.01946316473186016, -0.046772826462984085, -0.04023943096399307, 0.006039007101207972 ]
<p>Will a CFL light bulb and an incandescent light bulb, in separate respective closed systems, produce exactly the same amount of overall temperature increase over time?</p> <p>Assume you have two identical closed systems with gray walls, with a system input of 20 watts of power each. </p> <p><strong>EDIT added for clarity: (On the packaging of the CFL light bulb the large print equivalent wattage is irrelevant... the input current of both bulbs is a consistent 20 watts of power each. The comparison wattage vs. the actual wattage of the CFL is off subject.)</strong></p> <p>One has a CFL, one has an ordinary incandescent light bulb. Will both systems increase in heat the exact amount, every hour?</p> <p>Due to conservation of energy it shouldn't matter if one light source is more efficient, right?... it's the same amount of energy input. One light makes more heat one makes more light, but the light when it hits the gray wall is converted to heat, right?</p> <p>There is no such thing as loss of energy... it's just converted to another form of energy... and light is converted to heat, right?</p> <p>The back story of this question is my wondering that if my wife leaves an incandescent light bulb on in the winter time it's not so bad because even though no one is in the room it's still heating up the room. On the other hand if she leaves on a CFL it's more efficient but it should still add heat to our "system," i.e., our home.</p>
g5401
[ 0.0260208398103714, 0.008376860059797764, 0.03690316900610924, -0.03466537967324257, -0.00701891491189599, -0.05941276252269745, -0.0013320422731339931, 0.0029938349034637213, -0.056753598153591156, -0.03358277305960655, 0.007451401092112064, 0.03216248005628586, -0.030790505930781364, -0.01918511837720871, -0.005033633206039667, -0.023139717057347298, 0.026787148788571358, -0.0480879470705986, 0.041902247816324234, 0.04995475709438324, 0.007995800115168095, 0.015001579187810421, 0.037750426679849625, -0.06688378006219864, -0.03566039353609085, -0.005774759687483311, -0.009176223538815975, -0.02657564915716648, -0.07893539220094681, -0.0019332924857735634, 0.007380292285233736, 0.015274174511432648, 0.018993526697158813, -0.03303160145878792, -0.08898795396089554, -0.007441676687449217, 0.06012539193034172, -0.016113411635160446, -0.009003526531159878, -0.024095645174384117, 0.017725903540849686, 0.09357281029224396, 0.019274592399597168, -0.03726194053888321, 0.03161817044019699, -0.024868328124284744, -0.02889656461775303, 0.038249172270298004, -0.04280586913228035, 0.037430498749017715, -0.015848960727453232, -0.008840811438858509, 0.001192871481180191, 0.0479336641728878, 0.05830890312790871, -0.02542577125132084, -0.023354386910796165, -0.05022156611084938, 0.022968687117099762, 0.019602041691541672, 0.028853807598352432, 0.0228126123547554, -0.01961807906627655, -0.04418884590268135, 0.014564196579158306, 0.02279188297688961, 0.07989431917667389, -0.056818731129169464, 0.03599011152982712, 0.005590608809143305, -0.025107719004154205, -0.019577762112021446, -0.03745422139763832, 0.010475742630660534, 0.09241979569196701, 0.02865772321820259, -0.011663523502647877, 0.012253161519765854, 0.0014197280397638679, 0.050653401762247086, -0.06697992235422134, -0.06527994573116302, 0.009671583771705627, 0.03564414009451866, -0.010324956849217415, 0.029799684882164, 0.031833622604608536, -0.01388803031295538, -0.02091902308166027, -0.005091378930956125, 0.009667843580245972, -0.0469859354197979, 0.09233459085226059, 0.023754464462399483, -0.041841186583042145, 0.0007202094420790672, 0.023050015792250633, 0.0010008795652538538, 0.0324929878115654, 0.006452085915952921, -0.024528035894036293, -0.03405885025858879, -0.03345632180571556, 0.004454871639609337, -0.057732246816158295, -0.022399628534913063, -0.0032429853454232216, 0.0018024054588750005, -0.09433940052986145, 0.013369725085794926, -0.04774564877152443, -0.05752437561750412, -0.016632232815027237, -0.010783420875668526, -0.03608164191246033, -0.025529196485877037, 0.031637925654649734, 0.002201731549575925, 0.04174375534057617, 0.01428226288408041, 0.006475938484072685, 0.040714506059885025, -0.007520857732743025, -0.009659037925302982, 0.016010675579309464, -0.0014690544921904802, 0.02733382023870945, 0.003944101743400097, 0.020494356751441956, 0.0018940831068903208, -0.060330864042043686, -0.021342819556593895, -0.004284910392016172, -0.013621523045003414, 0.06794257462024689, 0.02430044300854206, 0.06336111575365067, 0.03796592354774475, 0.012060180306434631, 0.0016252706991508603, -0.0037811556831002235, 0.019021227955818176, 0.0016689378535375, -0.011706823483109474, -0.04012519121170044, 0.04920722544193268, -0.032158274203538895, -0.01862277276813984, 0.021686041727662086, 0.045931894332170486, 0.02231242135167122, 0.04781895503401756, -0.01143905520439148, -0.009233820252120495, -0.011203977279365063, 0.0192501749843359, -0.09169480204582214, -0.018600214272737503, -0.052702128887176514, -0.07889976352453232, 0.009440402500331402, -0.02443693019449711, 0.056775521486997604, -0.07545386254787445, -0.015301624312996864, -0.029554815962910652, -0.019836433231830597, -0.048929594457149506, -0.003530899528414011, -0.06890542060136795, -0.047557052224874496, 0.02393900416791439, -0.013518491759896278, 0.06983093917369843, 0.026917265728116035, -0.009289142675697803, 0.07398729026317596, -0.0007671290077269077, 0.04512288048863411, -0.053424905985593796, -0.01571805775165558, 0.04902904853224754, 0.00988477747887373, -0.03968412056565285, -0.02652812749147415, -0.02582131326198578, -0.020955970510840416, -0.05924282968044281, -0.041537027806043625, 0.06816670298576355, -0.060793399810791016, -0.030145924538373947, 0.02085798792541027, 0.07528618723154068, -0.011087214574217796, 0.014482982456684113, -0.04347233846783638, 0.01627999357879162, -0.06697630137205124, -0.0002977847761940211, -0.03282064571976662, 0.005405154079198837, 0.05913796275854111, -0.012922178953886032, 0.024906042963266373, 0.04335149750113487, -0.0039334069006145, -0.05525243654847145, 0.031328581273555756, -0.064826600253582, 0.0031794102396816015, 0.005663078743964434, -0.010865322314202785, 0.05508503317832947, 0.05804970860481262, -0.019778061658143997, -0.017794685438275337, 0.017933959141373634, -0.012712054885923862, 0.024163832888007164, 0.02396906167268753, 0.08459518104791641, 0.014322903007268906, -0.03159051015973091, -0.04076138883829117, -0.02903672121465206, -0.041762735694646835, 0.0013693630462512374, -0.032381150871515274, 0.04314371198415756, -0.015425643883645535, -0.006836533546447754, 0.015215670689940453, -0.011635275557637215, 0.011747748591005802, 0.009667542763054371, 0.04159143939614296, 0.06539371609687805, 0.05195590853691101, 0.013822096399962902, 0.006352301687002182, 0.00010083894449053332, 0.01431672740727663, 0.0468384250998497, -0.004088891204446554, -0.02834283746778965, 0.07263906300067902, 0.005689308047294617, -0.01267851423472166, 0.031643934547901154, 0.01826413720846176, 0.043473970144987106, -0.0041236961260437965, -0.028079267591238022, -0.05460210517048836, -0.008671373128890991, -0.0010896436870098114, -0.032772134989500046, 0.004188996739685535, 0.02657943405210972, 0.054594736546278, -0.052378006279468536, -0.030918043106794357, 0.043988361954689026, 0.011589361354708672, -0.008426595479249954, 0.050169214606285095, -0.08008182048797607, -0.00854199007153511, 0.0027604438364505768, 0.029590971767902374, 0.04914221167564392, -0.01228378713130951, 0.033740825951099396, -0.003684516530483961, 0.06235708296298981, 0.022451192140579224, -0.00999910943210125, 0.01535035390406847, -0.019951891154050827, 0.030985303223133087, 0.0005695170839317143, -0.08126828819513321, 0.033309005200862885, 0.045229557901620865, -0.08313238620758057, 0.0017633672105148435, 0.0038969318848103285, -0.023952964693307877, 0.06697789579629898, 0.004154952242970467, 0.022974064573645592, 0.05509483814239502, 0.003104652976617217, -0.013862842693924904, -0.0035784130450338125, -0.018057430163025856, -0.013930721208453178, -0.034044552594423294, -0.01022886112332344, -0.007518112193793058, -0.024834519252181053, -0.033222779631614685, 0.02344576269388199, 0.008226757869124413, 0.03952477499842644, -0.095301054418087, -0.06973877549171448, 0.027996135875582695, -0.018116425722837448, -0.03461930528283119, 0.03509685769677162, -0.010217701084911823, 0.043018124997615814, -0.0019404403865337372, -0.022322455421090126, -0.018268007785081863, -0.03216293454170227, 0.020481254905462265, -0.04846832901239395, 0.021959923207759857, 0.023189727216959, -0.019498728215694427, -0.04499996080994606, 0.004095457959920168, -0.032890286296606064, -0.005755617283284664, -0.006916530430316925, -0.04514326527714729, -0.023823197931051254, 0.008368825539946556, 0.03454817458987236, -0.031950004398822784, -0.01960131898522377, 0.011066102422773838, 0.06884294748306274, -0.02334566041827202, -0.006746583618223667, 0.020255446434020996, 0.0583963580429554, 0.0006086751236580312, 0.003803243860602379, -0.03923920914530754, 0.02335016056895256, 0.009854688309133053, 0.03772062808275223, -0.009458104148507118, -0.018805792555212975, -0.0614335723221302, 0.0014783558435738087, 0.0803489238023758, -0.05244068801403046, 0.029540445655584335, 0.031698066741228104, -0.009052402339875698, -0.016856614500284195, -0.041712887585163116, 0.09682148694992065, -0.022778023034334183, 0.0069244927726686, -0.001438939361833036, -0.0351499505341053, 0.04493163526058197, 0.026598164811730385, -0.028303269296884537, -0.01882139779627323, 0.01652318798005581, -0.016460416838526726, 0.01869354397058487, -0.037125930190086365, -0.019913414493203163, 0.08669687807559967, -0.07541923969984055, 0.037161096930503845, 0.028229063376784325, 0.011743569746613503, 0.060668423771858215, 0.012601376511156559, -0.031783174723386765, 0.05791058391332626, -0.02401096373796463, 0.0008282714406959713, -0.007431441452354193, -0.0260480809956789, 0.02905704453587532, -0.004462637472897768, -0.00630239536985755, -0.023092973977327347, 0.007367911748588085, -0.04350060224533081, -0.02120707929134369, -0.011078202165663242, -0.013364586047828197, 0.05341159179806709, 0.015777215361595154, 0.05606260895729065, 0.03772500529885292, 0.007113548927009106, 0.06508849561214447, 0.029783936217427254, -0.001697139348834753, -0.0010871563572436571, 0.004240149632096291, -0.040507394820451736, -0.06562362611293793, -0.03398030251264572, 0.03071155957877636, -0.060010455548763275, -0.024556608870625496, -0.02582424320280552, 0.03418387100100517, 0.010906259529292583, 0.010772241279482841, 0.031794652342796326, -0.009843242354691029, -0.006113677751272917, 0.04017225652933121, -0.029263166710734367, 0.07181589305400848, 0.01979895681142807, 0.0010781128657981753, -0.026466667652130127, -0.021710747852921486, 0.02034030854701996, 0.009021259844303131, 0.045245103538036346, 0.014848114922642708, -0.023808658123016357, -0.038786739110946655, -0.05537424609065056, 0.021250803023576736, 0.03192908316850662, -0.0049947709776461124, -0.021641850471496582, -0.025341253727674484, 0.021575896069407463, 0.03317254036664963, -0.0032069713342934847, 0.0335770808160305, 0.0680471733212471, 0.03870359808206558, -0.007980325259268284, 0.030816227197647095, -0.0015967764193192124, 0.017102746292948723, 0.02195177786052227, -0.03670385479927063, -0.04896395280957222, -0.001953758532181382, -0.07030078023672104, 0.04017387703061104, 0.0357273668050766, -0.02380945347249508, -0.03903552144765854, 0.01194562017917633, 0.014525923877954483, 0.024361202493309975, -0.0037578323390334845, 0.02922736294567585, 0.03237035870552063, -0.021139834076166153, -0.02517169713973999, -0.009601875208318233, 0.012158620171248913, -0.009537596255540848, -0.006580510176718235, -0.027013923972845078, -0.03643852099776268, -0.07425151765346527, -0.006891277618706226, 0.014022436924278736, 0.039744969457387924, -0.00044729741057381034, 0.0274558924138546, 0.044428516179323196, -0.054234184324741364, 0.009137257002294064, -0.02666088566184044, 0.02149406261742115, -0.02277000993490219, -0.02490079402923584, -0.04103618487715721, 0.017297513782978058, 0.040636759251356125, 0.0211953092366457, 0.026752138510346413, -0.056011930108070374, 0.07791931182146072, 0.08773647248744965, -0.019570479169487953, -0.03129996359348297, 0.06649379432201385, 0.036440979689359665, -0.012891920283436775, -0.03367901220917702, 0.010282166302204132, 0.013748044148087502, -0.023952092975378036, -0.045083120465278625, -0.018149694427847862, -0.014826066792011261, 0.027524592354893684, -0.003616601461544633, -0.023531705141067505, -0.020858675241470337, 0.043668631464242935, 0.007385758217424154, -0.07103701680898666, -0.04118163138628006, 0.03739384189248085, -0.04292207956314087, 0.01637183129787445, -0.013138691894710064, 0.020592670887708664, 0.05905766785144806, -0.014718574471771717, -0.04153814911842346, -0.011363938450813293, -0.045477475970983505, -0.02519475668668747, 0.003764399327337742, 0.03236391395330429, -0.023590436205267906, 0.06254232674837112, 0.035859979689121246, 0.021313084289431572, -0.05187344551086426, 0.007531029172241688, 0.03751916438341141, 0.01819983869791031, 0.06914860755205154, 0.08538977056741714, -0.009266097098588943, 0.006443149875849485, -0.0273231640458107, -0.03379035368561745, -0.028493646532297134, 0.03365197032690048, 0.007422246038913727, 0.024703633040189743, 0.024406583979725838, -0.027760479599237442, -0.006034694612026215, 0.05479934811592102, -0.009118788875639439, -0.053165435791015625, -0.01623324304819107, -0.07287327945232391, 0.011899984441697598, 0.016274001449346542, 0.014872984029352665, 0.03671091049909592, 0.0407334566116333, 0.03443711996078491, 0.03519101068377495, 0.028695469722151756, 0.0495903380215168, 0.015482750721275806, 0.06702406704425812, 0.02148105949163437, -0.027985217049717903, 0.016339927911758423, 0.004386783577501774, -0.03589412569999695, 0.03410216048359871, -0.022866778075695038, 0.0004147869476582855, -0.028719834983348846, 0.02244705706834793, 0.06477869302034378, 0.07215099036693573, -0.040858540683984756, 0.02079864963889122, -0.017624108120799065, 0.024720512330532074, -0.02486034668982029, -0.03654734045267105, -0.045597534626722336, -0.005305012688040733, -0.0029065071139484644, -0.016838662326335907, -0.00609053997322917, -0.013136795721948147, 0.05585212633013725, 0.027577940374612808, 0.0505463145673275, -0.040311578661203384, 0.0027199287433177233, 0.05852887034416199, 0.000019675902876770124, 0.021383902058005333, -0.05796171724796295, 0.015986217185854912, 0.03376138582825661, -0.012587247416377068, -0.015446547418832779, -0.07094460725784302, -0.004573962185531855, -0.011441036127507687, -0.005192574579268694, -0.0235806442797184, 0.017195727676153183, 0.052119676023721695, -0.09795106947422028, 0.02170265093445778, 0.06012384966015816, -0.0349847786128521, 0.03974324092268944, 0.02787931263446808, -0.011496624909341335, -0.025633348152041435, 0.009109113365411758, 0.009821227751672268, -0.0254875086247921, -0.003842954058200121, -0.07102609425783157, -0.0693592056632042, -0.0018826475134119391, -0.003987872041761875, 0.012209420092403889, 0.00871427170932293, -0.05114253610372543, -0.03258043900132179, -0.03531580790877342, -0.002968535292893648, 0.08781702071428299, -0.019286904484033585, 0.057054370641708374, 0.03551292419433594, 0.024738701060414314, -0.005539951846003532, -0.004498813766986132, 0.011328593827784061, 0.004795989952981472, -0.011317980475723743, 0.008569012396037579, -0.01440203096717596, -0.011185606010258198, -0.013650474138557911, -0.028417538851499557, -0.026306336745619774, 0.06085778772830963, -0.021418394520878792, 0.0687679648399353, -0.007249032612890005, 0.014805645681917667, 0.07021482288837433, -0.06817365437746048, -0.0308513343334198, 0.03030330315232277, -0.0373934768140316, -0.07263897359371185, -0.027965638786554337, 0.00792577862739563, -0.0015934491530060768, 0.025423288345336914, -0.026028050109744072, 0.023283567279577255, -0.03887958824634552, -0.01161787286400795, 0.03963359817862511, -0.00942301657050848, -0.005549578461796045, 0.07539837062358856, 0.01719372533261776, 0.014913984574377537, 0.007838666439056396, -0.0203115064650774, 0.03845531493425369, -0.009065288119018078, 0.029104508459568024, -0.06673111766576767, -0.03088965453207493, -0.022665034979581833, 0.027973180636763573, -0.002964402548968792, -0.06332193315029144, 0.03334026038646698, 0.008943519555032253, -0.08206818997859955, -0.005996717605739832, -0.07201781868934631, -0.056009043008089066, -0.06442313641309738, 0.0475052073597908, 0.01146636251360178, -0.05268954113125801, -0.017775025218725204, 0.010652972385287285, -0.01486461516469717, -0.03777790069580078, 0.002111757406964898, -0.020661190152168274, 0.0501527413725853, 0.0006335136131383479, 0.05538177862763405, 0.021222341805696487, -0.03271452337503433, 0.03712819516658783, 0.013644921593368053, 0.014613914303481579, -0.0006021446897648275, -0.01725519821047783, -0.022649170830845833, -0.01979077234864235, 0.04483245313167572, -0.04754720628261566, 0.015895836055278778, -0.00921884085983038, -0.010618571192026138, 0.06770829111337662, 0.010930772870779037, 0.0482245609164238, 0.00004128739965381101, 0.011073078028857708, -0.03864915668964386, -0.02084587700664997, -0.05221446976065636, 0.02018100395798683, 0.006956000812351704, -0.05187147110700607, 0.011107594706118107, -0.0399429053068161, -0.036055367439985275, 0.006494621280580759, -0.00033120907028205693, 0.032091204077005386, -0.017037570476531982, -0.023654675111174583, -0.02717810496687889, 0.02333376184105873, -0.06218741461634636, 0.015334494411945343, -0.046358123421669006, 0.006887482479214668, 0.007532719988375902, 0.024666981771588326, 0.054497383534908295, -0.02795867808163166, 0.05756090581417084, -0.015872135758399963, -0.03213602676987648, 0.021518491208553314, -0.0402752123773098, 0.054137907922267914, -0.013078377582132816, -0.052421934902668, -0.003027083585038781, 0.05692144110798836, 0.0048927608877420425, -0.019564112648367882, 0.016844408586621284, -0.07578913122415543, -0.016403568908572197, 0.062219731509685516, 0.03229644522070885, -0.09465492516756058, 0.023910820484161377, -0.0215302687138319, 0.05559692159295082, -0.044761523604393005, 0.039421163499355316, -0.007593266200274229, -0.039636511355638504, 0.01401329692453146, 0.025344599038362503, 0.015451201237738132, 0.018815400078892708 ]
<p>This question is essentially a duplicate of <a href="http://physics.stackexchange.com/questions/67810/gibbs-paradox-why-should-the-change-in-entropy-be-zero">Gibbs Paradox - why should the change in entropy be zero?</a>. The question concerns the following situation: I have some gas of identical particles and they are in a box which has been partitioned into two halves by a removable divider. Now the question is "<strong>If I remove the divider, why should the change in entropy be 0?</strong>" The standard answer is given in the above-linked-to question. The main idea of the answer is that the particles are supposed to be considered indistinguishible. If you treat the particles this way, you find that there is no change in entropy when the partition is removed. </p> <p>I understand this answer, and I suppose it should work for identical atoms, but you can easily imagine a situation where you have a collection of objects which are distinguishible, say some nanoparticles with differing numbers of constituent atoms. </p> <p>Furthermore, you should be able to treat a gas of identical particles as classical distinguishable bodies, and still get the right answer from statistical mechanics. I would say this is a good check of understanding of statistical mechanics. </p> <p>If this isn't enough motivation to come up with an alternate resolution to the paradox, consider this paradox, which requires essentially the same resolution that the gibbs paradox does: Imagine two systems initially in thermal contact and in thermal equilibrium. Now suppose they are separated. Here we might think the entropy will decrease in this process because in the initial configuration the energy of both systems were allowed to change as long as their sum remained constant. After separation, the systems' energies are fixed at some value. Clearly the set of final states is a subset of the set of initial states, so the entropy has decreased. This is the analogy of the gibbs paradox where instead of the systems exchanging particle number, they are exchanging energy. I would expect it to have essentially the same resolution.</p> <p>So my question is, "<strong>Why should the change in entropy be zero, even in the particles are distinguishible?</strong>"</p>
g5402
[ 0.02246689982712269, -0.013368668965995312, 0.018453018739819527, -0.048900872468948364, 0.044327087700366974, -0.033195704221725464, -0.0254212599247694, 0.114768847823143, -0.00936636421829462, -0.02246592938899994, -0.020131977275013924, 0.024034908041357994, 0.03383265435695648, -0.04846121370792389, -0.02722146175801754, 0.03027920238673687, 0.020117176696658134, -0.03352458029985428, -0.004599836189299822, 0.055746935307979584, -0.022168995812535286, 0.014375786297023296, 0.04452095180749893, -0.061548084020614624, -0.012567575089633465, -0.07031471282243729, 0.041670627892017365, 0.0022204394917935133, -0.04363062605261803, 0.0003895515692420304, 0.02479669637978077, 0.03903665766119957, 0.0571395680308342, -0.07937567681074142, -0.03207266330718994, -0.057429369539022446, 0.11889925599098206, 0.01648521237075329, -0.0036383355036377907, -0.007559264078736305, 0.05284435674548149, -0.03264511004090309, 0.0024566093925386667, -0.03883508965373039, 0.009155891835689545, 0.05016076937317848, 0.05749867111444473, 0.017275555059313774, 0.047010019421577454, -0.021219957619905472, 0.03016427345573902, 0.031714729964733124, 0.01209297962486744, 0.015105650760233402, 0.05102984979748726, 0.02912319451570511, -0.0003084131167270243, 0.03546270355582237, 0.02558758109807968, 0.010965059511363506, 0.03071495331823826, -0.0023278649896383286, -0.0020797213073819876, -0.02672739326953888, -0.03370780125260353, 0.0007768822833895683, 0.010358705185353756, 0.06870526820421219, 0.034340132027864456, -0.012965092435479164, -0.026546752080321312, -0.026143992319703102, 0.026336075738072395, 0.008244733326137066, -0.023361263796687126, -0.046898383647203445, -0.0033364472910761833, -0.03142400458455086, 0.006221739109605551, -0.0173359178006649, -0.06064283475279808, -0.023255344480276108, 0.047428395599126816, 0.01178757008165121, 0.028539760038256645, 0.016782991588115692, 0.03064369596540928, -0.04511517658829689, 0.03478451818227768, 0.06824343651533127, 0.0049298349767923355, 0.03325382247567177, 0.08434873819351196, 0.02625340409576893, -0.03482783958315849, -0.006424846593290567, -0.010283362120389938, 0.022543249651789665, 0.0020333968568593264, 0.0260016992688179, 0.011237733997404575, -0.008081740699708462, 0.007258664816617966, 0.020815828815102577, -0.030171560123562813, -0.012106221169233322, -0.0006542598712258041, 0.047913193702697754, -0.02414659596979618, -0.011832792311906815, -0.011344862170517445, 0.004168924409896135, -0.006367113906890154, -0.0515693798661232, 0.007945115678012371, -0.0020384856034070253, 0.12954401969909668, -0.012217164970934391, -0.02238784171640873, 0.017002146691083908, -0.0026906735729426146, 0.035542212426662445, 0.0034705970901995897, -0.0008978492696769536, -0.044257789850234985, -0.04780697077512741, 0.028374403715133667, 0.03302663192152977, 0.043913066387176514, -0.0369742251932621, -0.015327583998441696, 0.021911712363362312, -0.04358971118927002, 0.047257985919713974, -0.006895373109728098, -0.0076017118990421295, 0.021306296810507774, -0.011435502208769321, 0.04039628058671951, -0.028417544439435005, -0.026778966188430786, 0.02471412718296051, -0.04359642416238785, 0.01585261896252632, -0.028572309762239456, -0.04050537198781967, -0.024059787392616272, -0.025622420012950897, 0.011896689422428608, 0.044759269803762436, 0.031148141250014305, 0.02231648936867714, 0.012237945571541786, 0.02008088305592537, 0.010082405991852283, -0.034572090953588486, 0.059173278510570526, -0.0011603099992498755, -0.003828722285106778, -0.008072460070252419, 0.042040057480335236, 0.008531748317182064, -0.00020010198932141066, -0.009792366065084934, -0.08652377128601074, 0.05336387827992439, 0.043313704431056976, -0.08538857102394104, 0.022447749972343445, -0.046545546501874924, -0.037758585065603256, 0.0026015620678663254, -0.06406760960817337, 0.08360456675291061, -0.006416430696845055, 0.010932039469480515, 0.046388834714889526, -0.007679924368858337, -0.008139385841786861, -0.008694964461028576, -0.04637294262647629, 0.020804129540920258, 0.06175561249256134, -0.049650102853775024, 0.022064024582505226, -0.009811139665544033, -0.002307533286511898, 0.029871689155697823, -0.058230116963386536, -0.007814602926373482, -0.01387033425271511, 0.028280630707740784, -0.06209642440080643, -0.024187937378883362, 0.023478971794247627, -0.0020480072125792503, 0.0038819615729153156, -0.020795192569494247, -0.09262661635875702, -0.016989901661872864, -0.021874865517020226, 0.01490353886038065, 0.0012566882651299238, 0.01763784885406494, 0.01730888895690441, -0.015507795847952366, -0.05215824022889137, -0.019970586523413658, -0.02275247871875763, 0.013521815650165081, 0.03269423544406891, -0.019731169566512108, -0.03450342267751694, -0.06116778030991554, 0.030959630385041237, -0.014126289635896683, 0.061470746994018555, 0.02406182326376438, 0.053864359855651855, -0.01185695268213749, -0.03651013225317001, 0.019640104845166206, -0.004655926022678614, 0.01913883537054062, -0.025085587054491043, -0.008554978296160698, -0.04010014981031418, -0.05783012509346008, -0.04018085077404976, 0.1040993332862854, -0.038866642862558365, 0.021208688616752625, 0.018495652824640274, 0.0006266564014367759, -0.02201659604907036, 0.00119676417671144, -0.029959455132484436, 0.006846349220722914, 0.032762542366981506, -0.008111480623483658, 0.046685490757226944, -0.03405733406543732, -0.037792835384607315, 0.029763517901301384, 0.05216524749994278, 0.00883452594280243, -0.03877072036266327, -0.04682266339659691, 0.007280588150024414, -0.017360465601086617, -0.016924340277910233, 0.006048452574759722, -0.03367229178547859, -0.021012436598539352, 0.024991264566779137, -0.01792110502719879, 0.06312214583158493, 0.03338118642568588, -0.030832478776574135, -0.02814001962542534, -0.004390420857816935, -0.08166593313217163, 0.011537427082657814, 0.06114013493061066, -0.02428966388106346, -0.03481927141547203, 0.0019898107275366783, 0.013597026467323303, -0.004245506599545479, -0.023111924529075623, 0.01781006157398224, 0.045881837606430054, 0.0071550351567566395, 0.09478629380464554, 0.0038971384055912495, 0.013386067934334278, 0.037001434713602066, 0.006784427911043167, 0.02664290927350521, 0.03215987980365753, 0.006160000804811716, 0.05672662332653999, -0.07366185635328293, 0.07415297627449036, 0.03280315548181534, -0.06447651237249374, 0.010057543404400349, -0.008836501277983189, -0.00011556356912478805, 0.011741023510694504, 0.02302529476583004, 0.06372641772031784, 0.014996611513197422, -0.010645780712366104, -0.02698518894612789, -0.005979293957352638, -0.012201075442135334, -0.07103607803583145, -0.013569468632340431, 0.014855744317173958, 0.0019262105925008655, 0.011599690653383732, -0.027099620550870895, 0.019697241485118866, 0.05529579520225525, 0.06535983085632324, -0.07248745113611221, 0.018670005723834038, -0.03719734773039818, 0.025437185540795326, 0.011481333523988724, 0.03137541189789772, 0.007029891945421696, -0.016792168840765953, -0.026372132822871208, 0.0028166284319013357, -0.002179901348426938, -0.005068231374025345, 0.05096590146422386, -0.031454749405384064, 0.021438762545585632, -0.008102796971797943, 0.05325847119092941, -0.0019158697687089443, 0.002620257902890444, 0.012775163166224957, -0.042852114886045456, -0.0026603988371789455, -0.025294382125139236, 0.023580174893140793, -0.0023186143953353167, -0.017077380791306496, 0.021596739068627357, -0.03464427962899208, -0.06202516704797745, -0.018076462671160698, -0.029216274619102478, -0.061432335525751114, 0.01754169352352619, 0.017709923908114433, 0.021510113030672073, 0.012366839684545994, -0.0492057241499424, 0.0262733306735754, -0.02989785000681877, 0.013920570723712444, 0.06962515413761139, -0.0072374483570456505, 0.0032243405003100634, 0.005452409386634827, 0.001734828925691545, 0.016227299347519875, 0.021817471832036972, -0.008256200700998306, -0.01941668801009655, -0.03022575192153454, -0.02475198544561863, 0.007579495664685965, -0.007836036384105682, -0.005237469915300608, 0.02838115394115448, -0.07095266878604889, 0.030427761375904083, 0.07098467648029327, 0.031459372490644455, -0.002901883563026786, -0.03949020802974701, 0.00650512520223856, -0.0002608817885629833, -0.026806320995092392, -0.015042881481349468, -0.03992840275168419, -0.07025198638439178, 0.002319624647498131, 0.030111929401755333, -0.022674519568681717, 0.047238923609256744, 0.04736145958304405, -0.018961139023303986, -0.04850929602980614, 0.024730060249567032, -0.04033167287707329, -0.0517735630273819, -0.030771469697356224, 0.036804601550102234, -0.005231090355664492, 0.0068719577975571156, -0.014107870869338512, -0.05190827697515488, -0.0386044904589653, 0.030977733433246613, 0.04660707712173462, 0.015218433924019337, 0.01762958988547325, -0.02419121004641056, 0.02727583236992359, -0.014500796794891357, -0.03495649993419647, -0.023342519998550415, 0.0725184828042984, -0.05160878971219063, -0.054384373128414154, -0.05315091833472252, -0.019521895796060562, 0.0270064789801836, -0.05241865664720535, -0.009196662344038486, -0.019349630922079086, -0.045896016061306, -0.02890200726687908, 0.0008027303265407681, 0.020057057961821556, 0.0017414484173059464, -0.0628676563501358, -0.03716778755187988, 0.02098124474287033, -0.027987178415060043, 0.005303196143358946, 0.023056063801050186, 0.008964546024799347, -0.007239475380629301, -0.0034721551928669214, -0.055492352694272995, 0.026951950043439865, 0.000884766282979399, 0.05916477367281914, 0.023783618584275246, -0.00008710061956662685, -0.04261286184191704, -0.055689748376607895, 0.006117282435297966, 0.056177157908678055, -0.014566539786756039, 0.02808547578752041, -0.033150143921375275, 0.04546000808477402, -0.06365961581468582, 0.04803227633237839, -0.033693745732307434, 0.04997817054390907, 0.06542564183473587, 0.01966274529695511, -0.01399112120270729, -0.014622082002460957, 0.027833720669150352, -0.017889652401208878, -0.018887890502810478, -0.025182927027344704, -0.030393095687031746, -0.06485248357057571, -0.014268804341554642, 0.019751984626054764, -0.0045795016922056675, -0.05516764521598816, -0.041135046631097794, -0.0192708857357502, -0.049277447164058685, -0.006071992684155703, -0.009932943619787693, 0.016646116971969604, -0.004128090105950832, 0.0006014630780555308, 0.03914362192153931, 0.03173896297812462, -0.027233881875872612, 0.036448437720537186, -0.03903971239924431, 0.036129895597696304, -0.009351362474262714, -0.02851114235818386, 0.0030658647883683443, -0.0015763783594593406, -0.02052551694214344, 0.04819989204406738, 0.0037889217492192984, 0.006459492724388838, 0.015799308195710182, -0.05063590779900551, 0.045050714164972305, -0.0040006013587117195, -0.04057057574391365, -0.019373180344700813, 0.08168329298496246, 0.03078947402536869, -0.009458444081246853, -0.0005992049700580537, -0.0738077312707901, -0.013494113460183144, -0.0010134234325960279, -0.04528595879673958, 0.0032727918587625027, 0.032417330890893936, 0.07260779291391373, 0.0005372355226427317, 0.08312400430440903, -0.06359854340553284, 0.034989647567272186, -0.020791513845324516, -0.03902815282344818, 0.05625348538160324, -0.04964793846011162, 0.03874408081173897, 0.0202627032995224, 0.012337954714894295, 0.004368877038359642, 0.04499053210020065, -0.022253215312957764, 0.008913148194551468, -0.01042255386710167, 0.0303183626383543, 0.030568134039640427, -0.0005964043084532022, 0.06371338665485382, 0.041428323835134506, 0.017162872478365898, 0.008089371956884861, -0.0063763936050236225, -0.04442870616912842, -0.049169380217790604, -0.03527940437197685, 0.01755758561193943, -0.012123732827603817, 0.004023367539048195, -0.0036632250994443893, -0.04901496693491936, -0.007758776657283306, -0.015780407935380936, -0.0008655833080410957, -0.056498486548662186, 0.05350389704108238, 0.03234078735113144, 0.06833549588918686, -0.0421919971704483, 0.05660144239664078, -0.0519169457256794, -0.02213985100388527, -0.04570386931300163, 0.045344483107328415, 0.009123834781348705, 0.014113092795014381, -0.002764846431091428, -0.05252658575773239, -0.015254801139235497, 0.033632565289735794, 0.009609675966203213, -0.03398788347840309, -0.05182389169931412, -0.03363119065761566, 0.019162137061357498, -0.01737276464700699, -0.03707999736070633, -0.01706329919397831, -0.03202323988080025, -0.050419483333826065, 0.03649306669831276, 0.007021364755928516, 0.0628337487578392, 0.03110865317285061, 0.051789864897727966, -0.022213969379663467, 0.03331686928868294, -0.01074671559035778, -0.016703471541404724, 0.002297505736351013, 0.04612255468964577, -0.10113312304019928, -0.0057404981926083565, -0.021318823099136353, 0.008673724718391895, 0.034917861223220825, 0.0011925589060410857, 0.02459200844168663, 0.08841731399297714, 0.0371309258043766, 0.03952988609671593, 0.014873440377414227, -0.04661284014582634, -0.021294506266713142, -0.04739416390657425, -0.01397368311882019, -0.05648275092244148, 0.0017905550776049495, 0.03472742810845375, -0.03183933347463608, -0.019772853702306747, 0.06185317039489746, -0.06717528402805328, -0.01531300786882639, 0.028587529435753822, 0.058955807238817215, 0.014327927492558956, -0.09843875467777252, 0.0060592712834477425, -0.0031289884354919195, 0.0022837345022708178, 0.03195996955037117, -0.0523817241191864, 0.007806725800037384, -0.023798024281859398, 0.03278210014104843, -0.026600070297718048, -0.04585626348853111, 0.011011825874447823, -0.057903360575437546, -0.021847737953066826, 0.03358590602874756, 0.005313648376613855, -0.018947118893265724, 0.010179032571613789, 0.0013101877411827445, 0.016534369438886642, -0.0005857828655280173, 0.005902015138417482, -0.04955814406275749, 0.03875027969479561, -0.027478698641061783, -0.040472742170095444, 0.03774477541446686, -0.006734560243785381, -0.003822948317974806, -0.002426355378702283, -0.009937012568116188, -0.0019906642846763134, -0.021488651633262634, 0.07103268802165985, 0.054347068071365356, -0.06172261759638786, 0.04441986605525017, 0.060120679438114166, 0.06588391959667206, -0.03368530794978142, 0.015908749774098396, 0.000920003280043602, 0.04053522273898125, -0.021925676614046097, -0.03140830248594284, -0.06815396994352341, 0.02267327904701233, 0.052205879241228104, -0.009292452596127987, -0.029560668393969536, 0.015086197294294834, 0.04819802939891815, 0.010560664348304272, 0.016950486227869987, 0.06491680443286896, 0.04129054769873619, 0.007498551160097122, -0.08634134382009506, -0.011357991024851799, -0.039519231766462326, -0.019651591777801514, -0.04432905465364456, -0.04801927134394646, 0.043312788009643555, 0.03289089351892471, -0.005914857145398855, 0.025618134066462517, 0.029878737404942513, -0.0024267437402158976, -0.003721366636455059, 0.006328623276203871, 0.01664310321211815, 0.0020117657259106636, -0.03440557420253754, 0.05382832512259483, 0.04984284192323685, -0.028746483847498894, -0.007257404271513224, -0.04868435487151146, -0.005624423269182444, -0.00629224069416523, -0.051709990948438644, -0.03059864230453968, 0.04710162803530693, 0.005505214910954237, 0.04379648715257645, 0.024671759456396103, 0.03242474049329758, -0.01149971317499876, 0.005968694109469652, 0.015658525750041008, -0.0075215226970613, -0.06374143064022064, -0.012670289725065231, 0.04238174110651016, -0.01757665164768696, 0.030855325981974602, 0.00008760057971812785, -0.018957048654556274, 0.0224765632301569, 0.04175505414605141, -0.0007342793978750706, 0.008446059189736843, -0.04386889562010765, 0.012138997204601765, 0.06086120009422302, 0.03756524249911308, 0.04862920194864273, -0.06425607204437256, 0.02745789662003517, 0.0019466193625703454, -0.02402809076011181, 0.006779806222766638, 0.010101623833179474, -0.021061083301901817, 0.01902950182557106, -0.000035958702937932685, -0.011863681487739086, 0.00571456691250205, 0.01949206367135048, 0.0242349561303854, 0.08218304067850113, -0.02878180891275406, -0.035879913717508316, -0.06076917052268982, -0.05810939893126488, -0.028083084151148796, 0.07561774551868439, -0.03389693796634674, -0.0019808837678283453, -0.004552172031253576, -0.029186058789491653, -0.04072776064276695, -0.04632873088121414, -0.03593660891056061, 0.003418687731027603, 0.006287061609327793, 0.027269607409834862, 0.04854118451476097, 0.0204865001142025, 0.05160529911518097, 0.0018229251727461815, 0.020195679739117622, -0.026670094579458237, 0.02646346017718315, 0.031623877584934235, 0.022303922101855278, -0.03471960127353668, -0.01206310372799635, -0.017331305891275406, 0.021201079711318016, 0.08306390792131424, -0.03439174219965935, -0.04582729935646057, -0.07906290143728256, -0.04735471308231354, 0.024086838588118553, 0.034383781254291534, -0.029485605657100677, -0.08269105851650238, -0.104430191218853, -0.04184717312455177, 0.01285109855234623, 0.0379265658557415, -0.06166119500994682, 0.034732721745967865, 0.02766646258533001, -0.01946931704878807, 0.005092673469334841, -0.011689292266964912, 0.012714333832263947, -0.05167296901345253, 0.05167197808623314, 0.002704296028241515, 0.008122462779283524, 0.034880008548498154, 0.03166797384619713 ]
<p>I am confused about the current and voltage. My intuitive example would be that of a pipe of say water. The diameter of the pipe determines the amount of water flowing per second but the pressure is comparable to voltage. Am I right?</p> <p>And what is the difference between voltage source and current source? In what class our electric sockets on the wall do fall?</p>
g5403
[ 0.07361117005348206, 0.019598878920078278, -0.010308020748198032, -0.03665623813867569, 0.042284250259399414, 0.014780094847083092, 0.05951864272356033, -0.02174745872616768, -0.05603184923529625, -0.025687485933303833, -0.040658146142959595, 0.02490239404141903, -0.024660645052790642, 0.04296087473630905, 0.032899800688028336, -0.0028142831288278103, 0.01653669960796833, -0.009616459719836712, 0.0036833828780800104, -0.03269131854176521, -0.025578733533620834, -0.026433486491441727, 0.017686784267425537, -0.022757628932595253, -0.032781932502985, -0.0005590426153503358, -0.014201733283698559, -0.053921688348054886, 0.05544572323560715, -0.022431906312704086, -0.016729231923818588, 0.006208050064742565, 0.045182064175605774, -0.000508936180267483, -0.023231593891978264, -0.002382877981290221, 0.04062320291996002, -0.004995689261704683, 0.03157264366745949, 0.011714659631252289, 0.021712902933359146, 0.003977777436375618, 0.021412130445241928, 0.022785604000091553, -0.032053522765636444, -0.044326405972242355, -0.03662779927253723, -0.01942516677081585, -0.016387104988098145, -0.04535279795527458, -0.044073522090911865, 0.014449716545641422, 0.03471171483397484, 0.0332798957824707, 0.03910701349377632, -0.03290330991148949, 0.03821874037384987, -0.04416729882359505, 0.01694094017148018, 0.000668638211209327, -0.01859605871140957, 0.039360735565423965, 0.018523359671235085, 0.0003167100949212909, -0.00508552510291338, -0.05475570261478424, -0.05401010438799858, 0.007342280354350805, 0.04221338406205177, 0.02676762081682682, -0.04057225212454796, -0.08053797483444214, 0.004293621052056551, -0.06705816090106964, 0.03466304764151573, 0.02610558643937111, 0.017995445057749748, -0.031410664319992065, 0.015158470720052719, 0.004912018310278654, 0.05702879652380943, 0.003995555453002453, -0.03455502167344093, 0.04507919028401375, 0.01319727674126625, -0.04384637251496315, -0.04448387771844864, 0.00590452179312706, 0.04240671172738075, -0.020841725170612335, -0.028404496610164642, -0.05266141891479492, 0.09195291250944138, 0.03969412297010422, -0.030252153053879738, -0.013306659646332264, -0.028407469391822815, 0.032335564494132996, 0.05824083834886551, 0.06054360419511795, -0.012466173619031906, -0.08656265586614609, 0.021062860265374184, -0.052090778946876526, -0.02707752026617527, 0.017060182988643646, 0.051634784787893295, 0.016746170818805695, -0.036486223340034485, -0.026687277480959892, 0.0036202706396579742, -0.0466027595102787, -0.04768376797437668, 0.0035643568262457848, -0.026062559336423874, -0.02372417412698269, 0.010737019591033459, 0.02883077599108219, 0.015787171199917793, 0.12597520649433136, -0.0024253365118056536, 0.004408831708133221, 0.010787343606352806, 0.029607797041535378, 0.03146927058696747, 0.011089957319200039, 0.009861145168542862, -0.0032655023969709873, -0.03032608889043331, -0.016016103327274323, 0.0457477904856205, 0.0004981615929864347, -0.04577799141407013, -0.005804155487567186, 0.07828570902347565, 0.010197675786912441, 0.014447825960814953, -0.06411305069923401, 0.016502832993865013, -0.01140214130282402, 0.05050553381443024, 0.05717519670724869, -0.005875986069440842, -0.053555045276880264, -0.05177973955869675, -0.021645495668053627, -0.051314253360033035, -0.0036175420973449945, 0.030122671276330948, -0.0010874505387619138, 0.06149493157863617, 0.030475853011012077, 0.031414225697517395, -0.02933666668832302, 0.02674424648284912, -0.06916099041700363, -0.04263382777571678, -0.027506539598107338, 0.01358221098780632, 0.004182211123406887, -0.0012941963504999876, -0.05226394161581993, 0.04096636176109314, 0.025208912789821625, 0.0013106628321111202, -0.07220763713121414, 0.06293156743049622, 0.028696026653051376, 0.03662022203207016, -0.03592049330472946, -0.020083680748939514, -0.003761935280635953, 0.01416358258575201, 0.035461485385894775, 0.034937143325805664, 0.014437184669077396, 0.020054571330547333, -0.03888914734125137, 0.04902619123458862, 0.03691220283508301, -0.002699554432183504, -0.01729041151702404, 0.025096029043197632, -0.01508590579032898, -0.004171597771346569, 0.016329888254404068, -0.06633222848176956, -0.007139841094613075, -0.015937965363264084, -0.02710547484457493, -0.09665028750896454, -0.03742983192205429, 0.03743935748934746, 0.016367372125387192, -0.024600079283118248, -0.019277144223451614, -0.004228990990668535, -0.06388600915670395, -0.043570976704359055, 0.007289507891982794, -0.013526979833841324, -0.01273238193243742, 0.05496342107653618, 0.05480577424168587, -0.008356811478734016, 0.08052986860275269, -0.017902232706546783, -0.02079167775809765, -0.0045875320211052895, -0.02255256101489067, 0.05302773043513298, 0.01633572205901146, 0.021499767899513245, 0.04501805454492569, -0.08734340965747833, -0.021225063130259514, -0.02926797978579998, -0.0060994187369942665, -0.058889225125312805, -0.01045545469969511, 0.018888700753450394, -0.09224243462085724, 0.05536193028092384, -0.023350216448307037, -0.07561254501342773, -0.011468900367617607, 0.0007004397339187562, -0.054624781012535095, 0.022464852780103683, 0.0016770233632996678, -0.05370861664414406, -0.01467290148139, -0.00022205666755326092, -0.006330277770757675, 0.032311417162418365, 0.025700394064188004, 0.03772775083780289, 0.0028395974077284336, -0.011134527623653412, -0.025796176865696907, 0.018998177722096443, -0.04020838439464569, 0.028616657480597496, 0.02687274105846882, -0.03706517070531845, 0.010616622865200043, 0.06337269395589828, 0.009059589356184006, 0.0024794943165034056, 0.06929043680429459, 0.0024207436945289373, -0.032099977135658264, -0.026415690779685974, 0.06850485503673553, -0.0035274133551865816, -0.0329815112054348, 0.01569313183426857, 0.01336222980171442, -0.013541925698518753, -0.045384906232357025, -0.02696659043431282, 0.029261210933327675, 0.03720453381538391, 0.07247112691402435, -0.016089700162410736, 0.029734209179878235, 0.03564152121543884, 0.0035475275944918394, 0.007167696487158537, -0.009018845856189728, 0.011381564661860466, -0.014206993393599987, -0.05652064085006714, -0.014250384643673897, -0.013439727015793324, -0.08158183097839355, 0.00976128876209259, -0.054002098739147186, 0.042077235877513885, -0.05009046569466591, -0.016959693282842636, 0.03616048023104668, -0.0864512249827385, -0.006125208921730518, 0.019009515643119812, -0.0957842469215393, 0.0765325278043747, -0.014574737288057804, -0.040572550147771835, -0.005162219516932964, -0.006077766418457031, -0.001352732884697616, -0.012162970378994942, -0.025747420266270638, -0.0009330063476227224, 0.03538138419389725, 0.014251918531954288, -0.012935740873217583, -0.034379828721284866, -0.003930107690393925, 0.0015397125389426947, -0.012676375918090343, -0.022785121574997902, 0.004892328754067421, 0.013792963698506355, 0.04495323821902275, -0.027061449363827705, -0.011765471659600735, 0.005895016249269247, 0.04902331158518791, -0.011760425753891468, 0.018229521811008453, 0.05280384421348572, -0.03532356023788452, -0.01976618729531765, 0.009533688426017761, -0.02512407675385475, -0.008424715138971806, -0.003181070787832141, 0.0007943512755446136, -0.07346514612436295, -0.0419817678630352, -0.016201721504330635, 0.04811730235815048, 0.01376172062009573, 0.038218844681978226, 0.00046870121150277555, 0.0621955506503582, -0.042469631880521774, -0.026777422055602074, -0.01664668880403042, -0.03655325248837471, -0.051288850605487823, -0.015482110902667046, 0.05745330825448036, -0.04810679703950882, 0.06298541277647018, 0.03742365539073944, -0.0041290149092674255, 0.05452185869216919, 0.019447920843958855, 0.005422435235232115, -0.015322122722864151, 0.002856387058272958, -0.005415801424533129, 0.011874073185026646, 0.00018575992726255208, -0.018193338066339493, 0.025963593274354935, 0.013493943959474564, 0.1110621839761734, 0.021698053926229477, -0.0005803901003673673, -0.02994760125875473, -0.01546318270266056, -0.010234416462481022, 0.013768301345407963, 0.013238615356385708, -0.02492118813097477, -0.03549790754914284, 0.005593682173639536, -0.05791556090116501, 0.04273681342601776, 0.03409947454929352, -0.07088413089513779, -0.05242343991994858, 0.012580336071550846, 0.02763298526406288, -0.028952928259968758, -0.06986162811517715, 0.02740192413330078, 0.024932997301220894, -0.018350135535001755, 0.03127605840563774, -0.009640485979616642, -0.02874206006526947, 0.013063382357358932, 0.00671638548374176, -0.04570264369249344, 0.014080540277063847, 0.05934864282608032, 0.0299869142472744, 0.03999951481819153, 0.006616064812988043, -0.005416187923401594, -0.010089660063385963, 0.007539126090705395, 0.04632498323917389, -0.012553141452372074, -0.05643611028790474, 0.026169683784246445, -0.0028704272117465734, -0.05959353595972061, -0.0497237890958786, 0.030815690755844116, 0.026104023680090904, 0.04362061247229576, 0.0022086454555392265, -0.03582077473402023, 0.03668728098273277, -0.046163514256477356, -0.013126161880791187, 0.03074605017900467, 0.0011995690874755383, 0.06289024651050568, 0.021036271005868912, 0.06637749075889587, -0.039863359183073044, 0.0009337630472145975, -0.03500228002667427, 0.018294258043169975, -0.006886879913508892, -0.0033797211945056915, -0.038008157163858414, 0.0570489726960659, -0.014553132466971874, 0.05116407200694084, 0.04890769347548485, 0.09619593620300293, 0.020272497087717056, 0.016664203256368637, -0.008357305079698563, 0.01244672667235136, -0.04974062740802765, 0.0035809935070574284, 0.031824614852666855, 0.06523848325014114, 0.008599676191806793, -0.03787342831492424, -0.02408054657280445, 0.005102246999740601, 0.030584445223212242, 0.001916724955663085, -0.013117611408233643, 0.04135492816567421, 0.07080446928739548, -0.009715823456645012, -0.02233649417757988, -0.027332870289683342, 0.06994885206222534, 0.10440356284379959, -0.009054664522409439, -0.04043108969926834, -0.027071885764598846, -0.0048403386026620865, 0.022478526458144188, -0.04778460040688515, 0.025500429794192314, -0.012202785350382328, 0.007320345379412174, 0.015597992576658726, 0.01581634022295475, 0.00025530587299726903, -0.10323922336101532, 0.013703127391636372, 0.029624443501234055, 0.009084767661988735, -0.03482510894536972, 0.007587688509374857, -0.027374863624572754, -0.037907764315605164, 0.0014339364133775234, -0.026091596111655235, -0.005601102020591497, -0.004994403105229139, -0.03898472711443901, -0.031143207103013992, -0.038646895438432693, -0.10558892786502838, -0.02091079391539097, 0.008913942612707615, 0.009796731173992157, -0.04662928357720375, -0.0036800424568355083, 0.08375068008899689, -0.0020130856428295374, 0.010658404789865017, -0.0025337794795632362, 0.00629102298989892, -0.057712044566869736, -0.048042040318250656, -0.020573822781443596, -0.014069869183003902, 0.059380922466516495, -0.029395248740911484, -0.006054953671991825, -0.034838542342185974, 0.0005108563345856965, -0.02214343100786209, -0.004733464680612087, 0.022788621485233307, 0.07880843430757523, 0.01129849161952734, 0.02208174206316471, -0.009725215844810009, 0.0008664766792207956, -0.018980009481310844, 0.02555810660123825, -0.012083180248737335, 0.03884832188487053, -0.045779503881931305, -0.01462817844003439, -0.019238896667957306, -0.009397944435477257, -0.048627838492393494, 0.07643873244524002, 0.0919036716222763, -0.04604727774858475, 0.03920804336667061, 0.007193712517619133, 0.02807285636663437, -0.008512690663337708, 0.0044124536216259, 0.0017257704166695476, 0.03448445722460747, -0.052080973982810974, -0.02045639604330063, -0.016483958810567856, 0.014707057736814022, 0.014502122066915035, 0.032341331243515015, -0.007961707189679146, 0.05438731238245964, 0.02714821882545948, -0.06086178123950958, -0.006685364060103893, -0.0847720131278038, -0.015380172990262508, 0.08362246304750443, -0.001952941296622157, 0.05276454612612724, 0.025403987616300583, 0.0329076424241066, -0.022609658539295197, -0.06267160177230835, -0.00795498862862587, -0.03864098712801933, -0.04876897484064102, 0.05638642981648445, 0.009955992922186852, -0.02491731382906437, 0.019125280901789665, 0.035305894911289215, 0.019770387560129166, 0.05119346082210541, -0.013753076083958149, -0.017422441393136978, 0.005924572236835957, 0.024463899433612823, 0.03266027569770813, -0.030444039031863213, 0.10196895897388458, -0.024722188711166382, 0.06311347335577011, 0.003902978729456663, 0.01047754567116499, 0.04510648176074028, -0.03452254831790924, -0.03306976705789566, -0.021827077493071556, 0.029378850013017654, -0.017262602224946022, -0.02895047888159752, -0.013779811561107635, 0.06851481646299362, -0.018415112048387527, -0.006007686257362366, 0.03931534290313721, 0.011321616359055042, 0.07005816698074341, 0.04297855123877525, -0.02066626027226448, 0.002582794288173318, -0.05190606042742729, -0.006621359381824732, 0.015851248055696487, -0.06047012284398079, -0.08199172466993332, 0.00022899359464645386, -0.03553926199674606, 0.046707965433597565, 0.0062965829856693745, -0.0007500895881094038, -0.038231607526540756, 0.04179282486438751, -0.011140186339616776, 0.008811529725790024, -0.01043926365673542, 0.02270837128162384, 0.030794965103268623, 0.022186165675520897, 0.026501120999455452, 0.006232965271919966, 0.015434839762747288, -0.01831631548702717, -0.011881851591169834, 0.021578453481197357, -0.0022796986158937216, 0.00660948408767581, 0.09256503731012344, -0.020414765924215317, 0.05242398381233215, 0.03512585535645485, -0.0049661374650895596, 0.01579667627811432, -0.02598264254629612, -0.018345696851611137, 0.08270809054374695, -0.054012347012758255, -0.028064731508493423, 0.016370896250009537, -0.007442112546414137, 0.003541051410138607, -0.001665957155637443, -0.007467166520655155, 0.01248796097934246, -0.018204668536782265, -0.002211272716522217, -0.014223819598555565, 0.03094620443880558, -0.005447803530842066, -0.017345203086733818, 0.007211159914731979, -0.03620374575257301, 0.03189731389284134, 0.03301168233156204, -0.029654180631041527, 0.03663717210292816, 0.04119928181171417, 0.0013131769374012947, -0.036246102303266525, -0.02002326212823391, -0.0026221282314509153, 0.012427030131220818, 0.018882563337683678, 0.03653830662369728, -0.0342581570148468, 0.006818235386162996, 0.07105141133069992, 0.02045452408492565, 0.10357049107551575, -0.009333387948572636, -0.006585821975022554, 0.019201841205358505, -0.03744947165250778, -0.002473649336025119, -0.015343778766691685, 0.008574055507779121, -0.05368954315781593, -0.025962406769394875, 0.03174007683992386, 0.0028683936689049006, -0.02938578650355339, 0.024344908073544502, -0.04827776923775673, 0.03589025139808655, 0.028187280520796776, 0.03204241394996643, 0.01052859053015709, -0.05656363442540169, 0.008916359394788742, 0.02432727999985218, -0.039246127009391785, 0.023021869361400604, 0.023303937166929245, 0.019096704199910164, -0.037826117128133774, -0.06480970978736877, -0.010737660340964794, 0.013264835812151432, 0.00279314280487597, -0.0502828024327755, 0.008322068490087986, 0.008458119817078114, -0.007091011386364698, -0.009927932173013687, -0.03680923208594322, 0.012872057035565376, -0.014245101250708103, -0.011040573008358479, -0.017384875565767288, 0.03691979870200157, 0.02148319222033024, -0.034775279462337494, -0.024329571053385735, -0.021618731319904327, -0.08207571506500244, -0.01627436839044094, 0.0111822709441185, 0.015515814535319805, 0.03489400073885918, -0.009274386800825596, -0.019053999334573746, -0.017455995082855225, -0.003650055965408683, -0.009856916032731533, 0.013501639477908611, -0.0008797565824352205, 0.06024298444390297, -0.026106446981430054, 0.021106090396642685, -0.04767809435725212, -0.02342965081334114, 0.03102138265967369, -0.021023966372013092, 0.021894004195928574, -0.0517275407910347, 0.046929918229579926, -0.05610937252640724, -0.019475392997264862, 0.03609713912010193, 0.012363607063889503, 0.017331870272755623, -0.023434963077306747, -0.001065752818249166, 0.030098076909780502, -0.05234228074550629, 0.06664414703845978, 0.006748789455741644, 0.034631434828042984, 0.03910954296588898, -0.03902808949351311, 0.018768152222037315, -0.06947694718837738, -0.0011688953964039683, 0.004689269699156284, -0.019776606932282448, -0.009634642861783504, -0.08658101409673691, 0.05888141319155693, -0.05476072430610657, -0.03618038818240166, 0.03221513703465462, -0.029204923659563065, -0.05616433918476105, 0.05363504961133003, 0.018667610362172127, 0.07796135544776917, -0.007372710388153791, 0.012415891513228416, 0.045998673886060715, -0.003139976877719164, -0.05013348162174225, 0.0041623590514063835, 0.0003082023176830262, -0.02410360798239708, 0.02927820011973381, 0.011467020958662033, 0.038123853504657745, -0.07870350033044815, 0.0149137694388628, -0.008158556185662746, 0.003468103939667344, -0.002668489934876561, -0.008202378638088703, -0.06823257356882095, -0.0074303331784904, 0.02415166050195694, 0.012431972660124302, 0.047952570021152496, -0.0002903493877965957, 0.02217847853899002, 0.020428428426384926, -0.0266477819532156, 0.02254129946231842, -0.028443748131394386, -0.04828166589140892, -0.023774823173880577 ]
<p>This question was asked to me.</p> <p>My first thought was that electrons may ionise the air and potential difference that was applied may increase or decrease the current which should have been observed. I'd like to know whether this is the right reason or if there is any other reason which I should take into account.</p> <p>$$hv-w.f=hv'=eV$$ where $V$ is stopping potential , my second question is: if there isn't a vacuum will that stop potential change?</p>
g5404
[ 0.012681338004767895, 0.0011161135043948889, 0.011780627071857452, 0.040536247193813324, 0.08160845935344696, 0.07382576912641525, 0.00386826042085886, 0.06755967438220978, -0.036383140832185745, 0.0036184152122586966, -0.0028603149112313986, 0.04768985137343407, -0.03713587671518326, 0.07674859464168549, -0.03910510614514351, 0.016292396932840347, 0.063544362783432, -0.053646769374608994, -0.005301969591528177, -0.05725768953561783, -0.012754635885357857, -0.042410481721162796, -0.02134302631020546, -0.0750572457909584, -0.03247952088713646, -0.0005017202929593623, 0.0025158708449453115, 0.03862065449357033, 0.0004740761942230165, -0.011806603521108627, 0.00985390692949295, 0.02310001663863659, 0.029447143897414207, -0.026767566800117493, -0.05321059003472328, -0.025717351585626602, 0.07980013638734818, 0.05739205703139305, -0.030439674854278564, -0.03077581524848938, -0.018571438267827034, 0.012900923378765583, 0.060624152421951294, -0.012046078220009804, -0.023225583136081696, -0.06843592971563339, 0.022115051746368408, -0.011915693059563637, 0.06697962433099747, -0.033505696803331375, 0.006817948073148727, 0.014123226515948772, 0.002605058718472719, 0.009335449896752834, 0.034520648419857025, -0.011800832115113735, 0.02275736816227436, -0.03470715135335922, 0.08785630762577057, 0.027928709983825684, -0.030760474503040314, 0.012269973754882812, 0.048705462366342545, 0.026162078604102135, 0.006132622715085745, -0.02242925390601158, -0.05979308485984802, -0.021011028438806534, 0.000559185747988522, 0.014051038771867752, -0.005296063143759966, -0.030293885618448257, -0.05860758200287819, -0.05246055871248245, 0.03714202344417572, 0.06005237251520157, -0.0007809091475792229, -0.029188068583607674, 0.09569461643695831, -0.01582186482846737, -0.04167908430099487, -0.04290103539824486, 0.023558631539344788, -0.008423669263720512, 0.07420910894870758, -0.05476682260632515, 0.005256301257759333, -0.0024346327409148216, -0.00009051421511685476, -0.05453500524163246, 0.004055205266922712, -0.0533217191696167, 0.03883529454469681, -0.015747230499982834, 0.007125247735530138, -0.024683840572834015, 0.01848677173256874, 0.09844508022069931, 0.011361999437212944, 0.014846605248749256, -0.03153396025300026, -0.06227540224790573, 0.02642204239964485, 0.015005089342594147, -0.05898663029074669, -0.035853855311870575, -0.04670675843954086, -0.032475028187036514, 0.01492331549525261, -0.003095580730587244, -0.027637256309390068, -0.06947733461856842, -0.08682761341333389, -0.05111919716000557, -0.02331947162747383, 0.008279616013169289, 0.025674495846033096, -0.04421288147568703, 0.00010160746023757383, 0.0425683967769146, -0.02688121236860752, 0.07498382031917572, -0.028338493779301643, -0.02840113639831543, 0.00461725564673543, -0.027626458555459976, -0.029488977044820786, -0.008561430498957634, 0.006821148097515106, -0.026100613176822662, 0.03287837654352188, -0.033536601811647415, -0.024530280381441116, 0.018337424844503403, -0.021860726177692413, -0.01942780613899231, 0.026500403881072998, 0.0015912683447822928, 0.06864522397518158, -0.056642670184373856, 0.04860726371407509, 0.0006608235999010503, 0.01264452189207077, -0.032568152993917465, -0.005343375261873007, -0.023497501388192177, -0.0070037576369941235, 0.020874666050076485, 0.03648825362324715, -0.004987013526260853, 0.013250413350760937, 0.06409745663404465, -0.0011888400185853243, -0.03859323263168335, -0.03167501837015152, -0.04752383008599281, 0.018743272870779037, 0.04740237817168236, 0.034029971808195114, 0.010053491219878197, -0.00046826511970721185, 0.030742965638637543, -0.009750529192388058, -0.02667883411049843, -0.04709184914827347, -0.01454069186002016, -0.0029691902454942465, -0.008329336531460285, -0.0036990069784224033, -0.008270435966551304, -0.07342609763145447, 0.010157734155654907, 0.034562066197395325, 0.06701645255088806, 0.040554698556661606, 0.05865161865949631, 0.06058042496442795, 0.007913422770798206, 0.015582483261823654, 0.008331114426255226, -0.028604015707969666, 0.0030173531267791986, 0.028890011832118034, -0.05403820052742958, 0.009310895577073097, 0.03675318509340286, -0.032799478620290756, 0.023328052833676338, -0.11743120104074478, -0.049483492970466614, -0.03463742509484291, -0.01521447952836752, 0.020106416195631027, -0.007158251479268074, -0.05018134042620659, 0.004476394969969988, 0.006298471707850695, -0.022497719153761864, -0.05834253132343292, 0.026661518961191177, -0.09953219443559647, 0.0434674434363842, 0.044031910598278046, 0.041110675781965256, 0.041720736771821976, 0.000305939611280337, 0.02135554514825344, -0.05476846545934677, 0.05209020897746086, -0.006535419262945652, 0.02894774079322815, 0.05318953096866608, 0.0466492660343647, 0.03099381923675537, -0.03612358495593071, 0.0584091879427433, 0.00831365492194891, 0.04971979185938835, -0.03132225200533867, -0.011845279484987259, -0.004297805950045586, -0.0570073239505291, 0.02882036380469799, -0.014523233287036419, -0.04039870575070381, -0.04756096750497818, 0.011415937915444374, -0.0929744765162468, -0.0006336935912258923, -0.01601133868098259, -0.019921204075217247, -0.004218048881739378, 0.005950557999312878, -0.02824069745838642, 0.022136438637971878, 0.05713387206196785, -0.021131986752152443, 0.01533084362745285, 0.022152215242385864, -0.06847698241472244, -0.013045934960246086, -0.019960766658186913, 0.00039076709072105587, 0.07576676458120346, 0.03904114291071892, -0.03261416777968407, -0.028527434915304184, -0.014958208426833153, -0.00428647780790925, 0.010529052466154099, -0.0003633168525993824, -0.03189212456345558, -0.01810833439230919, 0.09562592953443527, -0.040178507566452026, -0.03952104598283768, -0.022800639271736145, 0.035580094903707504, -0.019954819232225418, -0.013002232648432255, -0.013310814276337624, -0.0030803882982581854, 0.01510247215628624, 0.0263346079736948, -0.03734062239527702, 0.003993229940533638, -0.016953205689787865, 0.04449152946472168, 0.03587702661752701, -0.026209821924567223, 0.039632707834243774, 0.04661329463124275, -0.06018252670764923, 0.04306463897228241, 0.03340530768036842, 0.05227581039071083, 0.026082785800099373, -0.026097305119037628, 0.07058829069137573, -0.060677770525217056, -0.04840034246444702, 0.00695377541705966, -0.0417434386909008, 0.019151635468006134, 0.011444664560258389, 0.006511540152132511, 0.0036502284929156303, -0.01745859906077385, -0.059205714613199234, -0.012187679298222065, -0.04403539374470711, 0.026173220947384834, 0.051678646355867386, -0.025781285017728806, -0.041903410106897354, -0.019753972068428993, 0.04790903255343437, -0.03812432289123535, -0.036582592874765396, -0.00999380461871624, 0.015203061513602734, -0.0088052311912179, -0.02514815516769886, 0.02551787719130516, 0.042689792811870575, -0.008655483834445477, -0.035277657210826874, -0.018724171444773674, 0.014606540091335773, 0.01653318852186203, 0.004543295595794916, 0.018212465569376945, -0.023742448538541794, -0.021247992292046547, -0.025576211512088776, -0.037636615335941315, -0.018879679962992668, 0.024433789774775505, 0.014334344305098057, 0.0308893583714962, -0.0436532199382782, -0.005162284709513187, 0.014621151611208916, 0.014712453819811344, 0.07526934146881104, 0.0640186220407486, -0.009288491681218147, -0.015855886042118073, 0.021240144968032837, 0.02047405019402504, -0.020198604092001915, -0.0007738455897197127, -0.0053517455235123634, -0.04436859115958214, -0.04582153633236885, 0.0070377858355641365, 0.011342288926243782, 0.037024907767772675, 0.015007108449935913, 0.0218640323728323, -0.0014557302929461002, -0.008871709927916527, -0.0650346428155899, 0.03373530134558678, -0.0012341081164777279, 0.06446371972560883, 0.0057402318343520164, -0.011905728839337826, 0.0029839533381164074, -0.01950615458190441, 0.08200664818286896, 0.0012816647067666054, 0.0435107983648777, 0.0004694973467849195, -0.0367375910282135, -0.04805899038910866, -0.01725815050303936, 0.006958052050322294, -0.012501171790063381, 0.006248868070542812, -0.013267056085169315, -0.024347582831978798, 0.0041955942288041115, -0.0161709226667881, 0.006399673409759998, 0.03223321959376335, -0.04216296598315239, 0.03061331808567047, -0.02153390273451805, -0.056599296629428864, 0.005882083438336849, 0.01460426114499569, -0.012589434161782265, 0.049833714962005615, 0.03541244938969612, -0.000864788715261966, 0.033521637320518494, 0.01159424427896738, 0.022900907322764397, 0.050294216722249985, 0.03119662031531334, 0.010764244012534618, 0.0030017055105417967, 0.0029237002599984407, -0.026626547798514366, -0.04708008095622063, -0.056275803595781326, 0.03156176209449768, -0.01289941556751728, -0.07145919650793076, -0.022050730884075165, 0.02599416859447956, -0.05444562807679176, -0.008993360213935375, 0.008812082931399345, -0.01978312060236931, 0.0326245091855526, -0.0586107075214386, 0.00962191354483366, 0.06970690190792084, 0.06143953651189804, 0.02534451335668564, -0.0003980785550083965, -0.0015114850830286741, 0.0059163193218410015, -0.010295579209923744, 0.04752112552523613, 0.014597640372812748, -0.017381440848112106, -0.051069557666778564, -0.005722657311707735, 0.010829082690179348, -0.017466552555561066, -0.03268160670995712, -0.03174206614494324, -0.04780026525259018, -0.032056450843811035, 0.036572810262441635, 0.06831250339746475, -0.010317692533135414, 0.0159525778144598, 0.051163215190172195, -0.012867394834756851, 0.011086967773735523, -0.010550117120146751, 0.04328254610300064, 0.012273726053535938, -0.025799915194511414, 0.0012984855566173792, -0.015402855351567268, -0.00444768788293004, 0.027053622528910637, -0.047890134155750275, 0.007567682769149542, 0.0019231084734201431, 0.05249043554067612, -0.02990007773041725, -0.032035063952207565, -0.007081300485879183, 0.03814036771655083, 0.10641161352396011, -0.003630823688581586, 0.0012936999555677176, -0.036641042679548264, -0.044348474591970444, 0.05425674468278885, -0.03858283534646034, -0.031348876655101776, 0.05812956765294075, -0.027853358536958694, -0.03223206847906113, 0.015649396926164627, 0.009831489995121956, -0.011754384264349937, 0.026057854294776917, -0.04459540173411369, -0.008051675744354725, -0.023814603686332703, 0.0030340675730258226, 0.013036851771175861, -0.02445330284535885, 0.036527760326862335, 0.04535575211048126, 0.032275162637233734, 0.04043182358145714, 0.002835111925378442, -0.05572446063160896, 0.002372708637267351, -0.0667639821767807, -0.05485298112034798, 0.010323840193450451, 0.017715217545628548, -0.01756204292178154, 0.07301224768161774, 0.017980093136429787, -0.025592617690563202, -0.02626831829547882, -0.01621359772980213, -0.0032256203703582287, -0.04089825227856636, -0.028766192495822906, -0.015768174082040787, 0.04742840677499771, 0.01668509840965271, -0.03142087906599045, -0.02561022713780403, -0.038684215396642685, 0.030905164778232574, -0.0011420848313719034, -0.02769606187939644, 0.0726674273610115, 0.09597276151180267, 0.02506420947611332, -0.01174527034163475, -0.008733165450394154, 0.00003162657594657503, 0.01352775190025568, 0.05049785599112511, -0.05980028212070465, 0.021609311923384666, -0.00462244963273406, -0.009355765767395496, -0.039283640682697296, -0.025316622108221054, -0.0066034323535859585, 0.058327566832304, 0.04968256130814552, -0.05381220579147339, 0.01849949359893799, 0.008778451941907406, -0.0200059711933136, -0.015747368335723877, 0.04711195081472397, 0.009748997166752815, 0.026622183620929718, 0.054809313267469406, -0.08884169161319733, -0.034951865673065186, -0.03177881985902786, -0.10056595504283905, 0.03178029879927635, -0.00023808689729776233, 0.032751020044088364, -0.004498666152358055, 0.004285131581127644, -0.03129362314939499, -0.01233807671815157, -0.01741122640669346, 0.00019431077816989273, 0.03937654197216034, 0.01915612816810608, 0.058517277240753174, 0.02364044077694416, -0.003652375191450119, 0.003054368542507291, -0.03178625553846359, 0.01660134270787239, -0.01975562609732151, 0.054418787360191345, 0.012031447142362595, -0.028845926746726036, -0.03897153586149216, 0.012366238050162792, 0.08793086558580399, -0.048011280596256256, 0.0016919263871386647, -0.06500272452831268, 0.0071328748017549515, 0.06440141052007675, -0.014193718321621418, -0.04434980824589729, 0.0043391757644712925, 0.0007894227164797485, 0.017535341903567314, -0.017438190057873726, 0.020945489406585693, 0.046149469912052155, -0.006530475802719593, -0.005142224486917257, -0.06767531484365463, 0.1060543954372406, 0.018179941922426224, -0.005357725545763969, -0.017008552327752113, 0.03971937671303749, -0.020649636164307594, 0.00978011079132557, 0.017738990485668182, 0.045142993330955505, 0.03194860741496086, -0.023822396993637085, 0.04610079526901245, 0.007685340009629726, -0.05867190659046173, 0.02244163490831852, -0.019019538536667824, -0.029259268194437027, 0.02917092852294445, -0.02624463103711605, 0.00301029602997005, -0.0019105359679087996, -0.02202492579817772, 0.07461155951023102, -0.09193733334541321, 0.007542086765170097, 0.029751667752861977, -0.01578335277736187, -0.03169511631131172, 0.09729650616645813, 0.010706366039812565, 0.011386165395379066, -0.04080931469798088, 0.04638541489839554, -0.025181785225868225, 0.0010723500745370984, -0.028310367837548256, -0.019493872299790382, -0.07044923305511475, -0.03949364647269249, 0.04305477440357208, 0.04904627054929733, 0.030832631513476372, -0.0592162162065506, -0.01370619423687458, 0.04172203317284584, 0.055305637419223785, 0.006146758794784546, 0.026797829195857048, 0.009304785169661045, -0.024162404239177704, -0.014672618359327316, -0.015515781939029694, 0.034935612231492996, -0.011774574406445026, 0.016627032309770584, -0.017277058213949203, 0.0049142795614898205, 0.036759402602910995, 0.010169663466513157, 0.03476806357502937, 0.009109812788665295, -0.023769158869981766, -0.01569899544119835, 0.05585706606507301, 0.031111305579543114, 0.09496673941612244, -0.020150817930698395, 0.010795548558235168, 0.04695829004049301, 0.02950015664100647, 0.014267882332205772, -0.024632476270198822, -0.010148147121071815, -0.005023215897381306, -0.0024016238749027252, 0.005927500780671835, 0.04487786814570427, -0.0253987405449152, 0.004899081774055958, -0.008111814968287945, 0.0048141623847186565, 0.0136492270976305, 0.04341115429997444, 0.015860160812735558, 0.011637168936431408, 0.0018762820400297642, 0.01950686238706112, -0.018691321834921837, -0.02072076126933098, -0.005283882841467857, -0.025809042155742645, 0.0038972259499132633, -0.022464193403720856, 0.032009974122047424, -0.02774950861930847, 0.0480056032538414, -0.017544269561767578, -0.015381164848804474, 0.03210083022713661, -0.024829337373375893, 0.010476014576852322, -0.019205771386623383, -0.04482424631714821, 0.050727564841508865, 0.024767965078353882, 0.009473813697695732, -0.05323487147688866, -0.06945724785327911, -0.025440877303481102, -0.045452333986759186, -0.00815841369330883, -0.06751666218042374, -0.007837112061679363, 0.004647795110940933, 0.059632327407598495, 0.01527568232268095, -0.037900086492300034, 0.027936618775129318, -0.018327854573726654, -0.009868650697171688, 0.00849794689565897, 0.021309293806552887, -0.015257958322763443, -0.01579895243048668, -0.05821150913834572, -0.029270146042108536, -0.05561327934265137, 0.010811900720000267, -0.010130525566637516, 0.001358931651338935, 0.0028347657062113285, -0.014531312510371208, 0.08047331124544144, 0.009470067918300629, -0.05506983399391174, 0.01563636213541031, -0.002194818342104554, 0.006840492133051157, -0.019752927124500275, -0.03308400511741638, 0.030996479094028473, 0.032844677567481995, 0.02217835746705532, -0.02909919060766697, 0.00658301031216979, 0.008501225151121616, 0.0011501430999487638, -0.01606285572052002, -0.054297491908073425, 0.017396636307239532, 0.036895375698804855, 0.03781725466251373, 0.031669728457927704, -0.013669691048562527, 0.003879230236634612, -0.048551157116889954, 0.005230187904089689, 0.03526853024959564, 0.07157561928033829, 0.058131519705057144, -0.03664914518594742, 0.008587213233113289, 0.013317687436938286, -0.021894944831728935, -0.03170030564069748, 0.028704727068543434, 0.003510202979668975, -0.01722387783229351, -0.009778589941561222, 0.022320499643683434, -0.048402104526758194, -0.03158240392804146, 0.00644685747101903, -0.07939933240413666, -0.035958342254161835, -0.027111634612083435, 0.04528568312525749, 0.035775769501924515, 0.027854816988110542, -0.022429073229432106, -0.07299204170703888, -0.03925269469618797, 0.013302466832101345, 0.033535491675138474, -0.0066340225748717785, -0.02989475056529045, 0.005897753406316042, -0.007031117100268602, 0.05944153666496277, -0.005158755462616682, -0.0032340188045054674, -0.028898781165480614, -0.10510376840829849, 0.06778974831104279, 0.039761632680892944, -0.001024539116770029, -0.028447411954402924, 0.06413692235946655, 0.005054604262113571, 0.02561120316386223, -0.01499924249947071, -0.002902899170294404, -0.040714483708143234, 0.003546760883182287, -0.018919313326478004, -0.07787773013114929, 0.0013852979755029082, 0.011353123001754284 ]
<p>what is the ram-facing side of a satellite? What does it mean and why is it called "ram"-facing? Thanks.</p>
g5405
[ 0.007882770150899887, 0.0642443373799324, -0.010488633997738361, -0.04403107240796089, -0.013224056921899319, -0.000966749619692564, 0.004835844971239567, -0.04938231781125069, -0.001954601379111409, -0.02449362352490425, -0.027680136263370514, 0.06492529809474945, 0.059644415974617004, -0.018410077318549156, 0.027570392936468124, -0.01735822483897209, 0.04620969295501709, -0.004166606348007917, -0.03083868697285652, 0.05449486896395683, -0.03440732881426811, 0.04821233078837395, -0.03116215579211712, 0.013354036957025528, 0.0009185413946397603, 0.03172653168439865, 0.006387715693563223, -0.029845602810382843, 0.026802506297826767, -0.012432784773409367, 0.05782280117273331, -0.013546748086810112, 0.0460650660097599, -0.02428019791841507, -0.040906839072704315, -0.03806944563984871, -0.0417330376803875, -0.002647940069437027, 0.028966231271624565, -0.020397374406456947, -0.042927853763103485, -0.07843919843435287, -0.03778638318181038, 0.04307064041495323, 0.0034311162307858467, 0.019380228593945503, -0.06171936169266701, -0.022670762613415718, 0.04754210263490677, -0.0021099827717989683, 0.04183223098516464, -0.010383769869804382, 0.04884014651179314, -0.03276324272155762, 0.041236963123083115, -0.03937848284840584, -0.009572889655828476, 0.06755110621452332, 0.045033372938632965, 0.012948733754456043, 0.01650378853082657, 0.014256582595407963, -0.066156767308712, 0.03464921936392784, 0.08818883448839188, -0.06512404978275299, 0.04154660552740097, 0.009645870886743069, 0.0036092200316488743, 0.051328420639038086, 0.05227756127715111, 0.03044222854077816, -0.0143279442563653, -0.05245057865977287, -0.009345641359686852, -0.014461384154856205, 0.05349573865532875, 0.00008718460594536737, -0.010603833012282848, 0.015017230063676834, 0.04338318854570389, -0.04023906961083412, 0.00029314978746697307, -0.0649741142988205, 0.09780219942331314, 0.06356780230998993, -0.020584573969244957, 0.0324128083884716, -0.04562598094344139, -0.004404188133776188, -0.035959094762802124, 0.004297545645385981, -0.025180328637361526, -0.04431888461112976, 0.012266813777387142, -0.02774093858897686, 0.040828049182891846, 0.03124203160405159, -0.06627495586872101, 0.04111820459365845, 0.024874214082956314, -0.036587443202733994, 0.0493243969976902, 0.01809000037610531, -0.011443412862718105, 0.03617402911186218, -0.05314280837774277, 0.034665435552597046, 0.04249797761440277, -0.039776768535375595, -0.019280849024653435, 0.005166952032595873, 0.06807678192853928, -0.015510731376707554, 0.006847360637038946, 0.008922887966036797, 0.054216109216213226, -0.024139927700161934, -0.002819771645590663, 0.029516281560063362, 0.01908222958445549, -0.07166818529367447, -0.011058025993406773, 0.05999043583869934, -0.003994711209088564, -0.02978781796991825, 0.013575061224400997, 0.0014242959441617131, -0.013357486575841904, 0.037886399775743484, -0.009437584318220615, -0.00782740768045187, -0.012339821085333824, -0.07326038181781769, 0.12536825239658356, 0.05923333764076233, -0.047726161777973175, -0.036618661135435104, 0.01815318502485752, -0.020601067692041397, -0.006849539000540972, -0.05940835922956467, -0.020588018000125885, -0.009781735949218273, 0.0029810662381350994, -0.031719889491796494, 0.0016357946442440152, 0.018139420077204704, 0.013384110294282436, -0.002661904552951455, -0.0320228673517704, 0.03469417989253998, -0.044626373797655106, -0.0793500766158104, -0.01983771100640297, -0.019490182399749756, 0.002195548266172409, 0.02742118388414383, 0.00709662027657032, 0.050944842398166656, 0.01692420057952404, 0.1039007231593132, -0.04712213575839996, -0.024114927276968956, -0.05763176828622818, -0.02245486155152321, -0.07846193760633469, -0.05733400955796242, -0.0026555131189525127, 0.030912326648831367, 0.037662189453840256, -0.013753406703472137, 0.02863341011106968, 0.010158244520425797, -0.03727797046303749, 0.0038765135686844587, 0.052096325904130936, 0.06747249513864517, 0.08834138512611389, 0.041822925209999084, -0.011004100553691387, 0.0035755212884396315, 0.006240911781787872, 0.03178513050079346, -0.041453782469034195, -0.0625506043434143, 0.015443261712789536, 0.003153234487399459, -0.02652936801314354, 0.008522058837115765, -0.04863018915057182, 0.0029159679543226957, -0.04118241369724274, 0.06042230501770973, -0.02546701766550541, -0.07730267196893692, -0.004359484184533358, -0.018264660611748695, 0.022283967584371567, -0.0414268933236599, 0.005504780448973179, -0.013904239982366562, 0.057626742869615555, 0.044468753039836884, -0.020046617835760117, -0.006367981433868408, -0.023942194879055023, 0.01793518289923668, 0.0729331448674202, 0.004402589052915573, -0.04169994220137596, -0.030076656490564346, -0.01638736203312874, -0.013679944910109043, 0.024050837382674217, -0.01594626158475876, -0.04512486234307289, 0.0029126631561666727, -0.010533378459513187, 0.020515626296401024, 0.018528401851654053, -0.026255076751112938, 0.00024340738309547305, 0.021306563168764114, 0.007750265765935183, 0.0429292656481266, 0.00862391758710146, 0.024440061300992966, 0.04831039533019066, -0.011917104944586754, -0.023536406457424164, -0.07848489284515381, 0.05060265213251114, 0.03676259145140648, 0.009412613697350025, 0.012943427078425884, 0.010966751724481583, 0.06960589438676834, 0.003981438931077719, 0.0019068182446062565, -0.034937694668769836, 0.018049322068691254, -0.024180766195058823, 0.004433836787939072, 0.003985779359936714, -0.028268469497561455, 0.06257342547178268, 0.0003792126080952585, -0.011148780584335327, 0.03210219740867615, 0.03198646008968353, -0.050629518926143646, 0.0007267524488270283, 0.04247663915157318, 0.003482658416032791, -0.04970891773700714, -0.04600369185209274, -0.05064541473984718, 0.023672854527831078, 0.03797512501478195, -0.03618853539228439, -0.024355584755539894, -0.001816143631003797, 0.0449540838599205, 0.058929573744535446, -0.019667411223053932, -0.015822671353816986, 0.037957917898893356, 0.07499752193689346, 0.036047521978616714, 0.005517872050404549, 0.058929234743118286, 0.04276014119386673, 0.0125808734446764, -0.007379337679594755, 0.019926592707633972, 0.010723560117185116, 0.018955545499920845, 0.028634097427129745, -0.002536431420594454, 0.007433656603097916, -0.02842024527490139, 0.03208969533443451, 0.026083633303642273, -0.027461020275950432, 0.05136258900165558, -0.024152884259819984, 0.023419048637151718, -0.06064591184258461, -0.038285478949546814, -0.0207956675440073, -0.07051274925470352, 0.07018861919641495, -0.07295585423707962, 0.03057865798473358, -0.010318651795387268, 0.05108267068862915, -0.0430273599922657, 0.0017016874626278877, 0.00556921074166894, -0.004293728154152632, -0.007642194628715515, 0.023427721112966537, -0.040560971945524216, -0.057577431201934814, 0.03829837217926979, -0.038765039294958115, -0.07432162016630173, -0.09133362025022507, -0.02647245116531849, -0.04475546255707741, 0.0035322532057762146, -0.007091892883181572, 0.0049105011858046055, 0.01214123610407114, 0.029476433992385864, -0.06964144855737686, 0.01417782623320818, -0.004325795453041792, -0.017798714339733124, -0.0807223692536354, -0.0456705205142498, -0.02953830361366272, 0.05634479597210884, -0.0406072735786438, 0.04412107914686203, 0.013582229614257812, 0.004563259892165661, -0.009827647358179092, -0.037603363394737244, -0.0018267604755237699, 0.0033889657352119684, 0.017436878755688667, 0.017622102051973343, -0.07282666116952896, 0.08076953887939453, -0.022258823737502098, 0.07504832744598389, 0.02468937821686268, 0.001264872495085001, 0.01489820796996355, 0.0776541456580162, 0.04168727621436119, -0.011814095079898834, -0.0128262834623456, 0.03134651854634285, -0.014121225103735924, -0.033071368932724, 0.037856247276067734, 0.014725970104336739, 0.029392791911959648, 0.028111979365348816, 0.0233110710978508, 0.0013441592454910278, -0.0592433325946331, 0.08366145938634872, -0.007505638059228659, -0.013443294912576675, -0.017488790675997734, 0.051404427736997604, 0.01797468215227127, -0.01052820309996605, -0.014062141999602318, 0.03901050612330437, 0.02236400917172432, -0.07506683468818665, 0.01510611642152071, -0.016057854518294334, -0.04456990957260132, -0.0693025067448616, -0.007053499575704336, -0.02248399518430233, -0.037039726972579956, -0.05143473669886589, 0.011025184765458107, 0.007080541457980871, -0.060235217213630676, -0.028952183201909065, 0.029740113765001297, 0.01020234264433384, 0.0279212798923254, -0.048873383551836014, -0.011659183539450169, -0.012132538482546806, 0.03435337543487549, 0.015411114320158958, 0.00265751825645566, -0.028472991660237312, 0.005447812378406525, -0.005539456848055124, 0.05223410204052925, -0.0018805097788572311, -0.019399654120206833, -0.045074462890625, -0.012615001760423183, 0.04561585560441017, -0.06039389967918396, 0.029329126700758934, -0.037088148295879364, 0.005612170323729515, 0.012088175863027573, 0.04382042586803436, -0.0019438271410763264, -0.011277101002633572, -0.010794584639370441, -0.020785870030522346, 0.03430425375699997, -0.0005917600938118994, -0.014214792288839817, -0.01181918103247881, 0.03320556506514549, 0.039276015013456345, 0.03646435961127281, 0.008053408935666084, 0.04798715561628342, 0.05913439765572548, -0.038714852184057236, 0.09005429595708847, 0.0593559555709362, -0.012968787923455238, -0.01771770976483822, 0.031205467879772186, -0.03258636221289635, -0.042907457798719406, -0.013368004932999611, 0.014829286374151707, -0.01875527761876583, 0.0019739398267120123, 0.017646944150328636, 0.011942264623939991, 0.06011785566806793, 0.03944876790046692, 0.0033512189984321594, 0.036714740097522736, 0.006493093445897102, 0.042542874813079834, -0.0006139030447229743, 0.0034120911732316017, 0.00034987926483154297, -0.010600554756820202, 0.012185624800622463, 0.013679001480340958, -0.004464911296963692, -0.013591524213552475, -0.022074922919273376, 0.03114817664027214, 0.07642876356840134, -0.016200026497244835, -0.015693387016654015, 0.04922885820269585, -0.06828013807535172, 0.002622542204335332, -0.04821106791496277, -0.03326830267906189, -0.03876010328531265, -0.007600509561598301, -0.036872513592243195, -0.03822337090969086, 0.02660452201962471, 0.032543353736400604, -0.03537881001830101, -0.051044926047325134, -0.0014971471391618252, 0.038211602717638016, 0.05321098864078522, 0.04290837422013283, -0.004483410157263279, -0.04648163542151451, 0.022921761497855186, 0.01304556429386139, -0.04194808006286621, 0.053460508584976196, -0.021269047632813454, 0.038040269166231155, -0.028499232605099678, 0.03939459100365639, -0.03684341534972191, -0.060001667588949203, -0.016046514734625816, -0.01360095851123333, 0.039426468312740326, 0.003999658860266209, 0.022805936634540558, -0.01784907467663288, -0.02501537837088108, 0.01539582759141922, -0.04119277745485306, -0.019798656925559044, -0.0049934894777834415, 0.015716196969151497, -0.00697040930390358, -0.058343641459941864, -0.0155692333355546, -0.05507253482937813, -0.02982236258685589, -0.03715742379426956, -0.02104920521378517, -0.05609713867306709, 0.02184372767806053, 0.020522769540548325, 0.04698683321475983, -0.034923020750284195, 0.03747040778398514, 0.029127782210707664, 0.03894691541790962, 0.029599826782941818, -0.009458933025598526, 0.0079573979601264, 0.02142270654439926, -0.033009447157382965, 0.02876177988946438, 0.007109770085662603, -0.08058817684650421, -0.007136551663279533, -0.0023021481465548277, -0.015347158536314964, 0.023578599095344543, 0.026047782972455025, 0.002896368270739913, 0.04866548627614975, -0.0629831850528717, -0.03233380988240242, 0.008234777487814426, 0.012562022544443607, -0.0031179762445390224, -0.037089232355356216, -0.0639481469988823, 0.022177109494805336, 0.058197084814310074, 0.027570510283112526, -0.03591050207614899, 0.05567259341478348, 0.03900916874408722, 0.05870193615555763, -0.035772018134593964, -0.040627870708703995, 0.04939135164022446, 0.048903707414865494, 0.06280158460140228, -0.005436690058559179, 0.009019163437187672, 0.0744505375623703, 0.00939286220818758, 0.04046119004487991, -0.013524671085178852, 0.027570612728595734, -0.03160804882645607, -0.0057444386184215546, -0.002137419767677784, 0.006498830392956734, -0.023638276383280754, 0.0036773651372641325, -0.026926767081022263, -0.002868113573640585, -0.0065348646603524685, -0.003422164125367999, -0.02835753746330738, 0.03285868838429451, -0.0032955652568489313, -0.028176385909318924, -0.0258560199290514, 0.01299767941236496, -0.03762899711728096, -0.0319666787981987, -0.0018920570146292448, -0.0016208417946472764, 0.019929733127355576, -0.007845860905945301, 0.015228581614792347, -0.05140487477183342, -0.00903805810958147, -0.01774332858622074, 0.05136101320385933, 0.05970324948430061, 0.04623910039663315, 0.04328840970993042, -0.02037760429084301, 0.01224671769887209, -0.07255978882312775, 0.012490823864936829, 0.01068378146737814, -0.09465453773736954, 0.027151325717568398, -0.010333452373743057, -0.009000682272017002, 0.009895042516291142, 0.006298087537288666, -0.04867419973015785, 0.0509391650557518, -0.027623340487480164, -0.03345917537808418, 0.0020962508860975504, -0.0018280389485880733, 0.013984588906168938, -0.01747027412056923, 0.03242291510105133, -0.0385514460504055, 0.12744061648845673, -0.030900463461875916, -0.007925614714622498, 0.03340337052941322, -0.013660364784300327, 0.034786827862262726, -0.0005786766414530575, -0.0005030836327932775, 0.026767870411276817, -0.0015233673620969057, -0.013584555126726627, 0.014332927763462067, -0.030625177547335625, 0.031039735302329063, -0.0033099292777478695, -0.01518895011395216, -0.0022114834282547235, -0.006991737987846136, -0.01823914237320423, -0.05479040741920471, -0.0011007980210706592, 0.01685933768749237, -0.045477841049432755, 0.03333128243684769, 0.013498020358383656, -0.03558561950922012, -0.007881022058427334, 0.0057019079104065895, 0.051373500376939774, -0.002405366860330105, 0.03351516276597977, 0.03238575533032417, -0.02587132342159748, -0.008122448809444904, -0.01808600313961506, -0.029126053676009178, -0.07241243124008179, -0.0020013023167848587, -0.03236168995499611, -0.03127483278512955, -0.01034233346581459, -0.061005789786577225, 0.035267215222120285, -0.03633331507444382, -0.0021935165859758854, -0.010456697084009647, -0.036547619849443436, 0.0022366838529706, -0.021129807457327843, -0.06439519673585892, -0.042132169008255005, -0.0036019424442201853, -0.008530966006219387, -0.026063622906804085, -0.0980449691414833, -0.00542171485722065, -0.008894870989024639, 0.04093269631266594, 0.03176805004477501, -0.0012422559084370732, -0.0027336645871400833, 0.024994559586048126, 0.013131660409271717, -0.005988454911857843, -0.009283846244215965, -0.07372912764549255, 0.011632516048848629, 0.006264108698815107, -0.006175707094371319, 0.0645531564950943, -0.03084327094256878, 0.006406677886843681, -0.02912646159529686, -0.08478479832410812, -0.012836380861699581, 0.008556435815989971, 0.03178964555263519, -0.04265908896923065, 0.05659587308764458, 0.007839818485081196, 0.020548680797219276, -0.03404124826192856, -0.007827998138964176, 0.039309706538915634, -0.0276370607316494, 0.006034153047949076, -0.024863226339221, -0.01184606272727251, -0.02554020658135414, 0.046841979026794434, -0.04958183690905571, 0.011739201843738556, -0.10152605921030045, 0.0654122605919838, 0.017255548387765884, -0.026412196457386017, -0.0534953847527504, -0.05001986026763916, -0.019288014620542526, -0.01666649617254734, 0.03644923120737076, -0.027622366324067116, 0.026978181675076485, 0.02418047934770584, 0.02983907237648964, 0.04060133919119835, 0.055150359869003296, 0.03582225367426872, -0.017215443775057793, 0.06068923696875572, 0.05069523677229881, -0.046323373913764954, -0.021987423300743103, -0.039662715047597885, -0.041194990277290344, 0.042265329509973526, -0.011730729602277279, -0.008002557791769505, 0.026539046317338943, 0.02757425233721733, -0.01827075146138668, -0.002688777633011341, -0.050073862075805664, -0.016527220606803894, 0.005029640626162291, 0.013574986718595028, -0.006112055853009224, -0.04337172955274582, 0.012330492958426476, -0.03522182255983353, -0.00972603727132082, 0.0662219300866127, -0.03353743627667427, -0.016414647921919823, 0.002362853614613414, 0.049249641597270966, -0.005647349637001753, 0.024535376578569412, -0.006769873667508364, -0.0296607818454504, -0.047976020723581314, -0.01750284992158413, 0.019262488931417465, 0.021299416199326515, -0.0030659791082143784, 0.018000811338424683, -0.017694806680083275, -0.050884950906038284, -0.0078246695920825, -0.019629424437880516, 0.0497463122010231, 0.016668325290083885, -0.028678573668003082, 0.06177661567926407, 0.014418297447264194, 0.03247362747788429, 0.030958261340856552, 0.019680684432387352, 0.010068103671073914, -0.004126496147364378, 0.05505617707967758, 0.022041255608201027, 0.01963532157242298, -0.03970262035727501, -0.018017476424574852, 0.04698512703180313, -0.014171368442475796, 0.0008645841153338552, -0.024828733876347542, -0.04033518210053444, -0.03318846598267555 ]
<p>Wired magazine ran an <a href="http://www.wired.com/magazine/2011/04/st_equation_sodapop/" rel="nofollow">article</a> this month on carbonation in soft drinks.</p> <p>If all soft drinks are manufactured effectively identically, why do some types fizz more than others?</p> <p>For example, root beer is always extremely fizzy (and <a href="http://billybrew.com/beer-lacing" rel="nofollow">laces</a> well).</p> <p>In similar fashion, lemon-lime drinks like Sprite and Sierra Mist are very fizzy - but do not lace like root beer.</p> <p>Compare those to diet colas, which fizz slowly and/or minimally, and one is left to ponder.</p> <p>What is it about some types of drinks that make them hold and release their carbonation differently?</p>
g5406
[ 0.03131597116589546, 0.03954418748617172, 0.021536989137530327, 0.07472635060548782, 0.04260220006108284, -0.04165465757250786, 0.03747749701142311, 0.019057612866163254, -0.07316359132528305, -0.028584765270352364, 0.009088004007935524, -0.015151860192418098, 0.0424271784722805, 0.08784367144107819, -0.009690250270068645, -0.03205299749970436, -0.007906782440841198, -0.06015742942690849, 0.03384058550000191, 0.06863822042942047, 0.016055723652243614, -0.03562154620885849, -0.017483284696936607, -0.02376558445394039, -0.02326657436788082, -0.010848761536180973, -0.04602453112602234, -0.06455250829458237, 0.002095259027555585, -0.007614803500473499, -0.031379587948322296, -0.01195092499256134, -0.017887815833091736, 0.012819522060453892, -0.041721444576978683, -0.06197838485240936, 0.024299127981066704, 0.040122393518686295, 0.026843097060918808, 0.013865013606846333, 0.00807814672589302, 0.032933905720710754, 0.05125163123011589, -0.06590598821640015, -0.021227288991212845, -0.04149972274899483, -0.012913778424263, 0.034078001976013184, -0.02640371024608612, -0.027310306206345558, 0.015891773626208305, -0.006662995088845491, -0.0505329966545105, 0.004067874513566494, 0.0029623820446431637, 0.006798791233450174, 0.029799196869134903, -0.01754898950457573, -0.014414794743061066, 0.03003489412367344, -0.061491839587688446, -0.01760380156338215, 0.024369165301322937, 0.08017159253358841, -0.009244917891919613, -0.059064071625471115, -0.028702223673462868, -0.008017226122319698, 0.09123993664979935, 0.04276425391435623, -0.01396175380796194, -0.03076283074915409, 0.010979751124978065, -0.06733369082212448, 0.005301345139741898, -0.014427179470658302, -0.017260540276765823, 0.006152867805212736, 0.018539929762482643, -0.05026460438966751, 0.029205042868852615, 0.04926196485757828, -0.017895804718136787, 0.055457718670368195, 0.07049378007650375, 0.03159630298614502, -0.030861778184771538, -0.006375078111886978, 0.027532922104001045, 0.014344160445034504, 0.053072087466716766, -0.03279535472393036, 0.09925024956464767, 0.020965874195098877, -0.12137842178344727, 0.02520729787647724, 0.06127292662858963, -0.03005276620388031, 0.009845525957643986, -0.0650360956788063, 0.0186222642660141, -0.009831393137574196, 0.028139518573880196, 0.04439184069633484, -0.0010934047168120742, -0.006745550781488419, -0.037163544446229935, 0.05435490235686302, 0.011189207434654236, 0.021421782672405243, 0.007442611735314131, -0.010301901958882809, -0.0338013730943203, 0.04168912395834923, -0.05973847955465317, -0.03835916519165039, 0.04320419579744339, 0.06859864294528961, 0.035300709307193756, 0.0024246620014309883, 0.05287546664476395, 0.015701700001955032, -0.026773884892463684, 0.013907461427152157, 0.003500957740470767, -0.024065392091870308, -0.0014732878189533949, -0.05400196090340614, 0.036379557102918625, -0.019912641495466232, -0.026252279058098793, 0.019535575062036514, 0.00031896212021820247, -0.08302819728851318, -0.028307348489761353, 0.045332930982112885, -0.027141738682985306, -0.03007359988987446, 0.06187950074672699, -0.04831023886799812, 0.060484934598207474, 0.012011146172881126, 0.0541183203458786, 0.032325029373168945, 0.02420874498784542, -0.0010139432270079851, 0.002807564102113247, -0.025206446647644043, 0.02526703104376793, 0.029576238244771957, 0.006876827217638493, -0.022027786821126938, 0.047525376081466675, 0.02828838676214218, -0.020810358226299286, 0.022678431123495102, 0.043675485998392105, -0.007073196116834879, -0.07810371369123459, 0.07334589958190918, 0.010154381394386292, -0.06788889318704605, 0.007423668168485165, -0.03209683671593666, -0.04407361149787903, -0.014693373814225197, 0.07575025409460068, -0.00856237206608057, -0.08995877951383591, 0.04945365712046623, -0.060414914041757584, -0.0311947762966156, -0.03820992633700371, 0.08077964931726456, 0.08254833519458771, 0.005952594336122274, 0.019643539562821388, -0.07516998797655106, 0.028476614505052567, -0.022898821160197258, -0.006545220036059618, 0.030405068770051003, -0.05147278308868408, 0.0029296630527824163, 0.006995178759098053, 0.023765744641423225, 0.006616335362195969, -0.025831039994955063, -0.02834848314523697, 0.030557461082935333, -0.04418380931019783, -0.07149041444063187, 0.040400534868240356, 0.010333691723644733, 0.003267723834142089, -0.015262190252542496, -0.006786371115595102, -0.005041253753006458, -0.056317288428545, -0.014210691675543785, -0.0631738156080246, -0.0108900535851717, 0.004698286764323711, -0.041086118668317795, -0.03152156621217728, 0.013506166636943817, -0.04878852888941765, 0.016635728999972343, 0.04256349802017212, 0.0004326463968027383, 0.020338980481028557, -0.016469961032271385, 0.008972919546067715, -0.003445960348471999, 0.049411922693252563, -0.022867118939757347, -0.004146103747189045, 0.007375051733106375, 0.005048748105764389, -0.006466159597039223, -0.004002621863037348, -0.01423961203545332, 0.0057181548327207565, -0.02680169977247715, -0.0035697282291948795, -0.0423184335231781, -0.00939225684851408, 0.03129468858242035, -0.006310533732175827, 0.032853592187166214, -0.005033144727349281, -0.03849080950021744, -0.004582949448376894, 0.0038165636360645294, -0.02710578963160515, -0.03522831201553345, 0.044947732239961624, 0.028078339993953705, 0.02201964147388935, -0.019838755950331688, 0.010989831760525703, -0.017992345616221428, -0.004670971538871527, -0.012871797196567059, 0.03629205375909805, -0.07533774524927139, -0.015589691698551178, -0.0025710980407893658, -0.023866921663284302, 0.02770177647471428, 0.03648878261446953, 0.0063768052496016026, 0.02571807987987995, -0.022983767092227936, 0.05544836074113846, -0.027385469526052475, 0.0169723741710186, -0.0028617673087865114, 0.006855052430182695, -0.06839654594659805, -0.003015322145074606, -0.029818745329976082, -0.013348031789064407, -0.06787313520908356, -0.028212467208504677, 0.028240807354450226, -0.039902713149785995, -0.048672713339328766, -0.02077379636466503, -0.032423824071884155, 0.006378557067364454, 0.03401082381606102, 0.005292661488056183, -0.04112353175878525, -0.019180022180080414, -0.014196965843439102, -0.0011454180348664522, -0.01629623956978321, -0.021208956837654114, -0.031153280287981033, -0.024935195222496986, -0.020648231729865074, -0.024068299680948257, 0.015346554107964039, 0.012982623651623726, 0.021353047341108322, 0.023556582629680634, 0.024475131183862686, -0.011319695971906185, 0.008364341221749783, -0.044396910816431046, -0.002359942067414522, 0.023939212784171104, -0.009892350994050503, 0.020077990368008614, 0.011902916245162487, -0.014858082868158817, -0.03803715854883194, -0.019276225939393044, 0.02472575195133686, 0.06534543633460999, 0.06802226603031158, 0.029361233115196228, -0.014662849716842175, 0.004950692877173424, 0.0825449749827385, 0.008895373903214931, -0.030198628082871437, -0.018175266683101654, 0.04339074343442917, 0.011930778622627258, 0.03263785317540169, -0.028293557465076447, 0.04675798863172531, -0.03508269041776657, 0.0013157211942598224, 0.023975541815161705, 0.05757768079638481, -0.0024694106541574, -0.038361310958862305, -0.03376386687159538, 0.02348976954817772, 0.02330942265689373, 0.01877090521156788, -0.0006138508324511349, 0.02364514023065567, -0.014986615628004074, 0.016197560355067253, -0.04597154259681702, 0.03771984577178955, 0.03503302112221718, 0.023637205362319946, -0.021328190341591835, -0.08033545315265656, -0.05332820490002632, -0.010670753195881844, -0.031963881105184555, 0.042062923312187195, 0.06115775555372238, -0.037279024720191956, -0.009072227403521538, 0.03261524811387062, -0.03600834310054779, -0.01837291568517685, -0.03174393251538277, 0.05186588317155838, -0.01660361886024475, 0.029325461015105247, -0.03143556788563728, 0.024908918887376785, 0.06459338217973709, -0.02806767448782921, -0.02825363725423813, -0.04143247753381729, -0.024767186492681503, 0.008866513147950172, 0.01830287091434002, -0.006347960792481899, 0.005520872306078672, 0.06562080979347229, 0.060344334691762924, 0.010086859576404095, 0.007223218213766813, -0.007236177567392588, 0.004138208460062742, 0.0917012020945549, 0.009285835549235344, -0.014540723524987698, -0.09362590312957764, 0.03870983049273491, 0.04541230946779251, 0.03342566266655922, -0.049578774720430374, 0.026992162689566612, -0.039618704468011856, -0.01986442506313324, -0.023070208728313446, 0.05269264057278633, -0.0649835467338562, -0.044395845383405685, 0.028167614713311195, 0.07212749123573303, 0.038465678691864014, 0.017349420115351677, 0.0022239016834646463, 0.00680955033749342, -0.03389337658882141, 0.005938165355473757, -0.038052748888731, -0.038012631237506866, -0.03708474710583687, 0.06414403021335602, -0.010835179127752781, -0.01918601058423519, 0.006746810395270586, 0.009011580608785152, 0.015185603871941566, 0.0045104678720235825, 0.04424991458654404, 0.02242385223507881, -0.023935437202453613, -0.045351337641477585, 0.029627615585923195, -0.03160814195871353, 0.01621408388018608, 0.0007996847853064537, -0.017839942127466202, -0.003963183145970106, -0.038482628762722015, -0.07297252863645554, 0.00436190003529191, 0.05841788649559021, -0.021318713203072548, 0.0119057921692729, 0.016446152701973915, 0.0015885423636063933, 0.002603626111522317, 0.0047241151332855225, 0.07428823411464691, 0.01555611565709114, -0.0042657009325921535, -0.009715733118355274, -0.017225010320544243, -0.041975490748882294, 0.01683272235095501, -0.0074767922051250935, 0.01563061960041523, 0.03196803480386734, -0.023622781038284302, -0.01802597939968109, 0.008273543789982796, -0.00905255600810051, 0.017065037041902542, 0.013266919180750847, 0.01380511000752449, -0.023284340277314186, 0.00720660574734211, 0.08020719140768051, -0.009684424847364426, 0.04965375363826752, 0.06486962735652924, 0.00489930110052228, -0.0031179762445390224, 0.011139306239783764, 0.009005492553114891, 0.06023363023996353, -0.02372019737958908, 0.04594781994819641, -0.11115580052137375, -0.07990230619907379, 0.011488084681332111, 0.038943950086832047, -0.058396872133016586, 0.021382544189691544, -0.011219628155231476, -0.006957397796213627, 0.04769192636013031, 0.008147135376930237, -0.01497895922511816, 0.028430696576833725, -0.030859587714076042, -0.038749810308218, 0.041200462728738785, -0.030461430549621582, -0.052414730191230774, 0.0026562209241092205, 0.017825661227107048, -0.07145517319440842, -0.045057833194732666, -0.009186869487166405, -0.024062609300017357, 0.021850034594535828, -0.01676497422158718, 0.030824938789010048, 0.015830762684345245, 0.015026452951133251, -0.014930437318980694, -0.020742740482091904, -0.05200883373618126, -0.018593041226267815, -0.01820393092930317, 0.006888580974191427, 0.005022728815674782, 0.03647424280643463, -0.00791956577450037, -0.00043724323040805757, -0.004377743694931269, -0.006735816597938538, -0.04223234951496124, -0.007250223308801651, 0.06946447491645813, 0.06036902591586113, -0.028171909973025322, -0.007223715540021658, 0.008249776437878609, 0.046227917075157166, -0.02582712285220623, 0.015867924317717552, -0.02357153221964836, 0.01733982190489769, -0.033703770488500595, 0.024020345881581306, 0.036218319088220596, -0.03743728995323181, 0.04103910177946091, 0.03989225998520851, 0.06279486417770386, -0.033610034734010696, 0.006263666786253452, 0.0001977249630726874, 0.004962200298905373, -0.003780428785830736, -0.0037609077990055084, 0.0542299784719944, 0.038010820746421814, -0.02863016352057457, -0.019058017060160637, -0.03581218793988228, -0.010205496102571487, -0.033849604427814484, 0.048956356942653656, 0.001479902770370245, -0.011080433614552021, 0.030188370496034622, -0.001471872441470623, 0.026029758155345917, 0.0009498740546405315, -0.03642157465219498, 0.019825970754027367, -0.05885882303118706, 0.026950757950544357, 0.06564994156360626, 0.01788831502199173, 0.03149566054344177, 0.0031634503975510597, -0.010753736831247807, -0.03998295217752457, 0.03562942519783974, -0.018194297328591347, 0.06922510266304016, -0.09140028059482574, -0.012644468806684017, -0.03132595494389534, 0.0913134515285492, 0.027872228994965553, -0.009631052613258362, 0.07441005110740662, -0.014019887894392014, 0.0046435389667749405, -0.024246247485280037, -0.04609912261366844, 0.005455342587083578, 0.014979740604758263, 0.006880773231387138, 0.04018622264266014, 0.03312386944890022, -0.0063874926418066025, 0.04717373847961426, -0.038981810212135315, -0.042171329259872437, -0.004921705927699804, 0.05492531508207321, 0.007213355507701635, -0.01153675839304924, 0.010356998071074486, -0.05338741093873978, 0.0031784370075911283, -0.05334053188562393, 0.03918798267841339, 0.044598288834095, -0.05393132567405701, 0.04773598536849022, 0.002712296787649393, -0.018171874806284904, -0.027844291180372238, -0.05034841224551201, 0.02150975540280342, 0.031581439077854156, 0.020232543349266052, 0.037718575447797775, 0.01275897491723299, -0.021563634276390076, -0.06991449743509293, 0.08493972569704056, 0.00445691030472517, -0.0050077592022717, -0.043107353150844574, 0.001029957551509142, 0.011003898456692696, -0.039634544402360916, -0.024991704151034355, -0.011610963381826878, -0.014497600495815277, -0.002444963902235031, -0.007912677712738514, -0.06783318519592285, -0.006300770211964846, -0.011841154657304287, -0.056164033710956573, -0.039856214076280594, -0.004665785934776068, 0.05807660520076752, 0.037163861095905304, -0.009345892816781998, -0.004831764381378889, 0.05006717890501022, 0.003488323651254177, 0.07106759399175644, -0.08573213219642639, 0.03760407865047455, -0.11806388199329376, 0.05935876816511154, 0.02601751685142517, -0.05149945244193077, -0.021396787837147713, -0.06832343339920044, -0.04261183738708496, -0.03754659369587898, -0.028089407831430435, 0.005115904845297337, -0.054940953850746155, 0.01636352203786373, 0.027667269110679626, -0.0178576298058033, 0.06163652986288071, -0.03635881841182709, -0.013408849015831947, 0.03887924179434776, -0.03542438521981239, 0.013482182286679745, 0.030959438532590866, -0.03625286743044853, -0.02851307950913906, 0.08543015271425247, -0.019362375140190125, 0.014490602537989616, -0.1041807308793068, 0.036776117980480194, 0.018642578274011612, -0.022741774097085, -0.00612803315743804, 0.014164594933390617, -0.016910208389163017, 0.0857122391462326, -0.02416463941335678, 0.05391146242618561, 0.004148694220930338, -0.05136548727750778, 0.016427114605903625, 0.022778576239943504, 0.012442940846085548, -0.0033194103743880987, 0.02106696367263794, 0.03310384228825569, -0.0004417365125846118, 0.024963971227407455, -0.014985539019107819, 0.020932292565703392, 0.009584113955497742, -0.05366085469722748, -0.06793752312660217, 0.00796608254313469, 0.03485708683729172, 0.03355378285050392, 0.024803683161735535, 0.0018673838349059224, -0.009277408011257648, 0.012036551721394062, 0.03056190349161625, 0.013709060847759247, -0.024135638028383255, -0.04790159687399864, 0.001840971875935793, -0.05015559121966362, 0.015385200269520283, 0.025151370093226433, -0.02872745878994465, -0.004182904493063688, 0.05864844098687172, 0.022982288151979446, 0.015525046736001968, 0.027278957888484, -0.021184952929615974, -0.020474432036280632, -0.026811599731445312, 0.05163954943418503, -0.04683731496334076, 0.024877706542611122, 0.004715827293694019, -0.0098688043653965, -0.026370132341980934, -0.02515687607228756, 0.04020151495933533, 0.023295920342206955, -0.042932841926813126, -0.06854401528835297, 0.00785062462091446, 0.02109665609896183, 0.0023603024892508984, 0.03391304984688759, 0.027365539222955704, 0.03310572728514671, 0.00259433058090508, 0.01914503239095211, 0.03159908950328827, 0.0028888622764497995, -0.022439658641815186, 0.006183624267578125, 0.019206875935196877, -0.004924359731376171, -0.003300527110695839, -0.034025974571704865, 0.009168442338705063, 0.009778100997209549, 0.040360257029533386, -0.013073443435132504, 0.028693977743387222, -0.03328623250126839, -0.04670257493853569, -0.015170793980360031, -0.05324786156415939, 0.002030756790190935, 0.023665688931941986, -0.0202526543289423, 0.023580601438879967, 0.01224720012396574, 0.013871091417968273, -0.011163422837853432, 0.0028444556519389153, 0.004049219191074371, -0.02152698114514351, -0.05626129359006882, 0.029815582558512688, 0.04623478278517723, -0.05026986822485924, -0.007179778069257736, 0.09283933788537979, 0.009611551649868488, 0.008785649202764034, -0.024232663214206696, -0.02158675342798233, 0.007073787972331047, -0.026000211015343666, -0.017641274258494377, 0.011363547295331955, -0.004174855072051287, 0.03366278111934662, 0.05347590520977974, -0.015394313260912895, -0.05206426605582237, -0.03014192543923855, 0.004475385881960392, -0.014946886338293552, 0.01920938864350319, -0.040726371109485626, 0.0029347813688218594, 0.02214951626956463, 0.049973007291555405, 0.07250543683767319, -0.033091843128204346, -0.10178252309560776, 0.009625150822103024, -0.03588990122079849, -0.007775848265737295, -0.019135423004627228, 0.03766439110040665, -0.011129459366202354, 0.030009835958480835 ]
<p>More specifically, in quantum field theory books, we usually have this:</p> <p>\begin{equation} Z = \int D(\bar{\psi}, \psi) e^{-S + \int_0^\beta d\tau \sum_l [\bar{\eta}_l (\tau) \psi_l (\tau) + \bar{\psi}_l (\tau) \eta_l (\tau) ]} \hspace{10mm} (1) \end{equation}</p> <p>where $S = \int_0^\beta d\tau \sum_l (\bar{\psi}_l (\tau) \partial_\tau \psi_l (\tau ) +H(\bar{\psi},\psi))$ is the action, and $H$ is the Hamiltonian of the system.</p> <p>Can I instead start off with the Hamiltonian in diagonal form and include the source term in, say, a momentum basis? So that</p> <p>\begin{equation} Z = \int D(\bar{\psi}, \psi) e^{-S + \int_0^\beta d\tau \sum_k [\bar{\eta}_k (\tau) \psi_k (\tau) + \bar{\psi}_k (\tau) \eta_k (\tau) ]} \end{equation}</p> <p>where $S$ is now $\int_0^\beta d\tau \sum_k (\bar{\psi}_k (\tau) [\partial_\tau +\epsilon_k]\psi_k (\tau ))$.</p> <p>Or do I have to start off with equation (1) and apply various transformations to the Hamiltonian and the rest of the exponent until $H$ it is in a diagonal basis? - If this is the case, the resulting source term in the momentum basis could be extremely complicated after the transformations are performed.</p> <p>Thanks! </p>
g5407
[ 0.004719932097941637, -0.010780767537653446, -0.003092536237090826, -0.09706998616456985, 0.05902574211359024, -0.014474231749773026, 0.04311772808432579, 0.018696054816246033, 0.011212204582989216, 0.011095663532614708, -0.028790183365345, 0.014619143679738045, -0.03379276767373085, -0.016155358403921127, 0.013576016761362553, -0.020357592031359673, 0.05120817571878433, -0.012415209785103798, -0.00047075841575860977, -0.010812046937644482, -0.052395906299352646, 0.0365605354309082, 0.0127819012850523, -0.048749346286058426, -0.013613986782729626, -0.059764645993709564, -0.056425128132104874, -0.06608087569475174, -0.010282326489686966, -0.02939159981906414, -0.04492708668112755, 0.0200557392090559, 0.03162979334592819, -0.02247944101691246, -0.04082125425338745, 0.02806917391717434, 0.09669332206249237, -0.008828234858810902, 0.005710827652364969, -0.059186700731515884, -0.0004671543138101697, -0.057571351528167725, 0.001661990536376834, -0.01236287597566843, -0.030176404863595963, -0.030272645875811577, 0.007514864206314087, -0.008614795282483101, -0.038153085857629776, 0.09114439785480499, 0.001994306920096278, 0.044045381247997284, 0.019433891400694847, 0.017450282350182533, -0.04554968699812889, 0.09729208797216415, 0.0429198257625103, -0.07399208098649979, 0.0007728280615992844, 0.06529591232538223, -0.024452654644846916, -0.035894762724637985, -0.019370514899492264, -0.036227237433195114, 0.020598847419023514, -0.00333566521294415, -0.05509604141116142, 0.001465321285650134, -0.033039242029190063, -0.014092919416725636, -0.01343871746212244, -0.029527654871344566, 0.08153262734413147, -0.022661354392766953, 0.05091920122504234, 0.04037383943796158, 0.013024644926190376, -0.009390998631715775, 0.014732344076037407, 0.01543971337378025, 0.017604095861315727, -0.06143886595964432, 0.07586117833852768, -0.03984681889414787, -0.00693137850612402, 0.02298390492796898, 0.03313058987259865, 0.008630961179733276, 0.007904109545052052, -0.0022383600007742643, -0.0033419651445001364, 0.03705110400915146, -0.0011132415384054184, 0.061263203620910645, -0.021471668034791946, -0.046245548874139786, -0.06265220791101456, -0.006516313645988703, 0.057464104145765305, 0.0031798805575817823, -0.026664970442652702, 0.02264281176030636, -0.0004785794299095869, -0.02760300040245056, -0.048780616372823715, -0.021736497059464455, 0.030398298054933548, -0.05808207392692566, 0.036471910774707794, 0.007630493491888046, -0.07005881518125534, 0.009844547137618065, -0.0013584825210273266, 0.031154898926615715, -0.10700982064008713, 0.015012072399258614, 0.012799966149032116, 0.01245980616658926, -0.029276207089424133, 0.04658512398600578, 0.019309042021632195, -0.004655464086681604, 0.04593225196003914, 0.014474930241703987, -0.012905159965157509, 0.008914494886994362, -0.0505482442677021, 0.05082005634903908, 0.07878796011209488, -0.05657750740647316, 0.02338932827115059, -0.031020084396004677, 0.015907548367977142, -0.010698258876800537, 0.03176315501332283, -0.0010709408670663834, 0.04087740182876587, 0.02617899887263775, 0.02516486681997776, 0.05855545029044151, -0.020205432549118996, -0.03396109491586685, 0.013541731983423233, -0.04505596682429314, 0.014430196955800056, 0.04064800962805748, 0.01179603673517704, -0.022304369136691093, 0.024245526641607285, 0.02773464284837246, -0.03090033121407032, 0.029258694499731064, 0.0048320177011191845, 0.02132178097963333, 0.019039200618863106, -0.002046554582193494, 0.051209256052970886, -0.022178450599312782, 0.027192045003175735, -0.07952077686786652, -0.002698160009458661, 0.009921962395310402, 0.024524202570319176, -0.0037397576961666346, 0.011689532548189163, 0.02153095416724682, 0.03709324449300766, -0.05095600709319115, -0.011913822032511234, -0.05167492479085922, 0.058846596628427505, 0.03340260311961174, 0.008685209788382053, -0.0029693287797272205, 0.00841553695499897, 0.08203268051147461, -0.029195012524724007, 0.012429812923073769, 0.007596899755299091, 0.007347612641751766, -0.010436693206429482, -0.014826239086687565, 0.0143789853900671, -0.05335869640111923, 0.00040451070526614785, 0.025596870109438896, 0.007804080843925476, 0.09648969024419785, -0.038149263709783554, 0.019108012318611145, -0.026260189712047577, 0.0340006947517395, 0.031031958758831024, 0.06543030589818954, -0.013783959671854973, 0.014721149578690529, 0.01922360248863697, -0.08636648952960968, 0.012204509228467941, 0.012515264563262463, -0.01321594137698412, 0.051830317825078964, -0.030656389892101288, 0.002732237335294485, 0.03615240752696991, -0.002781225834041834, 0.044251762330532074, -0.0033372421748936176, 0.010740717872977257, -0.02625413052737713, 0.03165639564394951, -0.06846365332603455, -0.04634286090731621, 0.05020266771316528, -0.013204677030444145, -0.025199297815561295, 0.055502984672784805, 0.01593635417521, -0.04223666340112686, 0.06708390265703201, -0.06515119969844818, 0.020128626376390457, 0.006506415084004402, -0.02759108506143093, -0.04100973531603813, 0.001009396044537425, -0.013233997859060764, 0.03380252420902252, -0.013800571672618389, 0.004864417016506195, -0.03742188587784767, 0.01586422510445118, -0.045922089368104935, -0.04230151325464249, 0.027858661487698555, 0.02754046581685543, -0.025133850052952766, 0.006633775308728218, 0.028911981731653214, 0.010327210649847984, -0.019335227087140083, -0.005865659099072218, -0.011579209938645363, 0.020988617092370987, 0.015151777304708958, -0.008817468769848347, 0.008354361169040203, 0.052146170288324356, -0.04278171807527542, 0.01604156196117401, -0.013379628770053387, -0.020610030740499496, 0.005443353671580553, -0.03434145450592041, -0.05776732787489891, -0.052657440304756165, -0.009296479634940624, -0.02651990018785, 0.01981327310204506, 0.026476852595806122, 0.014455868862569332, 0.019664207473397255, -0.03331684321165085, 0.0736779272556305, -0.0501914881169796, 0.014310329221189022, 0.016419799998402596, -0.03890657424926758, -0.008889403194189072, 0.008517114445567131, -0.07134155929088593, 0.0485515221953392, -0.007374541833996773, 0.02262931503355503, -0.02093731239438057, -0.0458059124648571, 0.0009360527619719505, -0.00707843666896224, 0.040277205407619476, -0.004790933337062597, -0.04446551203727722, -0.017386063933372498, -0.05732578784227371, 0.04379134997725487, 0.01600102335214615, -0.008634006604552269, 0.02181943692266941, 0.008846824988722801, -0.015017326921224594, -0.004544330760836601, 0.018013862892985344, 0.05632123351097107, 0.05196152627468109, 0.016068486496806145, -0.023126887157559395, -0.002279979409649968, 0.019746629521250725, -0.10773167014122009, 0.008401724509894848, 0.08339933305978775, -0.0038024892564862967, -0.019011039286851883, -0.00486827502027154, 0.05035329982638359, 0.042114779353141785, 0.03543604165315628, -0.06473000347614288, -0.0077168308198452, -0.024343939498066902, -0.005925766658037901, 0.0038914065808057785, 0.009489398449659348, 0.008007329888641834, -0.0018480735598132014, -0.01719140075147152, -0.02430260367691517, 0.024232737720012665, -0.054983288049697876, 0.0067466325126588345, -0.022481346502900124, -0.04771417751908302, -0.03697328269481659, -0.006505703087896109, 0.0242761317640543, 0.05478491261601448, 0.06268908083438873, -0.05925743654370308, 0.007104464806616306, -0.06464909762144089, -0.023899560794234276, -0.01846456527709961, 0.0015961542958393693, 0.024747047573328018, -0.018823469057679176, -0.06513430923223495, 0.00433331448584795, -0.0031646760180592537, -0.0048218462616205215, -0.016408534720540047, -0.01995396427810192, -0.04267076402902603, -0.023182015866041183, -0.0019430755637586117, 0.042954519391059875, -0.012176547199487686, -0.08081243187189102, 0.051545847207307816, -0.027264490723609924, 0.005058063194155693, -0.034149568527936935, -0.0519164614379406, 0.008547247387468815, 0.009728560224175453, 0.014217101037502289, -0.011795096099376678, 0.06912330538034439, 0.05137437954545021, 0.09632699936628342, 0.05747001990675926, -0.010168978944420815, 0.008896336890757084, -0.06148795038461685, 0.0034528884571045637, 0.025945516303181648, -0.03076268918812275, 0.023715835064649582, -0.04029132053256035, -0.03743169084191322, -0.011336296796798706, -0.006027101539075375, 0.025315459817647934, -0.005511276889592409, 0.07233341038227081, -0.01880168356001377, 0.014798726886510849, -0.03547873720526695, 0.027622465044260025, 0.011718343943357468, -0.0032618676777929068, 0.01450128760188818, -0.007934987545013428, -0.029968474060297012, 0.001207426656037569, 0.034085094928741455, 0.035917025059461594, 0.042821548879146576, 0.029557984322309494, 0.02080865204334259, 0.033429741859436035, 0.04779708385467529, -0.031196188181638718, -0.04931481555104256, 0.017526155337691307, -0.0050567700527608395, 0.0012209403794258833, 0.037875350564718246, -0.00846688263118267, 0.01970483362674713, -0.02081470377743244, 0.06600499153137207, -0.04164738580584526, -0.02427152916789055, 0.0363595150411129, 0.03982323408126831, -0.017970554530620575, 0.033914562314748764, 0.0345940887928009, -0.017246566712856293, 0.03438863903284073, -0.045583371073007584, -0.017247362062335014, -0.059571605175733566, 0.006355588790029287, 0.009418332017958164, -0.014605569653213024, 0.008143635466694832, 0.023672210052609444, -0.02274388074874878, 0.004392016679048538, 0.004693995695561171, 0.06559199839830399, 0.03250416740775108, 0.04127226397395134, 0.04110443964600563, 0.0329289510846138, 0.014828301034867764, 0.08309393376111984, -0.01733124814927578, -0.013031400740146637, -0.009815714322030544, -0.04687560349702835, 0.030057335272431374, 0.018700318410992622, 0.008005335927009583, -0.06749401986598969, -0.005526021122932434, -0.06433849036693573, -0.021003419533371925, 0.012983173131942749, -0.014580046758055687, 0.04651607200503349, 0.017137976363301277, 0.02018493041396141, -0.003993201535195112, -0.03843060880899429, 0.03800872340798378, -0.038373932242393494, -0.08945351094007492, 0.0399019829928875, 0.013316547498106956, -0.04516296833753586, 0.04122529178857803, 0.028388841077685356, -0.011764072813093662, 0.006770219188183546, -0.006441818084567785, -0.03124658763408661, 0.018033621832728386, -0.02319280244410038, -0.007201966363936663, -0.032673440873622894, -0.03538403660058975, -0.027193395420908928, 0.027430929243564606, -0.0046791089698672295, -0.0356292687356472, -0.07292303442955017, 0.08274626731872559, -0.05557824298739433, -0.05212778225541115, 0.08270560950040817, -0.002993346191942692, -0.002976392861455679, -0.03195689618587494, 0.042993415147066116, -0.01484155748039484, 0.006032568868249655, -0.0354326032102108, 0.0062735071405768394, -0.07174640893936157, 0.019388487562537193, -0.014448793604969978, -0.011438537389039993, 0.02413158304989338, 0.015907704830169678, 0.033249031752347946, 0.007523045409470797, -0.018436163663864136, 0.017009682953357697, -0.0032690903171896935, 0.008872144855558872, 0.033430200070142746, -0.019610455259680748, -0.04194623976945877, -0.0109257185831666, 0.06442269682884216, -0.035347625613212585, -0.026847152039408684, 0.014059212990105152, 0.0018264219397678971, -0.04100329056382179, 0.02092345431447029, -0.05706408992409706, 0.011858412064611912, 0.0028741166461259127, 0.003964023664593697, 0.07474485784769058, 0.04525747522711754, 0.015745265409350395, 0.033562347292900085, 0.003684563096612692, 0.010207097977399826, -0.02434895932674408, -0.0019867606461048126, 0.012477228417992592, -0.04754716530442238, 0.007230296730995178, 0.011351022869348526, -0.014357762411236763, -0.06549607217311859, 0.030316052958369255, -0.04463299363851547, -0.038104098290205, -0.03090915083885193, 0.018708255141973495, 0.046034056693315506, -0.05496307089924812, -0.07991231977939606, -0.0015106524806469679, -0.006383503321558237, 0.025167562067508698, 0.0224680807441473, -0.013837062753736973, 0.01964365318417549, -0.05152413249015808, -0.06393060088157654, -0.029928850010037422, 0.018033090978860855, -0.026737814769148827, 0.007766408380120993, -0.024256274104118347, -0.04428205266594887, 0.031746283173561096, -0.007011478766798973, -0.06806892901659012, -0.009805119596421719, 0.05504798889160156, -0.013661175034940243, -0.05511811375617981, -0.007346486207097769, -0.051020242273807526, 0.05500752851366997, -0.07218846678733826, 0.0012590824626386166, -0.04181746393442154, 0.019319897517561913, -0.013800669461488724, 0.01974874921143055, 0.051440559327602386, 0.018418176099658012, 0.027861904352903366, 0.0229581780731678, 0.03343401476740837, -0.03202492371201515, 0.007843910716474056, 0.041710712015628815, 0.02312675304710865, -0.029207296669483185, 0.06390957534313202, -0.0015739816008135676, 0.04610695689916611, -0.012206978164613247, -0.02218455635011196, 0.009353707544505596, 0.022273622453212738, 0.029425324872136116, 0.05034913122653961, -0.01592838019132614, -0.022039184346795082, 0.021265989169478416, -0.07566806674003601, 0.01175687462091446, 0.02357906475663185, 0.0025283859577029943, -0.004088180605322123, 0.02223445102572441, -0.05171937867999077, 0.02066081389784813, 0.006219607777893543, 0.0031200062949210405, -0.06841094046831131, 0.0075799585320055485, -0.027473052963614464, -0.019924145191907883, -0.03444989398121834, 0.029216371476650238, 0.04070861637592316, 0.0036774417385458946, 0.025761445984244347, 0.01656099036335945, 0.055550478398799896, 0.02182304672896862, 0.02776063233613968, 0.008971897885203362, -0.0033463293220847845, 0.007442041300237179, -0.02514357678592205, 0.01939573511481285, 0.0482533760368824, 0.022179972380399704, 0.06009627878665924, -0.0564996600151062, 0.02934090979397297, 0.04536024108529091, -0.0068086255341768265, -0.07529202103614807, 0.035535626113414764, 0.08903864026069641, 0.03484872728586197, 0.05683765187859535, 0.07200087606906891, -0.012669728137552738, 0.03484969213604927, 0.002544340444728732, 0.0065727015025913715, 0.06197110936045647, -0.032105423510074615, 0.001738493680022657, 0.0702003687620163, -0.02353503927588463, 0.03948047384619713, -0.016176417469978333, -0.05356360226869583, 0.029358159750699997, -0.032145652920007706, 0.049312666058540344, -0.024482883512973785, 0.02487991936504841, -0.008650862611830235, 0.021133549511432648, 0.004164996091276407, 0.01270356122404337, 0.031305257230997086, -0.051455236971378326, -0.051269061863422394, 0.023546842858195305, 0.04030246660113335, -0.03587503731250763, -0.13794726133346558, 0.0014058926608413458, 0.036639727652072906, 0.02543415129184723, -0.06790889799594879, -0.019226739183068275, -0.02250312827527523, -0.021501116454601288, 0.05142439156770706, 0.058730173856019974, -0.016835037618875504, -0.019899295642971992, 0.007871650159358978, -0.03936804085969925, -0.006024900823831558, -0.02457301691174507, 0.0019193310290575027, 0.03248261660337448, 0.012380870059132576, -0.011906427331268787, 0.06775408238172531, 0.032005295157432556, 0.019952699542045593, -0.06462414562702179, -0.047166064381599426, 0.03391341492533684, -0.004850092343986034, 0.004540738649666309, 0.05279454216361046, 0.0468486025929451, -0.011440823785960674, -0.010019694454967976, -0.02386847883462906, 0.03998284041881561, -0.040619924664497375, -0.06315283477306366, -0.03514552861452103, 0.011474191211163998, 0.04399098455905914, 0.023988377302885056, 0.025083960965275764, 0.017638327553868294, -0.029319360852241516, 0.016911659389734268, -0.00022725366579834372, 0.020461929962038994, -0.043238215148448944, 0.023935610428452492, -0.00752620305866003, 0.002192460233345628, -0.009161892347037792, 0.0026777861639857292, 0.03717879578471184, -0.07734569162130356, 0.0009487594943493605, -0.026375677436590195, 0.03314441442489624, -0.0038736669812351465, 0.02253943309187889, -0.04162215813994408, -0.04728791117668152, -0.03363042324781418, 0.029979586601257324, -0.0006509119411930442, -0.01283500250428915, 0.002272680401802063, 0.02391783334314823, -0.0023558009415864944, -0.016778014600276947, 0.023806780576705933, 0.030596911907196045, -0.02571273408830166, 0.006879778113216162, -0.01580803468823433, -0.1012255996465683, -0.009899542666971684, 0.025945087894797325, 0.003382025519385934, -0.034657835960388184, -0.03468439728021622, 0.008296262472867966, -0.005694533232599497, -0.05762261152267456, -0.030911967158317566, -0.009199593216180801, -0.002244145143777132, 0.004916418343782425, -0.03723054379224777, -0.06921887397766113, -0.07152566313743591, 0.045409318059682846, -0.025273112580180168, 0.010871791280806065, -0.0666998103260994, 0.018490958958864212, 0.010705559514462948, 0.010223071090877056, -0.020279671996831894, 0.0064256745390594006, 0.007881139405071735, 0.10275815427303314, -0.018496917560696602, 0.002129111671820283, 0.06722448766231537, -0.026060115545988083, 0.035671308636665344, 0.02443111315369606, 0.008898125030100346, -0.024094799533486366, 0.028936779126524925, 0.011335586197674274, 0.007447557523846626, -0.0191911980509758, -0.022294139489531517, -0.022421136498451233, 0.006655661854892969, -0.0355631448328495, -0.043213650584220886, -0.01756921038031578, 0.07596049457788467 ]
<p>First of all, I know there's a much alike question <a href="http://physics.stackexchange.com/questions/15762/what-is-a-wave">here</a> but this is not duplicate since I couldn't find there the answer I'm seeking. My problem is the following: I know that intuitively we have a wave when we have some quantitiy (that as I see can be anything) oscilating at each point in space. So for instance, electromagnetic waves are composed of electric and magnetic fields oscilating on each point of space.</p> <p>Now, this is vague and imprecise. It is not clear at first how to model this mathematically and what properties this thing should have. However there's the wave equation:</p> <p>$$\nabla^2 \psi = \dfrac{1}{v^2} \dfrac{\partial ^2}{\partial t^2}\psi,$$</p> <p>but asking some physicists they told me that not every wave obeys that equation. That anything obeying that equation is really a wave, but that there are waves which evolve differently, some that are nonlinear and all of that.</p> <p>In that case it seems everything is totally vague. A wave is something that moves like a wave, some of those things obeys a certain equation and the others can obey equations totally different. In that case it becomes a little bit difficult to grasp what really is a wave and how do we treat waves with precision.</p> <p>So, what is a wave and how waves are preciselly dealt with in some mathematical framework?</p>
g5408
[ 0.03280891105532646, -0.013588493689894676, -0.006515180226415396, 0.01839674450457096, 0.08044902235269547, -0.029136203229427338, 0.01983930729329586, 0.04367585480213165, -0.030057083815336227, -0.05689741298556328, 0.00041272168164141476, 0.011273150332272053, 0.0006329328753054142, 0.04256260395050049, 0.01578412391245365, -0.06731344014406204, 0.009302202612161636, 0.00919866282492876, 0.038522835820913315, -0.045620519667863846, 0.04046650603413582, 0.029744353145360947, 0.0770118236541748, -0.015312912873923779, -0.05100025236606598, -0.000707675120793283, 0.008584141731262207, -0.031573690474033356, 0.06918767839670181, -0.0021068863570690155, -0.01670645736157894, 0.05428799241781235, 0.095053531229496, -0.02751687727868557, -0.014014004729688168, -0.02166847325861454, -0.014385590329766273, -0.0005743733490817249, 0.03356508910655975, 0.007192813325673342, 0.015397101640701294, -0.02541845664381981, -0.018972184509038925, -0.009644732810556889, 0.04274863377213478, -0.011342155747115612, -0.03075023554265499, -0.03160880506038666, -0.016985764726996422, -0.004199273884296417, -0.011956178583204746, -0.01785019040107727, 0.08325569331645966, 0.009830313734710217, 0.039434414356946945, 0.028180204331874847, 0.04381279647350311, -0.0007516690529882908, 0.10542111098766327, 0.003636842593550682, 0.0017351461574435234, 0.01440675649791956, 0.049005575478076935, 0.0918048843741417, 0.0034585536923259497, -0.039460401982069016, -0.06253179162740707, -0.03590751066803932, 0.01583748310804367, -0.060548510402441025, 0.03918847814202309, -0.08023203164339066, -0.0002252830017823726, -0.03875387832522392, -0.0009808165486901999, 0.027075529098510742, -0.020796077325940132, -0.004964231513440609, -0.008889223448932171, -0.027904247865080833, 0.006836540997028351, -0.016666678711771965, 0.014132861979305744, 0.038286127150058746, 0.035556893795728683, -0.01787935569882393, -0.04620984569191933, -0.020048698410391808, 0.013155912980437279, -0.008600501343607903, 0.03937891125679016, 0.0183723047375679, 0.046331003308296204, -0.014536794275045395, 0.0009521387983113527, -0.0008635427220724523, -0.03455004096031189, 0.04845765605568886, 0.01992364227771759, 0.020855357870459557, -0.05708840489387512, -0.009761864319443703, 0.036207787692546844, -0.005770046263933182, 0.00975466426461935, -0.015286656096577644, -0.007645131088793278, 0.03204578906297684, 0.0065193576738238335, 0.015514468774199486, -0.030383076518774033, -0.0065138875506818295, -0.04025387763977051, -0.047209784388542175, -0.09491311013698578, -0.05151265859603882, -0.010155024006962776, 0.05004668980836868, 0.030345065519213676, 0.07961272448301315, 0.048379406332969666, 0.0016647148877382278, 0.03365185856819153, 0.051978569477796555, 0.06791595369577408, -0.0025239218957722187, -0.00669939024373889, -0.02621658518910408, 0.044933855533599854, 0.02758483961224556, 0.08552636951208115, 0.028895828872919083, -0.04148688539862633, 0.021154142916202545, -0.02094087563455105, 0.03412368521094322, -0.017628170549869537, -0.02694559283554554, 0.02695639245212078, -0.0055078971199691296, 0.004361947067081928, -0.052339162677526474, 0.00541789410635829, -0.013830944895744324, -0.04985306039452553, 0.008010754361748695, 0.02400708943605423, -0.02712751366198063, 0.04252460226416588, -0.006596725899726152, 0.023718301206827164, 0.04771130159497261, -0.02146098203957081, -0.010518302209675312, 0.029963398352265358, 0.008411266840994358, 0.01874631643295288, 0.00031401519663631916, 0.007598907221108675, 0.001669225050136447, 0.05732458457350731, 0.006778863724321127, -0.004428887739777565, 0.04610271379351616, -0.045568227767944336, -0.021507522091269493, 0.0029274343978613615, -0.05207393318414688, 0.023069607093930244, 0.04018420726060867, 0.009537138044834137, -0.019692888483405113, -0.0249649491161108, 0.026866892352700233, 0.03449809178709984, 0.12687337398529053, 0.03751150891184807, -0.010502931661903858, 0.02996686100959778, 0.008978045545518398, -0.05513200908899307, -0.05608999356627464, -0.026668019592761993, -0.049596596509218216, -0.05143856257200241, 0.06947540491819382, -0.007875306531786919, -0.012362118810415268, -0.03160911425948143, -0.01579238474369049, -0.008938710205256939, -0.042621318250894547, 0.026468422263860703, 0.02208811789751053, 0.01794220693409443, 0.030769720673561096, -0.014098559506237507, -0.004471192602068186, -0.010594476014375687, 0.005253076087683439, 0.023679599165916443, 0.0553254708647728, 0.08204951882362366, 0.06665659695863724, 0.040270060300827026, 0.020499760285019875, -0.010402665473520756, -0.03026469610631466, 0.03678547218441963, 0.025944985449314117, 0.04655074700713158, -0.030428925529122353, 0.04486573860049248, 0.02563471905887127, -0.07626780867576599, -0.0005921275005675852, -0.028305374085903168, 0.009816156700253487, -0.070355623960495, -0.008712422102689743, -0.014167365618050098, -0.030417487025260925, 0.0786643996834755, 0.036467429250478745, -0.006582031957805157, 0.036097992211580276, -0.041383132338523865, -0.028516389429569244, 0.007167036645114422, 0.013203848153352737, -0.0414879210293293, 0.02692979946732521, -0.0014167079934850335, -0.04748694598674774, 0.053105466067790985, -0.0008191309752874076, -0.03896958753466606, -0.019008619710803032, 0.014037398621439934, -0.014009346254169941, -0.005905961152166128, 0.014614425599575043, -0.024997862055897713, -0.03691987320780754, 0.030082516372203827, -0.06878432631492615, 0.04978884384036064, 0.006615855731070042, -0.032289206981658936, -0.016153231263160706, 0.03154626488685608, -0.057973138988018036, -0.03929326310753822, 0.004946080967783928, 0.006515578366816044, -0.03925711661577225, -0.019609510898590088, 0.04277779161930084, -0.02009105123579502, 0.00035898899659514427, 0.022882891818881035, -0.017288992181420326, 0.005941046867519617, 0.03993311896920204, -0.0194579865783453, -0.0034006754867732525, -0.013373613357543945, 0.040703184902668, -0.027960069477558136, -0.026561671867966652, 0.017428699880838394, 0.002381750149652362, 0.005119572393596172, -0.0030767580028623343, -0.028226671740412712, -0.03379930928349495, 0.028990382328629494, -0.012890336103737354, 0.00941113568842411, -0.02628503553569317, 0.0020578783005476, 0.02823115512728691, -0.03823823854327202, -0.0036909596528857946, 0.048423442989587784, -0.05284963920712471, 0.040662143379449844, -0.049431461840867996, -0.015942372381687164, -0.020397711545228958, -0.020008308812975883, -0.01841776818037033, -0.06080609932541847, 0.03436203673481941, -0.08603782951831818, 0.05385800823569298, -0.020358406007289886, -0.05746248736977577, -0.0251950453966856, 0.010313541628420353, 0.027325890958309174, 0.03237337991595268, 0.033347729593515396, -0.00771375373005867, 0.06449081748723984, 0.026326263323426247, -0.005433404818177223, -0.035385847091674805, 0.015502816997468472, 0.035089585930109024, 0.020970994606614113, 0.06750444322824478, -0.05754648149013519, 0.007303749676793814, -0.03369623050093651, 0.01200431864708662, -0.009286620654165745, -0.02841244451701641, -0.023879023268818855, -0.02786596678197384, -0.0656832903623581, -0.05406176671385765, -0.0041076685301959515, 0.021276285871863365, 0.08493226766586304, 0.004308078438043594, 0.004239049274474382, 0.015300163067877293, -0.06099472939968109, -0.023725083097815514, 0.01191632729023695, -0.00417342921718955, -0.067278191447258, -0.036145422607660294, 0.00028429250232875347, -0.07346437126398087, -0.013592459261417389, -0.040103979408741, 0.05398011580109596, 0.03321373462677002, 0.027298564091324806, -0.047924116253852844, 0.01968899555504322, 0.0006495785200968385, -0.021042486652731895, 0.061401620507240295, -0.004603233188390732, -0.044294729828834534, 0.014813871122896671, -0.053806889802217484, 0.027506347745656967, 0.021550452336668968, -0.021405786275863647, 0.0013060373021289706, -0.021675171330571175, 0.05788779258728027, 0.10311979800462723, -0.028003212064504623, -0.012642154470086098, -0.012619925662875175, -0.009874611161649227, -0.049802690744400024, 0.04495999962091446, 0.02129519172012806, -0.012896917760372162, -0.0056038531474769115, 0.06761739403009415, 0.01731153577566147, -0.017156437039375305, 0.000048843106924323365, 0.03974594548344612, -0.023645324632525444, -0.003665388561785221, 0.02297382242977619, 0.019306806847453117, -0.030282549560070038, -0.016895484179258347, -0.016621209681034088, -0.01053690817207098, -0.009463313966989517, -0.006671751383692026, 0.028271391987800598, 0.03810587525367737, -0.052846167236566544, 0.034991852939128876, 0.013913887552917004, 0.021899951621890068, 0.020985493436455727, 0.03602457046508789, -0.013598071411252022, 0.029422147199511528, -0.03806907311081886, -0.02419455535709858, 0.01220890786498785, 0.06957052648067474, -0.03898449242115021, -0.017036395147442818, 0.02507247030735016, -0.051446862518787384, 0.058025069534778595, 0.03886299207806587, 0.007636670954525471, 0.016857435926795006, -0.02460230141878128, 0.01790252886712551, 0.016437267884612083, 0.03195899724960327, -0.07674911618232727, -0.01668895035982132, -0.0472179651260376, -0.031705889850854874, 0.03476022183895111, 0.013937425799667835, -0.09001446515321732, -0.024877432733774185, 0.07266027480363846, 0.03689493611454964, -0.029565127566456795, 0.01494287233799696, 0.036340147256851196, 0.02189572900533676, 0.06639868021011353, 0.015517394058406353, -0.0193278007209301, -0.008690788410604, 0.055797088891267776, 0.05868298187851906, 0.033643610775470734, -0.018592625856399536, -0.01901411823928356, -0.02045506238937378, 0.0006216091569513083, 0.04019534960389137, 0.08175424486398697, -0.051600441336631775, -0.001383850583806634, -0.07959061861038208, 0.016454843804240227, 0.023198440670967102, 0.009674347005784512, 0.057854827493429184, -0.0013144253753125668, -0.012406834401190281, -0.01665124110877514, 0.0037810311187058687, 0.009473904967308044, -0.0359448678791523, 0.002884612651541829, -0.04300874099135399, 0.000711896107532084, -0.03366773575544357, 0.07727542519569397, -0.001354288193397224, -0.07338257133960724, -0.01813402585685253, -0.015071329660713673, -0.01885358802974224, -0.00841207429766655, -0.009901117533445358, -0.026776853948831558, -0.03224097937345505, -0.0007405310752801597, 0.052466168999671936, 0.0031076157465577126, 0.005994644481688738, -0.05635309964418411, -0.003141120309010148, -0.05494409427046776, -0.09115248918533325, -0.0037711181212216616, 0.038028836250305176, -0.010034667328000069, -0.020413445308804512, -0.00168873299844563, 0.02558392845094204, 0.018324539065361023, -0.024186871945858, -0.033101703971624374, -0.021163906902074814, -0.08720538765192032, -0.008561541326344013, -0.01406788732856512, 0.036263175308704376, 0.025057531893253326, -0.038518112152814865, 0.020717864856123924, -0.027302592992782593, 0.015074114315211773, -0.019283508881926537, -0.05424020439386368, 0.03780530393123627, 0.01514272391796112, 0.00541525986045599, 0.006234141066670418, -0.007657486479729414, -0.10007934272289276, -0.003985453397035599, 0.02275296114385128, -0.008850489743053913, 0.004906127229332924, -0.05742814391851425, 0.005743565037846565, -0.03114026039838791, -0.031148124486207962, -0.041048720479011536, 0.05617876723408699, 0.006507974583655596, -0.037895746529102325, -0.03919931501150131, 0.04630541428923607, 0.011821247637271881, -0.005729238037019968, -0.07055167108774185, 0.03502052649855614, 0.05647038668394089, -0.02308724634349346, 0.006075281649827957, 0.020315689966082573, -0.017835352569818497, 0.01349277701228857, -0.005762114655226469, -0.011966011486947536, -0.010849135927855968, 0.00010530576400924474, 0.06048019975423813, 0.012435194104909897, -0.07001516222953796, 0.0025167420972138643, 0.03595878556370735, 0.0477345734834671, 0.013961403630673885, -0.011400241404771805, -0.03911849856376648, 0.00492063257843256, 0.008787973783910275, 0.02677740715444088, 0.01677451841533184, -0.0643153190612793, 0.047815460711717606, 0.012151731178164482, -0.038469407707452774, 0.02584647387266159, 0.003320736810564995, 0.06566772609949112, 0.028889106586575508, 0.0077477749437093735, 0.012093174271285534, 0.06361877173185349, 0.023972880095243454, -0.023638205602765083, -0.0823553204536438, -0.03619278594851494, 0.0038320724852383137, -0.0007676921668462455, 0.0607018880546093, 0.028624314814805984, -0.029986420646309853, -0.055011898279190063, 0.0029887014534324408, -0.038891810923814774, 0.018018081784248352, 0.055382706224918365, -0.01558920368552208, -0.0819765105843544, 0.023603012785315514, -0.012096773833036423, 0.028159454464912415, -0.022202331572771072, 0.04056504741311073, 0.057642459869384766, -0.02418573945760727, 0.043556977063417435, -0.02562955766916275, 0.015439625829458237, 0.01584521308541298, 0.0004433203430380672, -0.0008619140717200935, -0.02547328732907772, -0.060062360018491745, 0.05170106887817383, 0.04089692234992981, 0.011277243494987488, 0.0430239699780941, -0.040837954729795456, -0.01527560967952013, 0.09696105122566223, -0.0280567929148674, -0.016094103455543518, 0.03381521254777908, 0.021157119423151016, 0.019770575687289238, 0.014972054399549961, -0.06870575249195099, -0.012615972198545933, 0.014580181799829006, -0.035484857857227325, 0.04849729314446449, 0.011596566066145897, -0.005797156598418951, 0.03455134108662605, -0.012152084149420261, 0.03246308118104935, -0.001522782607935369, 0.005747475195676088, 0.017990034073591232, 0.037882350385189056, -0.030252646654844284, -0.0006854133098386228, -0.030195040628314018, 0.009945504367351532, -0.031890928745269775, 0.041306547820568085, 0.01631452515721321, -0.016992643475532532, -0.007810173090547323, -0.060388967394828796, -0.016466112807393074, 0.01924258843064308, -0.01155817974358797, -0.0007810911047272384, -0.011960540898144245, -0.05988044664263725, 0.01620950922369957, 0.0321669727563858, 0.036627352237701416, -0.010960462503135204, 0.012695522978901863, -0.0034877059515565634, 0.04261279106140137, -0.0641026645898819, -0.040926605463027954, 0.02403952367603779, 0.027281293645501137, 0.040592439472675323, -0.030183790251612663, 0.006936318706721067, -0.035280317068099976, 0.0006057924474589527, 0.048495642840862274, -0.007349328137934208, -0.020505327731370926, 0.03949914127588272, 0.06020693853497505, 0.05122264847159386, -0.07386865466833115, -0.0010005672229453921, 0.020084241405129433, -0.0592537559568882, -0.10592528432607651, 0.021782102063298225, 0.010069862939417362, -0.034765299409627914, -0.02504677325487137, 0.02226102165877819, -0.0473674051463604, 0.041704967617988586, -0.03368797153234482, 0.013476954773068428, -0.04408879950642586, -0.050671037286520004, -0.02761550061404705, -0.023402348160743713, -0.005259927362203598, 0.040281932801008224, -0.0002702451020013541, 0.034439973533153534, 0.0003430053184274584, -0.024506423622369766, 0.011933732777833939, -0.03043496236205101, -0.018300652503967285, -0.043764155358076096, -0.0014716328587383032, 0.006081470288336277, 0.017298294231295586, 0.01762905716896057, -0.05692146718502045, 0.02352011576294899, 0.009090575389564037, -0.034625034779310226, 0.03269645944237709, 0.04439987614750862, 0.023924967274069786, -0.00330172898247838, 0.014964686706662178, 0.019346043467521667, -0.02752276323735714, 0.005181665997952223, -0.0549246221780777, -0.012757515534758568, -0.012504014186561108, -0.027511388063430786, -0.008458747528493404, -0.03311816230416298, -0.004097009543329477, -0.0206315815448761, 0.05648383870720863, 0.03501415625214577, -0.023953014984726906, -0.009192375466227531, -0.004070653114467859, 0.0006269336445257068, 0.020226866006851196, -0.005249570589512587, 0.01984768733382225, -0.012490636669099331, -0.002128572203218937, -0.056143227964639664, -0.045265428721904755, 0.001679757609963417, -0.009816327132284641, -0.017817821353673935, 0.038562316447496414, -0.03868388757109642, -0.0018842426361516118, 0.01675284281373024, -0.03569475933909416, 0.015064883977174759, -0.000013645721082866658, -0.05373002961277962, -0.007015411276370287, 0.01084846630692482, 0.010306233540177345, -0.08095558732748032, 0.02834101766347885, -0.0007506576948799193, -0.005700091831386089, -0.039091359823942184, 0.03859874606132507, -0.0371035635471344, -0.026498716324567795, -0.017598344013094902, 0.022340109571814537, 0.008013906888663769, -0.01254329178482294, 0.08314790576696396, -0.01173409167677164, -0.016070976853370667, 0.024516746401786804, -0.0339987650513649, 0.08554670214653015, -0.0186229906976223, -0.028537852689623833, -0.006054570898413658, 0.025618555024266243, 0.008981261402368546, 0.00590403052046895, 0.04814944416284561, 0.06221004202961922, -0.09582741558551788, -0.038693103939294815, 0.07125017791986465, -0.021054022014141083, 0.03964294120669365, -0.04406047612428665, -0.10926409065723419, -0.0007480310159735382, -0.013835610821843147, 0.06683305650949478, -0.007999751716852188, 0.040278419852256775, -0.008417600765824318, 0.02313581109046936, 0.030817780643701553, -0.059845779091119766, -0.05652507767081261, -0.019326219335198402, -0.026367755606770515 ]
<p>In order to derive the Lorentz transformation one can use the picture of a light clock. A Photons bounces back and forth between two mirrors. This is then observed in two different inertial systems. If the relative speed of the inertial systems is perpendicular to the propagation direction of the photon deriving, extracting the Lorentz transformation is easy and there are hundreds of examples on the web: </p> <p><a href="http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/lightclock.swf" rel="nofollow">http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/lightclock.swf</a></p> <p>However, I am trying to calculate this scenario if the relative motion between the Inertial systems is parallel to the direction of the light propagation:</p> <p><img src="http://i.stack.imgur.com/XfeMN.png" alt="Depiction of clock moving parallel to light propagation"></p> <p>In this case I simply get for the standing observer:</p> <p>$T_{Periode} = \frac{2 h}{c}$</p> <p>and for the moving observer:</p> <p>$ T_{Periode} = \frac{h + v_{rel} t}{c} + \frac{h - 2v_{rel} t}{c} = \frac{2h - v_{rel}}{c}$</p> <p>I can't see how this would lead me to the Lorentz transformation.</p>
g5409
[ 0.042014893144369125, 0.04516485333442688, -0.0033209379762411118, -0.010854890570044518, -0.006654434371739626, -0.003381153102964163, 0.061792973428964615, 0.009776362217962742, 0.01401540171355009, -0.012061742134392262, -0.027717581018805504, 0.060600876808166504, 0.04209397733211517, 0.01924956403672695, 0.014519862830638885, -0.026113642379641533, 0.10869864374399185, 0.00711123226210475, -0.0015022923471406102, 0.00018425274174660444, 0.0023065542336553335, 0.01766338013112545, -0.022773928940296173, -0.04073445126414299, 0.025489427149295807, -0.03573516756296158, 0.006522432900965214, 0.02255789190530777, -0.06754826009273529, 0.012734814547002316, 0.0005533475195989013, -0.0048117609694600105, -0.012115800753235817, -0.029916374012827873, 0.029568683356046677, -0.022209368646144867, -0.031587857753038406, 0.03234367445111275, -0.02599000558257103, 0.05709654092788696, 0.021555038169026375, 0.039927322417497635, -0.02489800564944744, 0.007008933462202549, 0.07562760263681412, 0.01597205176949501, -0.021716294810175896, 0.034611597657203674, -0.017729712650179863, -0.007976016029715538, 0.0007855129078961909, 0.03783894702792168, 0.04467129707336426, -0.022117098793387413, -0.0223720483481884, 0.03470159322023392, 0.06432586163282394, -0.04342096671462059, 0.08149479329586029, 0.05843180790543556, -0.0064575569704174995, -0.062141481786966324, -0.007443051785230637, 0.008422425016760826, 0.03151848539710045, 0.017164258286356926, 0.011694878339767456, 0.011099159717559814, -0.008641542866826057, -0.025625690817832947, -0.023394523188471794, 0.022998077794909477, 0.0029648891650140285, 0.01569497026503086, -0.03943494334816933, -0.007402683142572641, 0.015336466021835804, -0.0507306307554245, -0.011187301948666573, 0.01057157851755619, -0.03327857702970505, -0.0222437996417284, -0.02545078471302986, -0.03146204352378845, 0.08933688700199127, -0.042495813220739365, 0.03674589470028877, 0.04451244696974754, -0.017681332305073738, -0.029090048745274544, 0.04364170506596565, -0.021217236295342445, 0.06722854822874069, 0.02992127276957035, -0.050094105303287506, -0.03211754187941551, -0.09395599365234375, 0.05678455904126167, -0.001232010661624372, -0.005086422897875309, -0.047015950083732605, -0.011126425117254257, -0.0283245500177145, -0.0053385584615170956, 0.05039241164922714, -0.04692860692739487, 0.008577193133533001, -0.016259344294667244, -0.017777664586901665, -0.04868733137845993, -0.04485216364264488, -0.11422130465507507, 0.033338967710733414, -0.01452674251049757, -0.02391715720295906, -0.0700434148311615, 0.024302328005433083, 0.0819389671087265, 0.009386505000293255, 0.05705863609910011, 0.043309535831213, 0.00699151074513793, -0.06112408638000488, 0.030486125499010086, -0.0008906748262234032, -0.011924195103347301, -0.05420822277665138, -0.02402092143893242, 0.057113826274871826, 0.0015855062520131469, 0.017154429107904434, 0.036301687359809875, 0.01587497442960739, 0.015959735959768295, -0.046413883566856384, 0.020672371610999107, 0.07483438402414322, -0.010508074425160885, -0.029387308284640312, 0.002316234167665243, 0.028785647824406624, -0.05823128670454025, 0.021249786019325256, 0.005249537993222475, -0.014901536516845226, 0.04693994298577309, 0.014434386044740677, -0.020198797807097435, 0.0556827150285244, 0.013062331825494766, -0.011215640231966972, 0.10488659143447876, -0.022493083029985428, 0.028505273163318634, 0.05716679245233536, -0.0349077433347702, 0.011449838057160378, -0.017069952562451363, -0.026831066235899925, 0.012936514802277088, 0.07351185381412506, -0.030353905633091927, -0.039062872529029846, -0.04582006484270096, -0.04157133400440216, 0.0022608700674027205, 0.016138095408678055, -0.009328117594122887, -0.05092328414320946, -0.06432182341814041, -0.06443800777196884, -0.014912249520421028, 0.03180186450481415, 0.027293872088193893, 0.022952329367399216, 0.06329742819070816, -0.014125082641839981, -0.009458297863602638, -0.05290756747126579, 0.010652989149093628, -0.00622373353689909, -0.03797086700797081, 0.02397018112242222, -0.0539400652050972, 0.04178709536790848, -0.03546414524316788, -0.013066974468529224, 0.014850826933979988, -0.0832609310746193, -0.011180237866938114, 0.02373688295483589, -0.012514568865299225, -0.0005713678547181189, -0.03959918022155762, -0.03150293976068497, 0.002447538310661912, -0.00015816348604857922, -0.004301778040826321, 0.01222276408225298, 0.049612484872341156, -0.0035826030652970076, 0.03328254446387291, 0.04640179127454758, 0.03343529999256134, 0.01988418959081173, 0.017418405041098595, -0.01593104936182499, -0.012749740853905678, -0.027105271816253662, -0.006751507520675659, -0.021532882004976273, 0.024766741320490837, 0.016071636229753494, -0.011636755429208279, -0.008926582522690296, 0.029298335313796997, 0.034542132169008255, 0.02285681664943695, -0.024265987798571587, 0.0709492489695549, 0.03209914639592171, -0.021198131144046783, -0.004672454670071602, -0.05971476063132286, -0.015175463631749153, -0.04484487697482109, -0.03399854525923729, 0.01628262922167778, 0.017421571537852287, 0.0786394327878952, -0.019295796751976013, 0.02814740501344204, -0.08117205649614334, 0.04096933454275131, 0.06193077191710472, 0.04484944045543671, 0.01657016947865486, 0.04639698192477226, 0.030852660536766052, 0.0016187407309189439, 0.04536653310060501, -0.011758505366742611, -0.03473339602351189, -0.018502293154597282, 0.03314358368515968, -0.011434019543230534, 0.06334397196769714, 0.005389743018895388, -0.022583352401852608, -0.00745824258774519, 0.0247539933770895, -0.06466511636972427, 0.004744681529700756, -0.056233156472444534, -0.04766703397035599, -0.046005699783563614, -0.01072425302118063, 0.058605995029211044, -0.05481266230344772, -0.010877236723899841, 0.0009354004287160933, -0.08674749732017517, -0.012728534638881683, -0.00150536117143929, -0.01791495643556118, -0.016219016164541245, -0.02986595220863819, 0.028297368437051773, -0.021777620539069176, -0.013235058635473251, -0.017186325043439865, 0.031577445566654205, 0.06228455528616905, 0.0468687005341053, -0.030252760276198387, 0.017611710354685783, 0.049253951758146286, -0.038349393755197525, -0.0375920869410038, 0.02823219820857048, 0.022073647007346153, -0.01891695335507393, -0.019121725112199783, -0.032426100224256516, 0.009052039124071598, -0.09392190724611282, 0.014280651696026325, -0.008425150997936726, 0.013091267086565495, 0.06637363880872726, -0.060009121894836426, -0.032557085156440735, 0.02886815555393696, 0.020811235532164574, -0.033969998359680176, 0.04075305908918381, 0.0863436684012413, -0.04325416684150696, -0.003940694499760866, 0.014551534317433834, 0.034503404051065445, -0.024618685245513916, 0.029882432892918587, 0.044018812477588654, 0.02976088970899582, -0.01608780212700367, -0.03906455636024475, -0.014582348056137562, -0.0016701793065294623, 0.02852519415318966, -0.019207045435905457, -0.011792486533522606, 0.020734701305627823, 0.025878088548779488, -0.0034072273410856724, 0.028261709958314896, -0.026407700031995773, 0.02479172870516777, 0.008891277946531773, 0.05898885801434517, -0.027184445410966873, 0.017758086323738098, -0.01006429921835661, -0.025163408368825912, 0.07042059302330017, -0.003586976556107402, 0.019808052107691765, 0.005640227813273668, -0.024032246321439743, -0.022035785019397736, 0.004551879595965147, 0.00972003024071455, 0.0084553062915802, -0.020779315382242203, 0.00474507687613368, 0.0006437184638343751, -0.0410570465028286, 0.033596862107515335, -0.003369537414982915, 0.009361808188259602, 0.015599790960550308, -0.011152049526572227, -0.07454603910446167, 0.07444771379232407, 0.0401817187666893, -0.006596674211323261, 0.02354602888226509, 0.038114141672849655, 0.04440223053097725, -0.0337207168340683, 0.016322899609804153, -0.012215588241815567, -0.00463775172829628, -0.012618142180144787, 0.004292042460292578, 0.020140277221798897, 0.0004052997101098299, 0.0045166416093707085, 0.01610911823809147, 0.003454693593084812, 0.00984921958297491, -0.02571702189743519, -0.013406566344201565, 0.020904451608657837, -0.06807631254196167, 0.04144103452563286, -0.02763025276362896, 0.06946094334125519, -0.00922441016882658, -0.013672646135091782, 0.00027520215371623635, 0.01032289769500494, -0.01928865723311901, -0.012659415602684021, -0.014837936498224735, -0.08318107575178146, 0.07356119900941849, -0.024868972599506378, -0.019197460263967514, 0.05201556533575058, -0.02240482158958912, 0.012019254267215729, 0.04053768515586853, 0.02602635882794857, 0.071274533867836, 0.022696541622281075, 0.01990649476647377, 0.019947635009884834, -0.010440459474921227, -0.03480321168899536, 0.06449104845523834, -0.001767034875229001, -0.013840842992067337, -0.04029270261526108, 0.0012588738463819027, -0.004957277327775955, 0.0636628270149231, -0.0030851424671709538, -0.02236737124621868, -0.019299423322081566, 0.017744682729244232, 0.02588783949613571, -0.0029124259017407894, 0.004865972325205803, -0.04667843133211136, 0.04246584326028824, 0.010081813670694828, -0.04468673840165138, 0.012399788945913315, 0.05322476848959923, -0.04189451411366463, -0.00616685813292861, 0.01539461687207222, -0.042272597551345825, 0.059885360300540924, 0.06437616050243378, 0.05813451111316681, -0.01229545846581459, 0.04039576277136803, -0.026825936511158943, -0.0028557879850268364, 0.07768116146326065, 0.03201194480061531, -0.03823158144950867, -0.024015583097934723, 0.09088452160358429, 0.0504596009850502, -0.020571203902363777, -0.03532971069216728, -0.06687458604574203, 0.03777848184108734, 0.044486209750175476, 0.05438685789704323, 0.011689444072544575, -0.04123036563396454, 0.007639779709279537, 0.0015692561864852905, 0.06013386324048042, 0.043069515377283096, 0.03218061849474907, 0.027306634932756424, -0.03648757189512253, 0.036055196076631546, -0.022657256573438644, -0.06844104081392288, 0.08351995050907135, 0.00867905467748642, -0.0715930312871933, -0.012433012016117573, -0.07092872262001038, -0.008024490438401699, 0.07979153096675873, -0.03655267134308815, -0.0032710444647818804, -0.029890026897192, -0.007867946289479733, -0.025089053437113762, 0.024253271520137787, -0.013218262232840061, 0.040912315249443054, -0.016246719285845757, 0.019610755145549774, 0.015125024132430553, -0.02929062955081463, -0.004554632119834423, 0.010147319175302982, -0.033039554953575134, -0.006600544787943363, -0.024053912609815598, 0.000572499237023294, 0.024510886520147324, -0.048239532858133316, -0.0262016449123621, 0.013817565515637398, -0.010733086615800858, -0.021778715774416924, -0.00923918280750513, -0.009466169402003288, 0.05311356484889984, -0.0000632720475550741, -0.03553178533911705, -0.011881579644978046, 0.032939184457063675, -0.03047581948339939, -0.04074597731232643, 0.04184712842106819, -0.03985549509525299, 0.045747123658657074, 0.02708670310676098, -0.07387956976890564, -0.044636379927396774, 0.006236167158931494, 0.010561397299170494, -0.03570212051272392, -0.0031853443942964077, -0.0076489136554300785, 0.00880329217761755, 0.032454680651426315, 0.0020180956926196814, -0.01907951384782791, -0.053875308483839035, 0.02736646682024002, 0.023307405412197113, -0.024519115686416626, -0.015774240717291832, 0.025957278907299042, 0.018144037574529648, 0.07395502924919128, -0.02331562712788582, 0.03658292070031166, 0.05497565120458603, -0.013668831437826157, -0.024255601689219475, -0.0243016816675663, 0.0205007903277874, -0.03626890480518341, 0.017610954120755196, -0.011514359153807163, 0.017553268000483513, -0.050791896879673004, -0.013680078089237213, 0.02093624137341976, 0.005262034013867378, -0.062449220567941666, 0.03351430594921112, -0.01970462128520012, -0.0652923434972763, -0.004895900376141071, -0.016840554773807526, -0.05774717405438423, 0.011664239689707756, -0.022165218368172646, -0.005808154121041298, -0.017781304195523262, 0.023610159754753113, -0.02291267365217209, 0.07422495633363724, -0.015171037055552006, -0.00023389779380522668, -0.018596438691020012, -0.07233769446611404, -0.014457635581493378, 0.04044095799326897, 0.03205346316099167, -0.07204384356737137, 0.040615297853946686, 0.018297743052244186, -0.02844596467912197, 0.047091975808143616, 0.03830484673380852, -0.033727049827575684, 0.031845495104789734, 0.0263286754488945, 0.02013092301785946, 0.0047832694835960865, 0.03127231076359749, -0.013681000098586082, -0.0325225368142128, -0.0782875046133995, -0.013314778916537762, 0.06425771117210388, 0.0029398067854344845, 0.046615730971097946, -0.021768061444163322, -0.06541649252176285, -0.013391287066042423, 0.025194909423589706, 0.0005790611612610519, 0.027584221214056015, 0.018716152757406235, 0.009684709832072258, -0.013477897271513939, -0.02574816159904003, 0.059956472367048264, 0.001789459609426558, 0.028704015538096428, -0.013646994717419147, -0.032973021268844604, -0.08573233336210251, -0.007031573913991451, -0.016011128202080727, 0.0061211371794342995, 0.031799301505088806, 0.02108735218644142, -0.044214554131031036, 0.004545109812170267, -0.04740593209862709, -0.011208701878786087, -0.03553429991006851, -0.028616975992918015, -0.05454103276133537, -0.006750805769115686, -0.052343979477882385, -0.060822244733572006, 0.004303684923797846, 0.02060781605541706, -0.020693380385637283, 0.012033662758767605, -0.03334611654281616, 0.054332565516233444, 0.0017892344621941447, -0.06981141865253448, 0.03483512997627258, -0.003964776638895273, 0.023065809160470963, 0.030941331759095192, -0.1272009015083313, 0.031056789681315422, 0.037073828279972076, -0.013852741569280624, 0.02843409590423107, 0.02283673733472824, -0.023161474615335464, 0.02765551768243313, 0.0005903126439079642, 0.007709314581006765, -0.03465932980179787, 0.012826358899474144, -0.01597784273326397, 0.03946985676884651, 0.050100505352020264, -0.026158446446061134, -0.03601263463497162, -0.01772175543010235, 0.010242895223200321, 0.05274312570691109, -0.03794292360544205, 0.018555469810962677, -0.004196706227958202, -0.0009053482208400965, 0.05265292525291443, -0.043922897428274155, -0.05182503163814545, 0.0207825880497694, 0.053690098226070404, 0.03218181058764458, -0.006090268027037382, -0.00003078805821132846, 0.018833089619874954, 0.04214290902018547, 0.038034334778785706, 0.016925906762480736, -0.04041362181305885, 0.009339558891952038, 0.007781548425555229, 0.008085901848971844, 0.011268501169979572, -0.04424426704645157, -0.034546010196208954, 0.037085019052028656, -0.034018002450466156, -0.034810226410627365, 0.00730059714987874, 0.024031341075897217, -0.02014649659395218, -0.008778905496001244, 0.016394400969147682, 0.03246188908815384, -0.005935629829764366, -0.08510947227478027, -0.04625063017010689, -0.059697575867176056, -0.013421783223748207, -0.005714952014386654, 0.014620470814406872, 0.02717188559472561, -0.046177078038454056, -0.004950899165123701, 0.021865716204047203, -0.0036600560415536165, -0.0508711077272892, 0.0034807869233191013, -0.012041748501360416, 0.02220974862575531, -0.014148847199976444, 0.010519837029278278, -0.004401740152388811, 0.0023728441447019577, -0.08166712522506714, -0.010157897137105465, -0.07696228474378586, 0.016337672248482704, -0.034707289189100266, 0.03227896988391876, 0.006889462471008301, 0.010701152496039867, 0.019656168296933174, -0.033914610743522644, -0.026822712272405624, -0.04730954393744469, -0.06727375090122223, 0.018421895802021027, -0.010586810298264027, 0.002784027950838208, -0.037483662366867065, 0.011260036379098892, 0.0339164063334465, -0.0030409672763198614, 0.008885851129889488, -0.012066398747265339, 0.01721297949552536, -0.0021613717544823885, 0.05375167727470398, 0.03383409231901169, 0.02565966732800007, 0.006002680864185095, -0.06772973388433456, -0.04384668916463852, 0.043445393443107605, 0.007365715224295855, -0.006625555455684662, 0.035804834216833115, -0.022974036633968353, -0.06134427711367607, 0.02956874668598175, -0.008313773199915886, 0.012101864442229271, 0.03592270240187645, 0.014763708226382732, 0.04449602589011192, -0.025567710399627686, -0.030800769105553627, 0.015214858576655388, -0.07336180657148361, 0.011060131713747978, -0.038420744240283966, 0.06078363209962845, -0.037433821707963943, -0.02560272254049778, -0.0793420746922493, 0.06652463972568512, 0.03631868585944176, -0.04424000903964043, 0.051870789378881454, 0.00009461658919462934, 0.006872728932648897, -0.010027437470853329, -0.05084770917892456, -0.04347935691475868, 0.02455114759504795, 0.004512025974690914, -0.08401879668235779, -0.012013021856546402, -0.01512119546532631, -0.024041099473834038, 0.0052507854998111725, -0.012943110428750515, -0.00013546990521717817, -0.01373933907598257, -0.03594106435775757, 0.0001919370552059263, 0.09993001818656921, 0.004006450995802879, 0.004718141630291939, 0.02310321293771267, -0.04101097956299782, -0.005153266247361898, -0.01724054105579853, 0.039844926446676254, -0.0007063238299451768, -0.013851129449903965, -0.06801632791757584, 0.012445186264812946, 0.03350678086280823, -0.01841074228286743, -0.015584859065711498, -0.05081067606806755, 0.07031577825546265 ]
<p>The formula for centripetal (radial) acceleration is well known, and there exist many proofs for it: $$||a_c|| = \frac{||v||^2}{r}$$</p> <p>However, all the proofs I've seen rely on the fact that it is <em>uniform</em> circular motion and the magnitude of the tangential velocity vector does not change. For instance, take the classic proof using similar triangles — the similarity can only be established if the final tangential velocity vector and the initial one are of the same length.</p> <p>In addition, take <a href="https://www.khanacademy.org/science/physics/two-dimensional-motion/centripetal-acceleration-tutoria/v/calculus-proof-of-centripetal-acceleration-formula" rel="nofollow">this</a> calculus based proof from Khan Academy, outlined as follows:</p> <p><img src="http://i.stack.imgur.com/7ysrf.png" alt="Image 1"> <img src="http://i.stack.imgur.com/lzHw6.png" alt="Image 2"></p> <p>For this proof to work, $\frac{\text{d$\theta $}}{\text{dt}}$ must be considered a constant, $\omega$, that does not depend on time. In the case of non-uniform circular motion, however, this is not always true as since there exists a tangential acceleration along with a radial one, $\omega$ must depend on time and is not necessarily a constant value.</p> <p>Intuitively I understand that the centripetal/radial acceleration depends only on the difference in orientation between two tangential velocity vectors, and that their magnitudes do not matter -- hence the formula intuitively holds true in the non-uniform case. However, how would you go about modifying either of the proofs presented so that they are still valid in this case? Or alternatively, is there another proof that holds valid even when there exists tangential acceleration?</p> <hr> <p>As per the suggestion of one of the answers, I let $\omega$ vary with time and took its derivative as $\alpha(t)$. This is my work so far. Unfortunately, I am stuck after the last step.</p> <p>$$\overset{\rightharpoonup }{p}(t)=r \cos (\theta (t))\cdot\hat{i}+r \sin (\theta (t))\cdot\hat{j}$$ $$\overset{\rightharpoonup }{v}(t)=-r \sin (\theta (t))\cdot\omega(t)\cdot\hat{i}+r \cos (\theta (t))\cdot\omega(t)\cdot\hat{j}$$ $$\overset{\rightharpoonup }{a}(t)=(-rcos(\theta(t))\cdot\omega(t)^2 - rsin(\theta(t))\cdot\alpha(t))\hat{i} + (-rsin(\theta(t))\cdot\omega(t)^2 + rcos(\theta(t))\cdot\alpha(t))\hat{j}$$</p> <blockquote> <p>From here on, $\theta(t)$ is represented as just $\theta$ for brevity and clarity</p> </blockquote> <p>$$\overset{\rightharpoonup }{a}(t)= -\omega(t)^2(rcos\theta\cdot\hat{i} + rsin\theta\cdot\hat{j}) -\alpha(t)(rsin\theta\cdot\hat{i} - rcos\theta\cdot\hat{j})$$</p>
g5410
[ 0.12657809257507324, 0.015437159687280655, 0.01475145947188139, -0.014715317636728287, 0.0403120294213295, -0.0220742579549551, 0.08664609491825104, -0.015392559580504894, -0.04599592089653015, 0.030585138127207756, 0.020549504086375237, 0.01443001814186573, -0.030933644622564316, 0.014652750454843044, -0.009167429991066456, -0.02702319249510765, -0.00630706362426281, -0.05366571247577667, -0.009322027675807476, 0.09585551917552948, -0.005116654559969902, -0.013410106301307678, -0.02469579316675663, -0.04107770696282387, 0.004131482448428869, -0.03293677791953087, -0.02158084511756897, -0.020325571298599243, -0.052108727395534515, -0.012650585733354092, 0.017276616767048836, -0.060793112963438034, 0.002985440194606781, -0.028103355318307877, 0.014875886030495167, -0.010531661100685596, 0.03422028198838234, -0.006912300828844309, 0.05124310776591301, -0.021955670788884163, 0.028993168845772743, -0.00872992817312479, 0.05351674184203148, 0.015372894704341888, 0.02704395353794098, -0.046876080334186554, 0.01626415178179741, 0.0036460624542087317, -0.020931269973516464, 0.05088923126459122, -0.064136803150177, 0.013077796436846256, 0.045132994651794434, -0.01418368797749281, -0.09795420616865158, 0.03869570046663284, 0.04847770929336548, 0.005454907659441233, 0.002259765053167939, 0.053957439959049225, -0.03908660635352135, -0.08070197701454163, 0.0012264986289665103, -0.026201156899333, 0.04333100840449333, -0.01616811566054821, 0.006899937987327576, 0.04501001909375191, -0.04235529154539108, 0.024070817977190018, 0.00739879347383976, -0.014969165436923504, 0.013037647120654583, -0.004057396203279495, -0.06030265614390373, 0.004744236823171377, 0.00040932270349003375, -0.02458825521171093, 0.004885380156338215, -0.029839739203453064, -0.03366732597351074, 0.07533596456050873, 0.0038155338261276484, 0.013516799546778202, -0.00952978152781725, -0.048499561846256256, -0.018130097538232803, -0.01816321350634098, 0.002196249086409807, -0.05068235099315643, 0.05115204304456711, -0.03968910500407219, 0.03793434053659439, 0.017786841839551926, 0.004439449403434992, -0.03631968051195145, -0.05556851625442505, 0.08209366351366043, 0.02536812052130699, 0.02670852467417717, 0.009622684679925442, 0.00135075394064188, 0.04969225078821182, -0.032077301293611526, 0.07396964728832245, -0.04469960182905197, 0.04687816649675369, -0.041068922728300095, 0.004601017571985722, -0.07445383816957474, -0.010876002721488476, -0.06531471014022827, -0.027969535440206528, -0.05204853042960167, -0.006868002004921436, -0.0373576395213604, 0.07374884188175201, 0.05698033422231674, 0.001498746918514371, 0.05620806664228439, 0.013479857705533504, 0.050240278244018555, -0.03186872601509094, 0.08768820017576218, -0.005117527209222317, 0.025916878134012222, -0.023304462432861328, -0.05561812222003937, 0.026306362822651863, -0.06593827903270721, -0.003051656298339367, 0.010283607989549637, 0.03397887945175171, 0.033702701330184937, -0.019121570512652397, 0.04208821430802345, -0.04517531394958496, 0.013434363529086113, -0.00045576001866720617, 0.0066657643765211105, -0.039986707270145416, -0.0692918598651886, 0.03891655057668686, 0.01840432547032833, -0.05415407195687294, 0.031497061252593994, -0.0399162583053112, -0.0030141540337353945, 0.038404062390327454, 0.0341033935546875, -0.004111564252525568, 0.017928799614310265, 0.0175494235008955, -0.019763370975852013, 0.002135324524715543, 0.000462729309219867, 0.0256196279078722, -0.019669709727168083, 0.00048199150478467345, 0.038892097771167755, 0.04385962337255478, 0.017952805384993553, 0.014604786410927773, 0.006751066539436579, -0.025101827457547188, -0.021019451320171356, 0.020597584545612335, -0.006773490458726883, -0.012658861465752125, -0.049782488495111465, -0.0007608150481246412, 0.08058895170688629, 0.04611695557832718, 0.01921568065881729, -0.01875120960175991, -0.0009177062311209738, -0.0061973510310053825, -0.017895104363560677, -0.09233596920967102, -0.020418724045157433, -0.06054192781448364, -0.012584737502038479, -0.04016284644603729, -0.030066970735788345, 0.01911361701786518, -0.021509801968932152, 0.02808823063969612, 0.004959470126777887, -0.06002134084701538, 0.018399357795715332, 0.05026751011610031, -0.03458604961633682, -0.021148717030882835, 0.058137934654951096, -0.05809299647808075, 0.008410543203353882, -0.017284490168094635, -0.02264990285038948, -0.025456175208091736, 0.04072137549519539, 0.004243826027959585, -0.023695027455687523, 0.05373868718743324, -0.006113475654274225, 0.045101746916770935, 0.004956517368555069, 0.044129256159067154, -0.07200965285301208, 0.017107322812080383, 0.0502423457801342, 0.006491014733910561, -0.0051179081201553345, -0.03425152599811554, 0.07045473903417587, 0.025879250839352608, -0.026109999045729637, 0.08820503205060959, 0.012045113369822502, -0.036425601691007614, 0.022516177967190742, -0.01589181274175644, -0.09208814799785614, -0.0052781011909246445, -0.06608498841524124, -0.02126510813832283, -0.014672891236841679, -0.04211430996656418, -0.04788922518491745, 0.026117756962776184, 0.07105638086795807, 0.007550264708697796, 0.016912447288632393, -0.04281647130846977, -0.022093499079346657, -0.008614744991064072, 0.006853723432868719, -0.02044415846467018, -0.027392975986003876, 0.049159836024045944, 0.0342145636677742, 0.039093296974897385, -0.02262546867132187, 0.003862938145175576, -0.018860282376408577, 0.015617170371115208, -0.06514068692922592, 0.05953683704137802, -0.0007188520394265652, -0.0033128787763416767, -0.03339700400829315, 0.0077576423063874245, -0.035459745675325394, -0.04466347396373749, -0.016670359298586845, 0.025975722819566727, 0.021663127467036247, -0.0421130545437336, 0.020909879356622696, 0.005278890021145344, -0.008378349244594574, -0.03403346613049507, 0.012484692968428135, 0.01761307381093502, 0.026486318558454514, -0.0497027263045311, -0.003235511016100645, -0.04067981615662575, 0.004767510574311018, -0.015602166764438152, 0.0472690649330616, -0.06525623798370361, 0.05861435830593109, -0.00035993632627651095, 0.11261626332998276, -0.031040659174323082, -0.002653983421623707, 0.019247736781835556, 0.00902564451098442, -0.03999495133757591, 0.01450260542333126, 0.003937008325010538, -0.04993024095892906, 0.011371307075023651, 0.053401973098516464, -0.03572975471615791, -0.009081498719751835, -0.005720566958189011, 0.017125608399510384, -0.001151571050286293, 0.006536473985761404, -0.029574517160654068, 0.00028574472526088357, 0.018204951658844948, -0.0355178602039814, 0.042176298797130585, -0.010340356267988682, -0.009694496169686317, -0.04525865986943245, 0.04376355931162834, -0.033961355686187744, 0.00603001844137907, -0.010555112734436989, -0.01514772605150938, -0.00953147653490305, 0.009771322831511497, -0.022920966148376465, -0.04418420046567917, -0.10087205469608307, 0.048318639397621155, 0.059600405395030975, 0.017862172797322273, 0.03200915828347206, -0.008232362568378448, 0.008105103857815266, -0.007610092870891094, -0.031161697581410408, -0.010199926793575287, 0.02140125259757042, 0.08154202997684479, 0.07771536707878113, -0.029423702508211136, -0.058334533125162125, -0.05259040370583534, 0.01681610941886902, 0.03760578855872154, -0.03904324024915695, -0.030393429100513458, 0.02105274237692356, -0.02401106432080269, -0.025844888761639595, 0.03006233088672161, 0.03173908591270447, 0.03619999438524246, -0.009572211652994156, -0.007893980480730534, -0.041091978549957275, 0.024634895846247673, 0.03355921059846878, 0.02953144907951355, -0.03222033753991127, -0.031172698363661766, -0.06933335959911346, -0.055710624903440475, 0.00006599152402486652, -0.03157640993595123, 0.026500198990106583, 0.04462004080414772, 0.04514588788151741, 0.04192067310214043, 0.03725869581103325, 0.03150775656104088, -0.052143629640340805, 0.019671902060508728, -0.026720181107521057, -0.02132100984454155, 0.03072582744061947, 0.033877890557050705, 0.02435440383851528, -0.03179371356964111, 0.0004794693668372929, 0.024855753406882286, -0.004713912960141897, 0.016062650829553604, 0.0011224033078178763, 0.010292449034750462, 0.03823402523994446, 0.029850322753190994, 0.02836637571454048, -0.029660960659384727, -0.010207590647041798, -0.00720679247751832, -0.027267983183264732, 0.0038771857507526875, -0.06681722402572632, 0.04021430015563965, -0.029174679890275, -0.04689653962850571, 0.04282505810260773, 0.006416108924895525, 0.06150088831782341, -0.001497513148933649, -0.004218940623104572, 0.011504384689033031, -0.01626191847026348, -0.02845647558569908, 0.053591664880514145, -0.041100867092609406, -0.001919441856443882, 0.05329211801290512, -0.05763448029756546, 0.02385837398469448, 0.014554694294929504, 0.012400130741298199, -0.04258323833346367, 0.04878479242324829, -0.027522645890712738, 0.018267011269927025, -0.016106467694044113, 0.015318474732339382, -0.007692867424339056, -0.03650170564651489, -0.050466373562812805, 0.045670170336961746, -0.01676551252603531, 0.01045456063002348, 0.04709649458527565, 0.0034167910926043987, 0.0329667404294014, 0.028738129884004593, -0.0068236710503697395, 0.0018812998896464705, -0.004017334897071123, 0.033461470156908035, -0.0065516200847923756, 0.054059624671936035, 0.0036873735953122377, 0.016756298020482063, 0.005153931211680174, -0.010783190838992596, -0.015822263434529305, 0.015446455217897892, 0.030413541942834854, 0.017271671444177628, -0.04364074021577835, 0.07251754403114319, 0.08559533953666687, 0.05008407682180405, -0.01567184366285801, -0.0003286203136667609, 0.022422553971409798, -0.014075704850256443, 0.006723286584019661, 0.023844603449106216, 0.02460271678864956, -0.006079440470784903, 0.01778525300323963, -0.015524492599070072, 0.07135353237390518, 0.023130668327212334, -0.029507504776120186, 0.004162494093179703, 0.04413466528058052, 0.0684344694018364, -0.040999144315719604, -0.056321531534194946, 0.08207833766937256, -0.0394737534224987, -0.017120935022830963, 0.011273720301687717, 0.009582451544702053, -0.021140579134225845, 0.025062089785933495, 0.03143350034952164, 0.03190784528851509, -0.04616621509194374, -0.024222075939178467, -0.030117928981781006, -0.021071860566735268, 0.010613065212965012, 0.002391575835645199, -0.036850057542324066, -0.019150912761688232, -0.01567099429666996, -0.04431883245706558, 0.04580787196755409, 0.006801024544984102, -0.021313613280653954, 0.014128422364592552, 0.0029491414315998554, -0.008115987293422222, -0.016549842432141304, -0.01954622194170952, -0.02623218670487404, -0.04486088082194328, -0.012810111977159977, -0.005974114406853914, 0.06245497614145279, 0.03584827855229378, -0.014246929436922073, 0.008433419279754162, -0.04367585852742195, -0.03430294618010521, 0.017056899145245552, -0.01837879978120327, 0.027026692405343056, 0.059774670749902725, -0.02132178097963333, 0.00005965183299849741, 0.03767045959830284, 0.02228776551783085, -0.02141672372817993, 0.005828594323247671, -0.01673542894423008, 0.008452733047306538, 0.015412477776408195, 0.03869761526584625, -0.03740885853767395, -0.05254005268216133, -0.015344622544944286, 0.006186013575643301, -0.07398302853107452, 0.026714911684393883, -0.021001677960157394, -0.027781760320067406, 0.012482710182666779, 0.036561593413352966, 0.030893981456756592, 0.021196642890572548, -0.0013352056266739964, 0.059380386024713516, 0.030309880152344704, 0.051753055304288864, 0.021771878004074097, -0.006727765314280987, -0.03613204136490822, -0.010195888578891754, -0.006082008592784405, 0.03754978999495506, -0.00884403008967638, -0.08198826014995575, 0.07078250497579575, 0.03665144369006157, 0.0036629056558012962, -0.05902624875307083, 0.03981062397360802, 0.007600798737257719, -0.0461706705391407, -0.05714936926960945, 0.03111325390636921, 0.006808917969465256, -0.008601495064795017, 0.009714026935398579, -0.0161608699709177, -0.05338699370622635, -0.06992089748382568, -0.014339967630803585, -0.003177642123773694, -0.02802533283829689, 0.045528117567300797, -0.05110703408718109, -0.0633663609623909, -0.005340551491826773, 0.039904698729515076, 0.004688926972448826, -0.1020246148109436, 0.05443345010280609, -0.04824688658118248, -0.006508755497634411, 0.04275180399417877, -0.04168413206934929, -0.0352327935397625, 0.0378873273730278, 0.0007281622383743525, -0.05019038915634155, -0.020905060693621635, 0.022908026352524757, 0.01265686098486185, -0.011084266006946564, -0.023302413523197174, -0.024249013513326645, 0.045131947845220566, -0.027642471715807915, 0.0829765722155571, 0.0007971388986334205, 0.0036198708694428205, -0.03039529360830784, 0.017421020194888115, -0.04646025598049164, 0.085485078394413, 0.011286602355539799, -0.04580392688512802, 0.010800040327012539, -0.014236369170248508, -0.014588405378162861, -0.007762155495584011, 0.01844196394085884, -0.04084939509630203, 0.012328753247857094, -0.053685881197452545, 0.008880672045052052, 0.030147995799779892, -0.02567148208618164, -0.042900122702121735, -0.011556710116565228, -0.028481047600507736, -0.009616115130484104, -0.052471823990345, 0.03952249139547348, 0.034570906311273575, -0.03754507005214691, -0.058918777853250504, 0.0075896126218140125, -0.0031806305050849915, 0.023299938067793846, -0.03554739058017731, -0.025484859943389893, -0.03651696816086769, 0.025078365579247475, 0.010344963520765305, 0.014516250230371952, 0.020758265629410744, -0.028380218893289566, 0.03899414464831352, -0.0004044448141939938, -0.008302455767989159, -0.00558155681937933, 0.004250798374414444, -0.04408852756023407, 0.038571689277887344, 0.009954705834388733, 0.006198480259627104, 0.040728580206632614, 0.019767235964536667, 0.054571375250816345, -0.020911067724227905, 0.022236954420804977, -0.026636820286512375, -0.023580064997076988, -0.0024862613063305616, -0.010130076669156551, 0.02105906419456005, 0.009206780232489109, 0.021905245259404182, 0.037635333836078644, 0.007158679887652397, 0.008731859736144543, -0.026662468910217285, 0.029289016500115395, 0.04239401966333389, -0.03981107845902443, 0.01752028800547123, -0.04206833243370056, -0.008997746743261814, 0.04093331843614578, 0.02734038420021534, 0.03448457643389702, -0.01859106309711933, 0.022123904898762703, 0.03772252798080444, 0.0022099276538938284, 0.020379837602376938, 0.012391227297484875, 0.0016208019806072116, -0.040418580174446106, -0.1323140412569046, -0.0688207596540451, 0.018829675391316414, 0.049243807792663574, -0.0848255529999733, -0.00850254949182272, 0.05367483198642731, -0.011713559739291668, -0.07140558958053589, 0.03023129515349865, -0.0026940004900097847, -0.010880575515329838, 0.03535551577806473, 0.04550956189632416, 0.028919856995344162, -0.05150594934821129, -0.05231203883886337, -0.027102027088403702, 0.02434699609875679, 0.0075919958762824535, 0.002758689457550645, 0.00012688316928688437, -0.026318727061152458, 0.002058124402537942, -0.0015790157485753298, -0.017540253698825836, 0.04715140908956528, 0.05392948538064957, 0.02831301838159561, 0.03639255836606026, 0.0034342685248702765, 0.04045047610998154, -0.04897536709904671, -0.03208232671022415, 0.022373909130692482, 0.02285999245941639, -0.011414535343647003, -0.023638591170310974, 0.04548323526978493, 0.010820431634783745, 0.002292294055223465, 0.04878335818648338, 0.0037471093237400055, 0.011441545560956001, 0.04377172514796257, -0.04387035220861435, -0.01963617280125618, 0.006952957715839148, 0.047607723623514175, 0.012720705941319466, 0.046062905341386795, 0.010373453609645367, 0.0208390261977911, 0.00798247940838337, 0.002830382902175188, 0.004939972423017025, -0.02646980620920658, -0.021658174693584442, 0.007644199766218662, 0.008901318535208702, 0.019429046660661697, 0.015101769007742405, -0.031125374138355255, 0.01593186892569065, -0.050657063722610474, -0.021617835387587547, 0.006277583539485931, 0.025978609919548035, -0.019281983375549316, -0.02683759666979313, 0.04070768132805824, -0.03328193351626396, -0.02661300264298916, 0.0483103021979332, -0.0006413315422832966, -0.03556118160486221, -0.019073374569416046, -0.013339214026927948, 0.04614466056227684, -0.10919712483882904, 0.025108125060796738, 0.021902916952967644, -0.013757054693996906, -0.05717957764863968, -0.05729488283395767, -0.04482076317071915, 0.0034235483035445213, 0.03297842666506767, -0.006032875273376703, 0.08407910913228989, -0.037188805639743805, 0.03478578105568886, -0.0031482421327382326, -0.002262973226606846, -0.02098269760608673, -0.06040162965655327, 0.0024927454069256783, -0.038137007504701614, -0.026324717327952385, 0.06411472707986832, -0.040639109909534454, 0.04681474715471268, 0.03229980543255806, 0.06427285075187683, 0.07152999937534332, -0.04506387189030647, 0.03309955820441246, 0.023745641112327576, -0.09790724515914917, -0.0213969387114048, 0.047949571162462234, -0.023212939500808716, 0.00777547899633646, -0.0065304930321872234, 0.03433401510119438, -0.04591270536184311, 0.03193427622318268, 0.01007595844566822, -0.013312414288520813, -0.01348001230508089, -0.009775364771485329, -0.017264969646930695, -0.06892623752355576, 0.006354678422212601 ]
<p>After reading <a href="http://www.nasa.gov/topics/technology/features/new-nano.html" rel="nofollow">this NASA article</a> about the "blackest material", the following stuck out to me.</p> <blockquote> <p>The tiny gaps between the tubes absorb 99.5 percent of the light that hits them</p> </blockquote> <p>Is it possible to create a material that absorbs, not just all visible light, but all electromagnetic radiation?</p>
g561
[ 0.035402875393629074, 0.03490448743104935, 0.008659630082547665, 0.021374382078647614, 0.02303258143365383, 0.058083899319171906, -0.060593605041503906, 0.060656119138002396, 0.001605185796506703, -0.04291357472538948, 0.06531926244497299, 0.05106143653392792, 0.026762476190924644, 0.0016627717996016145, -0.00345805287361145, 0.03732769936323166, 0.07761657983064651, 0.0072719077579677105, 0.010041993111371994, 0.04879187420010567, -0.006961950566619635, -0.021711891517043114, -0.01785743609070778, -0.05458381399512291, -0.04908423125743866, 0.049606189131736755, -0.028577180579304695, -0.021757865324616432, -0.007387150079011917, -0.0619235634803772, 0.03861788287758827, -0.029856642708182335, 0.005591534078121185, 0.002315661171451211, -0.04418965429067612, 0.006497170776128769, -0.06320931017398834, -0.028835946694016457, -0.03175245225429535, 0.043850548565387726, 0.005463413428515196, 0.03311913460493088, 0.009480456821620464, -0.02574450522661209, -0.03222227841615677, 0.015187815763056278, -0.007272241171449423, -0.00613392423838377, -0.026040121912956238, -0.05791500210762024, -0.0006936521967872977, -0.023135671392083168, 0.04020390659570694, 0.009817139245569706, 0.018151670694351196, -0.013621256686747074, -0.001775248791091144, -0.0560966320335865, 0.06583400815725327, 0.017418038100004196, -0.061882488429546356, -0.017107313498854637, -0.01825769618153572, 0.039412930607795715, -0.0018061441369354725, -0.015093482099473476, -0.033788371831178665, -0.02669285424053669, -0.008538256399333477, -0.010974058881402016, 0.00507824681699276, 0.02996431291103363, -0.016610251739621162, 0.00488132843747735, -0.03474865481257439, 0.020017145201563835, -0.059654880315065384, 0.0962362289428711, 0.007790697738528252, 0.011816761456429958, -0.03616194799542427, 0.02727261744439602, -0.03798724338412285, 0.032326363027095795, 0.07432958483695984, -0.04198057949542999, -0.010737438686192036, -0.06657068431377411, -0.04965301230549812, 0.04557089880108833, 0.03625580668449402, -0.005690575111657381, 0.033377647399902344, 0.00006850143108749762, 0.07636230438947678, 0.03907258063554764, 0.022112606093287468, 0.022367293015122414, -0.020833788439631462, -0.04809701442718506, -0.0078061423264443874, -0.047349486500024796, 0.024444885551929474, 0.012758136726915836, 0.022675437852740288, -0.01430601067841053, 0.011187472380697727, -0.037721626460552216, -0.030485309660434723, 0.03049113042652607, -0.04544375091791153, -0.04701944813132286, -0.06897573173046112, -0.012182545848190784, 0.019773928448557854, -0.013422812335193157, 0.07914196699857712, -0.03709090128540993, -0.010189048945903778, 0.057402148842811584, 0.05648644641041756, 0.021826809272170067, 0.019492169842123985, -0.0011191354133188725, 0.000733574794139713, -0.014064398594200611, -0.009884391911327839, 0.0013057761825621128, 0.019203508272767067, -0.043058812618255615, 0.030505632981657982, 0.011031988076865673, -0.02650720253586769, 0.010654008015990257, 0.010347842238843441, -0.010552898049354553, 0.026824332773685455, 0.000027729829525924288, 0.0008583947201259434, 0.013271491043269634, -0.016692550852894783, -0.056327320635318756, -0.0414888858795166, 0.014993103221058846, -0.013121480122208595, 0.014262283220887184, -0.021924201399087906, 0.04988082870841026, -0.002434168942272663, 0.014970019459724426, 0.025058943778276443, 0.035604529082775116, -0.0017804420785978436, -0.04994979128241539, -0.03588224574923515, 0.005689053796231747, 0.09030884504318237, 0.019287487491965294, 0.005430527031421661, 0.014436702243983746, 0.023690449073910713, 0.03420767933130264, 0.03236943855881691, -0.05509117245674133, -0.0404292494058609, -0.021767299622297287, -0.033082135021686554, -0.10296028852462769, 0.03898182511329651, -0.06289780884981155, -0.0013722142903134227, -0.028822489082813263, 0.008617326617240906, 0.04950863867998123, 0.024585483595728874, 0.0535518079996109, 0.10253873467445374, -0.06184186041355133, -0.014186271466314793, -0.024225939065217972, -0.021901505067944527, -0.004199393559247255, -0.008144049905240536, -0.019321352243423462, 0.028252914547920227, -0.035558730363845825, 0.04260688275098801, 0.003355450229719281, -0.005636713467538357, 0.025865472853183746, -0.04004983231425285, -0.009585894644260406, 0.011652967892587185, 0.02008621208369732, -0.00417286716401577, -0.020224466919898987, 0.049276042729616165, -0.018511919304728508, 0.01696225255727768, 0.012666590511798859, 0.029919814318418503, 0.06367513537406921, -0.018142955377697945, 0.020552612841129303, 0.05993502214550972, 0.005702884867787361, -0.07403779029846191, -0.041540492326021194, 0.0067937965504825115, -0.002215290442109108, 0.05849960818886757, 0.03557819500565529, 0.01706238090991974, 0.03266506269574165, -0.04291072115302086, -0.08183854818344116, -0.07814271003007889, 0.006775400135666132, -0.021584315225481987, -0.023957207798957825, -0.008312677033245564, 0.006317324936389923, -0.013722352683544159, -0.0006248701829463243, -0.021701112389564514, -0.032581035047769547, -0.05389875918626785, -0.059521544724702835, 0.03443697839975357, -0.01972244866192341, -0.05733392387628555, -0.039373259991407394, 0.024534039199352264, -0.03944822773337364, 0.06585977971553802, 0.014267404563724995, -0.016949033364653587, -0.018160799518227577, -0.06127588450908661, -0.006655263248831034, 0.04938839375972748, -0.026369353756308556, -0.05014916881918907, -0.0483589842915535, -0.01080107782036066, -0.02134069614112377, -0.04058576002717018, -0.010305712930858135, -0.01594538427889347, 0.02620049938559532, 0.03578504920005798, -0.049314241856336594, 0.007283378392457962, -0.013871285133063793, 0.01846843957901001, -0.025989551097154617, -0.008943445980548859, -0.0026443081442266703, -0.054212722927331924, -0.030522139742970467, 0.014197688549757004, -0.04358873888850212, 0.02173854038119316, 0.038170766085386276, -0.0339127853512764, 0.025764986872673035, -0.03409351781010628, -0.021347589790821075, -0.010419766418635845, 0.07807949185371399, -0.06403745710849762, 0.013555911369621754, 0.05665242299437523, -0.0012785985600203276, 0.0026789349503815174, 0.0669369027018547, 0.00029220347641967237, -0.036696162074804306, 0.029445480555295944, 0.0017468079458922148, -0.009225450456142426, -0.0033945434261113405, -0.026788217946887016, 0.0000861214502947405, 0.010801684111356735, -0.028358489274978638, -0.022713394835591316, -0.05088048428297043, 0.01895979233086109, 0.055017273873090744, -0.07103072106838226, -0.03665938600897789, 0.010437080636620522, 0.006981506943702698, -0.04134851321578026, 0.012365788221359253, 0.026636170223355293, -0.011278479360044003, -0.07625964283943176, 0.051487792283296585, -0.0027159140445291996, 0.0009322850964963436, 0.04517363756895065, 0.021102113649249077, -0.05190224200487137, 0.02262299321591854, 0.010829141363501549, -0.025714874267578125, 0.029597202315926552, 0.0007118961657397449, -0.003393241437152028, 0.03447269648313522, 0.009170775301754475, 0.04497702047228813, -0.011716671288013458, 0.01890154741704464, 0.04860880970954895, -0.029820840805768967, 0.08355481177568436, 0.004454880952835083, -0.005414069164544344, -0.040563520044088364, 0.002100919606164098, -0.04444584622979164, 0.045695655047893524, -0.006975975353270769, 0.02502169832587242, -0.02738826721906662, -0.03607717156410217, 0.0323902890086174, 0.047817401587963104, -0.009786608628928661, 0.009087378159165382, 0.02081778459250927, 0.004777473863214254, -0.014484965242445469, -0.03350374102592468, 0.056352533400058746, 0.034734852612018585, -0.0005256886361166835, -0.05207308754324913, -0.04065614938735962, -0.07710378617048264, 0.0055921063758432865, 0.035229600965976715, 0.034915100783109665, 0.0018403544090688229, 0.0069962553679943085, 0.024990888312458992, 0.04697548598051071, 0.060033611953258514, 0.00010167826258111745, -0.011526601389050484, -0.03105028159916401, -0.012577077373862267, 0.03231516480445862, 0.06583701819181442, 0.03823968023061752, 0.11164163798093796, -0.04426288977265358, 0.03938117250800133, -0.013912060298025608, 0.0657801702618599, -0.08939897269010544, -0.05510378256440163, 0.02758491225540638, 0.036055274307727814, 0.025958161801099777, 0.02906789630651474, 0.05392341688275337, -0.06085699424147606, -0.004865516442805529, -0.033745162189006805, 0.03358810022473335, 0.025453869253396988, -0.011094227433204651, -0.0031913258135318756, 0.023931220173835754, 0.011609580367803574, 0.011715959757566452, -0.027445005252957344, 0.028389200568199158, -0.015249659307301044, 0.011342703364789486, 0.011171530932188034, 0.03558744117617607, -0.012692486867308617, 0.0016355093102902174, -0.029729092493653297, -0.05416776239871979, -0.026437876746058464, 0.011171500198543072, -0.05562037602066994, -0.03181258589029312, -0.03634287416934967, -0.038252003490924835, -0.01748601347208023, -0.04594462364912033, 0.0036141087766736746, 0.022368229925632477, 0.07824934273958206, 0.06783146411180496, 0.029961349442601204, -0.03713616356253624, 0.010869181714951992, 0.015339383855462074, 0.015184899792075157, 0.0330084003508091, -0.016837963834404945, 0.016270076856017113, -0.0001877497270470485, -0.014932841993868351, -0.005787872709333897, -0.03708096966147423, 0.05391211807727814, 0.037468262016773224, -0.05657720938324928, -0.027567675337195396, -0.007841323502361774, -0.021707024425268173, 0.033249251544475555, -0.011308693327009678, -0.03769880160689354, 0.03246062621474266, 0.010450954549014568, 0.0205509252846241, 0.018095938488841057, 0.016975589096546173, 0.024667484685778618, -0.0030771230813115835, 0.03013632632791996, -0.03308477625250816, -0.01046836469322443, 0.03839736431837082, -0.04940712824463844, 0.013851705938577652, -0.031251899898052216, -0.050338633358478546, 0.07601543515920639, 0.03158623352646828, 0.06420476734638214, -0.04526054114103317, 0.002791123930364847, -0.012558294460177422, 0.06362036615610123, 0.07027103751897812, 0.032603487372398376, -0.03251523897051811, 0.018115181475877762, 0.06659261137247086, 0.003941168077290058, -0.06284288316965103, -0.011736813001334667, -0.02208435907959938, 0.01314795296639204, -0.03566015884280205, -0.024597521871328354, 0.026487741619348526, 0.11484622210264206, 0.03676280006766319, -0.00671709980815649, 0.0014927268493920565, 0.058902036398649216, 0.01712947152554989, 0.029477369040250778, -0.003623283002525568, -0.016359126195311546, 0.004657691810280085, -0.04779220372438431, -0.027638670057058334, -0.05064254626631737, 0.03479437530040741, 0.01718745008111, 0.02565518021583557, -0.015053893439471722, -0.0505027137696743, -0.058512549847364426, 0.0015742977848276496, -0.06983759999275208, -0.011900712735950947, -0.026504281908273697, 0.013388613238930702, 0.049112726002931595, 0.017753034830093384, 0.03216461092233658, 0.04772140458226204, -0.056426845490932465, 0.06490844488143921, -0.015989750623703003, -0.07656460255384445, 0.005787915550172329, -0.0014265448553487659, -0.011156206019222736, -0.031708892434835434, -0.03188815340399742, -0.029070226475596428, 0.06477171182632446, -0.010605165734887123, -0.012906767427921295, 0.0288639385253191, 0.03904789313673973, -0.017891349270939827, -0.019599294289946556, -0.04487225413322449, 0.016380494460463524, 0.01807902380824089, 0.0025041636545211077, 0.034019529819488525, 0.0164291150867939, 0.0000937749064178206, -0.04668981209397316, 0.008874624967575073, -0.060260530561208725, 0.012347014620900154, 0.005392287392169237, -0.058401986956596375, -0.04241664335131645, 0.05728937312960625, -0.02237369306385517, -0.05678097903728485, -0.05468962341547012, -0.03583914041519165, 0.002196436282247305, 0.04013699293136597, 0.01871727779507637, -0.011536569334566593, -0.04781326279044151, 0.007656825706362724, 0.06310538947582245, 0.03756313398480415, 0.06635221838951111, 0.028266437351703644, 0.005678809713572264, -0.006230230443179607, -0.008507177233695984, 0.005417871288955212, 0.06197066605091095, 0.03895782306790352, 0.02396427094936371, 0.0032661468721926212, 0.018976479768753052, -0.0019168651197105646, 0.06835662573575974, 0.09375372529029846, 0.08523716032505035, 0.026346739381551743, -0.037172671407461166, -0.0024820684920996428, -0.013215679675340652, -0.0108803054317832, -0.020415060222148895, 0.017730344086885452, 0.04038579389452934, 0.06644155085086823, 0.029914572834968567, 0.036402855068445206, -0.018727635964751244, -0.025722986087203026, 0.03781869262456894, -0.05067983642220497, 0.058681778609752655, 0.009463269263505936, 0.04685356095433235, -0.032731108367443085, -0.01297748927026987, -0.003390924772247672, 0.007052360102534294, -0.02839619107544422, 0.04327090084552765, 0.009815013036131859, 0.001262847799807787, -0.03603285551071167, -0.04185027256608009, 0.00800845492631197, -0.04575426131486893, -0.03140094503760338, 0.039795197546482086, 0.014195896685123444, -0.033991821110248566, 0.046812668442726135, 0.045625071972608566, 0.009800217114388943, -0.009389867074787617, -0.0406963974237442, -0.004493034444749355, 0.017835624516010284, 0.0045425547286868095, 0.06027781590819359, -0.034572526812553406, -0.0234355628490448, 0.0033455758821219206, -0.016937339678406715, 0.014512338675558567, -0.014895967207849026, -0.03428627923130989, -0.042911626398563385, -0.028760042041540146, -0.012192611582577229, 0.001254797214642167, 0.04121240973472595, -0.007396685425192118, -0.030813422054052353, -0.04460778459906578, -0.009562644176185131, 0.0027317951899021864, -0.023381972685456276, -0.01661672815680504, -0.026762355118989944, 0.033340997993946075, -0.004253976512700319, -0.049439433962106705, -0.023340264335274696, -0.06772220134735107, -0.012454557232558727, -0.07065888494253159, -0.050072081387043, -0.03543311357498169, -0.022747837007045746, 0.034797243773937225, 0.01719689555466175, -0.02052389271557331, -0.02863825485110283, -0.02725936472415924, -0.02055985853075981, 0.01658216491341591, 0.05771719291806221, -0.022679073736071587, 0.021256403997540474, 0.04975670576095581, 0.025270601734519005, 0.007775225210934877, 0.012572736479341984, 0.04107619822025299, 0.03599131852388382, 0.02764907293021679, 0.051745038479566574, 0.05784882977604866, -0.09347695857286453, 0.035628948360681534, 0.002240746980533004, -0.00653355335816741, 0.0012999994214624166, 0.03279043734073639, 0.08110834658145905, 0.002979842247441411, 0.08306024223566055, 0.003210265189409256, -0.00006274119368754327, 0.017867453396320343, -0.008210767060518265, 0.03845387324690819, -0.051969848573207855, -0.026603633537888527, -0.01182127557694912, -0.0501895472407341, -0.005811180453747511, -0.05748351290822029, -0.005801972933113575, 0.028786297887563705, -0.0590500570833683, 0.019189268350601196, -0.048215702176094055, 0.005967812146991491, -0.003866483923047781, 0.04169734939932823, -0.0038352033589035273, 0.01779354363679886, -0.01005410123616457, 0.006476483307778835, -0.028527822345495224, 0.010913524776697159, -0.02944146655499935, -0.011020051315426826, -0.023282812908291817, -0.04509652778506279, -0.1039205864071846, 0.027326028794050217, 0.0664495974779129, 0.0006636817124672234, 0.01578977331519127, 0.0064970324747264385, -0.009016650728881359, 0.03206070885062218, -0.010033473372459412, 0.009609207510948181, -0.0491449199616909, -0.02822321280837059, 0.013609356246888638, 0.02000425197184086, -0.015421280637383461, -0.03939729183912277, 0.02532106079161167, 0.020319271832704544, -0.02855869196355343, 0.018487658351659775, 0.022048283368349075, 0.033184051513671875, 0.023730788379907608, -0.04628615453839302, -0.03019237332046032, -0.06203204393386841, -0.004188933409750462, -0.018937021493911743, -0.03647162765264511, -0.003560752607882023, 0.01602734997868538, 0.018633395433425903, 0.00962300319224596, -0.0354827418923378, 0.02618919126689434, 0.06615463644266129, 0.09473451972007751, 0.012723064050078392, 0.03699864074587822, 0.023540174588561058, 0.0036888704635202885, -0.05232612416148186, -0.002720552496612072, -0.003247886896133423, 0.02279733680188656, 0.020784951746463776, -0.011339406482875347, -0.03466593101620674, -0.06749796867370605, -0.0074344114400446415, -0.04690181091427803, -0.008510923944413662, 0.0006825474556535482, -0.004464772529900074, -0.015962889418005943, 0.005392030812799931, 0.006266152486205101, -0.04653666540980339, -0.033327143639326096, 0.027790699154138565, -0.005381961818784475, -0.03330432251095772, -0.015521123073995113, 0.014321310445666313, -0.01709960401058197, -0.018664268776774406, -0.03523382544517517, -0.04516392573714256, -0.03418871387839317, -0.030446374788880348, 0.02585943229496479, -0.027762282639741898, 0.022981852293014526, 0.01198347844183445, -0.03574357554316521, -0.06224782392382622, 0.0439637154340744, 0.030886227265000343, 0.007290429901331663, 0.10547803342342377, -0.046328913420438766, 0.0022998542990535498, -0.008084269240498543, 0.01348572876304388, 0.03331958130002022, 0.021294541656970978, 0.03640967980027199, -0.06561771035194397, -0.029056664556264877, 0.004263924900442362, 0.01005333662033081, 0.043614838272333145, -0.024819625541567802 ]
<p>I am reading the two concepts mentioned in the title. According to the definition of torque and moment of inertia, it would appear that if I pushed on a door, with the axis of rotation centered about its hinges, at the door-knob, it would be difficult, relative to me applying a force nearer to the hinges. However, I just experimented with my front door, and it would appear to be the converse, what am I misunderstanding?</p> <p>Definition of torque: $\tau=r\times\vec{F}$, where r is the length of the lever arm (the distance from the axis of rotation to the point of application of the force).</p> <p>EDIT:</p> <p>Also, what does it mean for torque to be perpendicular to the rotation?</p>
g5411
[ 0.00997157022356987, 0.011438215151429176, 0.00335987051948905, -0.024182498455047607, 0.016394736245274544, -0.04815426468849182, 0.07920389622449875, -0.005890486761927605, -0.03583831712603569, 0.014459105208516121, -0.015772143378853798, -0.05016760155558586, -0.019842304289340973, -0.020319519564509392, 0.05076178163290024, 0.005926771555095911, 0.047901496291160583, 0.037806667387485504, 0.05963373929262161, 0.05371398851275444, 0.02424006350338459, -0.0033104445319622755, -0.07432220131158829, -0.03892936557531357, 0.004103869199752808, 0.02935626171529293, 0.001122605288401246, 0.04482574015855789, 0.0017228624783456326, -0.008775245398283005, 0.012317062355577946, 0.019660070538520813, 0.019252879545092583, -0.07518653571605682, -0.0651930645108223, -0.00951040256768465, 0.01628422923386097, 0.032188668847084045, 0.05171828344464302, -0.008250831626355648, -0.007024859543889761, -0.028875820338726044, -0.0158699844032526, 0.01143061276525259, -0.010419921018183231, 0.0032917680218815804, -0.025364462286233902, 0.03088342770934105, 0.03194873407483101, -0.024731185287237167, -0.019571008160710335, -0.04011579230427742, 0.03644092381000519, -0.04171593487262726, -0.022950051352381706, 0.002238623332232237, 0.061459410935640335, -0.002860515145584941, 0.021811604499816895, 0.04395117983222008, 0.008623473346233368, -0.01541026122868061, -0.02201705239713192, 0.016277097165584564, 0.048681147396564484, 0.004852005746215582, 0.07873352617025375, 0.02368752844631672, 0.013350475579500198, -0.04268847033381462, -0.037555038928985596, -0.050083864480257034, 0.05205250531435013, -0.04954291880130768, -0.046526577323675156, 0.0206241887062788, 0.015186588279902935, 0.009400218725204468, 0.00030017158132977784, 0.013693506829440594, -0.03405372425913811, -0.04016811400651932, 0.018816521391272545, 0.028992166742682457, 0.09420458972454071, 0.009405309334397316, -0.014494367875158787, 0.03704734891653061, 0.09061991423368454, 0.016951508820056915, 0.07825373858213425, -0.020713578909635544, 0.01191707793623209, 0.013646293431520462, -0.05674209073185921, -0.031676460057497025, -0.017580661922693253, 0.09431275725364685, 0.058328017592430115, 0.046671949326992035, 0.00035305367782711983, -0.037796176970005035, -0.006277395877987146, -0.0418616347014904, 0.02448275126516819, -0.04790116101503372, 0.034796107560396194, -0.014865637756884098, -0.06591473519802094, -0.011890344321727753, -0.061496030539274216, 0.004944815766066313, -0.027927109971642494, -0.0256305243819952, 0.00827078241854906, -0.047766126692295074, 0.052575692534446716, 0.020742198452353477, 0.022849127650260925, 0.04170427843928337, -0.02320481278002262, 0.040370095521211624, 0.006081876344978809, 0.07762938737869263, -0.013132928870618343, -0.02758105844259262, -0.05185924097895622, -0.032933276146650314, 0.043300993740558624, -0.03505993261933327, 0.0012023183517158031, -0.005506104789674282, -0.006321114953607321, 0.03423754870891571, 0.042208537459373474, 0.03817129135131836, -0.022243192419409752, -0.0008381921797990799, 0.0023046396672725677, 0.0017559414263814688, 0.01834980957210064, 0.024367768317461014, 0.011908884160220623, 0.038656994700431824, -0.045921411365270615, 0.03357807174324989, -0.05088089406490326, 0.002903267042711377, 0.05323418974876404, 0.007394949905574322, -0.012753892689943314, 0.054292213171720505, -0.0336705707013607, 0.010353614576160908, 0.02600853331387043, -0.0025015827268362045, 0.011926667764782906, -0.0018459456041455269, -0.00036006112350150943, 0.0675501674413681, -0.006686639040708542, -0.006024030037224293, 0.00939357653260231, -0.030957171693444252, -0.015350911766290665, -0.005124268587678671, -0.0557950995862484, -0.017557304352521896, 0.0073988791555166245, -0.04311694577336311, -0.03730226680636406, 0.036679498851299286, 0.02673167921602726, -0.03418032452464104, 0.007348541170358658, 0.018043136224150658, -0.016898298636078835, -0.061037175357341766, 0.006946372799575329, -0.03025457262992859, -0.016211355105042458, 0.005885903723537922, -0.00045438067172653973, -0.009026780724525452, -0.05910801142454147, -0.040483977645635605, 0.053263697773218155, 0.021722136065363884, -0.05718746408820152, 0.015676843002438545, -0.009599431417882442, -0.04494583606719971, -0.0026970161125063896, 0.07423466444015503, -0.02998511493206024, -0.009425442665815353, 0.01147688739001751, -0.011682133190333843, -0.00897904671728611, 0.06289849430322647, -0.07142851501703262, 0.004086723085492849, 0.06235793977975845, 0.07193249464035034, -0.005687145981937647, 0.029485415667295456, -0.033516015857458115, 0.013026095926761627, 0.0988956168293953, 0.0036909892223775387, -0.0056239101104438305, 0.030866509303450584, 0.013433561660349369, -0.018357299268245697, -0.020220642909407616, -0.04107442870736122, -0.017155731096863747, 0.045238424092531204, -0.026311222463846207, -0.04405508190393448, -0.002683213446289301, -0.04652300104498863, 0.003569228807464242, 0.00024727481650188565, -0.05784691125154495, -0.0256667360663414, -0.022481132298707962, 0.029321424663066864, 0.005917277652770281, -0.03563342243432999, -0.0021643899381160736, -0.02632436342537403, -0.017748307436704636, 0.043404072523117065, 0.01666489988565445, 0.01155867986381054, 0.025500917807221413, 0.03574967011809349, -0.02970260940492153, -0.01288066990673542, 0.04389938339591026, -0.03650221228599548, 0.019131340086460114, 0.03190821409225464, -0.0013065413804724813, -0.020084239542484283, 0.07395967096090317, -0.05226646736264229, 0.043644536286592484, 0.011010754853487015, -0.0023695738054811954, -0.026148857548832893, -0.062109749764204025, -0.0051811314187943935, -0.024228518828749657, 0.02607000432908535, -0.005094518885016441, -0.019609563052654266, -0.026959359645843506, -0.023101547732949257, -0.0021335671190172434, -0.006361665669828653, 0.063418909907341, 0.005628389306366444, -0.003238565055653453, -0.006398046854883432, -0.04679681733250618, 0.04335668683052063, 0.02231781557202339, 0.016056418418884277, 0.005189765710383654, 0.11934018135070801, -0.04424413666129112, 0.008281480520963669, 0.010221848264336586, -0.04631209746003151, -0.018511902540922165, 0.03258231282234192, -0.01835659146308899, -0.039483457803726196, -0.08111359924077988, 0.018916476517915726, 0.0063569312915205956, 0.047570135444402695, 0.01213886123150587, 0.0030939080752432346, -0.023580599576234818, -0.006279155611991882, -0.03777172043919563, 0.036228932440280914, 0.009086644276976585, 0.02593117766082287, 0.03631152957677841, -0.014634168706834316, 0.03722931444644928, 0.015093055553734303, -0.006287754513323307, -0.021078728139400482, -0.024757275357842445, 0.010700302198529243, 0.005918825510889292, -0.034742288291454315, 0.03909808397293091, 0.005655221175402403, 0.007604977581650019, 0.0015154565917328, -0.027057413011789322, -0.02282031811773777, -0.021112941205501556, 0.05140748620033264, -0.08634625375270844, -0.006236928980797529, -0.02402365580201149, -0.03474223613739014, -0.04885244742035866, -0.049461573362350464, -0.013708791695535183, 0.010508873499929905, -0.028486963361501694, 0.046908359974622726, -0.010470433160662651, -0.04718731716275215, -0.0345834344625473, 0.0443551242351532, 0.031151743605732918, 0.060124874114990234, -0.06814546883106232, 0.02942982316017151, 0.003162928856909275, -0.06042715907096863, 0.0424436554312706, 0.05861867219209671, -0.011939628049731255, 0.004331675358116627, -0.04809437319636345, 0.05277049541473389, -0.005520767532289028, 0.028227441012859344, -0.002447724575176835, 0.04638301953673363, 0.04543048515915871, -0.04147609323263168, -0.02564118430018425, 0.03782767057418823, 0.015362859703600407, 0.048488497734069824, -0.02766493149101734, 0.01146954670548439, 0.05964811146259308, 0.03516215831041336, 0.025998927652835846, -0.02388766221702099, 0.015846364200115204, -0.03916490077972412, 0.014637957327067852, 0.011922595091164112, -0.035459231585264206, 0.02024735137820244, -0.04141414165496826, 0.042695339769124985, 0.047003358602523804, 0.0032498689834028482, -0.0496101938188076, -0.05041971802711487, -0.015092811547219753, -0.00869724154472351, 0.042115941643714905, 0.07331787794828415, 0.011990953236818314, 0.006615139078348875, -0.03393521159887314, -0.00021992463734932244, -0.0066703432239592075, -0.020987043157219887, 0.05452267453074455, -0.05464816093444824, 0.019462423399090767, -0.04118327051401138, 0.01842420920729637, 0.03819594159722328, -0.00852564163506031, 0.04013211652636528, -0.02437831647694111, -0.03639128804206848, -0.0026460313238203526, 0.0010436002630740404, -0.004329640418291092, 0.012845230288803577, 0.06272675096988678, -0.03236842527985573, -0.06633790582418442, 0.01811085268855095, -0.04154640808701515, 0.0063100093975663185, 0.06703772395849228, 0.012619866989552975, 0.012155134230852127, 0.022598937153816223, -0.06593120843172073, 0.024369435384869576, 0.04397732764482498, 0.0803351178765297, -0.0030140234157443047, 0.028138184919953346, -0.029281513765454292, 0.039237502962350845, 0.013680164702236652, 0.04375267028808594, -0.021598607301712036, -0.023998400196433067, 0.019289493560791016, -0.026792485266923904, -0.07039733231067657, -0.02487555332481861, 0.03661339730024338, 0.0013698487309738994, 0.05488279089331627, 0.018576499074697495, -0.02207168936729431, 0.06251553446054459, 0.039063721895217896, 0.031528882682323456, 0.08855804055929184, 0.000606585992500186, -0.0030444867443293333, 0.017757052555680275, 0.02070198394358158, 0.04859934374690056, 0.029124800115823746, -0.036251917481422424, -0.02170480787754059, -0.024671955034136772, 0.043602198362350464, -0.02399563603103161, 0.05441921949386597, -0.04369491711258888, -0.005662481300532818, 0.00649613793939352, 0.02864585444331169, -0.028837433084845543, -0.02662370726466179, 0.04739203304052353, 0.009452066384255886, -0.003984836395829916, -0.10370998829603195, 0.03354024142026901, -0.009735222905874252, -0.04194488748908043, -0.017845170572400093, 0.016533393412828445, -0.09279484301805496, -0.008013281039893627, -0.0026596083771437407, -0.05559411272406578, 0.05881974473595619, 0.0198472049087286, -0.022547930479049683, -0.012512325309216976, -0.04218623787164688, -0.0390586219727993, -0.0359165221452713, -0.02032976970076561, -0.020026713609695435, 0.03333912789821625, 0.023350749164819717, -0.0027613271959125996, -0.01152043230831623, 0.021966436877846718, -0.07056108117103577, -0.007530738599598408, 0.0023054126650094986, -0.05058940127491951, -0.006591904908418655, 0.023474305868148804, 0.04088882356882095, 0.040966663509607315, 0.062364645302295685, -0.001057035056874156, -0.013044764287769794, -0.01744707114994526, -0.042338963598012924, -0.076840840280056, 0.013800092972815037, -0.05399211496114731, -0.013288861140608788, -0.01854328066110611, -0.00009931031672749668, -0.00388834485784173, 0.03658996894955635, -0.004071291070431471, 0.049873288720846176, 0.10222024470567703, -0.046262577176094055, -0.050179701298475266, -0.05108344554901123, 0.05434178188443184, 0.03849375620484352, -0.000808662676718086, -0.038968537002801895, -0.0018737917998805642, -0.09206818789243698, 0.03740796819329262, -0.03823694586753845, 0.020144261419773102, -0.034486111253499985, 0.025794174522161484, 0.05358438566327095, -0.005398019682615995, -0.043810922652482986, 0.04370783269405365, 0.04341888427734375, 0.04520241543650627, -0.02844190038740635, 0.016556957736611366, -0.0011342044454067945, -0.005456462502479553, 0.001241603516973555, 0.008318687789142132, -0.03756842762231827, -0.003432788420468569, 0.0546463243663311, 0.03549330681562424, -0.01823931746184826, -0.0821290835738182, -0.026181897148489952, 0.013759265653789043, 0.004334406927227974, 0.01804606430232525, -0.069806769490242, 0.04697921499609947, -0.035253025591373444, 0.04747433960437775, 0.0526110865175724, -0.0627618134021759, -0.03374532610177994, -0.030322792008519173, 0.0679636150598526, -0.03485467657446861, 0.016609881073236465, -0.039182525128126144, -0.0049056243151426315, -0.048498205840587616, -0.014464645646512508, -0.0064790332689881325, -0.09010885655879974, -0.009903354570269585, -0.005242874380201101, -0.10077018290758133, -0.000013430701073957607, 0.005768627859652042, -0.06832662969827652, 0.03506651148200035, -0.05696135386824608, -0.00485427537932992, -0.0156769547611475, 0.038053348660469055, 0.05978187918663025, -0.033874478191137314, -0.017432909458875656, -0.03831854462623596, 0.06386370956897736, 0.007729524280875921, 0.021976467221975327, -0.005987638607621193, 0.029661277309060097, -0.031058847904205322, -0.009716592729091644, -0.026730723679065704, 0.006125352811068296, 0.06584419310092926, 0.03016246296465397, -0.053570643067359924, -0.0014388482086360455, -0.013901608996093273, 0.03249654918909073, 0.08361630886793137, -0.04842052981257439, 0.009304167702794075, -0.014425557106733322, -0.005713033024221659, 0.01687927544116974, -0.05487264320254326, -0.0023436276242136955, -0.020002808421850204, 0.019633973017334938, 0.0033777339849621058, -0.05527060106396675, -0.017880629748106003, 0.04366561025381088, 0.0070248618721961975, -0.04300682619214058, 0.02250034175813198, -0.028234943747520447, -0.029859868809580803, 0.031314667314291, 0.046331737190485, -0.017823662608861923, 0.014594553969800472, -0.014337982051074505, 0.07408018410205841, 0.0162679310888052, 0.027457883581519127, 0.07719677686691284, 0.04858388751745224, 0.003100472269579768, -0.008846559561789036, -0.014377872459590435, 0.019236180931329727, 0.02605617232620716, -0.003783614607527852, 0.05190998688340187, 0.05875414237380028, 0.000994384754449129, 0.02438037097454071, -0.005448944866657257, 0.03866153582930565, -0.04439665377140045, -0.04315907135605812, 0.04060779884457588, 0.017457298934459686, 0.011184516362845898, -0.011207809671759605, -0.011487863957881927, -0.009803930297493935, -0.05950196087360382, 0.01831422559916973, -0.08298094570636749, 0.0576142892241478, 0.03390737622976303, -0.0010290603386238217, 0.010541824623942375, -0.07620973140001297, -0.06861841678619385, 0.02365642972290516, -0.029129544273018837, 0.011620362289249897, -0.04492693021893501, 0.027302641421556473, -0.005985647439956665, 0.041682999581098557, 0.02403564751148224, -0.018398674204945564, -0.061878953129053116, 0.02018396370112896, -0.026967283338308334, -0.030663209035992622, -0.00425688736140728, -0.027718860656023026, -0.029729710891842842, 0.02189585193991661, -0.029135392978787422, -0.007293439470231533, -0.04314885661005974, 0.035024382174015045, -0.028353411704301834, -0.04025648534297943, 0.007753558456897736, 0.015492351725697517, -0.03700747713446617, -0.04499295726418495, -0.024279698729515076, 0.03492866829037666, -0.039782289415597916, 0.03594576194882393, 0.0232296884059906, -0.0006591113051399589, -0.011699275113642216, 0.007006740663200617, 0.02993944101035595, -0.033650465309619904, 0.021800989285111427, -0.025396155193448067, 0.007268642541021109, 0.00969799142330885, -0.021515462547540665, 0.04764876887202263, 0.03397688642144203, -0.027748558670282364, -0.05347245931625366, -0.06887151300907135, -0.010747643187642097, 0.016630718484520912, -0.02706802450120449, 0.027638381347060204, 0.012549502775073051, 0.04290691018104553, -0.007674528751522303, -0.054418936371803284, -0.04011606052517891, -0.08249468356370926, -0.004959700163453817, 0.01400955580174923, 0.0017527230083942413, 0.04641396924853325, -0.031667087227106094, -0.0037197726778686047, 0.019401490688323975, 0.04059350863099098, -0.02602563239634037, 0.015293552540242672, -0.016298353672027588, -0.0009638849296607077, 0.03588642552495003, 0.010951783508062363, 0.006955157965421677, 0.04434233531355858, 0.004313130397349596, 0.026835909113287926, -0.0068214163184165955, 0.019171953201293945, -0.009273665957152843, 0.04703580588102341, 0.024449830874800682, 0.036587391048669815, -0.001253296504728496, -0.008847102522850037, 0.01978868991136551, 0.022719886153936386, -0.0030596971046179533, 0.0011432740138843656, 0.01128806546330452, -0.006961263716220856, 0.03768163174390793, -0.04757978394627571, -0.0380241833627224, 0.00942094624042511, 0.002672437811270356, -0.06271462887525558, -0.033700089901685715, 0.010847947560250759, 0.007501171436160803, -0.04995747655630112, 0.000981682795099914, 0.03472217172384262, -0.04036012664437294, 0.06039823964238167, 0.00381508469581604, -0.020923567935824394, 0.02045484259724617, 0.02020709216594696, 0.020975420251488686, -0.027642011642456055, -0.025598911568522453, 0.012164297513663769, -0.02348765730857849, -0.034430067986249924, -0.01709809899330139, 0.029116177931427956, 0.027730736881494522, 0.06567192822694778, -0.026382090523838997, -0.005893087945878506, -0.09442610293626785, -0.041674818843603134, 0.01531730592250824, 0.014889327809214592, -0.06122581660747528, 0.012566829100251198, 0.06619910895824432, -0.0013457790482789278, -0.02137545309960842, 0.0004929171409457922, 0.017115535214543343, -0.07205066829919815, 0.01872967928647995, -0.02010180987417698, -0.03490948677062988, 0.022311441600322723 ]
<blockquote> <p><strong>Possible Duplicate:</strong><br> <a href="http://physics.stackexchange.com/questions/7584/how-do-we-know-that-some-radioactive-materials-have-a-half-life-of-millions-or-e">How do we know that some radioactive materials have a half life of millions or even billions of years?</a> </p> </blockquote> <p>I understand how to calculate decay, but it seems to me that the formula leaves a lot to be desired. I learned in chemistry that radioactive decay occurs completely at random, which is why we have assigned half life times to radioactive isotopes. But how can we know for sure the half life of an isotope unless one waits for exactly half the sample to decay? For all we know, uranium has a much shorter half life, and all the samples are about to decay to half mass. Thanks for any help in clarifying. </p>
g191
[ 0.015597689896821976, 0.008170672692358494, 0.010774205438792706, 0.017308158800005913, 0.020417090505361557, -0.0026994699146598577, -0.0032436384353786707, 0.06291978061199188, 0.008466668426990509, -0.03045092523097992, -0.04122934490442276, 0.01708838902413845, 0.03824948891997337, -0.003441103035584092, 0.024900291115045547, -0.02553226239979267, 0.09583920985460281, -0.059593819081783295, 0.013890299946069717, 0.060349468141794205, -0.015235483646392822, 0.015378961339592934, 0.010065200738608837, -0.01052363682538271, -0.07652004063129425, -0.0357452891767025, 0.02097013033926487, 0.028483957052230835, 0.01190105639398098, -0.006688032764941454, -0.039263926446437836, -0.028379112482070923, 0.056199029088020325, -0.0025024593342095613, 0.03643535450100899, -0.05985879898071289, 0.005585726350545883, 0.025156725198030472, 0.04905485361814499, 0.014428375288844109, 0.025210440158843994, -0.0401654876768589, 0.06963421404361725, 0.002916117198765278, -0.018728649243712425, 0.0053154355846345425, -0.09460411220788956, 0.004423399455845356, 0.04573235288262367, -0.050413694232702255, -0.019313994795084, 0.03854318708181381, 0.05041282996535301, 0.04113101586699486, -0.04784058406949043, -0.02441093511879444, -0.0023158800322562456, -0.007859539240598679, 0.09525956213474274, -0.03371403366327286, 0.06386637687683105, -0.06271259486675262, -0.0025087527465075254, 0.03536368906497955, 0.09228835999965668, 0.046243779361248016, -0.035101424902677536, 0.008717088960111141, 0.047522932291030884, 0.036662470549345016, 0.02302626520395279, 0.018585264682769775, -0.032656822353601456, -0.02393363229930401, -0.058755043894052505, -0.0025037522427737713, 0.02659379132091999, 0.06748979538679123, 0.05157462880015373, 0.06335318833589554, -0.018126605078577995, -0.014751669019460678, 0.023578228428959846, 0.0687195211648941, -0.024214256554841995, 0.024467574432492256, -0.07670601457357407, 0.016170574352145195, -0.035132478922605515, 0.04808757081627846, 0.010915648192167282, -0.015313480980694294, 0.008650023490190506, 0.04604874923825264, 0.04239137843251228, -0.01737212762236595, -0.03869440034031868, 0.065342478454113, -0.03232644498348236, 0.05597032606601715, 0.013322397135198116, -0.03252892941236496, -0.02181846834719181, -0.03278113529086113, -0.038675565272569656, 0.02821890078485012, -0.019053321331739426, 0.01830786094069481, -0.0277877077460289, -0.005122237838804722, -0.021098867058753967, 0.025501074269413948, -0.06755740940570831, 0.0031206223648041487, 0.031385261565446854, 0.03902212902903557, 0.05689985677599907, -0.022213168442249298, 0.015790462493896484, -0.004276986233890057, 0.007925264537334442, 0.047425318509340286, -0.016217520460486412, -0.03093467280268669, -0.02070923149585724, -0.05102526396512985, 0.008762774057686329, 0.009170792065560818, -0.0041047558188438416, 0.04472579434514046, -0.004932853858917952, 0.04302925243973732, -0.02694212645292282, 0.03596702590584755, -0.03544273599982262, 0.07036300003528595, 0.023286862298846245, 0.06816917657852173, -0.05601798743009567, -0.007753410376608372, -0.0009252461604773998, 0.011180047877132893, -0.012271993793547153, -0.00402083108201623, -0.0802728682756424, 0.08869458734989166, -0.03264588862657547, -0.01855648308992386, -0.00004916684338240884, 0.0240030474960804, 0.03545837476849556, 0.03551536053419113, 0.0051888516172766685, -0.02453622780740261, 0.01101741474121809, -0.02304970473051071, 0.02086244896054268, -0.054971031844615936, -0.02628033608198166, 0.051246266812086105, 0.029295414686203003, 0.019608940929174423, -0.055019836872816086, -0.01550538931041956, -0.0035077251959592104, 0.012196005322039127, 0.03511224314570427, -0.05490713566541672, -0.0007811811519786716, -0.07091473042964935, -0.026091614738106728, 0.01158782560378313, 0.043873995542526245, 0.05762476474046707, -0.022979678586125374, 0.06235075369477272, 0.046738337725400925, -0.025490982457995415, -0.023273253813385963, 0.0024288417771458626, 0.01959880441427231, -0.03168409317731857, 0.054430313408374786, -0.0004629871982615441, -0.017280830070376396, 0.039206720888614655, 0.04458801448345184, -0.007327890023589134, -0.026390893384814262, 0.038746871054172516, -0.03138233348727226, -0.04486823081970215, 0.03488576039671898, 0.027743414044380188, 0.00822519138455391, -0.01044679805636406, -0.007574631832540035, -0.0706300139427185, 0.03376728668808937, 0.047777581959962845, -0.02449241653084755, -0.022178705781698227, -0.030730877071619034, 0.030502961948513985, 0.06842563301324844, -0.003568242536857724, -0.006613411009311676, 0.009991709142923355, 0.03148959204554558, -0.017898892983794212, 0.036979690194129944, 0.022497791796922684, -0.020011983811855316, 0.05708421394228935, 0.011067165993154049, -0.021150868386030197, -0.08274121582508087, 0.004957776982337236, 0.04681950807571411, 0.014070423319935799, 0.02109697461128235, -0.013001636601984501, -0.025016332045197487, 0.003620009869337082, -0.012881115078926086, 0.03895660489797592, -0.0613790825009346, -0.004595205187797546, 0.0031823001336306334, 0.00553481699898839, -0.03749877214431763, 0.012743504717946053, -0.005587133578956127, -0.027221353724598885, 0.0031598499044775963, 0.05332820862531662, -0.005908389110118151, -0.0592661090195179, -0.013166716322302818, 0.010147486813366413, -0.025404395535588264, -0.040399204939603806, -0.038335416465997696, 0.04093557223677635, -0.0065290192142128944, -0.08101817220449448, -0.008811944164335728, -0.06589268893003464, -0.0025187302380800247, 0.05742831155657768, -0.0065148635767400265, 0.0063236309215426445, 0.001238208613358438, -0.00598507234826684, -0.010922973975539207, -0.016197312623262405, -0.05194131284952164, 0.038058873265981674, -0.05779426172375679, -0.002013354329392314, 0.02070339396595955, -0.02158321812748909, 0.049509525299072266, 0.018362706527113914, -0.03032437153160572, -0.06084931641817093, -0.028537752106785774, 0.025550412014126778, 0.016094716265797615, 0.02446676976978779, 0.031785815954208374, 0.023120790719985962, 0.02157963439822197, 0.04900838062167168, -0.040840812027454376, -0.005514690652489662, 0.011680050753057003, -0.014429560862481594, -0.003350947517901659, -0.0010346770286560059, 0.011063861660659313, 0.019306914880871773, -0.010662988759577274, 0.07683839648962021, -0.007437942083925009, -0.02903658337891102, 0.010727249085903168, -0.03092854842543602, 0.04088457301259041, -0.01931084878742695, -0.0381174273788929, -0.009174979291856289, 0.012555649504065514, -0.03274345025420189, -0.014619537629187107, 0.04165114462375641, 0.03396352380514145, -0.03174612298607826, -0.050052572041749954, -0.005348305683583021, 0.01873394474387169, -0.08055062592029572, -0.005144140217453241, -0.024923400953412056, -0.006797128822654486, 0.014913992024958134, -0.023891780525445938, -0.014464807696640491, -0.007109903730452061, 0.0055291783064603806, -0.021295353770256042, 0.0431455597281456, 0.0009477388230152428, -0.007139019668102264, -0.05323445424437523, -0.020609978586435318, -0.05164401978254318, 0.022781487554311752, 0.0038056205958127975, -0.09530837833881378, -0.012751637026667595, -0.06698402762413025, 0.025815339758992195, 0.0276634581387043, 0.00193901383318007, -0.007254813797771931, -0.043508537113666534, -0.011648191139101982, -0.06456397473812103, -0.029183702543377876, 0.007642967160791159, 0.027737978845834732, -0.011995164677500725, -0.002563140820711851, -0.07431979477405548, -0.04741375520825386, -0.014418483711779118, 0.003184075467288494, -0.007163067348301411, -0.013641116209328175, 0.003264352213591337, -0.0009365050354972482, -0.02684764750301838, 0.05650624260306358, 0.039120208472013474, 0.0023448271676898003, 0.016887182369828224, -0.018497752025723457, -0.012769770808517933, 0.011330729350447655, 0.027025366201996803, 0.0036284257657825947, -0.04517172649502754, 0.01655275747179985, -0.005392841529101133, 0.04180808365345001, 0.00949049647897482, -0.01110183447599411, 0.0894617810845375, -0.013663793914020061, -0.009176214225590229, -0.053931113332509995, 0.06403800845146179, -0.016174916177988052, -0.010944648645818233, 0.014328394085168839, 0.0707644522190094, 0.052015092223882675, 0.0737399235367775, -0.015122273936867714, 0.0003465058689471334, -0.009696903638541698, 0.06574754416942596, -0.010586761869490147, -0.0038876631297171116, -0.009213116951286793, 0.03827889263629913, -0.004316103644669056, -0.026379505172371864, 0.02565394528210163, -0.0053212204948067665, 0.003361790208145976, -0.02251911722123623, -0.025976233184337616, -0.01490203570574522, -0.004697029944509268, -0.02573896013200283, -0.018115634098649025, 0.006361393257975578, -0.05868407338857651, 0.023975780233740807, -0.0586278922855854, -0.026495566591620445, 0.04360681027173996, 0.00019466772209852934, -0.08204548060894012, 0.040679968893527985, 0.039924073964357376, -0.013909238390624523, -0.04414428025484085, -0.042303744703531265, 0.006352697964757681, -0.043580833822488785, 0.004636205732822418, 0.04262949898838997, 0.08860311657190323, 0.0003471893141977489, -0.07292978465557098, 0.08658017218112946, -0.045458100736141205, -0.0089586665853858, -0.00672347005456686, 0.02100578509271145, -0.039666324853897095, 0.015737732872366905, -0.016162626445293427, 0.002163259545341134, -0.023098593577742577, -0.03707176819443703, 0.009824981912970543, 0.009752361103892326, -0.013478032313287258, -0.05371946468949318, 0.004131948575377464, -0.008792757987976074, 0.03786904364824295, -0.009388442151248455, 0.011020305566489697, 0.026471717283129692, -0.016942067071795464, 0.052207447588443756, 0.042495667934417725, 0.00826976913958788, 0.03403313830494881, -0.06311653554439545, -0.0036203162744641304, 0.020350953564047813, 0.01852552779018879, 0.023709293454885483, 0.03874099627137184, 0.035802680999040604, -0.003924941178411245, 0.011257396079599857, 0.03499072045087814, -0.011060317046940327, 0.022296559065580368, 0.0023160900454968214, -0.005039065144956112, 0.03671031445264816, -0.029701152816414833, -0.007432968355715275, 0.0002907498273998499, -0.035592351108789444, -0.03227904066443443, 0.0037811968941241503, -0.038176264613866806, 0.024831371381878853, 0.06575131416320801, 0.00843951478600502, 0.09153114259243011, -0.043045349419116974, -0.09034035354852676, 0.06400971859693527, -0.003682071343064308, -0.07783319056034088, 0.03152098134160042, 0.018291492015123367, -0.03621461242437363, -0.0012905572075396776, 0.04064776375889778, -0.06800604611635208, -0.012872193939983845, 0.03636136278510094, -0.017070017755031586, -0.0023763254284858704, -0.015827151015400887, -0.05809491500258446, -0.008400438353419304, 0.015511072240769863, -0.0015306532150134444, -0.05573675408959389, 0.009245906956493855, -0.04087567701935768, 0.01848619058728218, 0.006354771554470062, -0.020869901403784752, -0.04407183453440666, 0.019012130796909332, 0.016218753531575203, -0.03375944495201111, -0.0024662865325808525, 0.03804510831832886, 0.059637680649757385, 0.0008157147676683962, -0.03498208895325661, -0.06941978633403778, -0.010325334034860134, -0.02799486741423607, 0.005833537317812443, -0.005523175001144409, 0.007068335078656673, 0.017794763669371605, 0.0004753550747409463, 0.02318628877401352, 0.04386655613780022, 0.07574797421693802, 0.03222908824682236, -0.003974309656769037, -0.04027601331472397, -0.019465791061520576, 0.014634443446993828, 0.049559902399778366, -0.02901051566004753, 0.042710497975349426, 0.00465822359547019, 0.03603123500943184, -0.06417832523584366, 0.04086460918188095, -0.057155609130859375, -0.02011495642364025, -0.043046798557043076, 0.014560570940375328, 0.04752587154507637, 0.007224671076983213, 0.019336530938744545, -0.09573175013065338, -0.08759693056344986, -0.009553849697113037, 0.0013492880389094353, 0.026172589510679245, 0.04587758705019951, 0.013953804038465023, -0.05243232473731041, -0.04572927579283714, -0.011680737137794495, 0.05450819060206413, -0.031795989722013474, -0.07147835940122604, 0.01696580834686756, -0.01585211046040058, 0.03971360996365547, 0.0332062803208828, 0.049408119171857834, 0.04535235837101936, 0.009142900817096233, -0.022816630080342293, -0.048525501042604446, -0.027009231969714165, 0.05976804718375206, -0.0032386884558945894, -0.011564276181161404, 0.03797765448689461, 0.042660512030124664, -0.013020161539316177, 0.0963813066482544, 0.010427788831293583, 0.0347612239420414, 0.007488400675356388, -0.02350422739982605, 0.05246339365839958, -0.021049538627266884, 0.07352478802204132, 0.0056794630363583565, 0.007996134459972382, 0.04048359766602516, -0.07272128015756607, -0.02527538500726223, -0.02821875922381878, 0.008422517217695713, 0.02777908928692341, -0.0012044199975207448, -0.007017839699983597, -0.027025394141674042, -0.05437833443284035, -0.005148952826857567, 0.0393376387655735, -0.029410725459456444, -0.046251267194747925, 0.021706443279981613, 0.011820858344435692, -0.05774916708469391, -0.03688645362854004, 0.004174604546278715, 0.02702273800969124, -0.026209507137537003, 0.014578117057681084, 0.008124872110784054, -0.016250593587756157, 0.02855837158858776, 0.016935104504227638, 0.026946034282445908, 0.02844434604048729, -0.031470395624637604, -0.07076257467269897, -0.0668952539563179, -0.050991155207157135, -0.01736932061612606, -0.03679932653903961, 0.012951148673892021, 0.01066548191010952, -0.015661127865314484, 0.05937625840306282, 0.030904972925782204, -0.025059334933757782, 0.038627661764621735, -0.027573486790060997, 0.027804499492049217, 0.0392267145216465, 0.03865406662225723, -0.03076965920627117, 0.021605664864182472, 0.0012125412467867136, -0.019025292247533798, 0.029651537537574768, -0.03643082082271576, -0.07377681881189346, 0.02396702952682972, 0.05727619305253029, -0.05021001771092415, 0.024707550182938576, 0.0019583050161600113, 0.009910044260323048, 0.018985671922564507, -0.012461992911994457, 0.001358636887744069, 0.058270201086997986, 0.0032986998558044434, 0.0005718643078580499, -0.0025972153525799513, -0.06315399706363678, 0.0006316343788057566, -0.04524983465671539, 0.04229523241519928, 0.018548157066106796, -0.007806259207427502, 0.037429675459861755, -0.05655099079012871, 0.018466420471668243, -0.004307385999709368, 0.08019225299358368, -0.02133367955684662, -0.07706848531961441, 0.03611235320568085, 0.010067043825984001, -0.050951119512319565, 0.01678568869829178, 0.0605834536254406, 0.05227849632501602, -0.05046604946255684, 0.002460620366036892, 0.02520415373146534, -0.036670323461294174, -0.07494141906499863, 0.03647162765264511, 0.01690775714814663, 0.05644521862268448, 0.057542722672224045, -0.007033911533653736, 0.04325694590806961, -0.04485822096467018, -0.024365276098251343, -0.007841442711651325, 0.0004230113991070539, -0.014339425601065159, -0.01471534464508295, 0.0017232649261131883, 0.03973860293626785, -0.05710620805621147, 0.023305131122469902, -0.016405530273914337, -0.014550567604601383, -0.026965511962771416, 0.021970978006720543, -0.034030795097351074, 0.047080766409635544, -0.000623813015408814, 0.0007955313194543123, -0.016174523159861565, 0.0336078405380249, -0.0009254305623471737, -0.012327484786510468, 0.053713228553533554, -0.04624819755554199, -0.06501537561416626, -0.009127333760261536, 0.036560509353876114, -0.040497444570064545, 0.02262616902589798, -0.019630398601293564, 0.02111230045557022, -0.02287895791232586, 0.048954110592603683, 0.036774106323719025, -0.02071022242307663, -0.0594652034342289, 0.002866602037101984, -0.024395497515797615, -0.06145622208714485, 0.020230213180184364, 0.0005214082775637507, -0.0077067092061042786, 0.028227832168340683, 0.08629777282476425, -0.029609575867652893, 0.007033329922705889, -0.007342809345573187, -0.03167082741856575, 0.01244026143103838, -0.021947678178548813, -0.02529679425060749, 0.025362703949213028, 0.0010277741821482778, -0.03459076210856438, -0.004538005217909813, -0.04242585599422455, -0.02608572691679001, -0.001713140169158578, -0.03390614688396454, 0.06157434359192848, -0.042474713176488876, -0.05438537523150444, 0.006199154071509838, 0.006300786975771189, -0.03921005129814148, 0.0037795931566506624, -0.001105590257793665, -0.007607294246554375, 0.024577807635068893, -0.002726604463532567, 0.036136381328105927, 0.011453229002654552, 0.027326680719852448, 0.0011950803454965353, 0.001731939148157835, 0.006720885634422302, 0.009986264631152153, 0.06168248504400253, -0.03657620772719383, -0.0204098392277956, -0.017344819381833076, 0.0360904335975647, -0.015352148562669754, -0.010505066253244877, -0.011232627555727959, -0.005515760742127895, -0.04885480925440788, -0.04580099508166313, 0.02789243496954441, -0.008131397888064384, -0.08110934495925903, -0.059870313853025436, 0.030431564897298813, 0.055169977247714996, 0.045733287930488586, 0.04034489393234253, -0.051582224667072296, 0.03143773227930069, -0.022431857883930206, 0.04605886712670326, 0.00024300577933900058, -0.03187547251582146, 0.0312565416097641, -0.040790338069200516, -0.003571053734049201, 0.03414638340473175, -0.020010696724057198, -0.025610588490962982, -0.043476082384586334 ]
<p>Some metal containers such as the Nissan Thermos ones, even if 100 C water is filled inside, the container is still cold to the touch on the outside. It won't be even warm:</p> <p><img src="http://i.stack.imgur.com/E3Cbs.jpg" alt="enter image description here"></p> <p>At the same time, some that look similar are so hot on the outside that holding it for a couple of seconds won't be possible:</p> <p><img src="http://i.stack.imgur.com/gg9pq.jpg" alt="enter image description here"></p> <p>Also, some teapot at Chinese restaurant or Vietnamese Restaurant, it can be boiling hot water inside, but the handle is also cold to the touch:</p> <p><img src="http://i.stack.imgur.com/mc5il.jpg" alt="enter image description here"></p> <p>The question is, for the Nissan one and the ones at Chinese restaurants, if the metal part is all connected, from where the liquid is, to the part that the hand can touch, why isn't the handle or outside too hot to hold, but can be not much different from room temperature?</p> <p>(the Nissan one is vacuum inside, but the metal container part is all part of a single piece.)</p>
g5412
[ 0.05229289457201958, 0.0026136713568121195, -0.008130800910294056, 0.03484279289841652, 0.08553683757781982, 0.005906791891902685, -0.017124611884355545, 0.03090212121605873, -0.061439160257577896, -0.00508396839722991, 0.02712709829211235, 0.00005405993579188362, -0.023735761642456055, 0.005886428523808718, 0.0021776098292320967, -0.03695594146847725, -0.029184730723500252, 0.007687586825340986, -0.014705190435051918, 0.02931147813796997, -0.028920715674757957, 0.018298644572496414, -0.02019890770316124, -0.06907694041728973, -0.0675709918141365, 0.0193849578499794, -0.01174995582550764, 0.021568920463323593, -0.05334858596324921, -0.013337579555809498, -0.06310312449932098, -0.014390752650797367, -0.05336238443851471, 0.004804536700248718, -0.03652367740869522, -0.02576780691742897, 0.05417940020561218, -0.014413573779165745, -0.03465468809008598, -0.005926449317485094, -0.021683335304260254, 0.013083337806165218, 0.0674038678407669, 0.0034227457363158464, 0.026244696229696274, 0.02504708804190159, -0.041899990290403366, -0.0077656349167227745, 0.012678712606430054, 0.007297532167285681, -0.00042906004819087684, -0.033094026148319244, -0.040331315249204636, -0.020726976916193962, 0.034060701727867126, -0.06365139782428741, -0.02631407417356968, 0.05823170021176338, 0.021233484148979187, 0.04388205707073212, 0.013493695296347141, 0.028066961094737053, 0.008713390678167343, 0.01404342707246542, -0.011902629397809505, 0.01810990460216999, -0.04188168793916702, -0.009581292979419231, 0.00965437013655901, 0.0022489619441330433, 0.021013231948018074, 0.024457870051264763, -0.006796466186642647, -0.019469503313302994, -0.017250677570700645, 0.030156921595335007, -0.06366509199142456, -0.00217335089109838, 0.0715397521853447, 0.019797420129179955, -0.03135586529970169, 0.04159427434206009, -0.03224882856011391, -0.009896672330796719, 0.012846569530665874, 0.03213532269001007, -0.04649000242352486, -0.011182030662894249, 0.039912596344947815, 0.05552302673459053, 0.016661785542964935, -0.008118885569274426, 0.053329162299633026, 0.060523610562086105, 0.024214843288064003, 0.03973707556724548, -0.0005187508068047464, 0.04181995615363121, -0.019329184666275978, -0.03072703443467617, 0.056617371737957, -0.058364130556583405, 0.06715049594640732, 0.029987091198563576, -0.0360528826713562, 0.017379462718963623, 0.018141232430934906, 0.06019824370741844, -0.029306000098586082, -0.028997551649808884, -0.009408668614923954, 0.01197167206555605, -0.06673572957515717, -0.013073460198938847, 0.07602785527706146, 0.02265951968729496, 0.047305215150117874, 0.047520481050014496, 0.01342596672475338, 0.0399833582341671, 0.033211950212717056, -0.002038612961769104, -0.04123767092823982, 0.012932470068335533, 0.05556893348693848, -0.039388418197631836, 0.04045514762401581, 0.02476426772773266, -0.026092801243066788, -0.043738704174757004, -0.046060193330049515, 0.05327526107430458, -0.08748520910739899, 0.012406310997903347, 0.021177133545279503, -0.01781558245420456, -0.011316180229187012, -0.006055271718651056, -0.00010052364086732268, -0.04155975952744484, 0.06278504431247711, -0.030261805281043053, -0.07439490407705307, 0.020311906933784485, -0.013403492979705334, 0.012599154375493526, -0.027113784104585648, 0.009438006207346916, 0.016139328479766846, -0.03267769142985344, -0.0007208588067442179, 0.03225767984986305, 0.05906810611486435, 0.030633319169282913, -0.022607123479247093, -0.018417390063405037, 0.047227125614881516, -0.09490056335926056, 0.03978274390101433, 0.0107579929754138, 0.01007594633847475, 0.03519844636321068, 0.06018104776740074, -0.013722607865929604, -0.015881869941949844, -0.029080040752887726, -0.0456765741109848, -0.025463778525590897, -0.019116902723908424, -0.05847911164164543, -0.09590937942266464, 0.056144412606954575, -0.06509890407323837, 0.09639998525381088, 0.07949507981538773, -0.041686318814754486, 0.040593262761831284, -0.01723909005522728, 0.04246944934129715, -0.04529799520969391, -0.024281255900859833, 0.0017211777158081532, 0.008226854726672173, -0.041613273322582245, -0.04877448454499245, 0.01818014308810234, -0.03597702831029892, 0.05562670901417732, -0.025266462936997414, -0.020426319912075996, 0.012416727840900421, -0.021961169317364693, 0.026770571246743202, 0.011980717070400715, 0.030221929773688316, -0.07938690483570099, -0.04929960146546364, -0.026875898241996765, -0.022300539538264275, -0.02418467402458191, 0.01803228072822094, -0.04400075227022171, 0.010876545682549477, 0.039059389382600784, -0.03961442410945892, 0.0002581404987722635, -0.013653825037181377, -0.004109205212444067, 0.008695580065250397, -0.02306278795003891, -0.004723723977804184, 0.037026453763246536, 0.01927550509572029, -0.04760296270251274, 0.021999070420861244, 0.07119638472795486, 0.05046946182847023, 0.012468788772821426, -0.004300263710319996, 0.04948226362466812, -0.008954278193414211, 0.0062679327093064785, 0.003467850387096405, -0.07211681455373764, -0.04894397035241127, -0.02935868315398693, -0.05309943109750748, 0.0016193826450034976, -0.0002786741533782333, 0.035729631781578064, -0.0450899675488472, -0.01968562975525856, 0.02380695566534996, -0.018253840506076813, -0.03511190786957741, -0.025619573891162872, 0.024765843525528908, 0.023578260093927383, -0.02903658151626587, 0.0667797103524208, 0.05595763027667999, -0.038998398929834366, -0.027071498334407806, 0.038046181201934814, -0.025834493339061737, -0.05302100256085396, 0.012556762434542179, -0.003946650307625532, 0.04415038973093033, 0.023209527134895325, 0.0035440209321677685, 0.0199893806129694, -0.044633880257606506, 0.04222814738750458, -0.04381536319851875, 0.02526993677020073, -0.019062425941228867, -0.01293597836047411, 0.00739510590210557, -0.05589606612920761, -0.0023062434047460556, -0.0315995030105114, 0.031086375936865807, 0.02802179753780365, 0.014380897395312786, 0.007433697581291199, -0.07819908112287521, 0.017780832946300507, 0.009919296018779278, 0.03809351846575737, 0.024650536477565765, 0.024862587451934814, -0.05097523704171181, 0.08419159799814224, 0.006712113507091999, -0.02369007281959057, -0.009715953841805458, -0.015723001211881638, 0.049250245094299316, -0.028970474377274513, 0.029607335105538368, 0.017493491992354393, 0.01084378082305193, 0.00489041255787015, 0.031895119696855545, -0.009216900914907455, -0.03809848800301552, 0.00982158537954092, -0.018543073907494545, -0.06186463683843613, 0.04004916176199913, 0.05095669999718666, 0.023291433230042458, 0.023354679346084595, 0.007417669054120779, 0.01887032575905323, 0.013940826058387756, 0.00617246562615037, 0.0002778110501822084, -0.00661112368106842, 0.033962346613407135, 0.0497308149933815, -0.012526681646704674, 0.035097550600767136, 0.049696486443281174, 0.0008765304228290915, -0.05045098066329956, -0.009223036468029022, 0.03719783574342728, -0.026367031037807465, 0.057153746485710144, 0.03375912085175514, -0.0187004953622818, -0.045320745557546616, -0.06407678872346878, 0.012969807721674442, -0.037617482244968414, 0.04329631105065346, 0.040848251432180405, 0.005707348231226206, -0.023935509845614433, 0.020324528217315674, -0.013072806410491467, -0.025273185223340988, 0.030472872778773308, 0.014021947048604488, -0.001345861703157425, 0.0075264680199325085, 0.03535137325525284, 0.009592766873538494, 0.03640657663345337, 0.04477072134613991, -0.009006179869174957, -0.034825630486011505, -0.008805237710475922, -0.01492313202470541, 0.002696251031011343, 0.043053291738033295, 0.06572207808494568, 0.02307339571416378, -0.04502337798476219, -0.04213918000459671, -0.015266151167452335, 0.014602445997297764, 0.0020682294853031635, 0.06455159187316895, 0.0002470472827553749, 0.030639104545116425, 0.010362816974520683, 0.026015661656856537, 0.028965342789888382, 0.025114217773079872, -0.03951514884829521, 0.015330891124904156, -0.07114140689373016, -0.019984329119324684, -0.030640633776783943, -0.008576011285185814, 0.001245819148607552, 0.02726215310394764, 0.05017822980880737, 0.04293303191661835, 0.034170228987932205, -0.0878877118229866, 0.008484357967972755, 0.060872405767440796, 0.02110307477414608, 0.04882454499602318, -0.004371580667793751, -0.012398861348628998, -0.016994209960103035, -0.022991547361016273, -0.021260354667901993, -0.0002160932490369305, 0.08034198731184006, 0.0027179978787899017, 0.05648929625749588, 0.01862000674009323, -0.005322635173797607, 0.050275590270757675, 0.022953946143388748, -0.01740250736474991, -0.06257174909114838, 0.06880472600460052, 0.03232232853770256, 0.027761129662394524, 0.007145710755139589, -0.024149026721715927, -0.042960524559020996, -0.11179237812757492, -0.017912130802869797, 0.00027480412973091006, 0.07651578634977341, 0.008524298667907715, 0.030703991651535034, 0.00662970868870616, 0.001304749632254243, -0.01274165790528059, 0.007628016639500856, -0.05196314677596092, 0.01400331687182188, -0.005849470850080252, 0.011662263423204422, -0.06256487965583801, 0.007598032243549824, 0.008010197430849075, 0.003632202511653304, -0.02162380889058113, -0.024308476597070694, -0.023556962609291077, 0.028952736407518387, -0.009201540611684322, 0.019410086795687675, 0.04236685112118721, 0.03635066747665405, -0.04777654632925987, 0.02303158864378929, 0.026155179366469383, 0.026638394221663475, -0.07463496923446655, -0.017559388652443886, 0.018868109211325645, -0.026252388954162598, -0.015637297183275223, 0.03972639888525009, -0.006857783067971468, 0.051012713462114334, 0.023770706728100777, 0.011542086489498615, -0.03796858713030815, 0.007017146330326796, 0.0076561179012060165, -0.004373917356133461, -0.0072218263521790504, 0.021441619843244553, 0.023139530792832375, -0.03956029936671257, -0.011834921315312386, -0.03356645256280899, 0.02717703767120838, 0.02598370425403118, 0.06541694700717926, -0.03351462259888649, 0.02079549990594387, 0.02426498755812645, 0.03946587070822716, -0.00980172399431467, 0.008244968019425869, 0.024975158274173737, -0.041640348732471466, -0.07083707302808762, 0.008658810518682003, -0.023319866508245468, -0.03360648825764656, -0.0074762278236448765, -0.037364162504673004, 0.0017912519397214055, -0.04203537106513977, -0.04615405574440956, 0.009205721318721771, -0.05389227345585823, 0.019696762785315514, -0.06359238177537918, 0.022064577788114548, -0.02192004583775997, -0.04443132504820824, 0.04048660770058632, -0.03906615450978279, -0.01091113593429327, 0.04604506865143776, 0.014039900153875351, 0.11150071769952774, 0.057525958865880966, 0.06819092482328415, 0.08435147255659103, 0.013775614090263844, 0.004119072575122118, -0.0013575602788478136, -0.014553395099937916, -0.017846254631876945, 0.009971853345632553, 0.01046388503164053, 0.0292771365493536, 0.03100946918129921, 0.007116406224668026, -0.015216550789773464, -0.017915833741426468, -0.008928905241191387, -0.04157424345612526, 0.03877715393900871, 0.058001503348350525, -0.047848764806985855, 0.011947731487452984, -0.004709609784185886, -0.027418658137321472, -0.020607909187674522, -0.0034486507065594196, -0.004907677881419659, 0.03765619173645973, -0.046569474041461945, -0.0551283024251461, -0.01118773128837347, -0.04952580854296684, -0.06091694161295891, 0.04653174430131912, -0.007053781766444445, 0.0016393607947975397, -0.05342889577150345, 0.055126652121543884, 0.01019818615168333, 0.025357870385050774, -0.010791877284646034, -0.03249368816614151, 0.037379033863544464, 0.08667983114719391, -0.04684842750430107, -0.009770678356289864, -0.046197813004255295, 0.0060247876681387424, -0.018000232055783272, -0.016560617834329605, -0.031288646161556244, 0.03766455873847008, -0.03215324878692627, -0.04996854439377785, 0.016370156779885292, -0.035050615668296814, -0.04267595335841179, -0.011974598281085491, 0.026597991585731506, 0.03475522622466087, 0.04063054919242859, 0.03066231682896614, -0.006318913772702217, -0.0620071217417717, -0.021535610780119896, 0.01626366563141346, 0.023982878774404526, 0.03281087800860405, 0.08404633402824402, 0.06400605291128159, -0.027505146339535713, -0.022500205785036087, 0.02665541134774685, -0.003909560386091471, 0.0482448935508728, 0.04505094140768051, 0.008670561015605927, 0.009751996025443077, 0.023525675758719444, -0.0033566595520824194, 0.0783919095993042, -0.08783438056707382, -0.03572218865156174, 0.010607819072902203, -0.05132736265659332, 0.0181666798889637, -0.0028643456753343344, 0.002144905272871256, -0.043076664209365845, 0.023083548992872238, 0.029764609411358833, 0.0018129601376131177, 0.035655438899993896, 0.006475385278463364, -0.007129755336791277, -0.08024494349956512, 0.02266523241996765, -0.01416377816349268, 0.023053009063005447, 0.015378494746983051, -0.025578442960977554, 0.02099657990038395, -0.08252059668302536, -0.016684982925653458, 0.014679878018796444, -0.02181430719792843, 0.029595181345939636, 0.020118840038776398, -0.008754887618124485, 0.007415336556732655, -0.020273718982934952, -0.08092457801103592, -0.01789005845785141, 0.0312851145863533, 0.011230211704969406, -0.0434873141348362, -0.023016849532723427, 0.016141509637236595, -0.033030733466148376, -0.03881276771426201, -0.011959437280893326, 0.007316570729017258, -0.006778557784855366, 0.00215097120963037, -0.03154589235782623, -0.018640877678990364, 0.05045316740870476, -0.014068369753658772, 0.05548291280865669, 0.020629776641726494, 0.0304060447961092, 0.03505149483680725, -0.01748541183769703, -0.04485710710287094, 0.023319866508245468, 0.05360312759876251, -0.005598051473498344, 0.03728413209319115, 0.02294294536113739, -0.005944014526903629, 0.028933707624673843, 0.01886828988790512, -0.011152100749313831, -0.005714507307857275, -0.09655378013849258, -0.020522665232419968, 0.03234915807843208, -0.024494173005223274, -0.020405760034918785, -0.050920698791742325, -0.012087814509868622, -0.042433060705661774, -0.030900852754712105, -0.027496105059981346, -0.0074925171211361885, -0.09209542721509933, 0.04909909889101982, 0.01335094403475523, -0.047734711319208145, 0.019974088296294212, 0.000835540471598506, -0.01887306198477745, -0.001082041417248547, -0.01746946945786476, 0.01848450116813183, -0.038744330406188965, -0.013767033815383911, 0.024587227031588554, 0.03603571280837059, -0.06589017063379288, -0.02956821210682392, 0.027158910408616066, 0.04359685629606247, 0.025360487401485443, -0.016451280564069748, 0.007604402024298906, 0.026641536504030228, -0.08164816349744797, -0.0005992634105496109, 0.01138532254844904, -0.047274548560380936, -0.0547775961458683, 0.011710640974342823, -0.007875277660787106, 0.008711205795407295, -0.007279514335095882, -0.03330519050359726, -0.014131036587059498, -0.0003761684929486364, 0.002358489204198122, 0.04539068788290024, -0.0007895070011727512, 0.05110618844628334, 0.028400864452123642, 0.049402981996536255, 0.01861579157412052, -0.07479675859212875, -0.0168011412024498, -0.02645220421254635, 0.007648678030818701, -0.002489348640665412, 0.007810443174093962, -0.03687778860330582, 0.024469483643770218, 0.041886020451784134, 0.027891000732779503, 0.010422886349260807, 0.06015313044190407, -0.010432785376906395, -0.041036270558834076, -0.03214516118168831, 0.04573478922247887, -0.04714056849479675, 0.012911357916891575, -0.019158892333507538, -0.014497392810881138, -0.038623202592134476, 0.05091419816017151, -0.05130976065993309, 0.042927082628011703, -0.01758870854973793, 0.002304209629073739, 0.0366203635931015, -0.026100559160113335, 0.0712142363190651, 0.03260042518377304, 0.013352788053452969, 0.017174459993839264, 0.0010169812012463808, 0.020966971293091774, -0.006474064663052559, 0.06690356880426407, -0.016858970746397972, 0.02086997963488102, 0.020778100937604904, -0.008964628912508488, 0.040582362562417984, -0.013893543742597103, 0.02310214936733246, 0.034952737390995026, 0.10978124290704727, 0.046956345438957214, -0.05982004851102829, 0.009391685016453266, -0.036645688116550446, -0.06547599285840988, -0.02087360993027687, -0.009774633683264256, -0.07760221511125565, -0.05138956382870674, -0.020308468490839005, 0.02431410923600197, -0.058479130268096924, -0.06169433519244194, -0.0037958126049488783, 0.03569865971803665, -0.04975803941488266, -0.04388158768415451, -0.04170748218894005, -0.05165208876132965, -0.0017098753014579415, -0.006196502596139908, 0.003955361433327198, -0.030872739851474762, 0.008774979040026665, 0.03745124861598015, -0.027118807658553123, -0.014311179518699646, -0.0047846101224422455, 0.01819024793803692, 0.0070024593733251095, -0.020428456366062164, 0.03553890809416771, 0.021198268979787827, -0.010828702710568905, -0.0594874806702137, 0.03363490104675293, -0.02786082960665226, 0.034233272075653076, -0.09585727006196976, 0.010426728054881096, -0.0803808718919754, 0.020764891058206558, -0.013478584587574005, -0.013162163086235523, -0.042211368680000305, 0.013605983927845955, -0.011830299161374569, -0.01018032431602478, -0.01667862758040428, 0.003488518064841628, 0.005397122353315353, 0.008818872272968292, 0.050793714821338654, 0.04561552032828331, -0.03574926033616066, -0.019869739189743996 ]
<p>When I whistle, I find that I can vary the volume by pushing more or less air through my mouth at once. However, when I increase volume past a point, I start to hear a blend of rushing air and a faint whistle sound. Why? Is the air just subtly pushing my lips out of shape, or is there some other maximum (such as size/shape of my mouth) that I'm encountering? Is there any adjustment I can make after I cross this point to continue whistling louder?</p> <p><strong>EDIT</strong></p> <p>Why is it possible for people to whistle louder with their fingers in their mouth?</p>
g5413
[ 0.006775617133826017, -0.003485980909317732, 0.0025587675627321005, 0.07738637179136276, 0.0059247370809316635, 0.02581102028489113, 0.03190455585718155, 0.04639784246683121, -0.0023749300744384527, 0.0018673116574063897, -0.0345541276037693, -0.0601339153945446, 0.044049981981515884, 0.05404408276081085, 0.03516823798418045, 0.026115771383047104, -0.004246504046022892, -0.033265385776758194, 0.016482047736644745, 0.06173611059784889, -0.02337663434445858, -0.0014852549647912383, 0.025411467999219894, -0.023626303300261497, -0.02077975682914257, -0.02429821528494358, 0.02127614989876747, 0.03148471564054489, -0.01927810348570347, -0.03702649474143982, 0.0036051117349416018, 0.07317481935024261, 0.023599043488502502, 0.0638570711016655, -0.01154089905321598, -0.015463369898498058, 0.054665371775627136, -0.03927973657846451, -0.04332401603460312, -0.007594621740281582, 0.054421599954366684, -0.10771539807319641, 0.023626089096069336, 0.0413830392062664, -0.0443701297044754, 0.013624356128275394, -0.021633461117744446, 0.007533211261034012, 0.027398454025387764, -0.0006616904865950346, 0.006500281859189272, -0.04540494456887245, -0.08283255994319916, 0.012440160848200321, 0.0050852010026574135, 0.0030682100914418697, -0.03665687143802643, -0.06440863758325577, 0.02730540558695793, 0.017132023349404335, -0.03150898218154907, 0.050903238356113434, 0.0354350283741951, 0.034450218081474304, 0.0424305759370327, 0.002849247306585312, -0.04107118397951126, -0.03688603267073631, -0.0255462434142828, 0.038871362805366516, -0.0048408773727715015, -0.028695838525891304, -0.0003918199217878282, -0.028340594843029976, -0.02208768017590046, 0.01956011727452278, -0.021766845136880875, 0.034530919045209885, 0.007558149751275778, 0.02054847776889801, 0.0678521916270256, -0.02648347057402134, 0.0320134311914444, -0.004791242070496082, 0.03983655944466591, -0.030760249122977257, 0.036025721579790115, -0.035504069179296494, -0.011220433749258518, -0.014377975836396217, -0.01988464780151844, -0.009950212202966213, 0.040067460387945175, -0.03218373283743858, -0.019965317100286484, -0.021089233458042145, -0.021231863647699356, 0.06095125898718834, 0.028348129242658615, 0.03980175033211708, -0.04772337153553963, 0.044839050620794296, 0.092837393283844, 0.07083124667406082, -0.06403086334466934, 0.015110097825527191, -0.021771259605884552, -0.009871983900666237, -0.02100992761552334, -0.023262478411197662, -0.07177326083183289, -0.02383548952639103, -0.004746273159980774, 0.015268608927726746, -0.01481225062161684, 0.008243538439273834, -0.06917494535446167, 0.06457607448101044, -0.02209281176328659, 0.047593023627996445, 0.045668404549360275, -0.0891009047627449, -0.01498904824256897, -0.04678348824381828, -0.03556347265839577, -0.03268681839108467, 0.022479623556137085, -0.009859658777713776, -0.005061062518507242, -0.04629547894001007, 0.035227786749601364, 0.03311947360634804, -0.015538707375526428, -0.03291647881269455, 0.0385906808078289, 0.015702322125434875, -0.024544136598706245, 0.023859944194555283, 0.029821794480085373, 0.0008565725293010473, 0.027692582458257675, 0.003673360450193286, 0.030708782374858856, -0.02596462145447731, -0.014012706466019154, -0.04246021807193756, -0.061522506177425385, -0.01130579598248005, -0.009794959798455238, -0.014373863115906715, 0.0310768261551857, 0.0006233231979422271, 0.013057910837233067, -0.01370065938681364, -0.024587007239460945, 0.0354684554040432, 0.02424086257815361, 0.046526044607162476, 0.004740228410810232, 0.009927122853696346, 0.038567930459976196, 0.0031687687151134014, 0.01783592626452446, 0.02726101316511631, -0.044247452169656754, 0.006515934597700834, -0.04050878435373306, -0.028301900252699852, -0.09194641560316086, 0.05341733619570732, 0.012180028483271599, 0.021866632625460625, -0.026144208386540413, -0.004995649214833975, 0.01544693112373352, 0.005341563373804092, 0.1005595326423645, -0.026032429188489914, 0.029810486361384392, -0.03603600710630417, -0.053950030356645584, 0.008984961546957493, -0.06746437400579453, -0.054997075349092484, -0.011411922983825207, -0.08184090256690979, -0.0431414358317852, -0.006136743817478418, 0.013150244951248169, -0.0035868354607373476, -0.018019037321209908, -0.08986984938383102, 0.019106710329651833, -0.013615252450108528, -0.030452050268650055, -0.0118084866553545, -0.019039209932088852, -0.05293633043766022, -0.0017554311780259013, 0.002027960726991296, -0.04134513437747955, -0.023290973156690598, 0.00019739555136766285, -0.051059868186712265, 0.006091558840125799, 0.056330930441617966, -0.010478153824806213, 0.006382555700838566, -0.004803737159818411, 0.04309854283928871, 0.014979043044149876, -0.012593955732882023, 0.04865339398384094, -0.03877502307295799, 0.031561221927404404, 0.06511972099542618, 0.0029439772479236126, -0.06274212151765823, 0.020657775923609734, 0.02487300895154476, -0.009743516333401203, -0.030785515904426575, -0.01238840352743864, 0.0018528419313952327, -0.03779599443078041, -0.05286981537938118, 0.023885034024715424, -0.04668501392006874, -0.02322135493159294, 0.022724464535713196, 0.0034935090225189924, 0.036159101873636246, -0.0455172136425972, -0.0047030202113091946, 0.004139427095651627, 0.03498202934861183, -0.05319882929325104, 0.028089048340916634, -0.03472209349274635, -0.04496777802705765, -0.000712491397280246, -0.06549743562936783, -0.01629064604640007, 0.04666341468691826, -0.02705640345811844, -0.018558112904429436, -0.03807593137025833, -0.05400411784648895, -0.024783091619610786, 0.034577447921037674, -0.049561791121959686, 0.033277157694101334, 0.0637185350060463, -0.0022955634631216526, -0.041559137403964996, -0.025350404903292656, -0.048490192741155624, 0.030306197702884674, -0.020899249240756035, -0.007463275454938412, 0.015395235270261765, 0.027872340753674507, -0.03011510521173477, 0.015217307955026627, -0.034105587750673294, 0.029144730418920517, 0.018600579351186752, 0.025948787108063698, 0.02269710972905159, 0.0011668188963085413, 0.009974190965294838, 0.08962318301200867, -0.019912423565983772, 0.034075427800416946, -0.04248523712158203, 0.02546444907784462, -0.062586210668087, -0.003436699975281954, 0.09320326149463654, 0.016262827441096306, 0.009874479845166206, 0.011349386535584927, -0.01850212551653385, 0.016188638284802437, 0.0424659289419651, 0.005128626711666584, 0.03774425387382507, -0.0017563409637659788, 0.004125656094402075, -0.018134787678718567, 0.004680839367210865, -0.0241123978048563, 0.0577249713242054, 0.001302296412177384, 0.05926261097192764, 0.07337848842144012, -0.02402825467288494, 0.004731185734272003, 0.01952173188328743, 0.022626254707574844, 0.0484793558716774, -0.0697144865989685, -0.006792322266846895, 0.00013165526615921408, 0.0012772477930411696, 0.06557859480381012, 0.011601058766245842, 0.007938805036246777, 0.0015042826998978853, 0.03816301375627518, 0.05039488524198532, -0.0030762588139623404, 0.0021484894677996635, 0.01069600973278284, 0.0029094344936311245, -0.07109779864549637, 0.020550502464175224, 0.004935706965625286, -0.052046820521354675, -0.019618935883045197, 0.025568798184394836, 0.009504859335720539, -0.015021120198071003, -0.04674433171749115, -0.004018112551420927, -0.03385834023356438, 0.02539297379553318, -0.04169338569045067, -0.03675132989883423, 0.005826279520988464, 0.022836878895759583, -0.003985395655035973, -0.049914974719285965, 0.027215341106057167, 0.0323646105825901, -0.005369329359382391, 0.004508961457759142, 0.029768720269203186, 0.07642640918493271, -0.006524092983454466, 0.0723157450556755, -0.005326036363840103, -0.058851659297943115, -0.007127039600163698, -0.042310819029808044, 0.002708572195842862, 0.05628133565187454, -0.001230061985552311, 0.016680853441357613, -0.015572763979434967, 0.03472838178277016, 0.004910680465400219, -0.04560781270265579, -0.08071979880332947, 0.055086664855480194, -0.0676833763718605, 0.0023062455002218485, 0.048943936824798584, -0.12705472111701965, -0.045151472091674805, 0.04876763001084328, -0.06953014433383942, -0.03261470049619675, 0.03805255889892578, -0.016868295148015022, -0.032309580594301224, 0.019098347052931786, 0.03652573004364967, -0.034189578145742416, 0.08026934415102005, -0.013539403676986694, -0.03884993866086006, -0.025112513452768326, 0.006706901825964451, -0.013468380086123943, -0.06000439450144768, 0.02765699289739132, 0.06598934531211853, 0.03301631659269333, 0.04834635928273201, 0.06197698041796684, 0.023983296006917953, -0.013360580429434776, -0.04335736483335495, 0.017468305304646492, -0.05941374972462654, -0.007727285381406546, -0.03721190616488457, 0.03674144670367241, -0.12317074835300446, -0.0436285026371479, -0.017905306071043015, -0.01083365548402071, -0.0017638184363022447, 0.049882806837558746, -0.0194416381418705, 0.01434419397264719, 0.04267944023013115, 0.002321191830560565, 0.0416279099881649, 0.027838585898280144, 0.017569860443472862, -0.0539994016289711, 0.02271324023604393, -0.04109867662191391, -0.024032168090343475, 0.05029875785112381, 0.040324047207832336, -0.03401195630431175, -0.06366480886936188, 0.02139906957745552, 0.003194937715306878, -0.022323977202177048, -0.03432275354862213, -0.029645109549164772, -0.007321472745388746, 0.020195579156279564, 0.015121976844966412, 0.040280915796756744, 0.04191445931792259, -0.01122360210865736, 0.05340912193059921, 0.020938144996762276, 0.03562553599476814, 0.02909357100725174, 0.07677160948514938, 0.047360941767692566, -0.028497517108917236, 0.03227180242538452, -0.026475902646780014, 0.021280284970998764, -0.02451036497950554, -0.024035023525357246, -0.02163052186369896, 0.04936210811138153, 0.03726052865386009, -0.02281329408288002, 0.022566791623830795, -0.008501719683408737, -0.009493388235569, 0.08137890696525574, -0.01714787445962429, -0.01740925759077072, -0.0030882731080055237, 0.029645157977938652, -0.043399378657341, -0.01565181463956833, 0.034584831446409225, 0.012052850797772408, -0.008055560290813446, -0.14352722465991974, -0.04270069673657417, -0.007421444170176983, -0.04375075548887253, 0.008042384870350361, -0.019899968057870865, -0.02009420469403267, -0.01310371421277523, -0.06483062356710434, -0.014970993623137474, 0.035711754113435745, 0.01128968596458435, 0.0067678457126021385, 0.036448560655117035, 0.04740988090634346, -0.01934668980538845, -0.029351510107517242, -0.06990160048007965, 0.023878127336502075, 0.005465662572532892, 0.011494617909193039, 0.045559175312519073, -0.0012159092584624887, 0.049786992371082306, -0.03368062525987625, 0.0442800372838974, -0.01925622671842575, -0.005314692854881287, -0.038742076605558395, 0.015428168699145317, 0.04021831229329109, -0.023980479687452316, 0.0666542798280716, 0.010715535841882229, -0.02777477353811264, -0.017782701179385185, -0.03577260673046112, 0.033850930631160736, 0.03589674085378647, 0.013305013068020344, -0.00843890756368637, 0.025576351210474968, -0.016401981934905052, 0.05809403955936432, -0.015800664201378822, 0.020065300166606903, 0.024642853066325188, 0.002850799122825265, 0.02671506069600582, 0.01035003550350666, -0.0430644191801548, 0.0023890540469437838, -0.00804272759705782, -0.00950976274907589, -0.018442882224917412, -0.01351853460073471, -0.0068867402151227, -0.014440029859542847, 0.007275308948010206, 0.01620667241513729, -0.005621484015136957, 0.043731775134801865, -0.022628385573625565, 0.012619676999747753, -0.009889948181807995, -0.010084200650453568, -0.021241653710603714, -0.0002407583815511316, -0.022382082417607307, 0.018410973250865936, 0.06165626645088196, -0.05125809833407402, 0.00969468429684639, -0.02017734944820404, -0.045952118933200836, 0.012980381026864052, 0.015578635036945343, -0.009470072574913502, 0.03476216644048691, -0.025182507932186127, -0.0522688664495945, 0.021396340802311897, 0.05513891577720642, 0.017207518219947815, 0.003779019694775343, 0.0079397764056921, 0.016514534130692482, -0.03180485963821411, -0.04315686970949173, 0.027698218822479248, -0.014030756428837776, 0.009200779721140862, -0.05067228898406029, 0.07783383876085281, -0.012295551598072052, 0.005648977588862181, 0.02922414429485798, 0.06653734296560287, -0.02080303616821766, 0.027220718562602997, 0.022397814318537712, 0.03550608456134796, -0.04175766929984093, 0.03769833967089653, -0.006024399306625128, 0.01658226177096367, 0.038469403982162476, 0.01001762691885233, 0.019421657547354698, -0.0675126314163208, 0.013550841249525547, -0.027259591966867447, 0.010245556011795998, -0.015513446182012558, 0.025623558089137077, -0.10812222957611084, -0.012035869993269444, -0.008275797590613365, 0.031332168728113174, -0.03012954629957676, -0.011538124643266201, 0.04299314320087433, 0.008167247287929058, 0.020327439531683922, -0.03439247980713844, -0.013445294462144375, -0.027928005903959274, 0.03946536034345627, 0.02358337491750717, 0.017074037343263626, -0.019107062369585037, 0.05481438338756561, -0.00023294064158108085, -0.009924204088747501, -0.021269874647259712, 0.014840641990303993, -0.04480503499507904, 0.015558136627078056, 0.01109988521784544, 0.03369418531656265, -0.01667592115700245, -0.04128875583410263, 0.03617098927497864, -0.012992918491363525, 0.003773159347474575, -0.06513496488332748, 0.010735921561717987, 0.038339339196681976, -0.03298542648553848, -0.0010080640204250813, 0.06243930011987686, 0.029445501044392586, -0.019714508205652237, 0.016092410311102867, -0.008999954909086227, -0.018925825133919716, 0.0034605874679982662, 0.021911650896072388, 0.019499940797686577, 0.015949998050928116, -0.0150460721924901, 0.029308533295989037, 0.06928786635398865, -0.045465137809515, -0.011924036778509617, -0.04347243532538414, -0.0008360334322787821, -0.023751532658934593, 0.00733942911028862, -0.009744414128363132, 0.030588893219828606, 0.0017614230746403337, 0.042770471423864365, -0.02125038020312786, 0.03762548044323921, -0.06558461487293243, -0.008566956967115402, -0.04513958841562271, -0.022930840030312538, -0.038813479244709015, 0.02746879681944847, 0.045948516577482224, -0.057839613407850266, 0.04706043004989624, -0.04157781973481178, -0.0018884248565882444, 0.02475912496447563, -0.04027606546878815, -0.06515577435493469, 0.060819096863269806, -0.026297811418771744, 0.012966521084308624, -0.013263151049613953, 0.08354503661394119, 0.03128407895565033, -0.005766700487583876, -0.03204675763845444, 0.02682407572865486, -0.037765223532915115, -0.005758954677730799, 0.016782525926828384, -0.044402383267879486, -0.05778003856539726, 0.004416963085532188, -0.007593113463371992, 0.05258313938975334, -0.05230993404984474, 0.00940016470849514, 0.017435725778341293, -0.016760777682065964, 0.013539471663534641, -0.04569447040557861, 0.01273943018168211, 0.07784846425056458, 0.06139785051345825, 0.07793483138084412, 0.007978049106895924, 0.01717257872223854, -0.03070145472884178, -0.06558845937252045, 0.01814286969602108, -0.03389468789100647, -0.006818608846515417, -0.03459230065345764, 0.06806036829948425, 0.005451848730444908, -0.0428006611764431, 0.025461345911026, 0.03158445283770561, -0.00928201712667942, 0.006810142192989588, -0.04611838981509209, 0.008295138366520405, -0.05905727669596672, -0.010993286967277527, 0.05056484043598175, -0.03884482756257057, 0.022769637405872345, 0.0199270062148571, -0.014805976301431656, 0.004592964891344309, -0.017917130142450333, -0.008007236756384373, 0.0828496590256691, -0.03340667113661766, 0.0514293909072876, 0.008400751277804375, 0.004733663983643055, -0.036301661282777786, -0.004117390140891075, 0.047296807169914246, 0.005755675490945578, -0.04201395437121391, -0.041060399264097214, 0.014807453379034996, 0.0055729690939188, 0.004272951278835535, 0.0059226942248642445, 0.04259166121482849, -0.03639531135559082, -0.005784773267805576, -0.021388502791523933, 0.042104337364435196, 0.01358654536306858, -0.009170310571789742, -0.02227291464805603, -0.013538235798478127, 0.03178722411394119, 0.02145545743405819, -0.004784269258379936, -0.06894174218177795, -0.01472626905888319, 0.026277324184775352, -0.0029635641258209944, -0.018753480166196823, -0.03911646455526352, 0.025759179145097733, -0.026322418823838234, -0.03801175206899643, 0.057944077998399734, -0.030631156638264656, -0.023861711844801903, 0.021864846348762512, -0.03055235743522644, -0.023699577897787094, -0.008292317390441895, 0.08933232724666595, 0.04047282785177231, -0.014772668480873108, 0.015170549042522907, 0.021990425884723663, 0.04587109386920929, -0.0007373585249297321, 0.013861468993127346, 0.019832730293273926, -0.07371759414672852, 0.049925465136766434, 0.03331928700208664, 0.000354903721017763, -0.011276118457317352, -0.02085624448955059, 0.04133732616901398, -0.033397264778614044, 0.029809407889842987, 0.02433263324201107, 0.03305462375283241, 0.007075138855725527, 0.048190854489803314, -0.01030762866139412, -0.06040549278259277, -0.031900327652692795, -0.018215356394648552, 0.024726245552301407, -0.0353056825697422, -0.0361274778842926, 0.04693758860230446, -0.04090382903814316, -0.059645555913448334 ]
<p>Recently, I have stumbled upon a YouTube video by Veritasium describing the conductivity of fire. My question is: how exactly does fire conduct electricity? I am a high school student; therefore appropriate language is expected. </p> <p><a href="http://youtu.be/a7_8Gc_Llr8?hd=1">http://youtu.be/a7_8Gc_Llr8?hd=1</a></p>
g354
[ 0.01693650707602501, 0.009754633530974388, 0.008315819315612316, -0.019316432997584343, 0.05317346751689911, 0.012089166790246964, -0.0002896518853958696, 0.055790044367313385, 0.022849561646580696, 0.026611153036355972, -0.032026320695877075, 0.03471861407160759, -0.010406415909528732, 0.04104809835553169, -0.006749703083187342, -0.03889058902859688, -0.016803335398435593, -0.04951063171029091, -0.01949048973619938, 0.026257995516061783, -0.03685234487056732, -0.008436881005764008, -0.004281274508684874, 0.0014596491819247603, 0.002023652894422412, -0.0410778746008873, -0.04463498294353485, -0.011466084979474545, -0.03852180019021034, -0.10537498444318771, 0.028536779806017876, -0.007233772426843643, 0.01629079505801201, -0.03423024341464043, -0.07406366616487503, 0.013788465410470963, -0.051994334906339645, -0.023876802995800972, -0.0028636620845645666, -0.003737925086170435, 0.02646828256547451, -0.03435416519641876, -0.00014478404773399234, 0.008614697493612766, -0.01500740833580494, 0.0019581939559429884, -0.020330969244241714, -0.05634065344929695, -0.01276469137519598, 0.005967816803604364, -0.014716319739818573, -0.017094148322939873, -0.033137381076812744, 0.00855023693293333, 0.017335999757051468, -0.039334625005722046, 0.019629521295428276, -0.012406234629452229, 0.036519855260849, -0.01895059645175934, 0.009878164157271385, 0.04890502989292145, -0.002631917130202055, -0.02962658368051052, 0.044781386852264404, 0.009794839657843113, -0.06686775386333466, 0.06452541053295135, 0.04493841156363487, -0.0004974824259988964, 0.007613196969032288, -0.02473287284374237, -0.030952678993344307, -0.028557874262332916, -0.009846958331763744, 0.025698207318782806, 0.03308198228478432, -0.04600181430578232, 0.031323205679655075, 0.027990998700261116, -0.032491594552993774, -0.018558524549007416, -0.03968386352062225, 0.03555537015199661, 0.049105335026979446, -0.04628529027104378, -0.018711380660533905, 0.024571580812335014, -0.024448592215776443, -0.037208061665296555, 0.017917973920702934, -0.020805474370718002, 0.1267593950033188, -0.016687000170350075, -0.013398579321801662, -0.011794098652899265, -0.049416303634643555, 0.037033017724752426, 0.057610612362623215, -0.002282104454934597, -0.01175625342875719, -0.0638171061873436, 0.05508195236325264, 0.005922941491007805, 0.004472584463655949, 0.006615723017603159, 0.008738325908780098, 0.000433733977843076, -0.0632224753499031, -0.03844338655471802, -0.03319550305604935, -0.05254341661930084, -0.01595216616988182, -0.03106536902487278, -0.02007661573588848, 0.046082429587841034, 0.057588379830121994, 0.001215863972902298, 0.06490461528301239, 0.011537842452526093, -0.012425253167748451, 0.023033002391457558, -0.001887607155367732, 0.011094157584011555, -0.05210307240486145, -0.05320708826184273, 0.04724219813942909, -0.011052554473280907, -0.03847958892583847, 0.03188074752688408, -0.05700984597206116, -0.01821364276111126, -0.02095763199031353, -0.02940218895673752, 0.01791967637836933, 0.044289201498031616, -0.0008347629336640239, 0.012817501090466976, 0.005914741661399603, -0.007714184001088142, 0.08094741404056549, -0.015949999913573265, 0.023109352216124535, -0.0721774622797966, -0.024934925138950348, 0.03636176139116287, -0.04848090559244156, 0.006390792783349752, 0.07682304829359055, 0.0015748811420053244, 0.03751932457089424, 0.03700451925396919, 0.055064789950847626, -0.04862489551305771, 0.029353318735957146, -0.04936008155345917, 0.021143687888979912, 0.01960248500108719, -0.002955818083137274, -0.03516124561429024, -0.013221953995525837, 0.011162904091179371, 0.018238073214888573, -0.02172335982322693, -0.033919807523489, -0.018566684797406197, -0.05500977113842964, -0.010137859731912613, 0.011628576554358006, 0.03669353574514389, -0.020543353632092476, 0.0020248095970600843, -0.003091958584263921, 0.06438116729259491, 0.008890245109796524, -0.01952406018972397, 0.03665522113442421, -0.027759721502661705, 0.03112553060054779, -0.02007894590497017, -0.04046770930290222, 0.03476307913661003, 0.019068961963057518, -0.0435638464987278, -0.009538526646792889, 0.016665734350681305, -0.042514003813266754, -0.02043377049267292, 0.002777490299195051, -0.0173802487552166, -0.08363206684589386, -0.03594394400715828, -0.008832331746816635, -0.0014601912116631866, 0.02333197556436062, 0.0014334263978525996, -0.031858425587415695, -0.024111533537507057, -0.010573595762252808, -0.03355829790234566, -0.034866273403167725, 0.010768459178507328, 0.0018173176795244217, 0.0012840299168601632, 0.056465085595846176, 0.018594518303871155, -0.030551239848136902, -0.005315037909895182, 0.048255663365125656, 0.021967794746160507, 0.022190846502780914, 0.02162904106080532, 0.04411141201853752, 0.008449235931038857, -0.0872587338089943, -0.007364585995674133, -0.035865481942892075, -0.058307550847530365, -0.06739674508571625, -0.0725695863366127, 0.024024352431297302, -0.037454795092344284, 0.040610168129205704, -0.002809548517689109, -0.06610991805791855, 0.02972256951034069, -0.01196744292974472, -0.03649778664112091, 0.026621179655194283, 0.043427474796772, -0.008707486093044281, 0.02009042166173458, -0.0003922225732821971, -0.04348919913172722, 0.0035537804942578077, 0.08495722711086273, -0.029315151274204254, -0.003135120728984475, -0.01578001119196415, -0.07291208207607269, -0.016180405393242836, -0.07784900069236755, 0.01486250665038824, -0.012073999270796776, 0.04159088805317879, -0.07932565361261368, 0.05453738570213318, 0.0509626679122448, -0.010282455943524837, 0.01718202792108059, 0.0260581374168396, 0.009008734486997128, 0.0019122341182082891, 0.06374716758728027, -0.02897605113685131, -0.05373411998152733, 0.001689997036010027, 0.024303166195750237, -0.003910607658326626, -0.005362129304558039, 0.05318094789981842, -0.05181547626852989, -0.02551841177046299, -0.026444625109434128, -0.09664927423000336, 0.015815995633602142, -0.034799396991729736, -0.015695618465542793, 0.03053751029074192, -0.04577653855085373, -0.016933193430304527, 0.03347733989357948, 0.004094588570296764, -0.010555988177657127, -0.07351867109537125, -0.011637761257588863, -0.024377096444368362, -0.009490047581493855, 0.06520041078329086, -0.055094920098781586, 0.006938115227967501, 0.029578857123851776, 0.0009101217146962881, 0.07017841935157776, 0.056054532527923584, -0.019915945827960968, -0.019618839025497437, 0.03674320504069328, -0.013320999220013618, -0.03519453853368759, -0.028247850015759468, -0.07070351392030716, 0.03784685209393501, -0.012807116843760014, -0.01919475942850113, 0.013477948494255543, 0.07625750452280045, -0.02899983339011669, -0.02399321459233761, 0.005443178117275238, -0.004324857611209154, -0.020150594413280487, -0.03800058364868164, -0.0073675536550581455, -0.033523302525281906, 0.03318636119365692, -0.017816560342907906, -0.05161282420158386, -0.00695433933287859, 0.01902403123676777, -0.00032130733598023653, 0.0010132560273632407, 0.015784669667482376, -0.027585633099079132, 0.02243996039032936, -0.02625216729938984, -0.0187499038875103, 0.04430555924773216, -0.005907815415412188, 0.04759736359119415, 0.015038466081023216, -0.03668200969696045, 0.048088353127241135, -0.004033488687127829, -0.00902183260768652, 0.026444602757692337, 0.03809294477105141, -0.033178988844156265, -0.05616970360279083, -0.029294125735759735, -0.04891728609800339, 0.017115896567702293, -0.0454162172973156, -0.037573520094156265, -0.010269131511449814, -0.00015130106476135552, -0.027489665895700455, -0.015027262270450592, 0.03491910174489021, 0.008513701148331165, 0.030721360817551613, -0.059200361371040344, -0.0643201544880867, -0.003391957376152277, -0.026832032948732376, 0.020721562206745148, -0.029935961589217186, -0.011434493586421013, 0.05404597893357277, 0.014579825103282928, 0.05353006348013878, -0.03299558162689209, -0.020805059000849724, -0.0396033376455307, -0.017095576971769333, -0.002725610276684165, 0.03316662460565567, 0.06557205319404602, -0.008617489598691463, 0.041689563542604446, 0.00871471967548132, 0.0009438240667805076, 0.012920184060931206, -0.007703560404479504, -0.01929323747754097, -0.0009708190336823463, 0.022716274484992027, 0.005808322224766016, 0.030081385746598244, 0.01702965795993805, -0.006437993608415127, -0.0269785039126873, -0.03520523011684418, 0.06032637506723404, 0.030192939564585686, -0.00762644037604332, 0.003017743583768606, 0.0013938092160969973, -0.05402591824531555, 0.028917714953422546, 0.025425253435969353, 0.08160102367401123, 0.06752143800258636, 0.056846778839826584, 0.02772790752351284, 0.020090078935027122, 0.02873324044048786, 0.027566317468881607, 0.01001190859824419, -0.0650721937417984, 0.007039640564471483, -0.03420199081301689, -0.028393331915140152, 0.005114209838211536, 0.028761856257915497, -0.10417024791240692, 0.03383909910917282, 0.05283462628722191, 0.020683806389570236, 0.023554595187306404, -0.019814061000943184, 0.05048239976167679, 0.04775216802954674, -0.005434503313153982, -0.013403401710093021, 0.047625262290239334, -0.018668167293071747, -0.06560792028903961, 0.0007878722972236574, -0.07866930216550827, 0.004133232869207859, 0.03593302145600319, -0.07281053066253662, -0.0581091083586216, -0.027811147272586823, 0.027578862383961678, 0.006688083987683058, 0.005947615951299667, 0.018145527690649033, 0.015492182224988937, 0.03351953253149986, -0.016036374494433403, 0.015868401154875755, -0.02499661035835743, 0.024967726320028305, 0.06632904708385468, 0.03089856170117855, 0.04471515864133835, 0.028582165017724037, -0.0004704637103714049, 0.009922902099788189, -0.015434208326041698, -0.010601318441331387, 0.0493910014629364, -0.06687076389789581, 0.028883911669254303, -0.027267713099718094, 0.060354165732860565, 0.03686520457267761, 0.08413943648338318, 0.04896250739693642, 0.037383779883384705, 0.023420492187142372, -0.018222646787762642, -0.0026301927864551544, -0.020249459892511368, -0.029201112687587738, 0.010812275111675262, -0.060170285403728485, 0.010665475390851498, -0.022586340084671974, 0.02569446712732315, -0.03815372660756111, -0.038432903587818146, -0.049144912511110306, -0.03811728209257126, -0.0031015542335808277, 0.017340904101729393, 0.00595623767003417, 0.036134570837020874, -0.041004057973623276, -0.04757065698504448, 0.011944431811571121, 0.04259781166911125, 0.029083341360092163, 0.017993023619055748, 0.026598462834954262, -0.057859666645526886, -0.03345910459756851, -0.00005279201650409959, 0.019314678385853767, 0.007534370757639408, 0.024926714599132538, 0.006253879051655531, 0.06274348497390747, -0.03198226913809776, 0.018748555332422256, 0.03602141886949539, -0.008382819592952728, -0.02341686189174652, -0.008022334426641464, 0.007980487309396267, 0.0025394910480827093, -0.0004534624167717993, -0.00349339353851974, 0.05509770289063454, -0.035309962928295135, 0.04590503126382828, -0.01877066120505333, -0.03912733122706413, 0.0031842398457229137, 0.07581596076488495, -0.03923565521836281, -0.015067803673446178, -0.020494021475315094, -0.05934625864028931, 0.04809099808335304, 0.0043492098338902, 0.03459528088569641, 0.02363278716802597, -0.01252940483391285, 0.015816161409020424, -0.05638101324439049, -0.003688426921144128, 0.01302138902246952, 0.07312548160552979, 0.014547392725944519, 0.015470234677195549, -0.02924693003296852, -0.02770007587969303, -0.017749520018696785, 0.05406736582517624, -0.055940207093954086, 0.042179808020591736, 0.03612840920686722, -0.008170032873749733, -0.10788094252347946, -0.001792705850675702, -0.00802499707788229, 0.009580552577972412, -0.00838455744087696, -0.003881308250129223, 0.024289973080158234, -0.025349363684654236, -0.030665826052427292, 0.016861896961927414, -0.027099525555968285, -0.07332436740398407, 0.050204455852508545, 0.02427860163152218, 0.0029491218738257885, 0.04218039661645889, 0.00894403737038374, -0.023951929062604904, -0.023618753999471664, 0.039462435990571976, -0.005583415739238262, -0.053284965455532074, 0.01184347365051508, 0.06843672692775726, 0.01814599521458149, -0.009506677277386189, 0.00007696424290770665, 0.05527212470769882, 0.07509993016719818, -0.02461746707558632, -0.018540887162089348, -0.0019677607342600822, 0.036715853959321976, 0.0242118239402771, -0.024550825357437134, 0.018404772505164146, 0.04414629191160202, -0.015283429995179176, 0.06788191944360733, 0.010276439599692822, -0.03578139841556549, -0.04181605577468872, 0.0006828962941654027, -0.0658552497625351, 0.02129540406167507, -0.008879008702933788, -0.02292579784989357, -0.05029958486557007, 0.06354162842035294, -0.09270694851875305, 0.038131121546030045, -0.01935805380344391, 0.030567392706871033, 0.09863130003213882, 0.06124366447329521, -0.02265016734600067, 0.040916167199611664, -0.06351357698440552, 0.020320743322372437, -0.0008262997725978494, -0.04776335135102272, -0.03666962310671806, -0.03157365322113037, 0.007929536513984203, 0.03831231966614723, 0.020508477464318275, 0.038169585168361664, 0.025268128141760826, -0.011921045370399952, 0.012532947584986687, 0.03735537827014923, 0.007423031143844128, -0.05008101090788841, -0.05859914422035217, -0.0026878213975578547, 0.020232342183589935, 0.04881253466010094, 0.0043513416312634945, 0.018006503582000732, 0.05759425461292267, 0.01876167394220829, 0.02230646088719368, 0.05764609947800636, 0.025630192831158638, 0.00623499508947134, -0.0077887787483632565, -0.012407609261572361, -0.04595985263586044, 0.10145649313926697, 0.01132176723331213, 0.09005701541900635, 0.04774577543139458, -0.023301927372813225, 0.023094603791832924, 0.01037251390516758, 0.042092472314834595, -0.04637257754802704, -0.05848848447203636, -0.02764599211513996, 0.012739328667521477, -0.0043037026189267635, -0.016125565394759178, 0.017681661993265152, 0.04629054665565491, -0.04408632963895798, -0.04856894165277481, 0.060446079820394516, -0.013287939131259918, 0.0024880245327949524, 0.028222041204571724, -0.032711807638406754, 0.05646220222115517, 0.034692686051130295, -0.03004881739616394, -0.011727448552846909, -0.020247913897037506, 0.05085905268788338, 0.037380073219537735, 0.03710807114839554, -0.02057080715894699, -0.03702087700366974, -0.05401025712490082, 0.040892813354730606, 0.05324047431349754, -0.004137781448662281, -0.016116240993142128, -0.018495390191674232, 0.011248591355979443, -0.03310307115316391, 0.011919264681637287, -0.04144943505525589, -0.033832285553216934, 0.014900296926498413, -0.04913632944226265, -0.015011746436357498, 0.0029215540271252394, -0.0024486971087753773, -0.022198697552084923, -0.03438924625515938, 0.030766906216740608, -0.004388365428894758, 0.00979521218687296, 0.009251919575035572, -0.05862300470471382, 0.007401981391012669, 0.0011586928740143776, 0.01277301274240017, -0.01016778964549303, 0.04342515021562576, 0.0548112727701664, 0.06163153797388077, -0.02390643022954464, -0.005467611830681562, -0.0007168951560743153, -0.0015827174065634608, -0.040671758353710175, 0.0446789525449276, -0.03582659363746643, -0.041621748358011246, -0.02739739790558815, 0.011710640974342823, 0.08451236039400101, 0.04535268619656563, -0.07393099367618561, 0.006014046259224415, -0.030579036101698875, -0.019528422504663467, 0.0013185228453949094, 0.0036363357212394476, 0.011196428909897804, -0.02930627018213272, -0.022667264565825462, -0.0179002545773983, 0.02288491278886795, 0.02801581844687462, 0.016590042039752007, -0.006867018528282642, -0.010408440604805946, 0.06668951362371445, -0.0007576315547339618, 0.02768213488161564, -0.00458767032250762, 0.05964275822043419, 0.01524268463253975, 0.006264141295105219, 0.03260288015007973, 0.02416934445500374, -0.012333023361861706, 0.014444531872868538, 0.018594572320580482, -0.01857829838991165, 0.03300999104976654, -0.08120191097259521, -0.04798804968595505, 0.015906304121017456, 0.04120893031358719, 0.025271961465477943, 0.020459327846765518, 0.021199442446231842, 0.002070606453344226, 0.015903979539871216, 0.00007492897566407919, 0.01966894045472145, 0.006105958949774504, 0.036036863923072815, 0.012010925449430943, 0.02139195241034031, 0.02374589815735817, 0.06272440403699875, 0.017611786723136902, 0.014799722470343113, 0.0056455377489328384, 0.0193746630102396, 0.01736905798316002, -0.0030224027577787638, 0.005300870630890131, 0.03208484500646591, -0.0028185148257762194, -0.05542345717549324, 0.00011847759742522612, 0.10275698453187943, -0.053998205810785294, -0.017540806904435158, 0.04737916961312294, 0.043418947607278824, 0.06223105266690254, -0.05413491278886795, 0.014279649592936039, 0.013662369921803474, -0.054677076637744904, -0.06641092896461487, 0.023065615445375443, 0.05464107543230057, -0.04550594463944435, 0.0077582914382219315, -0.023740816861391068, -0.01380147784948349, -0.003160251770168543, -0.05765688419342041, -0.05259426683187485, 0.00741184176877141, 0.036470379680395126, -0.019444512203335762, 0.020249266177415848, -0.038549210876226425, -0.009272956289350986, 0.02155587635934353, -0.005567790009081364, -0.02245352230966091, -0.07662501186132431, 0.007484178990125656, -0.06116795539855957 ]
<p>I read according to 'Newtonian' Mechanics any set of physical activity of particles can be reversed ( I think) so a set of complicated dynamic systems of particles and matter can reverse their 'behaviour'. Yet a Star collapsing towards a 'Black Hole' will probably not 'stop' and reverse it's behaviour. So could Gravity be considered part of the 'Arrow of Time'? Since entropy is part of this 'Arrow' could entropy have 'qualities similar to the qualities of Gravity?</p>
g5414
[ -0.012270860373973846, -0.0037345297168940306, 0.01760944537818432, 0.00211290898732841, 0.021896297112107277, 0.0060789138078689575, 0.047258973121643066, -0.025541406124830246, -0.02821376733481884, 0.018441693857312202, 0.06077836826443672, 0.04819238930940628, 0.05219191312789917, -0.0396977998316288, -0.011432626284658909, 0.051779914647340775, 0.046881865710020065, 0.020453834906220436, 0.010402755811810493, 0.043963685631752014, 0.024573802947998047, -0.025585072115063667, 0.0344843752682209, -0.06569083034992218, -0.06442592293024063, -0.007878090254962444, 0.0732891783118248, -0.023322854191064835, -0.0519653856754303, -0.03404228761792183, 0.07339291274547577, -0.027804337441921234, 0.0014058779925107956, -0.036025334149599075, -0.023813486099243164, -0.04802793264389038, -0.004823068156838417, 0.009286259301006794, 0.0315420962870121, -0.020180562511086464, 0.004022642970085144, -0.016646819189190865, 0.025762945413589478, 0.03126150742173195, 0.007229720242321491, -0.020463118329644203, 0.05545820668339729, 0.03087899647653103, -0.0017966977320611477, 0.0010893086437135935, 0.03475314751267433, 0.002567085437476635, 0.00774805061519146, 0.03474893420934677, -0.0020060192327946424, 0.007253088988363743, 0.020771078765392303, 0.024768739938735962, 0.04117206111550331, -0.011653323657810688, -0.06330280005931854, -0.008477436378598213, 0.012565490789711475, 0.020137082785367966, 0.01329046767205, -0.02586905099451542, -0.021464621648192406, -0.03471760079264641, 0.004117469768971205, 0.01148021500557661, 0.020690159872174263, -0.010461234487593174, 0.017938973382115364, 0.0337071493268013, 0.024999838322401047, 0.06585658341646194, -0.026928551495075226, 0.03950967639684677, -0.009383674710988998, -0.04356617480516434, -0.06928575783967972, -0.013563146814703941, 0.00019310902280267328, 0.019591985270380974, 0.09620052576065063, -0.03717123717069626, -0.009639997035264969, -0.01246461272239685, -0.03349189832806587, 0.02123929373919964, -0.0053084129467606544, -0.06664059311151505, 0.06258902698755264, 0.024846047163009644, 0.01622435636818409, -0.006736877374351025, -0.014883740805089474, 0.005903227254748344, -0.034537069499492645, 0.031112145632505417, -0.06255410611629486, -0.02074243500828743, -0.009144521318376064, -0.024749726057052612, 0.00039649775135330856, -0.05332740396261215, 0.01692184992134571, -0.01828964240849018, 0.006921201478689909, 0.025783320888876915, 0.014716221950948238, -0.021135447546839714, -0.014746474102139473, 0.00855179876089096, -0.04856519401073456, -0.013940664008259773, 0.08383588492870331, -0.009955299086868763, -0.037711091339588165, 0.031875673681497574, 0.013094471767544746, -0.009064639918506145, 0.013808846473693848, 0.012971351854503155, -0.056543488055467606, 0.019978104159235954, -0.001026035868562758, -0.02373364381492138, 0.028173839673399925, -0.014076472260057926, -0.012265913188457489, 0.02555391937494278, -0.026937976479530334, 0.04770151898264885, -0.051882073283195496, 0.020777903497219086, 0.023472826927900314, -0.04011831060051918, -0.012441061437129974, -0.01434163749217987, 0.0411568284034729, 0.011987031437456608, -0.0038796623703092337, 0.006009134463965893, 0.0012699789367616177, 0.046221308410167694, 0.009587250649929047, 0.015880867838859558, -0.030806899070739746, 0.01094779185950756, -0.01098737120628357, 0.055629193782806396, 0.007122545037418604, -0.05962361395359039, 0.0013242610730230808, -0.013279391452670097, 0.053087227046489716, 0.06456625461578369, 0.004248395562171936, 0.04649895057082176, 0.04064365103840828, -0.03359879553318024, 0.05478454753756523, 0.011584103107452393, -0.022231275215744972, 0.005479810293763876, -0.03626282885670662, -0.021159052848815918, 0.06304896622896194, -0.06007135659456253, -0.06773137301206589, 0.030795898288488388, -0.018025973811745644, 0.03521374985575676, 0.03724134340882301, -0.04835149273276329, 0.001565869664773345, 0.007823445834219456, -0.013216852210462093, -0.05357680842280388, -0.009695412591099739, -0.007876754738390446, -0.0025542215444147587, 0.055450186133384705, 0.012677925638854504, 0.0020135475788265467, 0.07328233867883682, 0.046201955527067184, -0.06945382058620453, 0.005936357192695141, 0.013346157968044281, -0.04423912987112999, -0.009453512728214264, 0.02770782820880413, 0.07430507242679596, -0.045728784054517746, 0.02026314102113247, -0.013615665026009083, -0.062489524483680725, 0.06889666616916656, 0.030892014503479004, 0.01454782672226429, -0.025790704414248466, -0.014684311114251614, 0.022467415779829025, 0.055070534348487854, -0.022773999720811844, 0.030220314860343933, -0.0043069166131317616, -0.0023169228807091713, 0.07603023946285248, -0.0020217495039105415, 0.02261536195874214, 0.03972335159778595, -0.030178099870681763, -0.005830415990203619, -0.05325188860297203, 0.030477430671453476, -0.004363365937024355, 0.05020013824105263, -0.07082121074199677, -0.020873354747891426, -0.034777943044900894, -0.06858779489994049, -0.0002609310031402856, 0.07135678082704544, -0.07081220299005508, -0.06747850030660629, 0.03949851542711258, -0.026539407670497894, -0.07955871522426605, 0.0367455929517746, 0.009861505590379238, -0.005563631188124418, 0.05838501825928688, -0.009559332393109798, 0.037786781787872314, -0.03601093217730522, 0.017214670777320862, -0.07522739470005035, -0.027899306267499924, 0.01563805527985096, -0.0011295864824205637, -0.03801727667450905, 0.014285160228610039, -0.0068296524696052074, -0.0371086522936821, -0.03238868713378906, 0.015415767207741737, -0.021677395328879356, 0.07544912397861481, -0.030694860965013504, -0.027389517053961754, -0.01080831978470087, 0.023052643984556198, 0.006133239716291428, 0.03459227457642555, 0.03395712748169899, -0.0614439882338047, 0.010298305191099644, -0.0065522086806595325, 0.00818475428968668, -0.01719626784324646, 0.03989848122000694, -0.04774775356054306, -0.044575829058885574, -0.055771488696336746, 0.010667335242033005, 0.034962788224220276, 0.09721650928258896, -0.028322923928499222, -0.02937200665473938, 0.008304647170007229, 0.011793918907642365, -0.01578572578728199, 0.050236776471138, -0.014479066245257854, -0.01812145486474037, 0.004064918030053377, -0.036966048181056976, 0.030253183096647263, 0.029793154448270798, -0.04062535986304283, 0.016311880201101303, -0.01827804557979107, -0.07403605431318283, -0.0031372644007205963, 0.0015445814933627844, -0.048551056534051895, -0.00011689160601235926, 0.007996306754648685, 0.03271294757723808, 0.0014635151019319892, 0.04189945384860039, -0.03284391760826111, 0.051965098828077316, 0.03649993985891342, -0.037882495671510696, -0.03787073865532875, -0.0044857836328446865, -0.026379242539405823, -0.011690943501889706, -0.009750842116773129, -0.003747801762074232, 0.04406222328543663, 0.045680686831474304, -0.06536731868982315, 0.009771039709448814, 0.024244194850325584, -0.057792335748672485, -0.017820294946432114, 0.02964170090854168, -0.023210925981402397, 0.03228675574064255, -0.008155692368745804, -0.004713451024144888, -0.020617974922060966, -0.03436855226755142, 0.036244459450244904, 0.02609207294881344, 0.013647550716996193, -0.03929927200078964, 0.028128616511821747, 0.018313415348529816, 0.04108019173145294, 0.04104875400662422, 0.015705754980444908, 0.015353980474174023, -0.04566007852554321, -0.0036986619234085083, -0.009530549868941307, -0.058197375386953354, 0.02773728035390377, 0.05624684691429138, -0.04885825142264366, 0.006776073481887579, -0.08444774150848389, -0.014864400029182434, 0.03763098642230034, 0.008241314440965652, 0.018296724185347557, 0.06778570264577866, -0.0007590333116240799, -0.005304699297994375, 0.007454732898622751, 0.06233902648091316, -0.06614470481872559, -0.02662886306643486, 0.034626804292201996, -0.019335901364684105, -0.023775413632392883, -0.0771048367023468, 0.07721440494060516, -0.008631385862827301, -0.0086900033056736, 0.01360847894102335, 0.06743557006120682, -0.0018120614113286138, -0.006402639672160149, -0.04972938448190689, -0.022650670260190964, -0.064703568816185, 0.01836506277322769, 0.016504647210240364, 0.01714172028005123, 0.03204116225242615, 0.022801171988248825, 0.008692455478012562, -0.033306509256362915, 0.0028757010586559772, 0.06291260570287704, -0.00415226723998785, -0.039815716445446014, 0.01400917861610651, 0.04717670753598213, -0.014277650974690914, 0.016561472788453102, -0.00111631047911942, 0.022518064826726913, -0.004767157603055239, 0.05569760501384735, -0.01971098780632019, 0.015919290482997894, 0.015456137247383595, 0.0055741677060723305, 0.01760796457529068, 0.0006453343667089939, -0.05571809038519859, 0.022648712620139122, -0.02658529207110405, -0.046289101243019104, -0.008456663228571415, 0.01986013725399971, -0.046900443732738495, 0.018410710617899895, 0.01920630782842636, 0.004672659561038017, -0.016583697870373726, -0.0019975381437689066, -0.028039511293172836, 0.0034766721073538065, 0.02514694072306156, 0.031083418056368828, 0.027596518397331238, 0.04571051895618439, -0.023693235591053963, 0.028652038425207138, -0.057958800345659256, -0.004423337988555431, -0.03463197126984596, -0.03612068295478821, -0.050708286464214325, -0.0051105753518640995, -0.004162184428423643, -0.010320045985281467, 0.03303837403655052, 0.024575568735599518, -0.012183768674731255, 0.0063956985250115395, -0.013010244816541672, 0.11660394817590714, 0.03899082913994789, 0.04458367079496384, 0.016201544553041458, -0.03168368339538574, 0.039040081202983856, 0.011326550506055355, 0.031119229272007942, -0.09051352739334106, -0.006191565655171871, 0.06585860997438431, -0.030781295150518417, 0.0008459113305434585, 0.02075856551527977, -0.03999822214245796, 0.10008511692285538, 0.009026193991303444, -0.012310891412198544, -0.0023864987306296825, 0.03814506158232689, 0.03459085524082184, -0.04737362265586853, 0.008993896655738354, -0.04497407749295235, 0.007364947348833084, 0.058211006224155426, -0.01742376945912838, 0.0007518036873079836, -0.050665922462940216, 0.008519204333424568, -0.009446044452488422, 0.0254594124853611, -0.0204798374325037, -0.04391825944185257, -0.04376900568604469, -0.014460276812314987, -0.046303439885377884, 0.05970439314842224, -0.06250707805156708, 0.00916507188230753, -0.054220035672187805, -0.06505104154348373, 0.04124655947089195, 0.035984478890895844, -0.01615416817367077, 0.010836469009518623, -0.04924420639872551, 0.006504355929791927, -0.0028210736345499754, -0.016972318291664124, -0.0261742752045393, 0.017977043986320496, -0.02455087937414646, 0.06400987505912781, 0.00509148882701993, 0.011498845182359219, -0.00449778325855732, -0.010889801196753979, 0.043217774480581284, -0.010345562361180782, -0.03942016884684563, -0.014754341915249825, 0.015773190185427666, -0.01764211244881153, 0.00021907061454840004, -0.022263934835791588, 0.010489216074347496, 0.028669340535998344, -0.014911995269358158, 0.027739286422729492, -0.030536320060491562, -0.032824840396642685, 0.02230042591691017, -0.04809020459651947, -0.03375524654984474, -0.02574171870946884, -0.01267271488904953, 0.0342196449637413, 0.025580691173672676, 0.007324166130274534, -0.0406784825026989, -0.0009278511861339211, -0.0209963321685791, 0.027813732624053955, -0.02286469005048275, -0.004912650212645531, 0.03432147204875946, 0.0028868806548416615, -0.09030644595623016, 0.05565556138753891, -0.03311691805720329, 0.0045594689436256886, -0.0037263298872858286, 0.0939604863524437, 0.050323277711868286, -0.02750740945339203, 0.021886300295591354, -0.00958101637661457, 0.03293555602431297, -0.047801028937101364, -0.026873210445046425, 0.008984270505607128, 0.0021782810799777508, 0.03866587206721306, 0.03859304264187813, 0.05327298119664192, -0.01678520254790783, 0.0339539535343647, 0.011270295828580856, 0.04764552414417267, 0.02854967676103115, -0.03033522330224514, 0.04061746597290039, -0.048928141593933105, -0.03309844434261322, -0.043701257556676865, -0.01984063908457756, 0.013358812779188156, 0.08874806016683578, -0.02550802193582058, -0.06328500807285309, -0.011744776740670204, -0.00673114275559783, 0.012522515840828419, -0.0009926108177751303, 0.031802646815776825, -0.05569233000278473, -0.005690363701432943, -0.010069568641483784, -0.03381020575761795, -0.008418972603976727, 0.04030362889170647, -0.05267946422100067, 0.005404037889093161, -0.06084882840514183, 0.029768412932753563, 0.016885317862033844, -0.014769756235182285, 0.012567619793117046, -0.07044235616922379, -0.001483169849961996, 0.0675075501203537, -0.013126049190759659, -0.033708665519952774, 0.009766110219061375, -0.01746026612818241, 0.028732571750879288, 0.01612386666238308, 0.049558669328689575, 0.03798583894968033, 0.0010974642354995012, 0.06213971972465515, 0.011836821213364601, 0.07158715277910233, -0.01163704413920641, -0.0695718303322792, -0.021663548424839973, -0.02192023955285549, -0.009718724526464939, -0.03029809147119522, 0.03189202770590782, -0.08546462655067444, 0.08203130215406418, -0.07356618344783783, 0.017367707565426826, -0.05709671229124069, -0.004303609486669302, 0.039558980613946915, -0.048932161182165146, -0.00273989443667233, -0.021124551072716713, 0.03538518771529198, -0.010019761510193348, -0.004321143962442875, -0.05592462420463562, -0.017705678939819336, -0.003264060942456126, -0.020040925592184067, 0.011505556292831898, -0.015013318508863449, -0.04426926374435425, 0.038818277418613434, -0.0021268739365041256, -0.052914097905159, -0.0034579767379909754, 0.07573653757572174, -0.04898080974817276, -0.004305008798837662, 0.0792999118566513, 0.016891544684767723, 0.011264168657362461, 0.0306589026004076, 0.008338069543242455, 0.07017611712217331, -0.036468442529439926, 0.01674807444214821, -0.01492907851934433, -0.02326134406030178, -0.02593226730823517, 0.0190769974142313, -0.00578797934576869, 0.03509495407342911, 0.01650131866335869, -0.04817302152514458, -0.01887650229036808, 0.05618572235107422, 0.008643376640975475, 0.08261532336473465, -0.03982793167233467, 0.04990400746464729, 0.023934578523039818, 0.04407527297735214, -0.014165766537189484, 0.01924208179116249, 0.043265145272016525, -0.01705760508775711, -0.053322795778512955, 0.06212232634425163, 0.02405381388962269, -0.0377754345536232, 0.020022662356495857, -0.025580937042832375, -0.009781958535313606, 0.007388333324342966, -0.013216491788625717, 0.029586421325802803, 0.03144023194909096, -0.03786821663379669, -0.057197388261556625, -0.005083749536424875, 0.007785700261592865, -0.04397967830300331, -0.023075921460986137, -0.004870132077485323, -0.03666847199201584, -0.009499482810497284, -0.02272578328847885, 0.0313856415450573, 0.030007028952240944, -0.06507930904626846, 0.014881156384944916, 0.038053371012210846, 0.004568755626678467, 0.032763078808784485, -0.037762757390737534, 0.026030011475086212, 0.07774703949689865, -0.049955036491155624, -0.037701062858104706, -0.013301430270075798, -0.007724854163825512, -0.06299801915884018, -0.0057125757448375225, 0.0031069896649569273, -0.06350547075271606, -0.03856993466615677, -0.011264876462519169, 0.020730113610625267, 0.027309663593769073, 0.04375411197543144, 0.04591067135334015, -0.0013180957175791264, 0.018999669700860977, 0.030017685145139694, -0.043221693485975266, 0.05655856058001518, -0.008352110162377357, 0.06681668013334274, 0.059270285069942474, -0.011459511704742908, -0.04369129240512848, 0.06100305914878845, -0.033847786486148834, -0.049297988414764404, 0.02968568727374077, -0.039410702884197235, 0.03052596002817154, 0.049085598438978195, -0.03539838641881943, -0.07274225354194641, 0.006613091565668583, 0.04566971957683563, 0.00922329816967249, -0.04284621775150299, 0.01808772422373295, 0.026224181056022644, -0.056267328560352325, -0.02132502757012844, -0.0723162516951561, 0.01886429265141487, 0.0013249587500467896, 0.0563732385635376, -0.024128582328557968, -0.0075478702783584595, -0.01089630089700222, -0.03980163112282753, -0.018513353541493416, -0.0359831266105175, -0.014664080925285816, -0.018663756549358368, -0.02814580127596855, -0.03044724278151989, -0.033420778810977936, -0.0393492616713047, -0.03210853412747383, -0.015302633866667747, -0.02746424823999405, 0.0022240555845201015, 0.002122825011610985, -0.04257165640592575, -0.0038277755957096815, -0.00436677411198616, -0.010077456012368202, 0.01361095067113638, -0.002046742243692279, 0.0336788184940815, -0.014484215527772903, 0.028302619233727455, 0.0008759363554418087, 0.002171804429963231, -0.0031826624181121588, -0.05922696366906166, 0.01873217709362507, 0.03234897553920746, 0.034329917281866074, -0.11215140670537949, 0.001499383244663477, 0.031262971460819244, 0.06615692377090454, 0.011125486344099045, 0.03525634855031967, -0.020663438364863396, 0.00230933609418571, -0.0074789454229176044, 0.029750119894742966, 0.06867111474275589, -0.06705624610185623, 0.023002315312623978, -0.04145088419318199, -0.010374329052865505, -0.023344997316598892, -0.00002983898957609199, 0.001322447438724339, -0.03501935303211212, -0.045402057468891144, -0.03329090401530266, -0.01598479598760605, 0.08824299275875092 ]
<p><strong>EDIT</strong>: I haven't forgotten to accept answer, the question is still open.. </p> <hr> <p>I need a clarification about Poisson brackets. </p> <p>I'm studying on Goldstein's Classical Mechanics (1 ed.).</p> <p>Goldstein proves that Poisson brackets are canonical invariants for any functions F and G. </p> <p>But there is a step that I can't understand.</p> <p>After some steps, he says that: </p> <p>$$ \tag{1} [F, G]_q,_p = \sum_k ( \frac { \partial G}{\partial Q_k} [F,Q_k]_q, _p +\frac {\partial G}{\partial P_k}[F, P_k]_q, _p)$$ </p> <p>After other steps, he writes:</p> <p>$$ \tag{2}[F,Q_k]= - \frac {\partial F}{\partial P_k}$$.</p> <p>and $$ \tag{3}[P_k, F]_q, _p = \sum_j \frac {\partial F}{\partial Q_j} [P_k, Q_j] + \sum_j \frac {\partial F}{\partial P_j}[P_k, P_j]$$ -></p> <p>$$ \tag {4} [F,P_k]=\frac {\partial F}{\partial Q_k}$$ </p> <p>and now he replaces these relations in the first expression I have written, obtaining:</p> <p>$$\tag {5}[F, G]_q, _p=[F, G]_Q, _P$$</p> <p>Why does he obtain in the second last step $\frac {\partial F}{\partial Q_k}$ and not $-\frac {\partial F}{\partial Q_k}$? $[P_k, F]=-[F, P_k]$ isn't it?</p> <p><strong>EDIT</strong>: Golstein starts from (1) and substituites $Q_k$ to $F$ and $F$ to $G$ and so he obtains (2). </p> <p>Then he substitutes $P_k$ to $F$ and $F$ to $G$ and obtains (3). </p> <p>Immediately after he writes (4), that according to me is opposite to (3). </p> <p>And so I have thought to a printing error. I have tried to substitute $-P_k$ to $F$ and I have obtained </p> <p>$$[-P_k, F]=\frac {\partial F}{\partial Q_k}$$</p> <p>Then, as $[-P_k, F]=[F,P_k]$, I can say that $$ [F,P_k]=\frac {\partial F}{\partial Q_k}$$. </p> <p>And so I can obtain (5).</p> <p>Could you confirm that my argumentation is correct? Many thanks</p>
g5415
[ 0.07149926573038101, -0.03839486092329025, -0.00968465581536293, -0.04705886170268059, 0.026992060244083405, -0.00010774046677397564, 0.020455533638596535, 0.05028432235121727, -0.05621316283941269, 0.031929366290569305, -0.10087913274765015, 0.005420437548309565, -0.08831171691417694, -0.012869789265096188, -0.02446603775024414, -0.035779040306806564, 0.053287066519260406, 0.06500014662742615, -0.00026264862390235066, -0.060347266495227814, -0.056142039597034454, 0.04623530060052872, -0.04514722898602486, 0.008867067284882069, 0.0020046306308358908, 0.00625253701582551, 0.04285312816500664, 0.01058280747383833, -0.050847072154283524, -0.01012511271983385, 0.028094559907913208, 0.009645713493227959, 0.05199204757809639, -0.010935884900391102, 0.010353301651775837, -0.048281725496053696, 0.053153060376644135, 0.00975189171731472, 0.03537697345018387, -0.05890769511461258, 0.007624332793056965, 0.02963373064994812, 0.028090449050068855, 0.06706786155700684, -0.010808221995830536, -0.05536169558763504, -0.002603536006063223, 0.023928280919790268, 0.0251633208245039, -0.06578594446182251, -0.01943361945450306, 0.046792663633823395, -0.03404197096824646, -0.03942974656820297, 0.006323707289993763, 0.060293566435575485, -0.0013817171566188335, 0.0029684214387089014, 0.013256173580884933, 0.02139231748878956, -0.002044282853603363, -0.04164210706949234, -0.009421141818165779, 0.0018607379170134664, 0.04435492306947708, -0.015369362197816372, 0.0006427793996408582, -0.0018512386595830321, -0.01790003851056099, -0.0007871852722018957, 0.013326743617653847, -0.03254213184118271, 0.04403223842382431, 0.019720328971743584, 0.035186685621738434, -0.023864319548010826, 0.00427766190841794, -0.026099923998117447, 0.040250733494758606, -0.03614117577672005, -0.01046057976782322, -0.0005912419874221087, 0.05945095047354698, 0.031130382791161537, -0.038177117705345154, -0.024167902767658234, -0.04870162904262543, -0.014774744398891926, -0.022321084514260292, 0.023111216723918915, -0.019719207659363747, -0.0002971860521938652, 0.009884165599942207, -0.013693420216441154, -0.043282896280288696, -0.02462289109826088, -0.03924664855003357, 0.033830057829618454, -0.03847043216228485, -0.027993986383080482, 0.007545046508312225, 0.02726406790316105, 0.043089400976896286, 0.008188013918697834, 0.020922118797898293, 0.007886488921940327, 0.018176399171352386, -0.020851489156484604, 0.001305007259361446, -0.04671788588166237, -0.008534572087228298, 0.02737271413207054, -0.0009617566247470677, -0.04271906614303589, -0.03308316320180893, 0.02247433550655842, 0.0784032791852951, -0.01391701027750969, -0.002972446847707033, 0.07636178284883499, -0.03807147964835167, 0.005105695687234402, 0.013658314011991024, 0.09202466905117035, 0.020067373290657997, -0.02833613008260727, 0.03614873066544533, 0.08638515323400497, 0.08199445903301239, 0.012781253084540367, -0.003194725140929222, 0.016725823283195496, -0.0008023849222809076, 0.016060546040534973, 0.06910112500190735, 0.050798360258340836, 0.029583478346467018, 0.020083557814359665, 0.04363144561648369, -0.00545815285295248, -0.04647110775113106, -0.025281578302383423, -0.03798692300915718, -0.0536721870303154, 0.004794982261955738, -0.041826531291007996, -0.010681839659810066, -0.02118399180471897, -0.006232289131730795, -0.00269138952717185, 0.006049802992492914, 0.023617280647158623, -0.01578798145055771, 0.00009692057210486382, -0.02338438853621483, 0.02891789749264717, 0.06857211887836456, 0.020166371017694473, 0.058829713612794876, -0.029648330062627792, 0.07458177208900452, -0.044833969324827194, 0.027305439114570618, 0.032853078097105026, 0.00031657531508244574, 0.0844775065779686, 0.017204158008098602, -0.03603058680891991, -0.022592371329665184, -0.049491651356220245, -0.03194732218980789, 0.011155962944030762, -0.01551884040236473, 0.025199459865689278, -0.00628151698037982, 0.03858418017625809, 0.006557498127222061, -0.023532496765255928, 0.01087938155978918, -0.003311948385089636, -0.010206813924014568, -0.008229825645685196, 0.04767819494009018, -0.0590030811727047, -0.03674187883734703, 0.007010642904788256, 0.008895916864275932, 0.011914929375052452, -0.06330524384975433, 0.03767888993024826, -0.03827899321913719, 0.0667516365647316, -0.028920510783791542, 0.06604773551225662, -0.01562580093741417, -0.013951783999800682, -0.0022231817711144686, -0.03624449297785759, -0.04068606346845627, -0.015062695369124413, 0.014758067205548286, -0.03219905495643616, 0.03353866562247276, -0.010167849250137806, 0.039119549095630646, -0.01795218512415886, 0.0018022482981905341, 0.008897334337234497, -0.027013497427105904, 0.000022979520508670248, -0.04170256853103638, -0.01757604256272316, -0.021692315116524696, 0.05510400980710983, 0.004327410366386175, 0.0037768224719911814, 0.028278453275561333, -0.017840802669525146, 0.005115584935992956, -0.010259236209094524, -0.0111454539000988, -0.021158728748559952, -0.02551487646996975, -0.00082165258936584, -0.025113146752119064, 0.02596307545900345, 0.05831058323383331, -0.018966831266880035, -0.05773472040891647, 0.06225971132516861, -0.10941708087921143, -0.028715532273054123, 0.0069247279316186905, -0.04170338809490204, 0.035393763333559036, -0.01030900701880455, -0.01504338625818491, 0.0066320146434009075, 0.021219857037067413, 0.03471236303448677, 0.057294558733701706, -0.05529951676726341, -0.017920654267072678, 0.05481863021850586, 0.02559967152774334, 0.027180174365639687, 0.06170853227376938, -0.034398000687360764, 0.03814547136425972, 0.019561102613806725, 0.025373142212629318, -0.029874393716454506, 0.010092243552207947, 0.010675203055143356, 0.011824040673673153, 0.00010540286166360602, -0.0383462980389595, -0.03481695055961609, 0.008425516076385975, -0.006515063811093569, -0.0038336114957928658, -0.01293144840747118, -0.03252151980996132, 0.03910267353057861, -0.08256465196609497, -0.01184258796274662, -0.0052818660624325275, -0.0041019669733941555, -0.029000788927078247, -0.0386057049036026, -0.04290269687771797, 0.040792278945446014, 0.00200326438061893, 0.03537194803357124, -0.022448115050792694, -0.03192037716507912, 0.01733960397541523, -0.030234739184379578, -0.0025948875118047, 0.02599717304110527, -0.0226911548525095, 0.06078357622027397, -0.017760083079338074, -0.01381921861320734, 0.008260941132903099, -0.03952130302786827, 0.016957934945821762, 0.061732884496450424, 0.03360700234770775, 0.042532358318567276, -0.027641143649816513, 0.061509910970926285, 0.02054712548851967, 0.009784710593521595, -0.014653461053967476, 0.03307044878602028, -0.04113372787833214, -0.038571085780858994, -0.0108029805123806, -0.04274692013859749, 0.05061030387878418, -0.02429933100938797, -0.04726359620690346, 0.05437936261296272, 0.05021854117512703, -0.02911023609340191, 0.026958037167787552, 0.029290566220879555, -0.0363299623131752, 0.05273214355111122, 0.02123895101249218, -0.0030088317580521107, -0.006923563778400421, -0.0044853962026536465, 0.0008584781899116933, 0.02810489758849144, -0.025358356535434723, -0.05081724375486374, -0.004405270330607891, -0.04699070006608963, 0.018557481467723846, -0.036610011011362076, -0.02066630870103836, -0.031192190945148468, 0.01946420408785343, -0.04219472408294678, -0.056096989661455154, 0.0072138928808271885, -0.0019574062898755074, -0.05158206820487976, 0.050164904445409775, -0.028434496372938156, 0.04098806902766228, -0.020952755585312843, 0.008078551851212978, -0.06084737554192543, -0.028641095384955406, -0.01564617082476616, -0.025664057582616806, -0.060527510941028595, 0.017878083512187004, -0.02064126543700695, -0.025942549109458923, -0.00016580741794314235, -0.07477124780416489, -0.01579303853213787, 0.030162444338202477, 0.0328461155295372, 0.010165766812860966, -0.010881678201258183, -0.043186988681554794, 0.04023195058107376, -0.01086372509598732, -0.01825903356075287, 0.002690456109121442, 0.021538272500038147, 0.0046609751880168915, 0.04578035697340965, 0.024281183257699013, -0.038274794816970825, 0.09320113807916641, -0.05629003047943115, 0.0016130018047988415, 0.0307182427495718, 0.019392941147089005, 0.008612407371401787, 0.024831026792526245, 0.03038790263235569, -0.025359924882650375, 0.02382311224937439, -0.012024418450891972, -0.0421174131333828, 0.05607343465089798, -0.04195385426282883, 0.06719924509525299, -0.042886145412921906, 0.027425892651081085, 0.05294543132185936, -0.0070164017379283905, -0.008484962396323681, 0.0010835332795977592, -0.0076441532000899315, 0.041116323322057724, 0.05146496370434761, 0.06089352071285248, 0.0040405732579529285, -0.026700647547841072, -0.007871683686971664, -0.007595970295369625, 0.029905159026384354, 0.054706450551748276, 0.02160315215587616, -0.03352970629930496, 0.040014658123254776, 0.009625958278775215, -0.07418419420719147, 0.06153169274330139, 0.001974655780941248, -0.010217748582363129, 0.04130478948354721, -0.01592571847140789, 0.013203896582126617, -0.056438103318214417, 0.009663852863013744, -0.0111562330275774, -0.0411403588950634, -0.02497517690062523, -0.016989372670650482, -0.02768828347325325, -0.0028885100036859512, -0.03305366262793541, -0.01623615063726902, -0.006682272534817457, -0.0494501031935215, 0.008511722087860107, 0.029374560341238976, -0.026980595663189888, -0.017762407660484314, -0.00421869195997715, -0.053492870181798935, 0.012246512807905674, 0.0040367539040744305, 0.013857285492122173, 0.010994709096848965, 0.06376189738512039, 0.1123126894235611, 0.013050859794020653, -0.018582217395305634, 0.04028526693582535, -0.04077066853642464, 0.03330109640955925, 0.04571251571178436, 0.025200845673680305, 0.027082335203886032, 0.0018616336164996028, 0.04696843400597572, -0.045586299151182175, -0.0069961161352694035, -0.03783383592963219, 0.035106267780065536, 0.031375810503959656, 0.005950450897216797, -0.03577779605984688, -0.039941322058439255, 0.028018293902277946, -0.0007576030329801142, -0.03686584159731865, 0.00017059047240763903, 0.020222967490553856, -0.06936056166887283, -0.004701156634837389, 0.03144501894712448, 0.07543319463729858, -0.039394114166498184, 0.011821691878139973, -0.02420586533844471, 0.011827768757939339, -0.04146697372198105, -0.01059949304908514, 0.02697751298546791, -0.050768498331308365, -0.006710392888635397, 0.06703346222639084, -0.02347639575600624, 0.04112383723258972, 0.04590478539466858, -0.054060328751802444, 0.026630762964487076, -0.05404166504740715, -0.04387032240629196, 0.01454438641667366, -0.026623684912919998, -0.05650656670331955, -0.023348504677414894, 0.028939837589859962, 0.027682457119226456, 0.00021517252025660127, -0.03148231282830238, 0.03393761068582535, -0.039974965155124664, -0.009488307870924473, 0.02450667694211006, -0.018453964963555336, -0.026512078940868378, -0.053287405520677567, -0.039986275136470795, 0.028587402775883675, -0.028041256591677666, -0.036179132759571075, 0.01955416053533554, 0.025887327268719673, -0.014960241504013538, 0.036803361028432846, -0.009557681158185005, -0.012308522127568722, 0.053505413234233856, 0.026348046958446503, -0.022383805364370346, 0.02975851483643055, 0.030722003430128098, -0.07437475770711899, 0.009759316220879555, 0.03935900330543518, -0.006996470969170332, -0.03317578509449959, 0.031187990680336952, 0.07934385538101196, -0.01634221524000168, 0.011060237884521484, 0.054926056414842606, 0.02483060210943222, -0.009602508507668972, 0.025498541072010994, 0.01559481117874384, 0.019796809181571007, 0.04416096955537796, 0.0161430686712265, -0.06830248981714249, -0.07095558196306229, -0.023787137120962143, 0.02721627987921238, 0.031140664592385292, 0.02312115952372551, -0.014735594391822815, -0.00869947299361229, -0.010673394426703453, -0.040677882730960846, -0.05398176610469818, 0.000107096646388527, 0.040046077221632004, -0.01558411493897438, -0.04300008341670036, -0.03152227774262428, 0.07260975986719131, 0.02449210360646248, -0.02440495975315571, -0.056321706622838974, -0.03917006030678749, 0.029088424518704414, 0.01187377329915762, -0.037651918828487396, -0.03698750212788582, 0.017573991790413857, 0.030047746375203133, -0.05240657180547714, -0.019287003204226494, 0.009499437175691128, -0.021413033828139305, -0.014493224211037159, -0.06296808272600174, -0.022960208356380463, -0.0019005739595741034, -0.05532916635274887, -0.008622243069112301, 0.0016681610140949488, 0.03380493074655533, 0.04748890548944473, -0.026700416579842567, -0.010289440862834454, -0.036278337240219116, 0.011280779726803303, 0.01917692832648754, -0.029478397220373154, 0.008592680096626282, 0.07517415285110474, -0.002756058471277356, -0.009629137814044952, 0.014913789927959442, 0.05345327779650688, 0.044727664440870285, 0.004688498564064503, 0.014174689538776875, 0.035793911665678024, 0.005628091283142567, -0.03958519920706749, 0.04671730101108551, -0.06566962599754333, -0.02339896559715271, -0.021235130727291107, -0.0032702372409403324, -0.01650061085820198, -0.01515395101159811, -0.0009432974038645625, -0.002356430748477578, -0.08519365638494492, 0.06307674944400787, -0.010476559400558472, 0.01948636956512928, 0.01625918783247471, 0.049087438732385635, -0.030156675726175308, 0.025507086887955666, -0.0717976838350296, 0.018434792757034302, 0.019701026380062103, -0.006346818525344133, 0.022578686475753784, 0.034070201218128204, -0.06512995064258575, -0.02368432842195034, 0.0031464474741369486, -0.0059425984509289265, 0.053566824644804, -0.06910558044910431, 0.005935765337198973, -0.005027326755225658, -0.00820544920861721, 0.010517450980842113, 0.013810819014906883, 0.07554614543914795, 0.03519810736179352, 0.03022034280002117, 0.03518949821591377, 0.011129289865493774, 0.03621121868491173, -0.05213390290737152, -0.07124103605747223, 0.027527542784810066, 0.00908371526747942, -0.018498321995139122, 0.02722923830151558, -0.015499559231102467, 0.01764056645333767, -0.025948774069547653, 0.009609222412109375, 0.08369781821966171, -0.026932114735245705, 0.037206970155239105, -0.008972005918622017, 0.0033310260623693466, -0.051460426300764084, 0.01995985582470894, -0.040457602590322495, 0.008983324281871319, -0.03652865067124367, 0.029066042974591255, -0.05599592253565788, 0.08597523719072342, 0.0553966760635376, -0.012321004644036293, 0.02483898401260376, 0.05957290902733803, 0.052622273564338684, -0.004331268835812807, -0.08525790274143219, -0.03890904784202576, -0.0012502410681918263, -0.0004937120829708874, -0.0932697132229805, 0.02115706168115139, 0.07264689356088638, 0.06452400237321854, 0.019053908064961433, 0.030162625014781952, -0.013234293088316917, 0.04740724712610245, 0.004927185829728842, 0.02964857406914234, 0.06436396390199661, -0.04891260340809822, -0.015339678153395653, 0.03682802990078926, 0.010837462730705738, 0.0003839571727439761, -0.008790976367890835, 0.018722767010331154, 0.013237184844911098, -0.0891336053609848, -0.006939796730875969, 0.03677752986550331, -0.010058087296783924, -0.009680129587650299, 0.03494805097579956, 0.03549846634268761, 0.005425617098808289, 0.042822837829589844, 0.007944714277982712, 0.04815131425857544, 0.00048152831732295454, -0.03046628274023533, -0.04925311729311943, 0.04360276088118553, -0.05453518405556679, -0.06145923584699631, -0.04712817072868347, 0.043212465941905975, -0.004271902609616518, 0.04114459827542305, -0.023717189207673073, 0.050458140671253204, -0.0033658770844340324, -0.0452292338013649, -0.0036226543597877026, 0.009884721599519253, -0.02935182675719261, -0.0033285196404904127, 0.007827341556549072, -0.017296243458986282, 0.019036060199141502, -0.003975904546678066, 0.01886245608329773, -0.010514741763472557, -0.05030263215303421, -0.002060886938124895, 0.03169332444667816, -0.010203425772488117, -0.021490046754479408, -0.07542363554239273, -0.024379264563322067, -0.003488334594294429, 0.021236740052700043, -0.00647662952542305, -0.04999963939189911, 0.010797510854899883, 0.05909925699234009, -0.031201276928186417, -0.033382710069417953, -0.0019020604668185115, 0.016186410561203957, -0.06610255688428879, -0.06230722740292549, -0.03108636662364006, -0.08048686385154724, -0.05416391044855118, -0.003498049918562174, -0.016821887344121933, 0.03726127743721008, -0.013733522035181522, -0.04974465072154999, 0.10279368609189987, -0.04407813400030136, -0.073896624147892, -0.05498363450169563, 0.02948921173810959, 0.026409978047013283, -0.0397082194685936, 0.027580007910728455, -0.029347680509090424, 0.018753381446003914, 0.038160596042871475, -0.010664582252502441, -0.03152564540505409, -0.0000318655111186672, 0.03407762572169304, 0.005143927410244942, -0.07170367240905762, -0.022262293845415115, 0.030673645436763763, 0.014127843081951141, -0.04096052795648575, -0.018034756183624268, 0.033858638256788254, 0.06728201359510422, -0.022227173671126366, 0.025837400928139687, -0.017821840941905975, 0.03140634298324585, 0.0006834428641013801, 0.04776411131024361, 0.017554933205246925, 0.014324693940579891, 0.026803012937307358, 0.00045251662959344685, -0.01955377496778965, 0.00015241437358781695, -0.043595001101493835, 0.031630657613277435, 0.045397497713565826 ]
<p>I have been searching on the Internet but have not found a derivation of the formula for the self gravitational potential energy of a sphere. Can someone show how to do this? I assume it involved 6 nested integrals (3 for each particle $dm$ and 3 for integrating the potential energy for all other particles).</p>
g5416
[ 0.06084809452295303, 0.07320326566696167, -0.0009741161484271288, -0.0011177173582836986, -0.01602308079600334, -0.023494184017181396, 0.008436991833150387, 0.01693257875740528, -0.059931837022304535, 0.05103310942649841, -0.05159635469317436, 0.015929624438285828, 0.02685489133000374, 0.028743354603648186, -0.04246054217219353, -0.007878103293478489, -0.000896837969776243, 0.023076144978404045, 0.0077016414143145084, 0.04598980396986008, 0.0077258809469640255, -0.043815016746520996, 0.021021772176027298, -0.054263267666101456, -0.04451219365000725, -0.008066742680966854, 0.0015077582793310285, 0.013054797425866127, -0.06070142984390259, 0.03409318998456001, 0.03107435069978237, 0.03672823682427406, 0.04813764989376068, -0.0016123077366501093, -0.04205981642007828, 0.01861109770834446, 0.06362660974264145, -0.000388185289921239, -0.041555870324373245, -0.029695801436901093, 0.003769696457311511, -0.04456708952784538, -0.029573291540145874, 0.051966700702905655, -0.007988453842699528, 0.017746882513165474, 0.043507374823093414, 0.04652506858110428, -0.015911491587758064, -0.09577720612287521, -0.03918904438614845, 0.05814986675977707, 0.06866671144962311, -0.04191502556204796, -0.02984803169965744, 0.03399520739912987, 0.0016101902583613992, -0.04291776567697525, -0.011861521750688553, 0.055077649652957916, 0.015086254104971886, -0.0532391257584095, -0.055302515625953674, 0.0038826032541692257, 0.05710054561495781, 0.008765657432377338, -0.07122323662042618, -0.004381672944873571, -0.04648969694972038, 0.03017774224281311, 0.047169774770736694, -0.0045086354948580265, -0.0036963645834475756, -0.03477034345269203, -0.05155998840928078, 0.01342195924371481, 0.05549241229891777, 0.05335475131869316, -0.042423710227012634, 0.00754938367754221, 0.04210051894187927, -0.017340146005153656, 0.058697085827589035, 0.010303650982677937, 0.011724346317350864, -0.05692673102021217, -0.019720423966646194, -0.035116683691740036, -0.08800960332155228, -0.007906326092779636, 0.04548666998744011, 0.03719710931181908, 0.016634393483400345, -0.009999154135584831, 0.02209031581878662, 0.012788401916623116, 0.0012440888676792383, 0.04383885860443115, -0.020359165966510773, -0.0290969368070364, -0.02726605348289013, -0.029430245980620384, -0.005143625196069479, -0.0036776545457541943, 0.005107743665575981, -0.07202982157468796, -0.015257700346410275, 0.05371234193444252, 0.07448339462280273, 0.0022758198902010918, -0.05029333755373955, 0.013991167768836021, -0.016544973477721214, 0.0006540700560435653, -0.04570676386356354, -0.04134437441825867, 0.08374518901109695, -0.02763461321592331, -0.008168993517756462, 0.06549022346735, 0.021990705281496048, 0.0766049399971962, 0.02551746927201748, 0.04605682194232941, -0.016959404572844505, 0.008518966846168041, -0.025851568207144737, -0.015270568430423737, 0.012776629067957401, -0.028127869591116905, 0.062287669628858566, -0.04856543615460396, -0.03063984401524067, -0.015957172960042953, -0.03601955622434616, -0.0020368159748613834, -0.0236209686845541, 0.01771022193133831, -0.032591596245765686, -0.009242669679224491, -0.024879874661564827, -0.04122716188430786, 0.03980224207043648, -0.023986240848898888, -0.02076457254588604, 0.04167024418711662, -0.003563688602298498, -0.05035419762134552, -0.05851564556360245, 0.04211391508579254, 0.04151555523276329, 0.07215986400842667, 0.07973586767911911, -0.10103317350149155, 0.07567228376865387, -0.026850758120417595, -0.0024785345885902643, 0.014368794858455658, 0.03472728282213211, 0.03979327157139778, 0.07339805364608765, 0.05727062001824379, 0.013627937994897366, 0.01886199228465557, -0.025321029126644135, 0.06534561514854431, -0.005784621927887201, -0.015171742998063564, -0.01952417381107807, -0.08264638483524323, 0.02948361448943615, 0.018870504572987556, -0.0047631594352424145, 0.016832927241921425, -0.061479873955249786, 0.028119908645749092, -0.039383262395858765, -0.01839875616133213, -0.05375002324581146, 0.09071225672960281, 0.07375268638134003, -0.003865751437842846, -0.00437734741717577, 0.00910147838294506, 0.014997917227447033, 0.000370441353879869, 0.011423318646848202, 0.006666875444352627, -0.00006270212907111272, 0.0010101383086293936, 0.0026918475050479174, 0.05931223928928375, 0.030491409823298454, 0.00478997640311718, 0.05481548234820366, 0.04571778327226639, 0.09654466807842255, 0.006951557472348213, -0.012303676456212997, 0.01444957870990038, 0.01313926000148058, 0.06075698137283325, 0.05894554406404495, 0.033782295882701874, 0.0480654239654541, -0.017274484038352966, 0.045526888221502304, -0.015496484935283661, 0.0274562556296587, -0.04700250178575516, -0.013198718428611755, -0.007865199819207191, 0.011259686201810837, -0.018617257475852966, 0.014495293609797955, 0.048314861953258514, -0.02907251939177513, -0.0003907060599885881, -0.026341328397393227, -0.00969405472278595, -0.08698603510856628, 0.035611726343631744, -0.026204301044344902, 0.02897992730140686, -0.00936836190521717, 0.08164771646261215, -0.04060223698616028, -0.012204883620142937, 0.03518817946314812, 0.004232076462358236, -0.044447917491197586, -0.01534978300333023, 0.008002646267414093, -0.029500635340809822, 0.0077954125590622425, 0.032835155725479126, -0.048600614070892334, 0.010190054774284363, -0.012860017828643322, 0.03317660838365555, -0.026534952223300934, -0.01253386028110981, 0.00834160577505827, 0.012930065393447876, 0.003000732744112611, 0.015178491361439228, 0.0613287016749382, -0.011042687110602856, -0.024543967097997665, 0.01890309900045395, 0.04119788855314255, -0.05528583750128746, -0.050655897706747055, -0.03252526372671127, -0.01913205347955227, 0.0653984397649765, -0.03965995833277702, 0.017361002042889595, 0.013262585736811161, -0.014392764307558537, -0.03072461485862732, -0.08974986523389816, 0.00909624807536602, -0.010727801360189915, -0.018008850514888763, -0.0536457784473896, 0.01456327922642231, -0.051958512514829636, 0.04525000602006912, 0.030738936737179756, -0.00351679022423923, 0.06830419600009918, 0.08037921041250229, -0.009164785034954548, 0.01726122759282589, -0.02933095209300518, -0.04149121418595314, 0.04729316383600235, 0.004092969931662083, 0.010351154021918774, -0.021538453176617622, -0.034095648676157, -0.009398045018315315, 0.042695824056863785, -0.004187051206827164, -0.0950070470571518, 0.04411608725786209, -0.008155596442520618, -0.022348051890730858, -0.03661344572901726, 0.03689521551132202, 0.008578612469136715, 0.005507745314389467, -0.010743001475930214, -0.005852032452821732, 0.06820983439683914, 0.02632443979382515, -0.034722935408353806, 0.019886624068021774, 0.06597647815942764, -0.04023924097418785, 0.037526704370975494, -0.015261123888194561, -0.009958081878721714, -0.023055102676153183, 0.023872561752796173, 0.027273356914520264, -0.019287927076220512, -0.0022212332114577293, -0.06055046617984772, 0.0020012997556477785, 0.039818063378334045, 0.037316206842660904, -0.014449195936322212, -0.024000421166419983, 0.005564081948250532, -0.020298806950449944, -0.030919410288333893, -0.01838858425617218, -0.019784187898039818, -0.011937498115003109, -0.03637651726603508, 0.020523371174931526, 0.03453265130519867, 0.00507572153583169, 0.022589635103940964, 0.010390526615083218, -0.021258285269141197, 0.014358408749103546, -0.01801128499209881, -0.022766605019569397, -0.053334034979343414, -0.029749970883131027, 0.041546545922756195, -0.018972231075167656, -0.03553665801882744, -0.07352029532194138, -0.059292685240507126, 0.03085741400718689, 0.0063324072398245335, -0.0064535848796367645, 0.033914756029844284, -0.053299520164728165, -0.03900332376360893, -0.05500062555074692, 0.03295935317873955, -0.010885074734687805, 0.01962166465818882, -0.020262613892555237, 0.0186916533857584, -0.025087431073188782, 0.00883365236222744, 0.03741101175546646, 0.00535160256549716, 0.011112513951957226, -0.028061028569936752, -0.006176760420203209, 0.07081238180398941, 0.01917347125709057, 0.052423618733882904, 0.012621459551155567, -0.008913619443774223, 0.01217327918857336, 0.028180589899420738, 0.028325002640485764, -0.06566253304481506, -0.03548062592744827, 0.00032941967947408557, 0.006143179256469011, 0.0033732762094587088, -0.0006844847230240703, -0.004394138231873512, -0.0259011872112751, -0.06284864991903305, -0.003051178762689233, -0.059982236474752426, -0.01050677988678217, -0.016329916194081306, 0.012976481579244137, -0.048024509102106094, 0.043635670095682144, 0.018490489572286606, 0.045454878360033035, 0.07737667113542557, 0.017425406724214554, 0.03374968469142914, -0.05786804482340813, 0.00138120970223099, 0.06419654190540314, 0.0024025789462029934, 0.005404593423008919, -0.04638160020112991, -0.012811778113245964, -0.010291524231433868, -0.006007042713463306, 0.031420160084962845, 0.018431153148412704, -0.030735567212104797, 0.015153375454246998, 0.04033977538347244, -0.022275062277913094, -0.016579996794462204, -0.007317485753446817, -0.021930312737822533, 0.06211007386445999, -0.00232574506662786, 0.011800328269600868, -0.07385549694299698, 0.007622600998729467, 0.008950809016823769, 0.022883215919137, -0.020331088453531265, 0.08459849655628204, -0.028187310323119164, 0.010623550973832607, -0.022595301270484924, -0.015704141929745674, -0.046408314257860184, -0.03146715462207794, 0.010199032723903656, -0.012135716155171394, -0.030201299116015434, -0.06668175756931305, 0.015910284593701363, -0.06477990001440048, 0.029726356267929077, 0.024462902918457985, 0.004689110908657312, -0.07099408656358719, -0.000045877495722379535, 0.04246217757463455, 0.03542007878422737, -0.01304095983505249, -0.009197644889354706, -0.07444621622562408, 0.007780422456562519, 0.001808043336495757, 0.012656906619668007, -0.015133542008697987, -0.026173584163188934, 0.03718437999486923, 0.08098821341991425, 0.009085629135370255, -0.022441329434514046, 0.038723014295101166, 0.047042012214660645, -0.04257079213857651, -0.03216957300901413, -0.029566239565610886, -0.02231774665415287, 0.02905852720141411, -0.05063819885253906, -0.0135703906416893, 0.012499593198299408, -0.009742764756083488, 0.07232251018285751, -0.033694684505462646, 0.030994515866041183, -0.015826229006052017, -0.003950523212552071, -0.023005610331892967, -0.016602719202637672, -0.01201101765036583, -0.020759398117661476, -0.01841926760971546, 0.019468573853373528, -0.057640500366687775, 0.04313451424241066, 0.019211923703551292, -0.020246164873242378, -0.013670713640749454, 0.004340114537626505, -0.07745739072561264, -0.029409175738692284, -0.018446234986186028, -0.04137103632092476, 0.011630309745669365, 0.010695639997720718, 0.059846196323633194, -0.019446762278676033, -0.03133475035429001, 0.024313917383551598, -0.03423041105270386, 0.014612594619393349, -0.030896421521902084, 0.0782109797000885, -0.0251358300447464, -0.04439590871334076, -0.034110166132450104, -0.008266804739832878, -0.023127151653170586, 0.006889108568429947, 0.0019126422703266144, -0.05122599005699158, 0.019855482503771782, 0.044611673802137375, 0.020179297775030136, -0.03364311903715134, 0.009244777262210846, 0.025869043543934822, 0.02059565670788288, 0.01571241393685341, -0.08071887493133545, 0.03314148262143135, 0.022298716008663177, 0.044808682054281235, 0.03176445513963699, 0.039398856461048126, 0.0244308914989233, -0.030971216037869453, 0.036341432482004166, -0.026584306731820107, 0.023205915465950966, 0.019530897960066795, -0.0012670322321355343, -0.00649828277528286, 0.004569576121866703, -0.021479731425642967, 0.008178393356502056, -0.0027211871929466724, 0.04269890487194061, 0.024184487760066986, 0.022171933203935623, -0.04165969043970108, 0.046810369938611984, 0.0033539074938744307, -0.06563811004161835, -0.02408452145755291, 0.09376036375761032, -0.0004594683414325118, -0.040865540504455566, -0.05042097717523575, -0.06845929473638535, 0.04701393097639084, 0.06889170408248901, -0.011603050865232944, -0.016958534717559814, 0.0027339658699929714, 0.07907063513994217, -0.006651866715401411, -0.05319806560873985, -0.04276275262236595, 0.005577622912824154, -0.029459625482559204, -0.058428626507520676, -0.004177791532129049, 0.0010647595627233386, 0.000946324784308672, 0.052636805921792984, -0.013027645647525787, -0.03548390418291092, 0.011208698153495789, 0.016401007771492004, -0.040822967886924744, 0.04597489908337593, 0.012743104249238968, 0.020396552979946136, -0.001429711701348424, -0.017397865653038025, -0.019023749977350235, -0.018662480637431145, -0.019058750942349434, -0.00869886763393879, -0.019021499902009964, -0.04911835491657257, -0.06253145635128021, -0.026608295738697052, -0.05495479330420494, 0.0014934963546693325, -0.0043515549041330814, 0.024227458983659744, 0.02636660449206829, -0.025698767974972725, -0.024482563138008118, 0.00408540852367878, 0.0019051114795729518, 0.040587544441223145, 0.010183867067098618, -0.015736375004053116, -0.014133311808109283, 0.014564898796379566, 0.0009362076525576413, 0.041894491761922836, -0.056455228477716446, -0.04369558393955231, 0.06727343052625656, -0.042832814157009125, -0.009951751679182053, -0.00005978189437882975, -0.0379486083984375, -0.006953966338187456, -0.018302256241440773, -0.0066895997151732445, -0.027659215033054352, 0.030194874852895737, -0.0464211031794548, 0.03975179046392441, 0.046820759773254395, 0.027604838833212852, -0.007074570748955011, -0.007442056201398373, 0.008169970475137234, 0.05613997206091881, -0.02372320182621479, 0.07286810874938965, 0.0012154338182881474, -0.03202696144580841, -0.052472010254859924, -0.0005798263591714203, 0.01755862683057785, 0.03008110262453556, 0.045120719820261, -0.033304180949926376, -0.005414326675236225, 0.02392072230577469, -0.005993208847939968, 0.0028877274598926306, -0.015337429009377956, -0.0394757017493248, -0.008316854946315289, 0.005558121018111706, 0.025956762954592705, 0.0211979690939188, -0.07313617318868637, 0.04044691100716591, -0.04150731861591339, -0.06398694962263107, 0.02435738779604435, -0.023353779688477516, -0.001259553013369441, -0.013114025816321373, 0.0009461977751925588, 0.01707163266837597, -0.0045093959197402, 0.0074440608732402325, 0.02342064492404461, 0.0023614647798240185, 0.003038786118850112, -0.01607581600546837, 0.024167554453015327, -0.04919175058603287, 0.03311958163976669, 0.033351100981235504, 0.0062043797224760056, -0.058954931795597076, -0.01511252112686634, 0.03592447191476822, -0.002453742315992713, -0.012815095484256744, 0.03978265821933746, -0.046106524765491486, -0.03919113427400589, -0.044831305742263794, 0.019498391076922417, -0.030468732118606567, -0.008531763218343258, -0.033913515508174896, 0.03018994815647602, 0.024093979969620705, -0.03130684420466423, 0.04878778010606766, 0.007117553614079952, -0.03182777017354965, 0.009458024054765701, 0.01170691754668951, 0.044972699135541916, 0.05500322952866554, 0.006517905741930008, 0.01790018007159233, -0.01355642732232809, 0.022325007244944572, 0.009244690649211407, -0.029322804883122444, 0.024773703888058662, -0.05988270416855812, 0.023140309378504753, 0.01831909455358982, 0.007688595913350582, 0.030514849349856377, 0.030349113047122955, 0.015087978914380074, -0.010900675319135189, -0.040073830634355545, 0.03788542374968529, 0.00436242064461112, -0.013567808084189892, -0.01623081974685192, 0.00752644706517458, 0.03104260563850403, 0.08926869928836823, -0.026675287634134293, 0.023265797644853592, -0.05369863659143448, -0.0251225046813488, -0.030936548486351967, 0.011724721640348434, 0.06736726313829422, 0.0014415931655094028, 0.06322845816612244, -0.010594877414405346, 0.056529439985752106, -0.020476914942264557, -0.009133603423833847, -0.033578429371118546, -0.023042788729071617, 0.013150986284017563, -0.050543785095214844, 0.023835796862840652, -0.005551645066589117, -0.0003619063354562968, 0.0235008355230093, -0.03434109687805176, -0.014835108071565628, -0.00033162414911203086, 0.002098387572914362, 0.035421986132860184, -0.0041819047182798386, 0.04391377419233322, -0.014979290775954723, -0.011677396483719349, 0.037396349012851715, -0.006253115367144346, 0.02219497784972191, -0.02572905644774437, 0.018597565591335297, -0.04342755302786827, -0.037412554025650024, -0.017650779336690903, 0.07349485158920288, -0.05225178226828575, 0.034779008477926254, -0.006057483609765768, -0.038432005792856216, 0.0160483680665493, 0.03325708582997322, -0.02729029208421707, -0.01633135974407196, -0.05810815095901489, 0.04270867630839348, 0.011704843491315842, 0.038935281336307526, -0.04734678566455841, 0.00622353982180357, -0.05848332867026329, 0.009161735884845257, -0.013459102250635624, -0.07185548543930054, 0.01897094026207924, 0.11549878865480423, 0.007490542251616716, 0.04977741837501526, -0.08920200169086456, 0.02586953714489937, 0.05789873003959656, 0.008452340960502625, -0.08951258659362793, -0.019478296861052513, -0.012085877358913422, -0.06370459496974945, 0.015952691435813904, 0.01925797015428543, -0.00875549204647541, 0.026989266276359558, 0.03650904446840286, 0.011520187370479107, -0.04742484912276268, 0.013486145064234734, 0.023398777469992638 ]
<p>Trying to get a better understanding of the relation between a SU(N) Yang Mill theory and its number of "color" <a href="http://www.stat.physik.uni-potsdam.de/~pikovsky/teaching/stud_seminar/Classical_Yang_Mills.pdf" rel="nofollow">space</a>.</p> <p>Most of the description I've found so far are either way to complex/specific. Yiannis answer on <a href="http://physics.stackexchange.com/questions/102941/how-many-physical-degrees-of-freedom-does-the-mathrmsun-yang-mills-theory">this post</a> is almost what I'm looking for, except I was hoping someone could provide addition sources and readings corresponding precisely to what he is describing. </p>
g192
[ 0.0033461202401667833, 0.04008451849222183, -0.024259544909000397, -0.052218738943338394, 0.026573147624731064, -0.009183915331959724, 0.05134110525250435, -0.018675101920962334, 0.029612837359309196, -0.03550250828266144, 0.021541180089116096, -0.03954465687274933, 0.09019728004932404, 0.02688591182231903, -0.025563152506947517, -0.03066573478281498, 0.024431776255369186, 0.058085571974515915, 0.014938995242118835, -0.06727614998817444, -0.02734123356640339, 0.02017315663397312, -0.008580553345382214, -0.06997676938772202, -0.03392845392227173, 0.005579203832894564, 0.03825632110238075, -0.0030822507105767727, 0.01753605529665947, -0.00992994848638773, 0.004497499205172062, -0.025023041293025017, 0.02189028263092041, -0.011306303553283215, -0.03523289039731026, 0.019071048125624657, 0.028051508590579033, 0.05267321318387985, -0.010993536561727524, -0.0014567499747499824, -0.04396815225481987, 0.01609603688120842, 0.005084446631371975, -0.009925976395606995, -0.00020856340415775776, 0.024106118828058243, -0.03492722287774086, -0.007851696573197842, 0.017781367525458336, 0.03222709894180298, -0.03885672241449356, 0.03540527820587158, 0.048371292650699615, 0.059561923146247864, -0.0119121503084898, 0.0476096048951149, 0.02271953597664833, -0.015254760161042213, 0.04292887821793556, 0.12025190889835358, 0.038823407143354416, 0.015843594446778297, -0.01761688105762005, 0.018186578527092934, 0.039779067039489746, 0.005910910665988922, -0.0033946565818041563, -0.052983932197093964, -0.012509500607848167, -0.06078307703137398, -0.026452677324414253, -0.08235146850347519, -0.0008399711223319173, -0.007096743676811457, -0.039385538548231125, 0.0031533963046967983, 0.028195785358548164, 0.03508611395955086, -0.012120275758206844, -0.02905665896832943, -0.06317876279354095, 0.01662151701748371, 0.0907197967171669, 0.014135037548840046, 0.07058782130479813, -0.03648830205202103, -0.015825826674699783, 0.01251509040594101, -0.013513520359992981, 0.008879458531737328, 0.003733064979314804, 0.027203449979424477, 0.03578856959939003, 0.007648948580026627, -0.012772892601788044, 0.01823183335363865, 0.0020729510579258204, 0.05604631081223488, -0.02269718609750271, -0.009842642582952976, -0.050428010523319244, -0.01928655244410038, 0.05452151969075203, -0.07026250660419464, 0.013245541602373123, -0.013514705933630466, 0.058300167322158813, -0.025393282994627953, -0.014363977126777172, 0.028571490198373795, -0.10676092654466629, 0.016399217769503593, -0.04166733846068382, -0.03669334575533867, -0.04772248491644859, -0.019348308444023132, 0.015260690823197365, -0.016937900334596634, 0.040847767144441605, 0.04912198707461357, 0.01616920344531536, 0.027337681502103806, -0.0494559071958065, 0.009725146926939487, -0.05204123631119728, -0.04575653001666069, 0.020253408700227737, -0.03534281626343727, -0.003674559062346816, 0.034822359681129456, 0.0078253373503685, -0.0467686653137207, 0.0007766140624880791, 0.01709446869790554, -0.005819979589432478, 0.00391262024641037, 0.012719265185296535, 0.0032399578485637903, -0.03515461087226868, 0.045414265245199203, -0.012581995688378811, -0.03728071600198746, -0.00004577679283102043, -0.06747649610042572, -0.022410061210393906, -0.0051535977981984615, -0.026565272361040115, 0.02049921452999115, -0.04202618822455406, -0.01653999648988247, 0.03904680907726288, 0.03900321573019028, 0.003283123252913356, -0.058111317455768585, -0.0136819276958704, 0.005155340768396854, 0.0110991932451725, -0.05068529024720192, 0.00036726100370287895, 0.009878170676529408, -0.03783492371439934, -0.08155000954866409, 0.020211124792695045, 0.013863704167306423, -0.03329216688871384, -0.06100839748978615, 0.026747077703475952, -0.02451210655272007, -0.05530669912695885, -0.09387296438217163, -0.02929569222033024, 0.00542965903878212, 0.028028899803757668, -0.013034956529736519, 0.03137895464897156, 0.053621403872966766, 0.03172365948557854, -0.03558603301644325, -0.039363883435726166, -0.025830058380961418, -0.03724204748868942, 0.009818712249398232, 0.00040410723886452615, -0.028549283742904663, -0.009275124408304691, -0.020885126665234566, 0.016295013949275017, 0.016754863783717155, 0.008624193258583546, 0.029848141595721245, -0.013655425980687141, 0.027225373312830925, -0.0012901982991024852, 0.0492783784866333, 0.0024954425171017647, -0.0015380897093564272, -0.00010367791401222348, 0.02482782118022442, -0.005037880968302488, -0.015622409991919994, -0.010569404810667038, 0.01126785483211279, -0.008831295184791088, -0.016093961894512177, 0.07875794172286987, -0.00872550718486309, 0.008350362069904804, 0.030756482854485512, -0.0006529783131554723, -0.015078105032444, -0.027503974735736847, -0.0374048687517643, 0.0281240101903677, 0.07471770793199539, -0.01264093816280365, -0.03435269370675087, -0.036144934594631195, -0.027934713289141655, 0.003316701389849186, 0.025525137782096863, -0.020855959504842758, -0.03500320017337799, 0.02846546471118927, -0.01045412290841341, 0.029180049896240234, -0.00682790158316493, -0.05836803838610649, -0.01518547348678112, 0.012009824626147747, 0.052065540105104446, -0.14856107532978058, 0.03873274102807045, -0.027001330628991127, -0.061931341886520386, 0.006333190016448498, 0.005692692939192057, -0.040047451853752136, -0.011557790450751781, 0.03895031660795212, 0.05582309514284134, 0.03371318802237511, 0.04648140072822571, -0.037158604711294174, 0.011981559917330742, -0.020494986325502396, 0.09363725036382675, 0.050351258367300034, -0.0627778023481369, -0.06063021719455719, 0.007787527982145548, -0.04377353563904762, -0.013712036423385143, 0.0024010692723095417, 0.003168323077261448, 0.009886769577860832, 0.005780255887657404, -0.03933660313487053, 0.014118434861302376, -0.07897166162729263, -0.05693803355097771, 0.04015237092971802, -0.059176329523324966, -0.030646445229649544, -0.0004776301502715796, 0.010998979210853577, 0.046690843999385834, -0.03734477609395981, -0.04660943150520325, -0.012727825902402401, -0.0005803934182040393, -0.03583921864628792, 0.041576988995075226, -0.004138682037591934, -0.012591788545250893, -0.06191883236169815, -0.020576898008584976, 0.003853446338325739, 0.008088327012956142, 0.016924111172556877, -0.03736492246389389, 0.014973030425608158, 0.03315576910972595, -0.05039381608366966, 0.02033933252096176, 0.004280316177755594, -0.06066203862428665, 0.008717639371752739, 0.00038613667129538953, -0.02149946615099907, 0.03636800870299339, -0.00927036628127098, 0.019289936870336533, 0.059915557503700256, 0.0520910806953907, -0.0440489687025547, 0.04757221043109894, 0.008097587153315544, -0.007455944083631039, 0.017920659855008125, 0.02404279075562954, 0.011775601655244827, 0.04468192905187607, -0.026268472895026207, -0.04178377240896225, 0.026906294748187065, 0.0660254955291748, -0.09483852982521057, 0.0031574442982673645, 0.03621099144220352, -0.04402484372258186, -0.028243575245141983, 0.00586407445371151, -0.00804851483553648, -0.01285584643483162, -0.08120827376842499, 0.006678457371890545, -0.002117696451023221, 0.0013534098397940397, -0.010346593335270882, -0.03269588202238083, -0.03337112441658974, -0.028366193175315857, 0.08490696549415588, -0.057183586061000824, 0.03969677537679672, 0.03159131109714508, -0.038975927978754044, 0.011150351725518703, 0.0021886243484914303, 0.016348550096154213, 0.06300702691078186, -0.07999812811613083, -0.018337279558181763, 0.023625513538718224, -0.052181314677000046, 0.0028307721950113773, -0.028902648016810417, -0.038710590451955795, 0.07312881946563721, 0.006840828340500593, 0.008400807157158852, 0.03493271395564079, -0.06627616286277771, -0.012154514901340008, 0.0004204892902635038, -0.0056485747918486595, -0.04594931751489639, 0.022047432139515877, -0.02192961424589157, -0.044200435280799866, 0.005421398673206568, -0.02497338503599167, 0.0026561920531094074, -0.007564298342913389, 0.03415118157863617, 0.014926421456038952, 0.02348797582089901, 0.05274363234639168, 0.02401694841682911, -0.02211175113916397, 0.05280012637376785, 0.012538865208625793, 0.007118422072380781, -0.020227866247296333, -0.011869583278894424, 0.027723126113414764, 0.0029925385024398565, 0.01878776028752327, -0.01719873957335949, -0.03315794840455055, -0.01047460176050663, -0.05410782992839813, -0.040647003799676895, 0.05431929603219032, 0.030840732157230377, -0.014806931838393211, -0.03001515381038189, 0.01725105009973049, -0.03100852109491825, 0.044166676700115204, -0.0101979561150074, 0.07266279309988022, 0.055356185883283615, 0.014136718586087227, 0.00718518253415823, 0.03796273097395897, -0.016067439690232277, 0.03968812897801399, 0.00925988145172596, -0.04610197991132736, -0.0038540675304830074, -0.06550414115190506, -0.08883486688137054, -0.02434193715453148, 0.04955087602138519, 0.006769389845430851, 0.014694190584123135, -0.009208019822835922, -0.030280258506536484, -0.013495175167918205, 0.03629366680979729, 0.07236723601818085, 0.02766360528767109, -0.002310018753632903, 0.004596969578415155, 0.0268461424857378, 0.07474987953901291, -0.019709032028913498, 0.07832437753677368, -0.027551960200071335, -0.043459441512823105, -0.026965094730257988, 0.02525336854159832, -0.11470174789428711, 0.0357881560921669, 0.019243981689214706, 0.004992239642888308, -0.05295909196138382, -0.007570281159132719, -0.003455545287579298, 0.05232236906886101, 0.02886960282921791, 0.011569363065063953, -0.05510972440242767, 0.03628108277916908, 0.03518330305814743, 0.02814822643995285, 0.01761496067047119, -0.020335735753178596, 0.0001721558510325849, 0.024888360872864723, 0.029686762019991875, 0.01097572036087513, 0.06506431102752686, -0.025315340608358383, 0.03216357156634331, 0.009510474279522896, 0.05015159398317337, -0.04384002462029457, 0.001916992710903287, 0.03348449617624283, 0.05738223344087601, 0.0394161231815815, -0.03416260704398155, 0.027747273445129395, -0.011695656925439835, -0.03092852607369423, -0.05178404226899147, -0.04144210368394852, 0.0028817979618906975, 0.03899332508444786, 0.019600536674261093, -0.0686563104391098, -0.011970113031566143, 0.004214093089103699, 0.02184777334332466, -0.037641461938619614, 0.019234485924243927, 0.02991572581231594, 0.009208411909639835, 0.006852945312857628, -0.037894368171691895, -0.03349201753735542, -0.026371190324425697, 0.0010991194285452366, 0.029548926278948784, -0.020693568512797356, -0.0023609523195773363, -0.07618732750415802, -0.02734881080687046, 0.030011774972081184, -0.0041335769928991795, 0.03180111572146416, -0.03325461223721504, 0.04325300455093384, -0.030452625826001167, 0.028966130688786507, -0.046504415571689606, 0.033128101378679276, 0.005316346418112516, 0.012996175326406956, -0.035657502710819244, 0.02346123941242695, 0.04475104808807373, 0.013119226321578026, 0.018990980461239815, -0.04188501089811325, 0.012119249440729618, -0.01216802280396223, -0.0002674427814781666, 0.004977594129741192, -0.06869086623191833, -0.004644995089620352, 0.020041102543473244, -0.0730161964893341, 0.038929056376218796, 0.0066846502013504505, -0.026186026632785797, -0.010495665483176708, 0.08258458971977234, 0.006372840143740177, 0.07121842354536057, 0.008685842156410217, 0.011323990300297737, 0.010556370951235294, -0.03477545455098152, 0.07210508733987808, -0.04739411175251007, -0.011390751227736473, -0.024891754612326622, 0.02788333036005497, -0.022430602461099625, 0.004962489008903503, 0.03799975663423538, 0.067979596555233, 0.03040243871510029, -0.03255737945437431, -0.0021923917811363935, 0.014197957701981068, -0.020379604771733284, 0.06470668315887451, -0.029421566054224968, 0.009633435867726803, -0.03188630938529968, -0.032012224197387695, 0.06505250185728073, -0.07532880455255508, -0.031367409974336624, 0.019141554832458496, -0.0009434999665245414, 0.021026987582445145, -0.0015596534358337522, 0.039460454136133194, 0.018203046172857285, 0.0027530372608453035, -0.01792169362306595, 0.02220989391207695, -0.015075040981173515, 0.06111539155244827, 0.02697623521089554, -0.007995271123945713, 0.05636715143918991, -0.01856967993080616, 0.055842649191617966, -0.01778491772711277, 0.009213259443640709, -0.0007579564116895199, -0.026886388659477234, 0.023028092458844185, 0.040393076837062836, -0.04873193800449371, -0.0005400783848017454, 0.0018326538847759366, -0.014770269393920898, -0.014625966548919678, 0.016264304518699646, 0.015149841085076332, -0.034259047359228134, -0.01604805886745453, 0.02493090182542801, -0.054467324167490005, 0.03560496121644974, 0.019548742100596428, 0.03736397251486778, -0.03961345553398132, -0.0036633694544434547, -0.0044540283270180225, -0.011727585457265377, 0.054552070796489716, 0.03640083968639374, 0.02117699384689331, 0.06053093448281288, 0.01411046739667654, 0.020046530291438103, 0.009729187935590744, 0.04232695326209068, -0.05937429144978523, -0.02820723131299019, -0.03530562296509743, 0.001993392361328006, -0.020917577669024467, 0.02554730884730816, -0.028589585795998573, -0.00005408063589129597, -0.028374847024679184, 0.02167022041976452, -0.04772507771849632, 0.04053901135921478, 0.015041667968034744, -0.02209855057299137, -0.0037067695520818233, 0.008277122862637043, -0.018841588869690895, 0.026441378518939018, 0.015250320546329021, 0.06331327557563782, 0.010962237603962421, 0.03234504163265228, 0.004415594507008791, 0.0026802970096468925, 0.08088863641023636, 0.04351407289505005, 0.06686294823884964, 0.04236454516649246, -0.008533118292689323, 0.054220572113990784, -0.053775765001773834, -0.07611224055290222, -0.017611579969525337, 0.01886315830051899, -0.02435675635933876, 0.007190153934061527, 0.011329193599522114, 0.030124038457870483, -0.00339502957649529, -0.04834672063589096, 0.00805078074336052, 0.0035442241933196783, -0.029962697997689247, -0.022729972377419472, 0.06726489961147308, -0.04631560668349266, -0.013692479580640793, -0.04048173502087593, 0.009332079440355301, 0.019897103309631348, 0.03664633631706238, -0.015796562656760216, 0.0719795748591423, -0.007560178637504578, 0.018107963725924492, -0.0038673398084938526, 0.010687176138162613, -0.012391509488224983, -0.03120851144194603, 0.012743747793138027, -0.04816700518131256, -0.021501922979950905, 0.0668695792555809, 0.07068152725696564, -0.07080575078725815, -0.03304160386323929, 0.00621062470600009, 0.03088724985718727, -0.009333064779639244, -0.03978720307350159, 0.0023702853359282017, -0.021396435797214508, -0.020225834101438522, -0.023377206176519394, -0.0011752545833587646, -0.02348334714770317, -0.019886638969182968, 0.00944767240434885, -0.09554915875196457, 0.006324728950858116, 0.013426311314105988, 0.011182622984051704, 0.04978305846452713, -0.07960091531276703, -0.004992898553609848, -0.02740994654595852, -0.0030247457325458527, 0.021423907950520515, -0.05880637466907501, 0.04263234883546829, 0.025292178615927696, 0.026820747181773186, 0.02078235149383545, -0.029253479093313217, -0.014781264588236809, 0.0339813269674778, -0.008402928709983826, 0.0254344679415226, -0.055345289409160614, -0.0028210545424371958, -0.014421804808080196, 0.01975330151617527, 0.029614591971039772, 0.005053428001701832, 0.04812125861644745, 0.034510038793087006, 0.019798053428530693, -0.012036816217005253, -0.05211576446890831, 0.03447600454092026, 0.013082216493785381, -0.005675090476870537, 0.06817766278982162, 0.05453583598136902, 0.005298231262713671, -0.0648304745554924, -0.0137267354875803, -0.01749340444803238, 0.01353654358536005, 0.026969367638230324, 0.01158420741558075, -0.001420194166712463, 0.034885846078395844, 0.061449091881513596, 0.03662930801510811, -0.06843335181474686, -0.038637030869722366, -0.04837160184979439, 0.043718475848436356, 0.04477584734559059, -0.0259951613843441, -0.009938092902302742, -0.0047189113683998585, -0.03006131201982498, -0.002909561153501272, 0.008166778832674026, -0.027468686923384666, 0.06455124914646149, 0.002897117054089904, 0.0380425788462162, -0.003810764756053686, -0.018869230523705482, -0.05096820369362831, 0.0296456441283226, -0.03132842481136322, 0.013841421343386173, -0.003003149526193738, -0.008975299075245857, -0.024317940697073936, -0.0372135229408741, 0.04554791375994682, 0.04187262803316116, -0.01644255593419075, 0.05188019946217537, -0.033619169145822525, -0.028667643666267395, -0.007657910231500864, 0.030564526095986366, -0.0580923818051815, 0.009066018275916576, 0.0016825174679979682, -0.01305820606648922, 0.029297158122062683, 0.011102072894573212, 0.015371570363640785, -0.05519763007760048, 0.04920648783445358, 0.0004236254026181996, -0.057371288537979126, -0.06813940405845642, -0.006625936832278967, 0.06214058771729469, 0.03159881755709648, 0.007859227247536182, -0.03529669716954231, 0.03955734521150589, 0.033300891518592834, 0.02280191332101822, 0.08263514935970306, -0.04141564667224884, 0.010521459393203259, -0.02530566416680813, 0.04875897616147995, -0.038394685834646225, 0.04498977214097977, -0.008549432270228863, -0.00817310530692339, 0.05143086984753609, 0.009745980612933636, -0.023572031408548355, -0.02696796879172325, -0.07812919467687607 ]
<p>What is thermal velocity? What is it's physical significance? <a href="http://en.wikipedia.org/wiki/Thermal_velocity" rel="nofollow">Wikipedia says</a>: </p> <blockquote> <p>The thermal velocity or thermal speed is a typical velocity of the thermal motion of particles which make up a gas, liquid, etc. Thus, indirectly, thermal velocity is a measure of temperature. </p> </blockquote> <p>But I cannot understand and comprehend it.</p>
g5417
[ 0.053355854004621506, 0.053020477294921875, 0.003425849601626396, -0.00988459587097168, 0.06567026674747467, -0.03662071377038956, 0.03472525626420975, 0.08561719208955765, -0.056097522377967834, -0.042498063296079636, -0.013013379648327827, 0.040872979909181595, 0.04123595356941223, 0.015409298241138458, 0.010182257741689682, -0.020887481048703194, 0.007870296947658062, 0.012896325439214706, 0.08538202941417694, 0.08585400134325027, -0.0057948133908212185, 0.03507375717163086, 0.0005471985205076635, -0.034260496497154236, -0.024931617081165314, -0.025547731667757034, -0.00855946447700262, -0.08596121519804001, -0.025209473446011543, 0.0023508858866989613, 0.006985201500356197, -0.0016444317298009992, 0.025620250031352043, -0.03554375469684601, 0.0035820910707116127, -0.01120863575488329, 0.02854870818555355, -0.04940398782491684, 0.0035079135559499264, -0.01707133837044239, -0.0019935104064643383, 0.028756767511367798, -0.015038826502859592, 0.01262020505964756, 0.047949910163879395, 0.05659914389252663, -0.025730108842253685, -0.006720328703522682, -0.05475793033838272, 0.06065955013036728, -0.01599808596074581, -0.0022664412390440702, 0.05014519765973091, -0.0029720573220402002, 0.007885719649493694, -0.04052348434925079, 0.022140629589557648, 0.03631383180618286, 0.042374204844236374, 0.0300977174192667, 0.05515230819582939, -0.0283953994512558, -0.02200324647128582, -0.033197760581970215, 0.03476909175515175, -0.004473580978810787, -0.015285965986549854, 0.02725427970290184, 0.04924025386571884, -0.0009778920793905854, 0.0020918832160532475, -0.025846481323242188, -0.04312548413872719, -0.04581902548670769, 0.00576514657586813, -0.05399637296795845, 0.005659261252731085, -0.030127035453915596, 0.02204100787639618, 0.019782627001404762, -0.005758864339441061, -0.006292709615081549, 0.014653153717517853, 0.05150150507688522, 0.02388744242489338, -0.01403291616588831, -0.05349590256810188, -0.006647162605077028, -0.009723789989948273, 0.010642372071743011, -0.018977081403136253, 0.04427861422300339, 0.07274962961673737, 0.05563991144299507, -0.031659867614507675, -0.00649483734741807, -0.06053098291158676, -0.008134490810334682, 0.01848328486084938, 0.04846150800585747, -0.017411313951015472, 0.01957116462290287, 0.05463802441954613, -0.013593174517154694, 0.04334673285484314, -0.010251284576952457, -0.018337247893214226, 0.00042056458187289536, -0.045443400740623474, 0.01479404978454113, -0.0016110307769849896, -0.034725576639175415, 0.007043018471449614, 0.012899821624159813, 0.001751106814481318, -0.014424002729356289, -0.02553682029247284, 0.022739415988326073, -0.02392379753291607, 0.04671043902635574, 0.034801024943590164, 0.07719319313764572, -0.002023156266659498, 0.012496878392994404, -0.02504802867770195, 0.0004897462204098701, 0.060249749571084976, -0.03166423738002777, -0.0004468467377591878, -0.0019372114911675453, 0.024820951744914055, 0.03553083911538124, -0.004420598968863487, 0.024713153019547462, -0.015330024063587189, 0.02481592632830143, 0.033309996128082275, -0.006521445699036121, -0.01903545670211315, -0.0023552044294774532, -0.02121400460600853, 0.0011695154244080186, 0.013920411467552185, -0.013707563281059265, -0.032155681401491165, 0.02902369201183319, -0.03583509474992752, 0.01878555491566658, 0.03919633477926254, -0.03071179986000061, 0.01262514479458332, 0.08718005567789078, -0.004441407043486834, -0.03314109891653061, 0.04720744863152504, -0.021644288673996925, 0.06586841493844986, 0.06292510777711868, 0.0193276759237051, 0.05376504361629486, 0.04731529951095581, 0.035437583923339844, -0.015320057049393654, 0.01075987983494997, -0.06717412918806076, 0.003652761224657297, -0.0034740513656288385, -0.03525732457637787, 0.008918069303035736, -0.07805942744016647, -0.06669571995735168, -0.02418004907667637, -0.08734381943941116, 0.053442519158124924, -0.012755370698869228, -0.023372549563646317, 0.04910031333565712, 0.030590824782848358, -0.021981967613101006, -0.047465745359659195, -0.038670141249895096, -0.011360909789800644, 0.06263002753257751, -0.053752195090055466, 0.007422467693686485, -0.009066637605428696, -0.0011766544776037335, -0.019389159977436066, -0.01566176675260067, 0.04759851470589638, -0.007194481324404478, -0.10268481075763702, -0.03807711601257324, 0.05305958166718483, 0.0015923196915537119, -0.022153569385409355, -0.001443032524548471, 0.007589524611830711, -0.0813160240650177, -0.020727355033159256, -0.013561377301812172, 0.00881732814013958, 0.002018897794187069, 0.01775939390063286, 0.01312155369669199, 0.00966514553874731, -0.04475434496998787, 0.019004318863153458, -0.041247665882110596, -0.0002253771963296458, 0.014937062747776508, 0.010069826617836952, 0.025193573907017708, 0.02056504786014557, 0.014824911020696163, 0.006820079404860735, 0.0014440908562391996, -0.0022660952527076006, -0.0118283461779356, -0.031977131962776184, -0.012125103734433651, -0.01183377206325531, -0.008329164236783981, -0.049199625849723816, -0.014501364901661873, -0.017738105729222298, -0.025461824610829353, -0.052599918097257614, 0.03881806880235672, 0.05026965215802193, -0.046001650393009186, -0.020266683772206306, -0.027606550604104996, 0.0284663587808609, 0.04451730474829674, 0.04912225529551506, 0.0035797362215816975, -0.009580318816006184, 0.011014985851943493, 0.043856408447027206, 0.036968883126974106, -0.07347524911165237, 0.004921832587569952, 0.02333480305969715, 0.040953584015369415, -0.03416483849287033, 0.019719025120139122, -0.0626092255115509, 0.007950087077915668, -0.013108172453939915, 0.031000187620520592, -0.05262573063373566, -0.008029043674468994, -0.01862235926091671, 0.03363117203116417, 0.015061432495713234, -0.026850543916225433, 0.031108424067497253, -0.05954241752624512, -0.018174612894654274, 0.0024383908603340387, 0.02680148556828499, -0.028034640476107597, -0.028647415339946747, 0.010729529894888401, -0.013330468907952309, -0.019367597997188568, 0.04637584090232849, -0.010767573490738869, -0.006036119069904089, 0.00482568982988596, -0.04183365777134895, 0.01803443394601345, -0.06107327342033386, -0.024284595623612404, -0.048209019005298615, 0.03811982646584511, -0.06341475248336792, 0.013116205111145973, -0.023666447028517723, 0.006252207327634096, 0.028987836092710495, -0.03347165137529373, 0.004277222324162722, 0.018824011087417603, -0.06621292978525162, -0.0033576011192053556, 0.04870191588997841, -0.002186379861086607, -0.06724054366350174, 0.003362820018082857, 0.025757290422916412, -0.02496832236647606, -0.0010936497710645199, 0.019085200503468513, 0.015739044174551964, 0.04342495650053024, 0.021411864086985588, 0.018524721264839172, -0.04439420998096466, 0.0029569133184850216, -0.04306107014417648, -0.02901364490389824, -0.008048354648053646, -0.01976727321743965, 0.02341327629983425, -0.05407886579632759, -0.013740826398134232, 0.02078479714691639, 0.007109507452696562, 0.05032249167561531, 0.036749646067619324, 0.03572399169206619, 0.055110856890678406, -0.047740787267684937, 0.02857598476111889, -0.0663888081908226, 0.019250232726335526, 0.016874972730875015, 0.015619168058037758, -0.03752024099230766, -0.037628173828125, -0.0113019784912467, 0.0011379143688827753, 0.022366318851709366, -0.01756206527352333, 0.03483818471431732, -0.05005466565489769, -0.010751847177743912, -0.07683884352445602, -0.05369095131754875, 0.005834968760609627, -0.0216508898884058, -0.004398015793412924, -0.04034193232655525, -0.04800936207175255, 0.006703018676489592, -0.006888772826641798, 0.061771441251039505, -0.02095009572803974, 0.06699732691049576, -0.013301275670528412, -0.0018735505873337388, 0.05025371536612511, 0.00006545221549458802, -0.0180355217307806, -0.002438930794596672, 0.010225677862763405, -0.05302400141954422, 0.029525158926844597, 0.06905461847782135, -0.02044518291950226, 0.018197545781731606, -0.04365028813481331, -0.03575841337442398, 0.06258027255535126, 0.04721500352025032, 0.010194789618253708, -0.013738028705120087, 0.008547535166144371, 0.004997465293854475, 0.001300509669817984, 0.0447477251291275, 0.04700421169400215, -0.03091466799378395, 0.029300743713974953, 0.0138108991086483, 0.02526930160820484, -0.035101599991321564, 0.005129717756062746, -0.03040480613708496, -0.06300994008779526, -0.044574666768312454, 0.012160815298557281, 0.038832955062389374, 0.0381300114095211, 0.026025719940662384, 0.0019787417259067297, -0.016335314139723778, -0.026809178292751312, 0.018160276114940643, 0.027019686996936798, 0.06626464426517487, -0.004488253500312567, 0.03586291894316673, -0.04707399383187294, -0.08052688837051392, 0.0041927495039999485, 0.0031317356042563915, -0.05622486770153046, 0.03436899185180664, 0.010528897866606712, -0.03482011705636978, -0.022789567708969116, 0.022550566121935844, 0.00010125909466296434, 0.009217001497745514, 0.005962260067462921, 0.015251779928803444, 0.035462066531181335, -0.030308138579130173, -0.03364981710910797, -0.011751532554626465, 0.0035410348791629076, 0.005863457452505827, 0.06672485917806625, 0.07511391490697861, -0.033359359949827194, -0.016624443233013153, -0.03160971403121948, -0.03237946704030037, 0.05449395999312401, 0.029199913144111633, 0.014995979145169258, 0.026951534673571587, 0.04537316784262657, 0.008834554813802242, -0.025170985609292984, 0.008750338107347488, 0.0490681529045105, -0.04797641932964325, -0.05786304920911789, 0.042413316667079926, -0.03206517547369003, 0.005276562180370092, 0.02344888262450695, 0.0827779471874237, 0.028640806674957275, -0.017069309949874878, 0.05074204131960869, -0.010490602813661098, 0.006946769542992115, 0.0024457252584397793, 0.03219614923000336, 0.010604172013700008, 0.03657403215765953, -0.02022000402212143, 0.07829447835683823, 0.01727614738047123, 0.006832787301391363, 0.0327470563352108, 0.03279298543930054, -0.01259005069732666, -0.008770192973315716, -0.038730647414922714, 0.001821195357479155, -0.012205960229039192, 0.0016486897366121411, -0.07599426060914993, -0.03727148473262787, 0.03481169044971466, 0.05473488196730614, -0.05508403852581978, -0.021144557744264603, -0.06166985630989075, 0.012081391178071499, -0.004980406258255243, -0.01534104160964489, -0.020954789593815804, -0.014671225100755692, -0.07655308395624161, 0.01577594503760338, 0.03895766660571098, -0.024572577327489853, -0.019902151077985764, -0.016431773081421852, 0.049977678805589676, -0.007761380169540644, -0.05958762392401695, 0.016812782734632492, -0.035867705941200256, -0.03658652305603027, -0.013551297597587109, 0.033416517078876495, 0.008390935137867928, 0.022130420431494713, 0.0028713643550872803, -0.015733597800135612, -0.0025263852439820766, -0.013571747578680515, -0.009368418715894222, 0.010560004971921444, 0.06048941612243652, -0.0160854272544384, 0.02834048680961132, -0.04168972000479698, -0.07969972491264343, 0.026458073407411575, 0.021554650738835335, 0.015746958553791046, -0.0006608585827052593, 0.0309576615691185, -0.008829304948449135, 0.05679899454116821, -0.05721534416079521, -0.0413164384663105, 0.020872240886092186, -0.0005051679327152669, 0.05115959420800209, -0.030764121562242508, -0.03587428107857704, 0.011500456370413303, -0.0013052080757915974, 0.02930534817278385, 0.033031463623046875, 0.032495006918907166, -0.00235188752412796, 0.00671363016590476, 0.010494853369891644, -0.015578730963170528, 0.029743121936917305, 0.03036121465265751, -0.052253082394599915, -0.041856952011585236, 0.03881792724132538, -0.05010944977402687, 0.08195947855710983, -0.09624724090099335, 0.014941933564841747, 0.0025215859059244394, -0.017928829416632652, -0.00845846626907587, -0.0034214062616229057, -0.013707268983125687, -0.01775728352367878, -0.015729648992419243, -0.060645800083875656, 0.02008870057761669, 0.012761113233864307, 0.055359531193971634, 0.008226919919252396, -0.007631762884557247, 0.05973455309867859, 0.016120124608278275, -0.09700244665145874, 0.0038073090836405754, -0.03392737731337547, -0.0609779991209507, -0.010970943607389927, 0.03640570119023323, -0.02612704038619995, 0.035860512405633926, -0.06235704943537712, 0.03595535829663277, 0.06837430596351624, 0.05881310999393463, 0.028504278510808945, -0.016116442158818245, 0.01199891697615385, -0.014864801429212093, 0.022865435108542442, -0.0383557491004467, 0.09935981780290604, -0.1258290559053421, 0.0024681829381734133, 0.021675897762179375, 0.02487926371395588, -0.004231019411236048, -0.03619051352143288, -0.037453245371580124, -0.02616667002439499, 0.014145723544061184, 0.022385239601135254, 0.026886170729994774, 0.022842969745397568, -0.07705505937337875, -0.03337972238659859, -0.030379530042409897, 0.015344466082751751, 0.013405672274529934, -0.03797336295247078, 0.0001474499294999987, -0.013392304070293903, -0.04209776222705841, 0.02949303574860096, 0.03747895732522011, 0.006592704448848963, -0.044925566762685776, -0.07129128277301788, 0.003589995438233018, -0.0028240804094821215, 0.03236296400427818, 0.020073946565389633, 0.013236564584076405, 0.015437476336956024, -0.03858672454953194, -0.025438951328396797, 0.04451713711023331, -0.045234616845846176, 0.005801621824502945, 0.006654681172221899, -0.0044548348523676395, -0.08921752870082855, -0.005386259872466326, -0.04402915760874748, -0.0396624393761158, -0.009602174162864685, 0.0320180207490921, -0.013837790116667747, 0.006394998170435429, -0.015589223243296146, -0.011913934722542763, -0.009349053725600243, -0.016290081664919853, 0.02669336274266243, 0.041826557368040085, -0.004648128524422646, -0.03670785576105118, 0.006938314530998468, 0.020914120599627495, -0.031102601438760757, 0.05506104975938797, 0.040574319660663605, -0.016546696424484253, -0.02054603584110737, 0.009133027866482735, -0.015009516850113869, -0.04685294255614281, -0.02622380293905735, -0.030099883675575256, 0.05052507296204567, -0.04009465500712395, 0.04588963836431503, -0.0026977243833243847, 0.09692803025245667, -0.011490407399833202, -0.07818488776683807, 0.08900455385446548, -0.0053424169309437275, -0.0006961603066883981, -0.01833617314696312, -0.060310110449790955, -0.025185860693454742, 0.03687799349427223, 0.007531816605478525, -0.03705916553735733, -0.037504952400922775, 0.03896721825003624, 0.09558181464672089, 0.028183717280626297, 0.04315406084060669, -0.04358820989727974, -0.05480418726801872, 0.0007841892656870186, -0.054013874381780624, -0.003955305088311434, -0.004458107519894838, -0.017759159207344055, -0.0686267539858818, -0.06340889632701874, -0.07054974138736725, -0.016060879454016685, -0.002192793181166053, 0.06632161140441895, 0.012032520025968552, 0.029541105031967163, 0.030216770246624947, 0.0024876983370631933, 0.015287044458091259, -0.027848966419696808, -0.03040299192070961, -0.0038400045596063137, 0.012226922437548637, -0.0010748966597020626, 0.0028760263230651617, 0.08566737174987793, 0.009260199032723904, -0.017625661566853523, 0.019615642726421356, -0.07852198928594589, 0.0152094392105937, 0.019274644553661346, 0.036304861307144165, 0.026944732293486595, -0.022411586716771126, 0.009135106578469276, 0.019275184720754623, 0.08080963045358658, 0.014109478332102299, -0.03791269287467003, -0.007612744811922312, 0.06323173642158508, 0.0220276340842247, 0.00995764508843422, 0.012537510134279728, 0.017040448263287544, 0.010936464183032513, 0.015253142453730106, 0.011458459310233593, -0.05909445881843567, -0.02055399864912033, 0.002836900530382991, -0.011233058758080006, -0.051947880536317825, 0.028791598975658417, -0.005207291804254055, 0.0376337505877018, -0.02133799158036709, -0.030888887122273445, 0.009161664173007011, -0.04509691148996353, -0.03906005993485451, 0.0006084752385504544, 0.04659154266119003, -0.00106840580701828, -0.003678620560094714, 0.04924808442592621, 0.06413682550191879, -0.05384993925690651, -0.010764775797724724, -0.014109489507973194, -0.02010944113135338, 0.025616811588406563, 0.020070495083928108, -0.014269095845520496, -0.02023847959935665, 0.017805900424718857, -0.011285889893770218, -0.030170729383826256, -0.01175075862556696, 0.05953602492809296, -0.013683577068150043, 0.015853261575102806, -0.035776905715465546, -0.06297222524881363, -0.011639447882771492, -0.03671916574239731, 0.03893560543656349, 0.011282176710665226, -0.03146601840853691, 0.031399037688970566, 0.06803296506404877, 0.0033081318251788616, -0.002165578305721283, -0.036264169961214066, 0.10735280811786652, 0.02239391952753067, 0.003703530877828598, 0.03255671635270119, 0.01770220696926117, 0.06952803581953049, 0.06140502169728279, -0.003137039951980114, 0.023992739617824554, -0.0625733807682991, -0.0945412814617157, -0.0395796112716198, 0.07890483736991882, 0.0090384716168046, -0.043133169412612915, 0.05494397133588791, 0.02678157389163971, 0.03017319180071354, -0.03818215802311897, -0.061564575880765915, -0.014302424155175686, -0.05556425079703331, 0.045496027916669846, 0.004262862261384726, -0.004037835169583559, -0.016236096620559692, 0.010515628382563591, 0.023188943043351173, -0.02707768604159355, -0.02837836742401123, -0.02496773563325405, -0.021884264424443245, -0.0038802726194262505 ]
<p><a href="http://www.mazda.com/mazdaspirit/skyactiv/engine/skyactiv-g.html" rel="nofollow">Here's a description</a> of new combustion engine improvement by Mazda, called SkyActive-G. They claim that in a "generic" engine...</p> <blockquote> <p>when the exhaust manifold is short, the high pressure wave from the gas emerging immediately after cylinder No. 3’s exhaust valves open, for example, arrives at cylinder No.1 as it finishes its exhaust stroke and enters its intake stroke. As a result, exhaust gas which has just moved out of the cylinder is forced back inside the combustion chamber, increasing the amount of hot residual gas</p> </blockquote> <p>I always though, that exhaust manifold and intake manifold are separated, so exhaust gases just can't possibly enter other cylinders combustion chambers as described in the above quoted text.</p> <p>Can exhaust gases be diverted into other cylinders as claimed in that text? </p>
g5418
[ -0.015121355652809143, -0.005033932160586119, 0.012353582307696342, 0.01712590828537941, -0.018930163234472275, -0.0011993552325293422, 0.030770933255553246, 0.030658623203635216, -0.07184534519910812, -0.016353465616703033, -0.0008907302399165928, 0.05681660398840904, 0.041323497891426086, -0.035398438572883606, 0.005134485196322203, 0.010071632452309132, 0.03199894353747368, 0.002237848471850157, -0.03481750190258026, 0.062331024557352066, -0.025136562064290047, 0.015115221031010151, 0.010646914131939411, -0.048779942095279694, 0.012105613946914673, -0.06253238767385483, 0.0478600338101387, -0.042033739387989044, -0.025379439815878868, -0.07407304644584656, 0.030788488686084747, -0.05036308243870735, 0.044835109263658524, 0.028382156044244766, -0.07595153898000717, -0.013769983313977718, 0.032787714153528214, -0.02827431820333004, -0.02360319159924984, 0.0014201090671122074, 0.01026246603578329, -0.007911394350230694, 0.06586889922618866, 0.03901297226548195, -0.02753330208361149, -0.0018904455937445164, 0.03725816309452057, 0.03693040832877159, 0.05821135640144348, -0.02116672694683075, 0.026231298223137856, -0.0291677787899971, -0.07350685447454453, 0.011699773371219635, -0.026841068640351295, 0.053823769092559814, 0.012179039418697357, -0.0045534842647612095, 0.07976541668176651, -0.023997873067855835, -0.07473444193601608, 0.012431448325514793, 0.06156731769442558, 0.006089447066187859, -0.050013381987810135, -0.030852066352963448, -0.11283665895462036, -0.03942900523543358, -0.0010608193697407842, -0.0262784231454134, 0.029075799509882927, 0.030834242701530457, 0.05570455268025398, -0.028473755344748497, -0.009768279269337654, 0.04598086699843407, 0.05016325041651726, -0.0012645971728488803, 0.01909932680428028, 0.027092842385172844, -0.019592221826314926, -0.03137968108057976, 0.023326093330979347, -0.006222488824278116, -0.06395134329795837, 0.02846243418753147, -0.02360471896827221, -0.01932726614177227, -0.03731736168265343, -0.02521747536957264, 0.04716544598340988, 0.04313918203115463, 0.04402254521846771, 0.0666733905673027, 0.00361605710349977, 0.0583510622382164, -0.04664667323231697, 0.047648921608924866, 0.014485892839729786, -0.00802863109856844, 0.01147510763257742, -0.04060136154294014, 0.04384804889559746, 0.04590163007378578, -0.015973832458257675, -0.0036548771895468235, 0.02226250059902668, 0.01288724783807993, 0.041659314185380936, -0.013701029121875763, 0.02271864004433155, -0.02966891974210739, -0.035169340670108795, 0.049135755747556686, -0.042782261967659, -0.029263153672218323, 0.054910436272621155, 0.055586688220500946, -0.009023591876029968, 0.005665060598403215, -0.0007453601574525237, 0.024635661393404007, -0.015815669670701027, -0.02317977137863636, -0.005794898606836796, -0.041840486228466034, 0.01688879169523716, -0.06084052100777626, 0.013040007092058659, -0.03895699232816696, -0.01929398998618126, 0.006204938516020775, 0.006624431814998388, 0.04993368312716484, 0.024861449375748634, -0.057375527918338776, 0.04376719519495964, -0.0016273511573672295, -0.013094952329993248, 0.05304424464702606, 0.012929526157677174, 0.01928333379328251, 0.023934945464134216, -0.03597867861390114, -0.028225436806678772, -0.015552897937595844, -0.03845072537660599, 0.05040748417377472, -0.029396802186965942, 0.018396994099020958, 0.013687166385352612, 0.0019062364008277655, 0.022052722051739693, 0.010049148462712765, -0.025418102741241455, 0.0008606754126958549, -0.013692243956029415, 0.0012007252080366015, 0.0036569908261299133, 0.008870253339409828, -0.009465274401009083, -0.02042449451982975, -0.009606139734387398, 0.010941612534224987, -0.07405838370323181, -0.039764802902936935, -0.08896496891975403, -0.0845712348818779, -0.004652165807783604, -0.023950012400746346, -0.028227312490344048, 0.053084298968315125, -0.06176842376589775, 0.008933520875871181, 0.035011451691389084, 0.02708645537495613, 0.1350744664669037, -0.012594745494425297, -0.01294204592704773, -0.0572274774312973, -0.02661631815135479, 0.019989021122455597, -0.03835224360227585, -0.05906365439295769, 0.03987640142440796, 0.03526841849088669, -0.06942089647054672, 0.001369575271382928, -0.001768016256392002, -0.014063520357012749, -0.015374499373137951, -0.0297580286860466, 0.052040744572877884, -0.019101973623037338, 0.026600543409585953, -0.06742773950099945, 0.0062889643013477325, -0.025185080245137215, -0.036095794290304184, 0.020128158852458, -0.0257945004850626, 0.019717002287507057, 0.039409663528203964, -0.025303944945335388, 0.08906253427267075, -0.02000122144818306, -0.008420607075095177, -0.02695315331220627, -0.0025303619913756847, -0.004201903939247131, 0.06573496758937836, 0.053673774003982544, 0.035219334065914154, 0.0226039569824934, -0.016805250197649002, 0.02423733100295067, -0.030546201393008232, 0.001965251751244068, 0.03940146788954735, -0.04630061984062195, -0.008376846089959145, 0.04519004002213478, -0.03537033125758171, -0.016957253217697144, -0.024205587804317474, 0.03217102959752083, 0.013539440929889679, -0.0403907373547554, 0.0013136856723576784, 0.01039234921336174, -0.051754213869571686, -0.04865868762135506, 0.017937179654836655, -0.0893491804599762, 0.02353404089808464, -0.013864707201719284, 0.04354273900389671, 0.0434969887137413, -0.0649893581867218, -0.016720879822969437, 0.025165613740682602, -0.028886951506137848, -0.02165558561682701, -0.020226826891303062, -0.014112072996795177, -0.04402456805109978, -0.010282570496201515, 0.030527973547577858, -0.03404872119426727, -0.012097478844225407, -0.048916976898908615, 0.004708404652774334, 0.022758057340979576, -0.03848974406719208, 0.004122322890907526, -0.05179791525006294, 0.001147148897871375, 0.029316797852516174, -0.004477653652429581, 0.021427500993013382, -0.035739071667194366, -0.02768184430897236, 0.05711866170167923, -0.0008649316732771695, -0.05490708351135254, -0.017831692472100258, 0.020296644419431686, -0.04536854103207588, -0.01587778888642788, -0.05484964698553085, -0.044153716415166855, 0.044307198375463486, 0.04672455042600632, 0.030611611902713776, -0.047500237822532654, 0.06957068294286728, -0.002087211236357689, -0.003783222520723939, -0.011279204860329628, 0.07801492512226105, -0.07289157807826996, 0.01767326146364212, -0.06663630902767181, -0.024774981662631035, 0.03174271807074547, 0.01733415015041828, -0.003928221762180328, -0.04763387516140938, -0.002577307168394327, -0.007292433641850948, -0.04154534637928009, -0.007404858712106943, 0.008439700119197369, 0.08354324847459793, -0.007666535209864378, 0.044980816543102264, 0.0018014941597357392, -0.002047572284936905, -0.0037734294310212135, -0.03070768527686596, -0.08306688815355301, -0.014827457256615162, -0.04896208643913269, 0.023165220394730568, -0.0241381973028183, 0.0200967900454998, -0.08692555129528046, 0.02265099063515663, 0.005838947370648384, -0.01449362188577652, 0.0014911938924342394, -0.04562941938638687, 0.029390254989266396, -0.02884812094271183, 0.008907419629395008, -0.015455711632966995, 0.013785657472908497, -0.029787348583340645, 0.004402752500027418, 0.07102639973163605, -0.04010007902979851, -0.010514633730053902, -0.01912774331867695, -0.028596440330147743, 0.0006108502275310457, 0.011534005403518677, 0.08182922750711441, -0.048358574509620667, -0.021126415580511093, 0.015373356640338898, 0.006120437756180763, 0.0028239500243216753, -0.07917951792478561, -0.030952291563153267, 0.05725819990038872, 0.04544743150472641, 0.011436841450631618, 0.013891706243157387, 0.014534484595060349, -0.0045228260569274426, 0.0037338060792535543, 0.015339257195591927, 0.023186875507235527, -0.021070189774036407, -0.024030599743127823, 0.021623941138386726, -0.009303431957960129, -0.008246690034866333, 0.02830563299357891, 0.018398964777588844, 0.04478294402360916, 0.02232479117810726, 0.02346532605588436, 0.001989773940294981, -0.06331916898488998, 0.02095019817352295, -0.017862992361187935, -0.023149413987994194, -0.015713773667812347, -0.004169059917330742, 0.019852569326758385, 0.0013510449789464474, -0.0009376778034493327, 0.019967395812273026, 0.02074364945292473, 0.0021618325263261795, -0.0338762030005455, 0.029304927214980125, -0.0016003173077479005, -0.01731642335653305, 0.02119135484099388, -0.019000129774212837, -0.018577609211206436, 0.03924494609236717, 0.0018879648996517062, -0.004080612678080797, 0.06373180449008942, 0.054638609290122986, -0.029501501470804214, 0.027017854154109955, 0.03275123983621597, -0.004998201970010996, 0.03807024285197258, -0.0009696388151496649, -0.007569936569780111, 0.021725349128246307, 0.02207118645310402, 0.022591587156057358, -0.03975332900881767, 0.008030139841139317, -0.0335918627679348, 0.02491014264523983, -0.021814141422510147, 0.026033634319901466, -0.030570318922400475, 0.0178348608314991, -0.03283734247088432, -0.0333792120218277, 0.037340711802244186, 0.05225082486867905, 0.02738944999873638, -0.004451126791536808, -0.0020118888933211565, 0.012213575653731823, 0.015310795977711678, -0.00802409928292036, -0.009136433713138103, 0.027154384180903435, 0.022273359820246696, -0.01917409524321556, 0.03392958268523216, -0.01924317143857479, 0.016017889603972435, 0.021409399807453156, 0.10792923718690872, -0.00941342394798994, -0.04556165263056755, -0.007793780416250229, -0.02994311973452568, 0.05904816463589668, -0.01745760068297386, 0.0003373668296262622, 0.03980199992656708, 0.07219018042087555, 0.07876864075660706, 0.011550948023796082, 0.022706957533955574, -0.03173813223838806, -0.024802640080451965, -0.011414581909775734, -0.026277588680386543, -0.013100731186568737, -0.03963067755103111, -0.0019314258825033903, -0.028368355706334114, 0.02979535050690174, -0.08658287674188614, 0.046190328896045685, 0.023639490827918053, 0.02129717357456684, 0.04979698732495308, 0.02659882977604866, 0.021448718383908272, -0.0142655149102211, 0.028854813426733017, -0.0013788063079118729, 0.005427256226539612, 0.0050985682755708694, 0.05635426193475723, 0.030811911448836327, -0.06995205581188202, -0.011825869791209698, -0.034919630736112595, 0.04445046931505203, -0.05746978148818016, -0.03168769180774689, -0.0544678159058094, 0.017695289105176926, 0.03970639780163765, -0.05347496643662453, -0.029673706740140915, -0.011789312586188316, 0.004391186870634556, 0.07157670706510544, 0.0025405443739145994, -0.026175009086728096, 0.02072240598499775, 0.03030163049697876, -0.025853445753455162, -0.0049975854344666, 0.03360661119222641, 0.004839146044105291, -0.003800099017098546, -0.020990904420614243, 0.012419730424880981, -0.000004326816906541353, 0.005408148281276226, -0.014945581555366516, -0.006187389604747295, -0.0049650720320641994, 0.003991652745753527, -0.004179646726697683, 0.04499528557062149, 0.037954043596982956, 0.05466131865978241, 0.0375368669629097, 0.046504490077495575, -0.04367026686668396, -0.014106255024671555, 0.004457398783415556, 0.0041728997603058815, 0.06029413267970085, -0.06480605155229568, 0.006573326885700226, 0.028485137969255447, 0.03594500944018364, 0.07206755131483078, -0.048379961401224136, -0.061295002698898315, 0.00932652410119772, -0.06311924755573273, 0.0015985053032636642, -0.030065977945923805, -0.03383307904005051, -0.002301698550581932, 0.00933054555207491, -0.0007336930138990283, -0.024974936619400978, -0.05259579047560692, -0.002973131835460663, 0.011857380159199238, -0.08513873815536499, -0.04936835169792175, 0.07173268496990204, 0.004057801328599453, -0.031259167939424515, -0.02299293875694275, 0.033118631690740585, 0.023896528407931328, -0.03069355897605419, 0.020064091309905052, -0.04196205362677574, -0.012627225369215012, -0.025230130180716515, -0.00437527010217309, -0.020303776487708092, 0.0066346884705126286, 0.008917126804590225, 0.000683001009747386, 0.04259350150823593, -0.02202661894261837, 0.05186157301068306, -0.02254200354218483, 0.06583283841609955, 0.07855621725320816, 0.025630371645092964, -0.0506397970020771, 0.004329370800405741, 0.04377789422869682, -0.04651032015681267, -0.019607722759246826, -0.03845100849866867, 0.009688451886177063, 0.031630098819732666, 0.01816732995212078, -0.004841502755880356, 0.0012540402822196484, 0.09217455238103867, -0.029993098229169846, -0.02640126645565033, 0.0024678956251591444, 0.029472583904862404, -0.037261150777339935, 0.002928231144323945, 0.04598101228475571, 0.006436827592551708, 0.02427545189857483, 0.0475766584277153, 0.06958749890327454, -0.020757200196385384, 0.0013783746398985386, -0.007679170463234186, 0.030556106939911842, -0.006001729983836412, -0.006853240076452494, -0.014508196152746677, -0.001918749650940299, 0.012897174805402756, 0.07640273123979568, 0.02551170065999031, 0.05296994373202324, -0.05011418089270592, 0.02533336542546749, -0.046516913920640945, 0.0324232280254364, -0.02959655225276947, -0.03840499371290207, -0.008431617170572281, 0.01889951340854168, 0.06834830343723297, -0.03092995285987854, 0.0022482499480247498, 0.017032023519277573, -0.05134505033493042, -0.02787453681230545, 0.024672357365489006, -0.02406783401966095, 0.0013971739681437612, -0.006744297221302986, 0.06298282742500305, -0.04122943803668022, -0.042539868503808975, -0.008609652519226074, 0.04096442461013794, -0.0442025326192379, 0.042120035737752914, -0.056532859802246094, 0.09549941122531891, 0.03358310088515282, 0.06872353702783585, 0.044102489948272705, 0.039323367178440094, 0.008354434743523598, -0.028386319056153297, -0.021500878036022186, 0.04971615970134735, 0.025055088102817535, 0.008663459680974483, 0.04966958612203598, -0.008336149156093597, -0.015396752394735813, -0.004879472311586142, 0.07781185954809189, -0.0008574219536967576, -0.002295863348990679, -0.03679472953081131, -0.011510265059769154, -0.06209908053278923, 0.025217769667506218, -0.006423372775316238, 0.06012053042650223, 0.006977765820920467, 0.012161573395133018, -0.019844476133584976, -0.047467853873968124, 0.02775619551539421, -0.062343139201402664, -0.059181876480579376, 0.027612844482064247, -0.00002304046938661486, -0.010272858664393425, -0.0351974219083786, -0.04016507416963577, -0.02594444900751114, -0.05982857197523117, -0.0075972541235387325, -0.008525732904672623, 0.0031602205708622932, 0.045881062746047974, 0.02299475111067295, -0.024182429537177086, 0.042752377688884735, -0.04860122874379158, 0.04521540552377701, 0.00020534146460704505, -0.010996652767062187, -0.024740373715758324, 0.010618211701512337, -0.028869042173027992, -0.012221438810229301, 0.0015738782240077853, 0.017416667193174362, -0.06598939001560211, -0.017699316143989563, -0.014948811382055283, -0.0007160373497754335, -0.047770626842975616, -0.05507694557309151, 0.08741641044616699, -0.03890673443675041, 0.03770683333277702, -0.002109314315021038, 0.033635299652814865, 0.053717322647571564, -0.004148298874497414, -0.021584387868642807, 0.007258412893861532, -0.031476739794015884, 0.0043498859740793705, -0.019352195784449577, 0.021219268441200256, -0.03504114970564842, -0.03756143897771835, -0.0057821450755000114, -0.034478094428777695, -0.04453341290354729, -0.01380513422191143, 0.05361079052090645, -0.0005650825332850218, 0.02737923339009285, -0.0173281691968441, 0.002477675909176469, 0.028242524713277817, 0.005303389858454466, -0.010311020538210869, -0.028499890118837357, 0.04119684174656868, 0.004967031069099903, 0.01769625023007393, -0.03496096283197403, -0.03251882269978523, -0.006098020821809769, 0.05031612515449524, 0.03651583567261696, -0.01522986963391304, 0.033168692141771317, 0.04308924451470375, 0.03141430765390396, -0.06021251901984215, -0.031598757952451706, -0.006399544887244701, 0.04222031682729721, -0.02526828646659851, 0.02324352227151394, 0.06302858144044876, -0.0000598702063143719, 0.006883860100060701, 0.06341259926557541, -0.02011808380484581, 0.018393756821751595, -0.0855456218123436, 0.001642310176976025, -0.046620648354291916, 0.07817495614290237, -0.00616186298429966, -0.07007928192615509, 0.04306449741125107, -0.055735595524311066, 0.014121892862021923, 0.0358242504298687, -0.0165877528488636, -0.0010421810438856483, 0.03879022225737572, -0.04434041678905487, -0.031056946143507957, -0.029375823214650154, -0.03650922328233719, 0.04408083111047745, -0.043980471789836884, -0.02170601114630699, -0.025050165131688118, -0.014574075117707253, 0.018862266093492508, 0.06568456441164017, -0.008082143031060696, -0.06118891388177872, 0.014742965810000896, -0.050388164818286896, 0.03270441293716431, 0.016321832314133644, 0.03444129601120949, 0.02380676381289959, -0.00024543871404603124, 0.024862075224518776, -0.00657486030831933, -0.011122526600956917, -0.043733008205890656, 0.0879870280623436, -0.03776388615369797, 0.041331011801958084, 0.019311625510454178, -0.027939390391111374, -0.0024179317988455296, -0.03318845108151436, 0.04042965918779373, -0.05919545888900757, -0.042490169405937195, 0.04155847802758217, -0.012625486589968204, 0.00557766854763031, 0.0017658190336078405, 0.022586314007639885, 0.00029300793539732695, -0.049880560487508774, -0.031221209093928337, 0.020343467593193054, -0.016877349466085434, -0.06267938762903214 ]
<p>For a time dependent wavefunction, are the instantaneous probability densities meaningful? (The question applies for instances or more generally short lengths of time that are not multiples of the period.)</p> <p>What experiment could demonstrate the existence of a time dependent probability density?</p> <p>Can an isolated system be described by a time dependent wavefunction? How would this not violate conservation of energy?</p> <p>I see the meaning of the time averaged probability density. Is the time dependence just a statistical construct?</p>
g5419
[ 0.028250284492969513, 0.020027868449687958, 0.022452523931860924, -0.038896236568689346, -0.018291201442480087, 0.006547176744788885, 0.005521134007722139, 0.012095313519239426, -0.023470070213079453, 0.004391056951135397, -0.01605987176299095, -0.05456286668777466, 0.021115312352776527, 0.05930858850479126, -0.017437465488910675, 0.0035208063200116158, 0.07763714343309402, 0.0064252521842718124, -0.0010571875609457493, 0.049501389265060425, -0.02798248827457428, -0.011117508634924889, -0.017076414078474045, 0.0006588896503672004, 0.015379609540104866, 0.01632743328809738, 0.04242826998233795, -0.05437283217906952, -0.03770697861909866, -0.008341515436768532, -0.0266112070530653, -0.0031763412989676, 0.04570028558373451, -0.03416653349995613, -0.010072391480207443, -0.039894960820674896, 0.009456999599933624, -0.0684807077050209, 0.03659797087311745, -0.0055725183337926865, -0.05221033841371536, 0.053612835705280304, -0.030978145077824593, -0.014223595149815083, -0.010934687219560146, 0.04156957566738129, -0.02095441147685051, 0.010950657539069653, -0.01786818914115429, -0.0014809867134317756, 0.017293160781264305, 0.009095695801079273, 0.04455381631851196, 0.018149880692362785, -0.014737625606358051, -0.031913258135318756, 0.05361905321478844, 0.033106729388237, 0.037998463958501816, 0.003742012195289135, 0.05620655417442322, 0.004703396465629339, -0.01296975277364254, -0.02334977686405182, 0.08021359145641327, -0.041831184178590775, 0.008919517509639263, -0.01844894140958786, 0.035800687968730927, -0.014836611226201057, 0.01444674376398325, -0.016859300434589386, -0.07400020956993103, -0.06447487324476242, 0.04368244856595993, 0.061918552964925766, 0.05592389777302742, -0.01501921471208334, 0.0072766197845339775, 0.05736503005027771, -0.030161406844854355, 0.03243487328290939, -0.0026242760941386223, -0.01984957791864872, 0.07784899324178696, -0.04006708040833473, 0.04414296895265579, -0.018984714522957802, 0.03399141505360603, 0.002030715113505721, 0.06237080320715904, -0.027421433478593826, 0.06553531438112259, 0.011929980479180813, -0.018403369933366776, -0.006401687394827604, -0.021753201261162758, 0.054181069135665894, 0.00036374235060065985, 0.06431691348552704, -0.012521478347480297, 0.03399386629462242, 0.0443887822329998, -0.02302040159702301, 0.007081403862684965, 0.0027881672140210867, -0.03126233071088791, -0.016943136230111122, -0.037780504673719406, -0.008387424051761627, 0.0162745863199234, -0.0055158077739179134, -0.02931887097656727, 0.03486233949661255, -0.0700877457857132, -0.04074393957853317, -0.0028313929215073586, -0.06807717680931091, -0.03549919277429581, -0.028767524287104607, -0.0176346804946661, 0.04125671833753586, -0.026992635801434517, 0.027158718556165695, -0.06257060170173645, 0.01665751449763775, -0.029045971110463142, 0.0524577796459198, -0.019797202199697495, 0.005988894496113062, 0.05816838890314102, 0.023804176598787308, -0.03891275078058243, 0.04369962215423584, -0.002123011276125908, 0.01873210072517395, 0.009715522639453411, 0.009603001177310944, -0.0050499956123530865, 0.03324850648641586, 0.004919260274618864, -0.03750684857368469, 0.011375611647963524, -0.011633657850325108, 0.030720805749297142, -0.02552654966711998, -0.014003390446305275, -0.03173983097076416, -0.013605451211333275, 0.02798265404999256, -0.019569985568523407, 0.039923518896102905, -0.05446348339319229, -0.07382895797491074, 0.03488178923726082, 0.022158456966280937, -0.03452807292342186, -0.009377546608448029, 0.008466162718832493, 0.04007319360971451, 0.03276311606168747, 0.02188139222562313, 0.0033326251432299614, 0.013845204375684261, -0.062857486307621, 0.0011177530977874994, 0.05963321030139923, -0.039844170212745667, 0.012184036895632744, -0.049142032861709595, -0.026445966213941574, -0.028410840779542923, -0.033703990280628204, 0.030727604404091835, -0.024364255368709564, 0.007645763456821442, 0.006146296393126249, -0.055466316640377045, 0.02605980820953846, -0.03395896404981613, -0.013333369046449661, 0.037074919790029526, -0.03183932229876518, -0.07744104415178299, 0.00722168106585741, 0.03301984444260597, 0.04768224060535431, 0.008582433685660362, -0.06253286451101303, 0.01922873966395855, 0.006873384118080139, -0.011015523225069046, -0.05270391330122948, -0.005395384971052408, -0.010736130177974701, -0.04371078684926033, 0.06403122842311859, -0.03298959136009216, -0.0059431022964417934, -0.0022191572934389114, 0.01504188310354948, 0.033952564001083374, 0.036530397832393646, 0.05557643249630928, 0.06314379721879959, 0.017086517065763474, -0.03769099712371826, -0.0011091312626376748, -0.01209105271846056, -0.03334552422165871, 0.05458596721291542, -0.030000513419508934, -0.021167434751987457, 0.045377667993307114, 0.035563476383686066, -0.035477686673402786, -0.05391736701130867, 0.016233185306191444, 0.012361635453999043, -0.005456768441945314, -0.03559926897287369, 0.032881539314985275, 0.05322093516588211, 0.025327499955892563, -0.003539819736033678, 0.018563229590654373, -0.02061564102768898, -0.029258906841278076, -0.03468899056315422, 0.04162028431892395, -0.038334619253873825, 0.0014399595092982054, -0.04984908178448677, 0.004412382375448942, 0.010831176303327084, 0.10579334199428558, -0.030025795102119446, -0.028489165008068085, -0.0009330704342573881, 0.01085959654301405, 0.011392926797270775, -0.011594314128160477, -0.013291471637785435, -0.009136603213846684, 0.019386792555451393, -0.10282652080059052, 0.00760996388271451, 0.01152739766985178, 0.0530657097697258, 0.010177401825785637, -0.034280966967344284, -0.005678925197571516, 0.034924693405628204, -0.01938306726515293, 0.026144076138734818, -0.03610416129231453, 0.005542668513953686, 0.046300649642944336, -0.08329807221889496, -0.07945997267961502, 0.025887129828333855, 0.008332890458405018, 0.01622142642736435, 0.006757049821317196, 0.009472506120800972, -0.03857269138097763, 0.027131447568535805, -0.05568324774503708, -0.03315160050988197, -0.007133391685783863, 0.013604368083178997, 0.04939230903983116, -0.01635519042611122, 0.021574469283223152, 0.011668720282614231, 0.04047746583819389, 0.019097326323390007, -0.01742459647357464, -0.00030580893508158624, -0.06158431991934776, 0.01815607398748398, -0.011287417262792587, -0.052367739379405975, 0.07089031487703323, 0.02836749330163002, -0.0887218490242958, 0.08109288662672043, -0.006567569449543953, -0.007505831774324179, -0.03038749285042286, -0.008168025873601437, 0.024457784369587898, -0.05198902636766434, -0.0026378436014056206, -0.07565384358167648, 0.024982403963804245, -0.061177656054496765, -0.08408353477716446, -0.009324396029114723, 0.00630720192566514, 0.0033253871370106936, -0.013135413639247417, 0.033760640770196915, 0.032204970717430115, 0.05028770864009857, 0.0828467458486557, -0.0468415804207325, -0.04433402046561241, -0.020344749093055725, -0.022663434967398643, -0.010045315138995647, 0.06521153450012207, 0.02014969289302826, -0.0006379071273840964, -0.08070606738328934, 0.011375710368156433, 0.01277920976281166, 0.003000896656885743, 0.030918173491954803, -0.07260503619909286, 0.0034653146285563707, -0.03404306620359421, -0.0130298538133502, -0.051006630063056946, 0.018444424495100975, 0.032221995294094086, -0.057219237089157104, -0.040821053087711334, -0.027404550462961197, -0.020732305943965912, 0.007848646491765976, -0.01759379170835018, 0.032322514802217484, -0.001532862544991076, -0.02587318792939186, -0.0389782078564167, 0.0012751163449138403, 0.028943903744220734, -0.052523039281368256, 0.020529761910438538, 0.030737731605768204, -0.029974408447742462, -0.03040745109319687, 0.00023327760573010892, 0.0011591421207413077, -0.0007566476706415415, -0.0028460784815251827, 0.058366719633340836, 0.08093736320734024, -0.000022432286641560495, 0.0060102553106844425, -0.013388155028223991, 0.04255015775561333, -0.04704652354121208, -0.0017569353803992271, 0.010918334126472473, 0.016569478437304497, -0.019769668579101562, 0.06814733892679214, -0.02097846195101738, -0.046957019716501236, -0.0773492306470871, 0.05611249431967735, -0.028721768409013748, 0.012823241762816906, -0.023328308016061783, 0.04324520379304886, 0.006556011736392975, 0.06237460672855377, -0.040839213877916336, -0.010162139311432838, 0.04122692346572876, 0.029431123286485672, -0.021610742434859276, 0.03663736954331398, -0.03002232126891613, -0.0012184157967567444, 0.022812189534306526, -0.041077688336372375, 0.05850566178560257, 0.00018947011267300695, 0.009784186258912086, 0.03898689150810242, 0.017409563064575195, 0.037446003407239914, -0.010700020007789135, -0.051169250160455704, -0.008054605685174465, -0.0380123071372509, -0.018824446946382523, 0.02672777697443962, -0.04856972396373749, -0.04205573722720146, -0.015908347442746162, -0.027592957019805908, -0.025793205946683884, 0.027299292385578156, -0.053466830402612686, 0.016546647995710373, 0.013426662422716618, 0.022544188424944878, -0.017394473776221275, -0.03757524862885475, -0.026245465502142906, 0.0322985015809536, 0.04412535950541496, 0.020654456689953804, -0.0470135360956192, -0.06786324828863144, -0.03667279705405235, -0.025063052773475647, -0.05197763815522194, 0.02055189572274685, -0.006454031448811293, -0.03682725131511688, 0.0063400049693882465, 0.09292885661125183, -0.05702734366059303, 0.017449721693992615, 0.07038318365812302, 0.0011013876646757126, 0.03488988056778908, -0.056978221982717514, 0.03549617528915405, -0.022489236667752266, 0.06421538442373276, 0.055811356753110886, 0.019619716331362724, -0.0394739955663681, -0.044466160237789154, 0.023074407130479813, -0.016149401664733887, 0.005534254480153322, -0.03263096883893013, -0.02465076372027397, -0.016971692442893982, -0.014620689675211906, 0.010694153606891632, 0.021677592769265175, 0.023966925218701363, 0.028255503624677658, -0.029871853068470955, 0.026384687051177025, 0.04079042002558708, 0.043359000235795975, 0.05573779717087746, -0.021133936941623688, -0.06629696488380432, -0.028438059613108635, -0.001955708023160696, -0.05656757578253746, 0.03630264103412628, -0.06743413954973221, -0.06988245993852615, -0.000356705131707713, 0.021736638620495796, -0.04360213130712509, 0.014006265439093113, 0.038147300481796265, 0.06330988556146622, -0.07779703289270401, -0.04004260152578354, -0.0201747827231884, -0.010306067764759064, -0.008602729998528957, -0.01873631961643696, 0.01731155626475811, -0.00886754784733057, -0.021035369485616684, -0.003436216851696372, 0.02037871815264225, -0.02416195161640644, 0.08225380629301071, -0.006377726327627897, 0.027642203494906425, 0.0028847400099039078, 0.021240396425127983, -0.030688121914863586, 0.050897032022476196, -0.01808825694024563, 0.05416514351963997, -0.016026204451918602, 0.010741977021098137, 0.040867917239665985, -0.002123048761859536, -0.0019387538777664304, -0.03666619956493378, 0.011272215284407139, 0.02338312566280365, -0.05119268596172333, 0.018046123906970024, 0.004425847437232733, 0.03159359470009804, 0.061234429478645325, 0.06352918595075607, -0.08974608778953552, 0.03359309583902359, -0.024100981652736664, 0.00817576888948679, -0.019388336688280106, 0.008829068392515182, -0.0088060786947608, -0.03221205249428749, 0.04036412388086319, -0.03260156512260437, 0.0411139577627182, -0.018894219771027565, 0.021292217075824738, -0.08416000008583069, 0.043716441839933395, 0.01013873890042305, 0.04340054839849472, -0.021685749292373657, 0.0014280725736171007, 0.0087996581569314, -0.03333365172147751, -0.07609276473522186, 0.026420023292303085, 0.008054056204855442, -0.013905489817261696, 0.04068922623991966, 0.03784744068980217, 0.04548780620098114, 0.008379253558814526, 0.04565044865012169, -0.012482876889407635, -0.08759640902280807, -0.03238397464156151, 0.01434189174324274, -0.01162081677466631, -0.001973067643120885, 0.0087773147970438, 0.019432637840509415, -0.04666922241449356, -0.030257103964686394, 0.0037206022534519434, -0.015392998233437538, 0.0011373740853741765, -0.028099065646529198, 0.05507108196616173, -0.03653400018811226, -0.015523617155849934, 0.011565795168280602, -0.04633663594722748, 0.016242925077676773, -0.0072278729639947414, 0.0007691275095567107, -0.031387098133563995, 0.04286835715174675, -0.019409410655498505, -0.04119616374373436, -0.010406703688204288, -0.02974604070186615, -0.03897276148200035, -0.0019796984270215034, 0.04960896074771881, -0.034878119826316833, -0.04607396945357323, -0.048419345170259476, 0.014586687088012695, 0.010673699900507927, 0.057483501732349396, 0.030488017946481705, -0.015610377304255962, -0.02821851521730423, -0.025613049045205116, 0.03162913769483566, 0.013090024702250957, -0.037451013922691345, 0.04325088486075401, 0.023943455889821053, 0.021177811548113823, 0.04138919711112976, 0.009955541230738163, 0.03558678925037384, -0.023435313254594803, 0.02490548975765705, 0.0017579798586666584, -0.01328334677964449, -0.03965584561228752, -0.012883215211331844, -0.01282392255961895, 0.03940396383404732, -0.06373590975999832, -0.04015044867992401, 0.013833767734467983, 0.04530441761016846, -0.05423630774021149, 0.014923732727766037, -0.017266996204853058, -0.004800721537321806, -0.019409622997045517, -0.025606058537960052, -0.007710779085755348, -0.00025161507073789835, 0.010772274807095528, -0.008964245207607746, -0.0281821396201849, -0.010740292258560658, 0.016626019030809402, -0.006811891682446003, -0.009298658929765224, 0.013004668056964874, -0.01669425144791603, 0.016250384971499443, 0.008241928182542324, 0.026972483843564987, 0.008480372838675976, -0.01054148655384779, 0.020182162523269653, -0.0577835738658905, 0.021308640018105507, 0.03151513263583183, -0.044983312487602234, 0.007116909604519606, 0.026430364698171616, -0.003395725041627884, -0.03583999350667, -0.02393219619989395, 0.050101589411497116, 0.06674584746360779, -0.004346254747360945, 0.003776766359806061, -0.000014646240742877126, -0.02203117124736309, 0.07430111616849899, -0.03440164402127266, -0.03853989392518997, 0.027227697893977165, -0.05367545783519745, 0.035500310361385345, 0.032549574971199036, -0.0012619083281606436, 0.04111092910170555, -0.054670512676239014, 0.09966319799423218, -0.027011189609766006, 0.054338883608579636, 0.09471512585878372, -0.06229540705680847, 0.002603166503831744, 0.019517607986927032, 0.0005321640055626631, 0.02984757535159588, -0.008999872952699661, 0.0296124629676342, 0.07224800437688828, 0.0037431283853948116, -0.03812085837125778, -0.015327471308410168, 0.030105536803603172, 0.010723701678216457, 0.00848948024213314, -0.010290559381246567, 0.026555128395557404, 0.037677448242902756, -0.00441714096814394, 0.008876260370016098, -0.02549486607313156, -0.015509516932070255, 0.00687649380415678, 0.008641811087727547, -0.019364554435014725, -0.01177187543362379, -0.02283290959894657, 0.06456317007541656, 0.049022406339645386, -0.08917485177516937, -0.016091352328658104, -0.062283020466566086, 0.04808134585618973, -0.011259022168815136, -0.02440919168293476, -0.04095565527677536, -0.0032517402432858944, 0.005188207142055035, 0.0384359247982502, 0.003398018656298518, 0.0321970097720623, 0.05273011326789856, -0.04550281539559364, -0.02070995606482029, 0.021611226722598076, -0.011786622926592827, 0.0009492404060438275, 0.03945967182517052, -0.020726138725876808, -0.09031899273395538, 0.037327349185943604, 0.026936976239085197, -0.06055639684200287, 0.03751126304268837, 0.015208493918180466, 0.005994483362883329, -0.014061623252928257, 0.018269173800945282, 0.09574825316667557, -0.01462655421346426, 0.023190058767795563, 0.0654669851064682, 0.0072141606360673904, -0.01777457632124424, 0.020853973925113678, -0.03123467043042183, 0.04303167760372162, -0.04327324032783508, 0.026320930570364, -0.058024752885103226, -0.060563940554857254, 0.03970082104206085, 0.03677884116768837, -0.00604392122477293, 0.001575945527292788, -0.03232564032077789, 0.025739939883351326, -0.008333265781402588, -0.04269089922308922, -0.013311801478266716, 0.009617503732442856, -0.0075152283534407616, 0.013154290616512299, -0.004809594713151455, -0.013227510266005993, -0.024086469784379005, 0.0454011969268322, 0.00479347025975585, -0.023529095575213432, -0.018851997330784798, 0.00297713465988636, -0.003460617270320654, -0.03709101676940918, -0.013575233519077301, -0.006768818479031324, 0.022728538140654564, 0.00130445696413517, 0.027507012709975243, 0.05384769290685654, 0.10319874435663223, -0.0597553625702858, 0.0683131292462349, -0.02933713234961033, 0.022673524916172028, -0.01762820966541767, -0.053917188197374344, -0.024202292785048485, 0.013582526706159115, -0.04300045594573021, -0.030564578250050545, 0.08266354352235794, 0.016844622790813446, -0.004523382522165775, 0.021094242110848427, -0.05730335786938667, 0.04656430706381798, -0.03973892703652382, -0.07937443256378174, -0.0008738308679312468, 0.039254412055015564, 0.041064515709877014, 0.026001688092947006, -0.04178491607308388, 0.022560516372323036, 0.01566586270928383, -0.023375820368528366, -0.004247093573212624, -0.03453381732106209, 0.0793834999203682, 0.011489050462841988 ]
<p>First of all, I should note that I'm a programmer and have only an extremely basic understanding of physics; I only know how to explain my question in layman's terms and I apologize if I'm unclear or unnecessarily verbose.</p> <p>If there's a rigid square object of size 1x1 and mass 1 on a two-dimensional frictionless plane, and while stationery it is struck by a force of strength 1 at exactly halfway along one of its sides from directly perpendicular to said side, like so:</p> <p><img src="http://i.stack.imgur.com/f8Pp0.png" alt="a picture of a square being struck by a force perpendicular to one of its sides"></p> <p>then my intuitive understanding is that it will begin traveling at a speed of 1 in the direction of the force.</p> <p>Similarly, if it is struck exactly on a corner by a force of strength 1 that is exactly perpendicular to the square's diagonal (at a 45* angle to its side), like so:</p> <p><img src="http://i.stack.imgur.com/bQF8O.png" alt="a picture of a square being struck by a force hitting it on the corner"></p> <p>then my intuitive understanding is that it will begin spinning (I don't know how fast) but remain stationery.</p> <p>What I don't know is how to work out what will happen if it is struck at any other point or from any other angle. For example, if struck three-quarters of the way down a side at an angle perpendicular to the side, like so:</p> <p><img src="http://i.stack.imgur.com/4qvUk.png" alt="a picture of a square being struck by a force partway down one of its sides"></p> <p>It seems as though it should cause it to begin moving (in some direction, at some speed) and spinning (at some speed), and the less perpendicular to the square's center of gravity the force is, the more it will spin and the less it will move. Is there a formula that, given the magnitude, angle, and impact point of the force, exactly how fast it will spin vs. how fast and in what direction it will move?</p> <p>More generally, how does one work out the answer to this sort of problem when applied to objects of other shapes/sizes/masses when impacted by other forces? Does it make a difference if the object is already moving or spinning? </p> <p>(Also, are any of my intuitive understandings actually entirely incorrect?)</p>
g5420
[ 0.026950132101774216, 0.019234012812376022, -0.000829388911370188, -0.02400246076285839, 0.025729410350322723, -0.006516939960420132, 0.0644787922501564, 0.012095682322978973, -0.03257587552070618, -0.010604633949697018, 0.0338832288980484, -0.015718664973974228, 0.06291647255420685, -0.049515992403030396, 0.04846493527293205, 0.027562623843550682, 0.047596413642168045, -0.054367899894714355, 0.06858865916728973, 0.07789731025695801, 0.002227618359029293, 0.007694660220295191, -0.001240923535078764, -0.0266391783952713, -0.03432384133338928, -0.06621260941028595, 0.020377036184072495, -0.03488447889685631, 0.0033683166839182377, 0.020353097468614578, -0.07701653987169266, 0.005935966968536377, 0.023093849420547485, -0.10077053308486938, -0.07378669828176498, 0.0033045271411538124, 0.011440595611929893, 0.03991863504052162, 0.021269861608743668, -0.014204555191099644, -0.005549344699829817, -0.03961140662431717, -0.023279907181859016, -0.03214362636208534, 0.03906133025884628, 0.002289337571710348, -0.01907145231962204, -0.028691360726952553, -0.007250807713717222, 0.01991340145468712, -0.06779886037111282, 0.015575028955936432, 0.07901177555322647, 0.00470362463966012, -0.049265552312135696, 0.05863438546657562, 0.07913788408041, -0.028323769569396973, 0.003956281580030918, 0.05966940149664879, -0.04178079962730408, 0.052919793874025345, -0.027174215763807297, -0.006135561969131231, 0.06000552698969841, -0.010862872004508972, -0.03170430660247803, -0.020264293998479843, -0.020361140370368958, -0.009046890772879124, -0.01870773546397686, -0.026781704276800156, 0.02171294391155243, -0.04924343526363373, -0.04457869380712509, -0.0065367273055016994, 0.0318092405796051, 0.0151888532564044, -0.05820811539888382, 0.05029994249343872, -0.017693880945444107, -0.02012396976351738, 0.033895812928676605, -0.018740713596343994, 0.09394420683383942, -0.05298740044236183, -0.017009595409035683, 0.029563605785369873, -0.012487626634538174, -0.0008045966387726367, 0.05959242209792137, -0.03248061239719391, 0.012469028122723103, 0.029899470508098602, -0.021464845165610313, -0.04068375006318092, -0.0010865562362596393, 0.034574396908283234, -0.04512558504939079, 0.019339224323630333, -0.03893805295228958, -0.020893868058919907, -0.0408954992890358, -0.051712363958358765, 0.011587458662688732, -0.007213626988232136, 0.036664191633462906, 0.0417245514690876, -0.054716743528842926, -0.048851579427719116, -0.03373214602470398, -0.03143040090799332, -0.05826918035745621, -0.020453594624996185, -0.013965282589197159, -0.0418255515396595, 0.08069878816604614, -0.0022044237703084946, 0.03458528220653534, 0.07230673730373383, -0.004853785969316959, -0.005585937295109034, -0.005382636561989784, 0.08956689387559891, -0.003013934940099716, 0.007468100171536207, -0.005835500545799732, 0.04557330906391144, 0.031970180571079254, -0.022169718518853188, -0.00210527959279716, -0.022846169769763947, 0.0003437314589973539, 0.008204425685107708, -0.03965870663523674, 0.09502467513084412, -0.020908024162054062, 0.04175407066941261, 0.034329984337091446, 0.023562796413898468, -0.03951757773756981, 0.03207983076572418, -0.024683477357029915, -0.009481623768806458, -0.0212970320135355, 0.025056976824998856, -0.030089735984802246, -0.01170726865530014, 0.052733324468135834, 0.014802428893744946, -0.005921094212681055, 0.07530000805854797, 0.004469920881092548, -0.06423883885145187, 0.03124929405748844, 0.024599986150860786, 0.03724813833832741, 0.0029873729217797518, 0.030720733106136322, -0.00930191483348608, 0.06971216201782227, -0.04795270040631294, 0.007967807352542877, -0.010763867758214474, -0.03078518807888031, -0.02056320756673813, -0.010623009875416756, -0.029985971748828888, -0.02397535741329193, -0.06523033231496811, -0.05055319890379906, 0.019180579110980034, 0.0407201424241066, 0.059958960860967636, -0.009668027050793171, -0.0018872481305152178, 0.014143426902592182, -0.04753587022423744, 0.03781905770301819, -0.010264835320413113, 0.03163890168070793, -0.0017878846265375614, 0.0367383249104023, 0.004226034972816706, 0.02271934412419796, -0.04320092126727104, 0.05654972791671753, 0.09593413770198822, -0.031907904893159866, 0.030418677255511284, -0.04081813618540764, -0.003983473405241966, -0.044578999280929565, 0.016283616423606873, -0.04695732891559601, -0.0040569007396698, 0.014025096781551838, -0.007790606468915939, -0.07826944440603256, -0.013001290149986744, -0.011583833023905754, 0.015169588848948479, 0.04486962407827377, 0.025980060920119286, -0.015357901342213154, 0.052969228476285934, 0.031337909400463104, 0.04410543292760849, 0.04975749924778938, 0.0233540590852499, -0.0030793575569987297, 0.0534149594604969, -0.013040909543633461, 0.05989576503634453, 0.019454125314950943, 0.010965225286781788, -0.019011404365301132, 0.04700988158583641, -0.01648894138634205, -0.0005743216024711728, -0.002348518231883645, 0.0018296402413398027, -0.006457907613366842, -0.040628135204315186, -0.05206838995218277, -0.011910304427146912, -0.03703511878848076, -0.013764600269496441, -0.010547158308327198, 0.049240607768297195, -0.03582392632961273, -0.0059951841831207275, 0.026455575600266457, -0.020822586491703987, 0.013272988609969616, 0.0009415671229362488, 0.017433658242225647, -0.00016905434313230217, 0.02369963563978672, -0.06384287774562836, 0.0943368524312973, -0.008734097704291344, -0.012954557314515114, -0.0133784469217062, 0.026359228417277336, -0.04338907077908516, 0.053828395903110504, -0.06620237976312637, 0.04542786628007889, 0.0929926186800003, 0.012831027619540691, -0.02190541662275791, -0.0642138421535492, -0.0013906583189964294, 0.024209391325712204, 0.0075082192197442055, -0.0220270287245512, 0.030196670442819595, -0.05184121057391167, -0.04546859487891197, -0.06310904026031494, -0.0208171047270298, 0.05120379477739334, 0.0300095546990633, -0.07207166403532028, 0.021088307723402977, -0.022471698001027107, 0.02552609145641327, 0.010205627419054508, 0.008344420231878757, -0.05785844102501869, 0.023406902328133583, 0.006551844533532858, 0.04621800035238266, 0.032348569482564926, -0.05547923967242241, 0.04141220822930336, -0.018817244097590446, -0.0339399054646492, 0.0480891577899456, 0.009624873287975788, 0.03570929542183876, -0.043858591467142105, 0.03444095700979233, 0.02039102092385292, -0.01725122146308422, -0.0011208771029487252, -0.017625801265239716, -0.060294900089502335, 0.010137733072042465, -0.029000451788306236, 0.031753361225128174, 0.061670828610658646, -0.03194383159279823, 0.039378996938467026, 0.040300402790308, -0.04061003774404526, -0.014246504753828049, 0.006940647028386593, 0.03270702809095383, 0.002428146544843912, -0.004123972728848457, 0.007437803782522678, 0.039054419845342636, -0.014182875864207745, 0.051043473184108734, -0.02869563177227974, -0.10824605077505112, -0.019744962453842163, 0.01618863455951214, -0.022120866924524307, 0.07872658967971802, -0.035349659621715546, 0.014849823899567127, -0.0831175222992897, -0.059379104524850845, 0.018285736441612244, 0.04959219694137573, -0.033852726221084595, 0.06582025438547134, -0.027419578284025192, -0.02101380005478859, -0.008374208584427834, 0.017637714743614197, 0.01742992177605629, 0.02832283452153206, -0.024972010403871536, 0.003816454904153943, -0.03117409162223339, -0.0030745116528123617, 0.0523129440844059, 0.0415736585855484, -0.022359468042850494, -0.027799410745501518, -0.07278706878423691, 0.019100487232208252, 0.027242491021752357, 0.015176757238805294, 0.03595564141869545, 0.06266219168901443, 0.03069351427257061, -0.047398265451192856, -0.010517469607293606, -0.006334643345326185, -0.011303567327558994, -0.034017808735370636, 0.037819862365722656, -0.03424113988876343, 0.01740686036646366, 0.006303964648395777, 0.09190802276134491, -0.03373485058546066, -0.03368790075182915, 0.00650499714538455, 0.05608058348298073, 0.018428700044751167, -0.0002752217114903033, 0.031378164887428284, -0.06169950217008591, 0.021643197163939476, -0.00496523967012763, -0.03409828245639801, 0.0017726919613778591, 0.003287564730271697, -0.019362716004252434, 0.016347382217645645, 0.03332052007317543, 0.010394222103059292, 0.010878929868340492, 0.039618346840143204, 0.005920183379203081, -0.07537293434143066, -0.010693556629121304, -0.0017631379887461662, 0.016916032880544662, 0.01828579045832157, 0.047032490372657776, -0.0001432822027709335, -0.014326626434922218, 0.0424065962433815, 0.008156631141901016, 0.023171167820692062, -0.014285980723798275, 0.022067323327064514, 0.00037914939457550645, 0.05468263104557991, 0.002295728540048003, -0.0027211683336645365, 0.05080197751522064, -0.03922947496175766, 0.015267865732312202, -0.04224295914173126, 0.01453745923936367, 0.045073941349983215, 0.031051961705088615, -0.010266441851854324, -0.03624625876545906, -0.00309164565987885, -0.022648120298981667, 0.011992729268968105, 0.023617258295416832, 0.03099857084453106, -0.024807503446936607, 0.0011943579884245992, -0.008081159554421902, 0.016146725043654442, 0.016169428825378418, 0.0014683986082673073, 0.008999953046441078, -0.028350966051220894, 0.020353076979517937, -0.024155542254447937, -0.058379750698804855, -0.036163002252578735, 0.033068254590034485, 0.03638928383588791, 0.001716797356493771, 0.03928523510694504, -0.02549838088452816, -0.036392271518707275, 0.02963426150381565, 0.030854305252432823, 0.017032664269208908, -0.00747982831671834, 0.0004746547492686659, 0.011800946667790413, 0.0500459261238575, -0.026386352255940437, 0.021291902288794518, 0.01769486628472805, -0.012557074427604675, 0.06179872527718544, 0.023725012317299843, 0.0381738655269146, -0.028429832309484482, 0.024586139246821404, 0.02792474627494812, 0.03922367841005325, 0.009399227797985077, -0.010119049809873104, 0.018381180241703987, 0.035210981965065, -0.006901766639202833, -0.01978013850748539, -0.001222433289512992, 0.03580909222364426, -0.0610978864133358, -0.017164211720228195, -0.005918413400650024, -0.05289221554994583, -0.05085378140211105, -0.022673390805721283, 0.004874218255281448, -0.06489540636539459, -0.04005269706249237, 0.022766070440411568, 0.0005948034231550992, 0.046531692147254944, -0.037561941891908646, 0.003229236463084817, -0.043332602828741074, -0.01199338212609291, -0.02227870561182499, -0.04225896671414375, -0.05559760704636574, 0.010841980576515198, -0.01429025735706091, 0.027795109897851944, -0.07367846369743347, 0.03279789537191391, -0.03825242072343826, -0.008069703355431557, -0.02238730899989605, 0.07033177465200424, 0.0292399562895298, 0.016818827018141747, -0.004750899970531464, -0.020547639578580856, -0.028587069362401962, -0.0001974353363038972, -0.01103794015944004, -0.046132560819387436, 0.054427459836006165, -0.027690628543496132, 0.0013446700759232044, -0.05292724445462227, 0.023863285779953003, -0.010034063830971718, 0.04534946382045746, -0.022080784663558006, 0.020151881501078606, -0.026457639411091805, -0.08179374039173126, -0.06397400051355362, -0.05894973874092102, 0.01637168787419796, 0.024033909663558006, -0.019839243963360786, -0.03321998938918114, -0.0032760712783783674, -0.039951141923666, 0.06365053355693817, 0.03375682607293129, 0.033855680376291275, 0.0009575342410244048, 0.03959408774971962, 0.053103625774383545, -0.054182134568691254, 0.0021514480467885733, 0.05488784238696098, 0.01813412457704544, 0.03178224712610245, 0.035509780049324036, 0.00410646153613925, -0.02900519035756588, 0.036338262259960175, 0.027409687638282776, 0.05814741179347038, 0.004772455431520939, 0.03469705209136009, 0.0011578038102015853, 0.02110983617603779, -0.07701924443244934, -0.01475531980395317, 0.005027778912335634, -0.019105495885014534, -0.041475117206573486, 0.0075120022520422935, 0.004326856229454279, 0.06397072225809097, 0.028358452022075653, 0.0031779571436345577, 0.00339239789173007, -0.02981039322912693, -0.06394876539707184, -0.029544997960329056, 0.022030441090464592, -0.05964747816324234, 0.06930990517139435, -0.034595564007759094, -0.04583626613020897, -0.025140855461359024, 0.041295018047094345, 0.04520310088992119, -0.06806443631649017, 0.000051798109780065715, -0.025179961696267128, -0.06855235248804092, 0.011208385229110718, 0.013309543952345848, -0.0510093979537487, 0.10440381616353989, -0.02134481444954872, 0.052203744649887085, 0.0020215394906699657, 0.04869742691516876, 0.0013967340346425772, -0.003792258445173502, -0.0033629063982516527, -0.0461624376475811, 0.013122507371008396, -0.024370409548282623, 0.03941825404763222, -0.004455254413187504, -0.004061935003846884, -0.035018760710954666, 0.018124988302588463, -0.05146431922912598, 0.04923248291015625, 0.06180809438228607, -0.03974708542227745, -0.006815887056291103, -0.02558181993663311, 0.04004823416471481, 0.036031030118465424, 0.028828442096710205, -0.02305922470986843, -0.007113833911716938, -0.05997270345687866, 0.08578386902809143, 0.008318033069372177, -0.01083735004067421, 0.0023175731766968966, 0.0007026066887192428, 0.02641897089779377, 0.02129179611802101, -0.06288280338048935, 0.006798882503062487, 0.015820782631635666, -0.07063736766576767, -0.056300535798072815, 0.015040388330817223, 0.011836029589176178, -0.05326814576983452, -0.05031268671154976, -0.035634417086839676, 0.009965640492737293, 0.043669190257787704, -0.024885280057787895, 0.009743097238242626, -0.0025912763085216284, -0.03181760385632515, 0.07448983937501907, -0.010379321873188019, -0.02593945525586605, -0.01648964174091816, -0.015984956175088882, -0.07176916301250458, 0.0008051019394770265, -0.005685034207999706, 0.00547892227768898, 0.0337446965277195, -0.0033661562483757734, 0.04995749145746231, -0.010335734114050865, -0.03296826407313347, -0.026382477954030037, -0.06277391314506531, 0.014122607186436653, -0.041045892983675, -0.025760171934962273, -0.018557434901595116, 0.01727011241018772, -0.055295102298259735, 0.02192673645913601, -0.0030219939071685076, -0.010523100383579731, 0.029914669692516327, 0.03817971795797348, 0.010939832776784897, 0.05553929880261421, -0.009557795710861683, -0.012533663772046566, 0.021455680951476097, 0.012706645764410496, 0.024916164577007294, -0.018855586647987366, 0.0075440481305122375, 0.0206103827804327, 0.06114781275391579, -0.011184418573975563, 0.026675403118133545, -0.04542291536927223, 0.01776880770921707, -0.010865757241845131, -0.05539415031671524, -0.041728511452674866, -0.0006563765346072614, -0.01713453233242035, 0.009731241501867771, -0.007428464945405722, -0.009096869267523289, -0.030129380524158478, 0.004372994881123304, -0.05488104373216629, -0.002073434880003333, 0.018468381837010384, 0.0053657605312764645, -0.010003273375332355, -0.0016654692590236664, -0.0709681510925293, -0.017460579052567482, -0.013131886720657349, -0.030176665633916855, -0.04565761238336563, 0.024322794750332832, -0.047962795943021774, 0.011379354633390903, 0.020302467048168182, -0.007808308117091656, 0.021742215380072594, -0.0634341910481453, -0.021306652575731277, 0.04973931983113289, 0.013174695894122124, 0.06925522536039352, -0.01685488224029541, -0.03176676109433174, 0.03770362213253975, -0.025737198069691658, 0.01888316124677658, 0.01293158158659935, -0.0009803290013223886, 0.011860446073114872, -0.04584512487053871, 0.0816354751586914, -0.03743951395153999, 0.048598289489746094, -0.00566000584512949, -0.05814385041594505, 0.026868382468819618, 0.00680047320201993, 0.009109382517635822, 0.06795668601989746, -0.036951009184122086, -0.022854620590806007, 0.021884238347411156, 0.05831979215145111, -0.03532112389802933, 0.010979822836816311, -0.013665064238011837, -0.020733114331960678, 0.02677924372255802, -0.04211205616593361, -0.006949275266379118, 0.028603756800293922, 0.010832666419446468, -0.012571399100124836, -0.0038255590479820967, -0.0342293381690979, 0.026296444237232208, 0.07391416281461716, 0.06060400977730751, -0.06304943561553955, -0.05618644505739212, -0.009487705305218697, 0.028322413563728333, -0.0015404854202643037, 0.029438350349664688, -0.01752394251525402, -0.04992739111185074, 0.044483769685029984, -0.05494158715009689, -0.03078833408653736, -0.01154196448624134, 0.03079098090529442, 0.020001502707600594, -0.010526699014008045, -0.008460192009806633, 0.025981847196817398, 0.020457644015550613, 0.023830607533454895, 0.0052486322820186615, 0.032723646610975266, -0.015073648653924465, 0.032948970794677734, 0.005693809129297733, -0.07692523300647736, -0.01676110550761223, 0.01568184792995453, -0.007651187013834715, -0.036420080810785294, -0.025001734495162964, 0.01158964540809393, -0.017473900690674782, 0.016877777874469757, 0.012913013808429241, 0.053548093885183334, -0.00589992618188262, 0.012867193669080734, 0.04384438320994377, 0.022740863263607025, 0.002370141912251711, -0.04262739419937134, -0.06552976369857788, -0.058081500232219696, -0.007644192315638065, -0.01073723379522562, -0.01613905467092991, -0.055086899548769, -0.015215673483908176, 0.012722772546112537, 0.04161154478788376, -0.01647830195724964, -0.0063896505162119865, -0.029048282653093338, -0.08091875910758972, 0.034737925976514816 ]
<p>I have asked this question before on other forums, but only got the classical answer of the impossibility of the probability interpretation for single particle in QFT. Now, there seems to be also doubt in multi particle interpretation of the Dirac "sea". while in QFT the multi particle seems to be the result of promoting the wavefunction to an operator. And some people claimed it is a multi picture of a single particle. So, is there any clearer explanation?</p>
g5421
[ 0.0233068335801363, 0.05021582171320915, 0.008055862039327621, -0.04806726053357124, 0.07374122738838196, -0.0006980992038734257, 0.020447595044970512, 0.053192779421806335, 0.006038897670805454, -0.040587250143289566, -0.026282677426934242, -0.018211031332612038, 0.02593083679676056, 0.04507433623075485, -0.032177552580833435, -0.011574218980967999, 0.04630338028073311, 0.0043641249649226665, 0.034571126103401184, -0.0072790831327438354, 0.016011178493499756, 0.021390119567513466, -0.005526010878384113, -0.03420981392264366, -0.018344106152653694, 0.004664148669689894, -0.0036674337461590767, -0.026706255972385406, -0.03552594035863876, -0.000013611120266432408, 0.05437515303492546, -0.007665419019758701, 0.006568226497620344, -0.06005670130252838, -0.011690022423863411, -0.06913352757692337, 0.05891747772693634, 0.026925161480903625, -0.008115368895232677, 0.010551094077527523, -0.021947307512164116, 0.01860683411359787, 0.022525165230035782, -0.017335955053567886, 0.013722140341997147, 0.04271984100341797, 0.011013626120984554, 0.02464543841779232, -0.030414095148444176, -0.057988524436950684, -0.013887573033571243, -0.023957516998052597, 0.012811611406505108, 0.05632834509015083, -0.055978912860155106, 0.0695304349064827, 0.007489547599107027, -0.021758561953902245, 0.043960459530353546, 0.06103011965751648, 0.010438255965709686, 0.07685914635658264, 0.01879623904824257, 0.005257127340883017, 0.03805074468255043, 0.006968360859900713, -0.02949235588312149, -0.004514314234256744, 0.012217420153319836, -0.011617672629654408, 0.011836839839816093, -0.09793440252542496, -0.00691343005746603, -0.007941712625324726, 0.005401854403316975, -0.0051237111911177635, -0.011573605239391327, 0.031868480145931244, 0.004403985105454922, -0.007647283375263214, -0.019468359649181366, -0.00924642477184534, -0.00973435491323471, 0.0026613592635840178, 0.017681598663330078, 0.02556803822517395, 0.06287477165460587, 0.008718966506421566, -0.007030804175883532, 0.012796730734407902, 0.005009498912841082, -0.007517595775425434, 0.02444533444941044, 0.04385446012020111, -0.016713665798306465, -0.027747364714741707, -0.05598055571317673, 0.0718616470694542, -0.07964447140693665, 0.05471282824873924, -0.0391726978123188, 0.03195980191230774, 0.0578828789293766, 0.010224642232060432, 0.000018812370399245992, -0.016404397785663605, 0.00044678192352876067, 0.021316686645150185, 0.05469455569982529, -0.027314607053995132, -0.08131492137908936, 0.002345662098377943, 0.04441598430275917, -0.010008102282881737, -0.02301075868308544, -0.027837276458740234, 0.06186354160308838, -0.052226472645998, 0.0083163408562541, 0.0416036956012249, -0.007714375853538513, 0.021925469860434532, 0.03659176826477051, 0.03599267080426216, -0.03253371641039848, -0.056737665086984634, -0.04566634073853493, 0.057526957243680954, 0.027194665744900703, 0.013974840752780437, 0.0464455746114254, 0.028427166864275932, -0.008710458874702454, 0.0350663922727108, -0.02443479187786579, -0.01854110322892666, -0.03322945907711983, 0.006883281748741865, 0.010878187604248524, 0.003980930894613266, 0.025706904008984566, -0.050603222101926804, -0.007029705215245485, -0.025387262925505638, -0.006188914179801941, -0.06665337085723877, 0.02076921984553337, -0.022980444133281708, -0.06587556004524231, 0.04036618024110794, 0.042709942907094955, 0.06871520727872849, 0.056324608623981476, 0.008233447559177876, 0.06471656262874603, -0.0003211077710147947, 0.033877916634082794, 0.014056398533284664, -0.05416951701045036, 0.00891959946602583, 0.03493179753422737, 0.014393769204616547, -0.027496561408042908, 0.015619948506355286, -0.05625376105308533, 0.028585057705640793, 0.03175878897309303, -0.02400369755923748, 0.010543370619416237, -0.05988384410738945, -0.007126001641154289, 0.004713393282145262, -0.0019624093547463417, 0.027765141800045967, 0.014678348787128925, 0.016902292147278786, -0.05136888101696968, -0.04791382700204849, -0.06399847567081451, 0.03908860683441162, -0.052129797637462616, 0.0368361659348011, -0.0048995851539075375, -0.057434145361185074, 0.00846336130052805, -0.03224607929587364, 0.00813471619039774, 0.0855007991194725, -0.021473903208971024, 0.055426064878702164, -0.030756443738937378, -0.034361280500888824, -0.007256395183503628, 0.024703150615096092, 0.06363733112812042, -0.013444389216601849, 0.03919506445527077, -0.048754483461380005, -0.0020349002443253994, 0.028525009751319885, 0.00976543128490448, 0.07189927995204926, 0.01738487184047699, 0.020696008577942848, 0.025572363287210464, -0.02992122806608677, -0.018879033625125885, 0.010363658890128136, 0.013891720212996006, -0.10866665840148926, 0.011901820078492165, -0.025931615382432938, -0.038269709795713425, -0.003240137128159404, 0.012508406303822994, -0.01166644785553217, 0.01250060647726059, -0.026646073907613754, 0.01664910651743412, -0.038171641528606415, -0.08197016268968582, -0.03592067211866379, 0.05255408212542534, -0.008594553917646408, -0.008014644496142864, 0.08064296841621399, -0.05203436315059662, -0.05030081048607826, -0.02541421540081501, 0.07161576300859451, -0.09989873319864273, 0.01270229835063219, -0.06535016000270844, 0.009478774853050709, 0.007647084537893534, 0.07008431851863861, -0.006284935399889946, -0.03358520194888115, 0.031656939536333084, 0.0600285567343235, -0.037340059876441956, -0.016344130039215088, -0.07172469049692154, -0.01782376319169998, 0.02659144066274166, 0.010417724028229713, -0.00019300343410577625, -0.025027893483638763, 0.0010542025556787848, 0.0211171992123127, 0.008084484376013279, -0.01796516217291355, -0.02312103472650051, 0.013955473899841309, 0.00489017553627491, -0.022863350808620453, -0.006709153763949871, 0.034341711550951004, -0.024280961602926254, -0.040256090462207794, 0.02364460378885269, 0.017459070309996605, -0.058738987892866135, 0.02830967679619789, 0.033183660358190536, -0.009079291485249996, 0.037716444581747055, 0.031034650281071663, 0.0012871775543317199, -0.04046745225787163, -0.00023627736663911492, 0.07791344076395035, -0.01732766255736351, 0.030880097299814224, -0.034046318382024765, -0.0010084433015435934, -0.009452860802412033, 0.0021736114285886288, -0.0018448486225679517, -0.0668536126613617, -0.048667505383491516, -0.037308093160390854, -0.010485885664820671, 0.022242238745093346, -0.012110172770917416, -0.052399393171072006, 0.03545987233519554, -0.01723119616508484, 0.02850843407213688, 0.042398981750011444, 0.01345966849476099, 0.010368735529482365, 0.06053749471902847, 0.016869211569428444, -0.04033854231238365, -0.035454027354717255, 0.010665307752788067, -0.02822727896273136, 0.01735350303351879, 0.06707637012004852, -0.03682662546634674, 0.004369884263724089, -0.004486816935241222, 0.04108796268701553, 0.0808626338839531, 0.025874363258481026, -0.03216356411576271, -0.03212512284517288, -0.01849072426557541, -0.04232397302985191, -0.013615160249173641, 0.03139766305685043, -0.023110900074243546, -0.010912973433732986, -0.044904861599206924, -0.0405871644616127, -0.03444448113441467, 0.06046796590089798, 0.027016663923859596, -0.030100129544734955, -0.025420550256967545, -0.03192836791276932, 0.04126613959670067, -0.03405905142426491, 0.07766804099082947, -0.022084468975663185, -0.016118455678224564, 0.004019616171717644, -0.0023791026324033737, -0.07146592438220978, -0.021838363260030746, -0.005284020211547613, 0.010286395438015461, 0.056862927973270416, -0.038850776851177216, -0.005029574036598206, -0.03334252908825874, -0.007574879564344883, 0.01236260961741209, -0.027074618265032768, 0.01361936517059803, -0.032021984457969666, 0.0016143250977620482, -0.019012130796909332, -0.006815937347710133, 0.05350487679243088, 0.050527174025774, 0.030689384788274765, 0.013739854097366333, 0.0038933581672608852, -0.0026374959852546453, 0.02567950077354908, 0.004462428856641054, 0.09421904385089874, 0.005252564791589975, 0.0028050215914845467, 0.026979265734553337, 0.06352529674768448, 0.03216373920440674, 0.02470218762755394, -0.02324083261191845, -0.01879214681684971, 0.017327357083559036, 0.048044607043266296, 0.00832713209092617, -0.04956492409110069, 0.03243613988161087, 0.029012594372034073, 0.01002019364386797, -0.030908767133951187, -0.03913440182805061, -0.020957691594958305, -0.02930722013115883, 0.03847832605242729, 0.03435191512107849, -0.019185254350304604, 0.024795472621917725, 0.006131171248853207, 0.014123588800430298, 0.03579821065068245, 0.04267307370901108, 0.04162219911813736, 0.007527121342718601, 0.007269010879099369, 0.0050273253582417965, 0.04328027367591858, -0.05601203814148903, -0.04049130529165268, -0.02710617706179619, -0.024780524894595146, 0.009354501962661743, -0.05200784280896187, -0.04894113913178444, 0.04589012265205383, 0.022223999723792076, -0.021095722913742065, 0.05111924186348915, -0.0557125024497509, 0.035825084894895554, 0.048987481743097305, -0.054286807775497437, -0.060124512761831284, -0.021926194429397583, -0.03518383577466011, 0.0016966708935797215, -0.010010634548962116, 0.04215807095170021, -0.030088068917393684, 0.01994970254600048, -0.0396542027592659, 0.022304601967334747, -0.016489986330270767, 0.07131629437208176, -0.007778531406074762, 0.009841486811637878, 0.05261938273906708, 0.01583005115389824, -0.03974881023168564, -0.011235032230615616, 0.033235710114240646, 0.027514388784766197, 0.011673626489937305, -0.0099482461810112, 0.019039055332541466, -0.04186707362532616, 0.03603517636656761, 0.020661355927586555, 0.01293069776147604, -0.07376452535390854, -0.016386093571782112, 0.006421311292797327, 0.0009455209947191179, -0.005588271655142307, 0.010734127834439278, -0.03163779899477959, 0.01489165611565113, 0.00039775282493792474, 0.04561351239681244, -0.03431331738829613, 0.017410770058631897, 0.09099612385034561, 0.005686112213879824, 0.02542126178741455, -0.014604448340833187, 0.0359494611620903, -0.00010142724204342812, -0.072076715528965, -0.041284359991550446, -0.029409613460302353, -0.05482567474246025, -0.028489816933870316, -0.0010020156623795629, -0.10271713882684708, -0.0023537129163742065, -0.023850034922361374, 0.000285280984826386, -0.046994004398584366, -0.01377126481384039, 0.021556884050369263, 0.0006624562083743513, -0.08591431379318237, -0.026065850630402565, -0.0077759078703820705, 0.048633135855197906, 0.027721036225557327, 0.015470767393708229, -0.05444980412721634, 0.02105051279067993, -0.05763551592826843, 0.007182679604738951, -0.010704735293984413, 0.030369650572538376, 0.02321512997150421, -0.06307779997587204, -0.01172944251447916, -0.029478944838047028, 0.009082361124455929, -0.06043960154056549, -0.022430213168263435, -0.05595317855477333, 0.03274541720747948, 0.006986695807427168, 0.01969568058848381, -0.020856183022260666, -0.06508117914199829, 0.035676077008247375, 0.042952362447977066, 0.010687957517802715, -0.023403184488415718, 0.005542166531085968, 0.018710963428020477, 0.013710425235331059, 0.06379801779985428, 0.007377905305474997, 0.035445671528577805, -0.00009742999100126326, -0.008684154599905014, -0.018025197088718414, -0.0003101270704064518, -0.014015731401741505, -0.02608817256987095, -0.07990362495183945, 0.04894021153450012, 0.04024992138147354, -0.018041202798485756, 0.031257763504981995, 0.03783388435840607, -0.04905117675662041, 0.01764674484729767, 0.0021591330878436565, 0.06386585533618927, -0.03939817100763321, -0.0859803557395935, -0.03504644334316254, 0.03959785774350166, -0.025292275473475456, -0.0240767952054739, -0.01538174133747816, 0.01617353968322277, -0.042719416320323944, 0.0006296706269495189, 0.012286427430808544, -0.011763736605644226, -0.0006967533845454454, 0.016885871067643166, -0.0154905766248703, -0.04884861409664154, -0.009682809002697468, 0.0012827090686187148, 0.012828782200813293, 0.05338282510638237, 0.07292968034744263, 0.029428860172629356, 0.01927812770009041, 0.022968271747231483, -0.03383605554699898, 0.03329237923026085, 0.0009399486589245498, 0.07943394780158997, 0.05748753249645233, 0.008102649822831154, 0.019611027091741562, 0.0260060615837574, 0.060939617455005646, -0.03687071427702904, 0.007872854359447956, -0.030581053346395493, 0.0255598034709692, 0.044410016387701035, -0.051094673573970795, 0.05534691363573074, 0.004272070247679949, -0.004266790580004454, -0.027346350252628326, 0.05190809443593025, 0.06911682337522507, -0.05241553485393524, -0.05176323279738426, -0.0424150675535202, -0.004663593601435423, -0.00976942665874958, -0.02656782977283001, 0.052176278084516525, -0.02748679183423519, -0.0005734899314120412, -0.00653343740850687, -0.0250091552734375, -0.013480830006301403, 0.02642473392188549, 0.02224087156355381, -0.05593886226415634, 0.04579467326402664, 0.02746288664638996, 0.025895938277244568, 0.07784325629472733, 0.01948985457420349, 0.055605750530958176, -0.04470035433769226, -0.022558648139238358, -0.057738009840250015, 0.017266707494854927, 0.034909311681985855, 0.006090802140533924, -0.05496248975396156, -0.027124561369419098, 0.07469204813241959, -0.022769855335354805, -0.018151871860027313, 0.028663255274295807, 0.042814143002033234, -0.05643611401319504, -0.0034416704438626766, -0.027124227955937386, -0.0029964253772050142, -0.031539976596832275, 0.014910690486431122, -0.00888039544224739, -0.047143787145614624, -0.0067770653404295444, -0.01624833047389984, 0.015924574807286263, 0.037185680121183395, 0.01805393025279045, 0.011700914241373539, 0.009931065142154694, 0.0008487284649163485, -0.020470844581723213, -0.030728016048669815, -0.05091249197721481, 0.006880780216306448, -0.017971221357584, -0.012902529910206795, -0.04621245339512825, 0.006020587403327227, -0.02593032643198967, -0.04414334148168564, -0.0586615614593029, 0.002100823214277625, 0.0005798779893666506, 0.010652661323547363, 0.04489300772547722, 0.0003950110112782568, -0.014678578823804855, -0.056521520018577576, -0.001483119442127645, 0.04958971589803696, 0.004732414148747921, -0.02488742209970951, 0.021433014422655106, -0.013258472084999084, 0.017358975484967232, 0.012763077393174171, 0.03102458268404007, 0.014863112010061741, -0.044106338173151016, 0.00857597216963768, -0.02886083349585533, 0.003812232054769993, 0.015620582737028599, 0.03821630775928497, -0.01441932749003172, -0.008619391359388828, 0.073683962225914, -0.031492456793785095, -0.058533065021038055, -0.05899880826473236, 0.08594109117984772, 0.014236358925700188, -0.11088559031486511, -0.036208052188158035, 0.030156681314110756, 0.014148129150271416, 0.008480115793645382, 0.04119259864091873, 0.0330447219312191, -0.0070978980511426926, 0.038946013897657394, -0.004212510772049427, -0.001327819307334721, -0.03714478015899658, -0.04663698375225067, 0.017423851415514946, -0.05048782378435135, -0.012520445510745049, -0.004496882203966379, 0.02378600277006626, -0.03309916332364082, -0.1114654615521431, 0.002810501493513584, -0.01710265874862671, -0.010627097450196743, -0.024402977898716927, -0.048118334263563156, 0.013408982194960117, 0.028206806629896164, -0.03410918638110161, -0.010784386657178402, 0.07707811146974564, 0.00270622200332582, 0.09026544541120529, 0.011200233362615108, 0.025564858689904213, 0.03766108304262161, -0.00417743157595396, -0.00036110045039094985, -0.020588479936122894, 0.029663555324077606, 0.016847115010023117, -0.0015428471378982067, 0.0020922503899782896, 0.026118887588381767, -0.02964603714644909, 0.043758783489465714, -0.07995489239692688, -0.02699892409145832, 0.03241632506251335, 0.07194764912128448, 0.016977718099951744, 0.08618192374706268, 0.04452262818813324, -0.01346310693770647, 0.0015987020451575518, -0.027002301067113876, -0.0112139992415905, 0.04494120553135872, -0.008333058096468449, 0.02508181519806385, -0.017400765791535378, 0.01665966771543026, -0.008368048816919327, -0.00815352238714695, -0.02838282287120819, -0.02428363263607025, 0.0388311930000782, -0.010709930211305618, -0.027099572122097015, -0.016464760527014732, 0.040067657828330994, -0.034178271889686584, -0.05106895789504051, 0.027918454259634018, 0.023771274834871292, -0.057048119604587555, -0.005356209352612495, -0.02237907238304615, -0.0552188903093338, 0.008406464010477066, 0.0009811471682041883, 0.023185230791568756, 0.0038130059838294983, -0.005761643871665001, -0.019366001710295677, -0.03799866884946823, 0.0018623507348820567, -0.03607696294784546, 0.051943596452474594, -0.005148035474121571, 0.039694007486104965, 0.01424005813896656, 0.012157149612903595, 0.017733879387378693, 0.025446439161896706, 0.013859003782272339, 0.0036385066341608763, -0.07250075042247772, -0.040898412466049194, -0.07022351026535034, -0.054444849491119385, 0.0494346097111702, -0.005239727906882763, -0.05978778377175331, 0.04016590490937233, -0.014889229089021683, 0.037899695336818695, 0.06268290430307388, -0.0721784234046936, -0.010959502309560776, 0.039908625185489655, 0.0038256424013525248, -0.01349096093326807, -0.0004228304896969348, -0.05483557656407356, 0.018906759098172188, -0.013101267628371716, -0.03246200084686279, -0.019066521897912025, -0.020212074741721153, 0.029892349615693092 ]
<p>Is the structural similarity between atoms ( smallest) and universe (biggest) a coincidence? Or there can a reason for this beyond imaginations?</p> <p>It seems like, if one starts travelling out from atoms... and grows bigger and bigger, one ends in a similar structure somewhere in the universe. Kind of a circular ring. </p> <p>PS: By structural similarity I mean : single nucleus and electrons revolving around in an atom, is structurally similar to planets revolving around the sun.</p>
g5422
[ 0.033471230417490005, 0.02286614663898945, 0.01375699695199728, -0.011309053748846054, -0.028743846341967583, 0.02772434428334236, -0.01043226383626461, -0.019074222072958946, 0.0015169112011790276, -0.05128839612007141, 0.000027676942409016192, 0.0019298280822113156, -0.000679461401887238, -0.027248725295066833, 0.018296897411346436, -0.018938099965453148, 0.006888282019644976, -0.06495431810617447, 0.02178221382200718, 0.0005441594985313714, 0.027039626613259315, 0.021900620311498642, -0.02716447412967682, -0.024688467383384705, -0.05672868713736534, 0.030587587505578995, -0.009425750002264977, -0.03767242282629013, 0.020448416471481323, 0.000287719041807577, 0.05882994830608368, -0.05959524214267731, 0.03393993154168129, -0.010520951822400093, 0.024586625397205353, -0.030685925856232643, -0.03399062156677246, -0.021992111578583717, 0.020375050604343414, -0.02982451021671295, 0.03451696038246155, 0.0017942962003871799, -0.017645731568336487, 0.01571890152990818, 0.03310312703251839, -0.046188436448574066, 0.02815067768096924, 0.020927168428897858, 0.08600253611803055, -0.05201369524002075, -0.044172756373882294, 0.08080966025590897, -0.02114040218293667, 0.030153706669807434, 0.008795849047601223, 0.04363340511918068, 0.05592840164899826, -0.019316140562295914, 0.07480497658252716, -0.0030480653513222933, -0.004951460286974907, 0.05346274375915527, -0.030987251549959183, 0.0780729427933693, 0.01391236949712038, 0.004959178622812033, -0.062035202980041504, 0.0037308689206838608, 0.05936194956302643, -0.017929816618561745, 0.019271085038781166, -0.012940151616930962, -0.03988519310951233, -0.017123745754361153, 0.043904997408390045, 0.061463650315999985, -0.009190374054014683, 0.03339064493775368, 0.012321379967033863, 0.0930694043636322, 0.013583497144281864, -0.046895965933799744, 0.03313830494880676, 0.06789114326238632, -0.002041539642959833, -0.015395436435937881, -0.008001659996807575, -0.018397880718111992, -0.03230844810605049, 0.04750233143568039, 0.021429583430290222, 0.000003851626843243139, 0.015441962517797947, -0.028094181790947914, -0.021738050505518913, -0.009164806455373764, -0.023502014577388763, 0.06063702702522278, 0.010479731485247612, 0.017218342050909996, -0.012600292451679707, 0.04085027053952217, -0.031896937638521194, -0.017051730304956436, 0.0398322269320488, 0.0009777580853551626, -0.021130964159965515, -0.019405420869588852, 0.032522618770599365, 0.019161906093358994, -0.05233222618699074, -0.07016553729772568, -0.014095264486968517, -0.01976301334798336, -0.01812565140426159, 0.033216264098882675, 0.06507883965969086, -0.04203886166214943, 0.05313270911574364, 0.03859052434563637, -0.004179994110018015, -0.016448019072413445, 0.009933813475072384, 0.03485512360930443, -0.03632989898324013, -0.023444686084985733, 0.039155296981334686, -0.036741919815540314, 0.020778043195605278, -0.04729032889008522, 0.05177765339612961, 0.005017770919948816, -0.010231423191726208, -0.013724792748689651, 0.012613439001142979, -0.000021620762709062546, -0.03799218684434891, -0.06749966740608215, -0.02385695092380047, 0.010332024656236172, -0.039825402200222015, 0.00420707743614912, 0.004833626095205545, -0.008258272893726826, -0.035549722611904144, 0.047336358577013016, -0.04806961491703987, -0.007538703735917807, -0.04393266886472702, -0.0036191940307617188, -0.0006349132163450122, 0.05316454917192459, 0.013056308031082153, -0.031880203634500504, -0.027775157243013382, 0.015178428031504154, 0.004585376940667629, 0.024614885449409485, -0.003269230481237173, -0.04780473932623863, 0.007519077975302935, -0.022133253514766693, 0.015148431994020939, 0.0011855937773361802, 0.017353663221001625, -0.009958027862012386, 0.016171516850590706, -0.019635844975709915, -0.025559833273291588, 0.00994549598544836, -0.048829175531864166, -0.0071099987253546715, -0.002039987361058593, 0.0430329404771328, 0.024492302909493446, 0.010459626093506813, 0.054171815514564514, -0.0599471777677536, 0.0062802559696137905, -0.026691127568483353, 0.0031982932705432177, -0.01561441458761692, 0.02364010363817215, 0.047574304044246674, 0.00571279413998127, 0.018719742074608803, 0.02274254523217678, 0.025035176426172256, -0.024583473801612854, -0.011950516141951084, 0.056562792509794235, -0.08082583546638489, 0.006719688884913921, 0.000993704772554338, 0.0031192621681839228, 0.010047146119177341, -0.022086067125201225, 0.013817841187119484, -0.0550021193921566, -0.013238872401416302, 0.02845493145287037, 0.040954191237688065, -0.004956831224262714, -0.010023119859397411, 0.03587291017174721, 0.039803724735975266, -0.03070436231791973, 0.03547972813248634, 0.02245457097887993, 0.03834223747253418, 0.008002139627933502, -0.015953879803419113, -0.047829240560531616, -0.03965888172388077, -0.01185627467930317, 0.014496398158371449, 0.026469649747014046, -0.011387413367629051, -0.055634066462516785, 0.07438267022371292, 0.012037482112646103, -0.07547733187675476, 0.05225207656621933, -0.02937636896967888, 0.04164262115955353, -0.010762396268546581, -0.022526880726218224, -0.004562624264508486, 0.061266522854566574, 0.009001088328659534, -0.08942968398332596, 0.051674675196409225, 0.040549810975790024, -0.016690323129296303, 0.05137474089860916, -0.0029678763821721077, 0.04214536398649216, -0.07540959864854813, -0.04816761240363121, 0.01512932125478983, 0.0475032664835453, -0.06501314043998718, -0.039338935166597366, 0.01647331565618515, 0.06344066560268402, -0.061814066022634506, 0.01894449256360531, -0.03536568582057953, -0.032575830817222595, 0.02720320038497448, 0.041592229157686234, -0.0056395274586975574, -0.05015673115849495, 0.023455984890460968, 0.02841770276427269, -0.031176503747701645, -0.010252497158944607, 0.02852732315659523, 0.018299508839845657, -0.0705627053976059, 0.024599594995379448, -0.03552054986357689, 0.02365989424288273, 0.016686923801898956, -0.0019494182197377086, -0.020388007164001465, -0.0043494077399373055, -0.03251232951879501, -0.04129251465201378, 0.007634511683136225, 0.003862883662804961, 0.010065766982734203, -0.019403256475925446, 0.02648383378982544, -0.042573656886816025, 0.025975966826081276, -0.001677805557847023, -0.009841092862188816, -0.0048253280110657215, 0.0009872287046164274, 0.00795272272080183, 0.01916959509253502, -0.04763931781053543, -0.011908110231161118, 0.0659172534942627, 0.0006595741724595428, -0.00536548625677824, 0.0022951525170356035, -0.035013943910598755, 0.04302093759179115, 0.025834186002612114, 0.013984118588268757, 0.04943979158997536, 0.09724903851747513, 0.039798084646463394, 0.055864110589027405, 0.02974630333483219, 0.04511383920907974, -0.09503607451915741, 0.0572502538561821, 0.0019968042615801096, -0.05524326488375664, 0.021638907492160797, 0.003764417488127947, -0.037170931696891785, 0.07471968233585358, -0.025854723528027534, -0.00380542129278183, -0.1022089347243309, -0.013960011303424835, -0.025930192321538925, 0.006197512149810791, 0.015341339632868767, 0.0549941211938858, -0.019133323803544044, 0.016438601538538933, 0.02593226730823517, 0.06203104555606842, 0.01986122690141201, 0.03288025036454201, -0.03564680740237236, 0.011703220196068287, -0.010986421257257462, -0.010583632625639439, 0.04802190884947777, 0.022003060206770897, -0.07059688866138458, -0.002685468876734376, -0.00913289561867714, -0.027611812576651573, -0.042327262461185455, -0.03761952370405197, -0.06719254702329636, 0.028442692011594772, -0.0643763542175293, -0.03995901718735695, -0.04575261473655701, 0.011632751673460007, 0.038915712386369705, -0.021910054609179497, -0.03438631072640419, 0.006518205162137747, 0.013861465267837048, -0.013855664059519768, 0.01017075777053833, 0.10359194874763489, 0.029588792473077774, 0.04208723083138466, 0.009431738406419754, -0.04304744303226471, 0.026113713160157204, 0.011347255669534206, -0.024610329419374466, 0.024232855066657066, -0.017148183658719063, 0.01645648665726185, 0.005423812661319971, -0.008625335991382599, 0.039408128708601, -0.06740491092205048, -0.0020693012047559023, -0.03441620245575905, 0.048393312841653824, -0.033448465168476105, -0.06407081335783005, 0.004490536171942949, -0.04473017156124115, -0.013532892800867558, 0.021167650818824768, 0.00032085934071801603, -0.05585339292883873, 0.02949412725865841, -0.005829528905451298, -0.02469673939049244, 0.08412609994411469, -0.007727038115262985, 0.06008012220263481, -0.011788612231612206, -0.05458072945475578, -0.02539738453924656, 0.04977291077375412, 0.019389552995562553, 0.02344699017703533, 0.0357021801173687, 0.04561717435717583, -0.06324602663516998, -0.02931041456758976, -0.06359490752220154, -0.053206898272037506, 0.0017699123127385974, -0.04401867091655731, -0.03382425010204315, 0.03154873847961426, 0.006841744761914015, 0.06139189377427101, 0.014802712947130203, 0.017739908769726753, 0.021051915362477303, 0.012150868773460388, 0.04140477627515793, -0.023796461522579193, -0.057148370891809464, 0.009010687470436096, -0.013542207889258862, 0.021010810509324074, -0.010645472444593906, 0.017151374369859695, -0.010513696819543839, -0.0415177084505558, -0.07319478690624237, 0.0032492445316165686, 0.08259500563144684, 0.021249976009130478, -0.01705213636159897, -0.00044628538307733834, 0.01160242035984993, -0.04092426970601082, 0.02487771213054657, 0.05473927780985832, 0.04559365659952164, -0.0372215174138546, 0.12330504506826401, 0.038351330906152725, 0.02814238704741001, 0.025577310472726822, 0.012212294153869152, 0.008278539404273033, 0.025918373838067055, -0.0005567042389884591, 0.020814554765820503, 0.015383142977952957, 0.037212271243333817, 0.058854829519987106, 0.03710956498980522, -0.025869321078062057, -0.019382433965802193, 0.020345386117696762, 0.06629795581102371, -0.0006161975907161832, 0.015966448932886124, 0.04263848811388016, 0.01130678504705429, -0.003872495610266924, 0.04205489158630371, 0.03966961428523064, 0.03678816929459572, -0.07704821974039078, -0.003783793654292822, -0.021858664229512215, -0.03537511080503464, 0.00492789875715971, 0.043609391897916794, 0.006371431052684784, -0.049141380935907364, -0.004783083219081163, -0.042201049625873566, -0.029082154855132103, -0.0036343098618090153, 0.021159108728170395, 0.024550970643758774, -0.01825074665248394, 0.007894761860370636, 0.03636736422777176, 0.06877200305461884, 0.054843720048666, -0.015506044961512089, -0.039584118872880936, -0.010118073783814907, -0.045699916779994965, 0.036486539989709854, -0.051762036979198456, 0.025582388043403625, -0.006675224285572767, 0.004965536762028933, 0.02437792532145977, -0.03400178253650665, -0.02833736315369606, -0.07403990626335144, -0.010386187583208084, -0.03969987481832504, -0.026572253555059433, 0.014389392919838428, -0.004308254923671484, -0.019492726773023605, 0.04394073411822319, 0.03245589882135391, -0.021008949726819992, 0.007608394138514996, -0.005995494779199362, -0.005887496750801802, 0.014273951761424541, -0.025581004098057747, 0.018475541844964027, 0.03036157600581646, -0.026552952826023102, -0.06646997481584549, 0.020400840789079666, -0.025301704183220863, 0.024692561477422714, 0.023988043889403343, -0.00832566898316145, 0.06493496149778366, 0.0008162761223502457, -0.006104466505348682, 0.011022848077118397, -0.02421841211616993, 0.06645912677049637, 0.027417588979005814, 0.005782239604741335, 0.01966722309589386, -0.009616914205253124, 0.03843247517943382, -0.06510532647371292, 0.010446388274431229, -0.01540383417159319, -0.019889097660779953, -0.0384153313934803, -0.009022222831845284, 0.013059882447123528, -0.03886795416474342, -0.05431631579995155, -0.0006501476746052504, 0.007557668723165989, 0.019959544762969017, 0.02329346165060997, 0.02379724197089672, -0.001906823250465095, 0.01766209676861763, -0.00006376610690494999, 0.00494159571826458, -0.011217255145311356, -0.004132486414164305, 0.0778231993317604, 0.0017713927663862705, -0.013225129805505276, 0.06437206268310547, 0.003427016781643033, 0.003901794319972396, 0.022453872486948967, -0.009142840281128883, 0.021099215373396873, -0.034700606018304825, -0.029791051521897316, -0.005653756204992533, -0.0099249929189682, -0.0195322185754776, -0.011481662280857563, 0.05328892543911934, 0.07168640941381454, 0.006576360668987036, -0.034595176577568054, 0.04354533925652504, -0.06883133202791214, 0.03357727825641632, -0.008722065016627312, 0.05353729799389839, 0.030145110562443733, -0.004575468599796295, -0.037720222026109695, -0.02491125278174877, -0.003190230345353484, 0.03434490039944649, -0.023408547043800354, -0.038987673819065094, 0.006038075778633356, -0.01940571703016758, -0.016355767846107483, -0.035553593188524246, 0.026295211166143417, 0.03806263953447342, 0.02006673626601696, -0.038151949644088745, 0.00370296579785645, -0.004180555231869221, -0.011975277215242386, -0.03917218744754791, 0.0017162341391667724, -0.019732225686311722, -0.007133085280656815, -0.02441546879708767, 0.07988195866346359, 0.008911289274692535, 0.014818337745964527, 0.036648500710725784, 0.03463498875498772, 0.012195445597171783, -0.02964646741747856, -0.013116452842950821, 0.026855409145355225, -0.03710866719484329, -0.013754012994468212, -0.013725883327424526, -0.010934751480817795, -0.031221413984894753, -0.028948428109288216, -0.060245580971241, -0.003664551069959998, -0.04500071331858635, -0.06513490527868271, -0.0072693475522100925, 0.013488484546542168, -0.02958325669169426, 0.02904263697564602, 0.00048635463463142514, -0.009303809143602848, 0.0637756958603859, -0.055771056562662125, -0.02985067293047905, 0.0198991522192955, 0.06974299252033234, -0.011085311882197857, 0.04450573772192001, 0.04847966134548187, 0.015354253351688385, -0.05053599551320076, -0.10936573147773743, 0.019519200548529625, -0.005528057925403118, 0.0010123446118086576, -0.05033332109451294, -0.011801701970398426, 0.019427143037319183, -0.07410112768411636, -0.02184153161942959, -0.029729261994361877, 0.06321355700492859, -0.01903165690600872, 0.07110361754894257, -0.02168281190097332, -0.017438454553484917, -0.05930107831954956, 0.03307601809501648, -0.023519445210695267, 0.06536846607923508, 0.012467319145798683, 0.01950985938310623, -0.050073012709617615, 0.0410093255341053, 0.0465017706155777, -0.036769360303878784, -0.0011817928170785308, -0.04792880639433861, -0.010483548045158386, 0.06489180028438568, -0.030223244801163673, -0.03691702336072922, 0.024260392412543297, -0.014838648959994316, -0.03969532251358032, -0.019707636907696724, 0.025445565581321716, 0.036933474242687225, -0.005528739653527737, 0.03757938742637634, -0.04233361780643463, -0.027949828654527664, -0.032951273024082184, -0.03563366457819939, -0.01569429226219654, -0.06230349838733673, -0.029166216030716896, 0.045485273003578186, -0.002706059953197837, -0.05593198165297508, -0.03346545994281769, 0.02629219740629196, 0.017018990591168404, -0.10123415291309357, -0.07490935176610947, 0.003907781094312668, -0.03911538049578667, -0.024119507521390915, -0.012140014208853245, 0.01627305895090103, 0.014099488966166973, 0.002615460893139243, 0.03284887969493866, -0.05848412215709686, 0.011672894470393658, -0.00545975798740983, 0.02700335532426834, 0.05164415389299393, 0.05067061260342598, 0.04745715484023094, -0.03170586749911308, 0.0753088891506195, -0.031380921602249146, 0.013639294542372227, -0.07922211289405823, -0.057296205312013626, -0.018049221485853195, -0.0224335677921772, 0.009159182198345661, -0.0058235591277480125, -0.00821574404835701, 0.06897265464067459, 0.05049063265323639, 0.0040724631398916245, -0.04758636653423309, -0.060432564467191696, -0.017065109685063362, 0.03192082792520523, -0.03285803645849228, -0.0466625802218914, 0.07951593399047852, 0.02434678003191948, -0.018779687583446503, 0.06562347710132599, -0.047953929752111435, -0.0010183134581893682, 0.04306897521018982, 0.01618419960141182, 0.023645155131816864, 0.033378031104803085, 0.06499867141246796, 0.004191883374005556, -0.004514005500823259, -0.01659053936600685, 0.06679088622331619, 0.04206375777721405, -0.042806752026081085, -0.008054852485656738, 0.008916877210140228, -0.014277360402047634, -0.0316874198615551, 0.01972946524620056, 0.03757436200976372, -0.04516918957233429, -0.06638702750205994, -0.009999314323067665, -0.0033177859149873257, 0.01207129005342722, -0.06193339452147484, -0.04197671636939049, -0.03904552012681961, -0.01810525916516781, -0.022786617279052734, -0.007493340875953436, -0.014503774233162403, -0.04171088710427284, 0.0023412369191646576, 0.018024111166596413, 0.027882369235157967, -0.005158829502761364, 0.004369622096419334, -0.06977003812789917, -0.0352177694439888, -0.003901967778801918, 0.018543964251875877, -0.051955122500658035, -0.04108044132590294, 0.017475085332989693, 0.005546125117689371, 0.026253145188093185, 0.03989708423614502, 0.020587630569934845, -0.034960873425006866, 0.041280634701251984, -0.08286699652671814, 0.012506545521318913, -0.01528728473931551, 0.011711071245372295, -0.0038305819034576416, -0.023727985098958015, 0.03148484230041504, -0.003439590334892273, -0.04652821645140648, 0.059765301644802094 ]
<p>I am very puzzled by the quintet of Higgs bosons in the MSSM: two charged, two scalars and a pseudoscalar. I wonder if they could be understood better if they were considered jointly with the three "bosons" that are "eaten" by the Higgs mechanism. For instance, if they were two charged bosons and a pseudoscalar one, then the whole set should be four charged, two pseudoscalars and two scalars, which seems more sensible if you wish, for instance, reorder them into chiral and dirac supermultiplets jointly with the higgsinos.</p> <p>I have been reminded of this question because it seems that now LHC is trying to guess if the discovered Higgs boson is a pseudoscalar or an scalar, and they are doing this by looking how it couples to ZZ, if it is to transversal or to longitudinal modes.</p>
g5423
[ 0.04907093942165375, 0.03807230293750763, 0.0013313560048118234, -0.013857394456863403, 0.06644705682992935, -0.04450604319572449, 0.024136710911989212, 0.0485161617398262, -0.0011080199619755149, 0.014823157340288162, -0.06499717384576797, 0.015452242456376553, 0.0014063065173104405, 0.05553751811385155, 0.0006823969888500869, -0.02951659820973873, -0.0460849329829216, 0.060887422412633896, 0.03966549038887024, 0.013979948125779629, 0.014516156166791916, 0.018246255815029144, -0.033840954303741455, -0.048185501247644424, -0.06197130307555199, 0.02196519449353218, 0.022036492824554443, -0.0030482206493616104, 0.052183546125888824, -0.05502697825431824, 0.039643216878175735, 0.012316370382905006, 0.06118299439549446, 0.0023043774999678135, -0.03710338473320007, -0.06680979579687119, 0.07632584124803543, -0.012744477950036526, -0.04869594797492027, -0.025823431089520454, -0.04243476316332817, -0.05901874229311943, -0.024660201743245125, -0.01808493584394455, 0.010698748752474785, 0.05516023933887482, 0.013396093621850014, 0.029869485646486282, 0.02003055065870285, 0.00767675181850791, 0.0898795872926712, 0.01646498031914234, 0.03267749771475792, 0.07254717499017715, 0.0005819303332827985, 0.03172949701547623, 0.046468209475278854, -0.011339603923261166, 0.08589329570531845, 0.006820795126259327, -0.009447860531508923, 0.04012760519981384, 0.009772227145731449, 0.007520732004195452, 0.05339495837688446, -0.01739601232111454, -0.03857399523258209, 0.017581462860107422, 0.003821936435997486, -0.013923904858529568, -0.026133611798286438, -0.01189198438078165, 0.03556923568248749, 0.0462677925825119, -0.02539338357746601, -0.030402004718780518, -0.02672053873538971, -0.0006214290042407811, -0.055999234318733215, -0.001237229909747839, 0.015978118404746056, -0.04928279668092728, 0.0037068487145006657, 0.015460082329809666, 0.051103562116622925, -0.02362370491027832, -0.011295183561742306, -0.012930515222251415, -0.03438861668109894, -0.021659711375832558, -0.060153644531965256, -0.08633876591920853, 0.026087205857038498, -0.002936007920652628, -0.05476279556751251, -0.06838630884885788, -0.008601675741374493, 0.022789355367422104, -0.014985524117946625, -0.006988854147493839, 0.005854325834661722, 0.03398093953728676, 0.03693480044603348, 0.0034406823106110096, -0.049410462379455566, 0.008296596817672253, 0.04280032590031624, 0.03518300503492355, 0.042621489614248276, 0.013187689706683159, -0.04640419781208038, 0.00795977097004652, 0.009613359346985817, -0.04029408469796181, -0.03948168829083443, -0.03734284266829491, 0.03606028109788895, 0.018762335181236267, -0.01804545894265175, 0.026600096374750137, 0.0352533757686615, -0.02484864741563797, 0.0274246446788311, -0.030390437692403793, 0.006177918985486031, 0.017261337488889694, -0.012425459921360016, 0.013726835139095783, -0.017561031505465508, -0.04038402810692787, -0.020986102521419525, -0.048284031450748444, 0.009797702543437481, 0.03679826855659485, 0.024793170392513275, 0.04357488080859184, 0.03803176060318947, 0.01256820559501648, -0.011753038503229618, -0.01746712625026703, 0.02148384042084217, -0.040650371462106705, -0.0003222298691980541, -0.005598151125013828, -0.006732705980539322, 0.003539390629157424, -0.028776070103049278, -0.03919583559036255, -0.032938651740550995, 0.008455857634544373, 0.10279253125190735, 0.06330890208482742, 0.019810818135738373, -0.045894086360931396, -0.05809793621301651, 0.029008109122514725, 0.0750780701637268, 0.012342422269284725, -0.011113855987787247, 0.042600762099027634, -0.03389883041381836, -0.018029671162366867, -0.029887134209275246, -0.025752214714884758, -0.056069161742925644, 0.018096573650836945, 0.06466460973024368, -0.005105651915073395, 0.008363918401300907, 0.028935233131051064, 0.008592887781560421, 0.010097651742398739, -0.03202112764120102, 0.07153596729040146, 0.05339683219790459, 0.07415656000375748, -0.011574401520192623, -0.06715021282434464, 0.03596562147140503, 0.0746113657951355, 0.006550883874297142, 0.027084173634648323, -0.03660528361797333, 0.025100912898778915, 0.015203230082988739, 0.010619481094181538, -0.02485203742980957, 0.037116359919309616, 0.06849966198205948, 0.025099044665694237, -0.0038696760311722755, 0.006113835610449314, 0.004903027322143316, -0.019395384937524796, 0.0697515606880188, -0.04088418558239937, 0.06479940563440323, -0.0032301160972565413, -0.017705097794532776, -0.03468416631221771, -0.011230114847421646, -0.022937439382076263, -0.005262470338493586, -0.003429495031014085, 0.029126979410648346, 0.020806070417165756, -0.019913777709007263, -0.03498280793428421, 0.06561735272407532, -0.03208717331290245, -0.043929871171712875, -0.044371455907821655, -0.022387854754924774, 0.007695407141000032, 0.02941282093524933, -0.058773357421159744, -0.0348210446536541, 0.03687134012579918, 0.019498789682984352, -0.011329112574458122, -0.08141424506902695, -0.03630092740058899, 0.014989483170211315, -0.020374568179249763, 0.044812850654125214, 0.03390385955572128, 0.015762336552143097, -0.06247760355472565, -0.019144127145409584, 0.04453841224312782, -0.005769904237240553, -0.016896285116672516, -0.02101053111255169, -0.04536186531186104, -0.036222103983163834, 0.003227048320695758, -0.04648512601852417, 0.018913740292191505, 0.027308152988553047, 0.012613311409950256, 0.09863206744194031, -0.008630364201962948, 0.012215765193104744, -0.021655574440956116, 0.04249082878232002, 0.014876332134008408, 0.06267035752534866, 0.019036103039979935, -0.0298711396753788, 0.01612096279859543, -0.0018785946303978562, -0.03181429207324982, 0.018238920718431473, -0.029664481058716774, -0.010181987658143044, -0.025787832215428352, 0.07653645426034927, -0.018154826015233994, -0.07551826536655426, -0.022769823670387268, 0.02008630521595478, -0.010631930083036423, -0.04051368683576584, 0.02084396407008171, -0.06208305433392525, -0.052975427359342575, 0.02256244607269764, -0.0002593924291431904, -0.039114199578762054, -0.01730191335082054, 0.0011840471997857094, -0.016345206648111343, 0.042710933834314346, 0.030652616173028946, -0.016125909984111786, 0.0009615116287022829, 0.013310941867530346, -0.014564943499863148, 0.006095205899327993, -0.08041545003652573, -0.007491142954677343, -0.007904230616986752, 0.020942116156220436, 0.007557894103229046, 0.012652471661567688, 0.008297041058540344, -0.055244188755750656, -0.03532206267118454, -0.029997700825333595, 0.04197625815868378, 0.0014773370930925012, -0.053197119385004044, 0.03039264678955078, -0.03424185886979103, 0.0074621024541556835, 0.03542115166783333, 0.046597905457019806, -0.003725126851350069, -0.06020427495241165, 0.0389462485909462, 0.007135688327252865, 0.012521528638899326, -0.02079126052558422, -0.004595783539116383, 0.038158174604177475, 0.008007478900253773, -0.035254694521427155, 0.019312866032123566, -0.013257412239909172, -0.0324239581823349, -0.031680140644311905, 0.05365166813135147, -0.043668705970048904, 0.032894548028707504, 0.007763160392642021, -0.007543460000306368, -0.03450509160757065, 0.029895514249801636, -0.022939370945096016, 0.032092295587062836, -0.007910707965493202, 0.03407769650220871, 0.045984212309122086, -0.028240639716386795, 0.009863746352493763, 0.04808025807142258, -0.023949744179844856, -0.025338467210531235, -0.05797595903277397, -0.00991215929389, 0.026610737666487694, -0.009592856280505657, 0.029311586171388626, 0.053157225251197815, -0.011335418559610844, -0.004408380016684532, -0.03274087980389595, -0.0025582383386790752, 0.05454550310969353, 0.02168714627623558, -0.00726004084572196, -0.0068380520679056644, -0.03559974581003189, -0.031842272728681564, -0.04135048761963844, -0.006891457363963127, -0.025855502113699913, -0.04396539926528931, 0.05427469685673714, -0.06703386455774307, 0.014280510134994984, 0.05731837451457977, 0.009257815778255463, 0.034830283373594284, -0.01841016486287117, -0.02554829604923725, -0.029184777289628983, 0.02918185479938984, -0.00883740745484829, -0.018788732588291168, 0.04303711652755737, -0.028769439086318016, -0.009599382989108562, -0.04185807332396507, 0.044110123068094254, -0.04154711589217186, -0.04984037205576897, 0.031774185597896576, 0.05386453494429588, 0.02133302390575409, -0.028919048607349396, -0.001305640209466219, 0.005934918764978647, 0.006463670637458563, -0.03505757078528404, -0.05731135979294777, 0.010892919264733791, -0.019216466695070267, 0.06879398226737976, -0.005704808048903942, -0.012359733693301678, 0.02410065568983555, 0.05740999057888985, -0.006563618313521147, 0.03459328040480614, 0.02400391362607479, 0.004156442359089851, -0.007896947674453259, -0.05702529475092888, 0.011941112577915192, -0.0364028736948967, 0.011207448318600655, -0.04685606807470322, -0.010562220588326454, 0.02170371636748314, -0.02813643217086792, 0.01208004541695118, -0.02572520449757576, 0.022097257897257805, 0.0053047132678329945, -0.01623811013996601, -0.028440196067094803, -0.032929252833127975, -0.0993928462266922, -0.037724558264017105, 0.01260156836360693, 0.004117551725357771, -0.03745954856276512, 0.09820450842380524, -0.014414101839065552, 0.008615762926638126, 0.03182957321405411, 0.036438800394535065, 0.05064435303211212, 0.024876775220036507, -0.04068867117166519, 0.014706423506140709, -0.011583147570490837, -0.017625581473112106, 0.018981756642460823, -0.03649970516562462, 0.03690950572490692, -0.030247239395976067, 0.004882837645709515, -0.018852371722459793, 0.10466352850198746, 0.006639290601015091, 0.04364557936787605, -0.043060943484306335, 0.004739753436297178, 0.08607511222362518, 0.003573742927983403, -0.04445713758468628, -0.00039015302900224924, -0.02570665068924427, -0.0039212568663060665, -0.11497323960065842, -0.01972745545208454, -0.052521850913763046, 0.06625572592020035, 0.04247051477432251, 0.021028604358434677, -0.016444245353341103, -0.02253347635269165, 0.055034343153238297, -0.02073546312749386, -0.04305510222911835, 0.015642385929822922, -0.016225360333919525, -0.025447307154536247, 0.018313875421881676, 0.06635263562202454, -0.02390616200864315, -0.005343044176697731, 0.06173780933022499, 0.007982353679835796, -0.013110694475471973, -0.020388854667544365, -0.005565289873629808, 0.007608606945723295, -0.056226953864097595, -0.0010947611881420016, 0.006783138494938612, 0.0019413677509874105, 0.08698740601539612, 0.005824754014611244, -0.029346764087677002, -0.028996000066399574, 0.011812732554972172, -0.05122062936425209, 0.06333320587873459, -0.0452241525053978, 0.0033391148317605257, -0.06815090030431747, 0.060412000864744186, -0.12157781422138214, -0.04817838966846466, 0.021779842674732208, -0.06594879925251007, -0.022356918081641197, 0.008079007267951965, 0.0340927392244339, -0.0034146695397794247, -0.03805767744779587, -0.0002317783801117912, 0.03677549213171005, -0.002526633208617568, -0.07268495857715607, 0.03836991637945175, -0.017324723303318024, -0.01132070180028677, 0.01623358204960823, -0.0014865659177303314, 0.02260877937078476, -0.0024496600963175297, -0.010477849282324314, -0.060686178505420685, -0.02626526542007923, 0.048134803771972656, 0.011765479110181332, 0.046664074063301086, 0.027553237974643707, -0.012219174765050411, 0.010941063053905964, -0.04418148845434189, 0.04533297196030617, 0.05399586260318756, -0.0414779968559742, -0.01828862354159355, 0.06839243322610855, -0.014232909306883812, -0.020718397572636604, 0.005093622952699661, 0.029579564929008484, 0.00038328111986629665, -0.03750146925449371, 0.03491580858826637, 0.007904755882918835, 0.05455441400408745, -0.0487365648150444, -0.0030039879493415356, 0.01902698166668415, -0.03155161440372467, -0.017995012924075127, 0.003083447925746441, -0.018275883048772812, -0.03608924522995949, 0.013886530883610249, 0.016960127279162407, 0.01625010557472706, -0.017547734081745148, -0.04439377412199974, 0.027310404926538467, 0.020060796290636063, 0.06358750909566879, -0.008774803020060062, -0.02433314174413681, -0.010492471046745777, 0.013866429217159748, 0.043131791055202484, -0.009756896644830704, -0.08331023901700974, 0.017541173845529556, 0.028204696252942085, 0.001619661576114595, -0.033039916306734085, 0.009704424068331718, 0.01730598323047161, 0.01680583506822586, -0.024707548320293427, -0.07905181497335434, 0.04600720480084419, 0.0024999489542096853, 0.005938775837421417, 0.010097241960465908, 0.006174997426569462, 0.035461876541376114, 0.00975614134222269, 0.007061467971652746, 0.024320010095834732, 0.004158153664320707, 0.06329706311225891, -0.020430458709597588, -0.011321541853249073, 0.01253454852849245, -0.024275396019220352, 0.007125804666429758, -0.03058846853673458, 0.06119847297668457, -0.062097787857055664, -0.0028672227635979652, -0.05085858702659607, 0.03315969929099083, 0.07958897948265076, 0.06323090195655823, 0.05158158391714096, -0.004250203724950552, 0.022883711382746696, 0.0023088427260518074, 0.01771269366145134, 0.03595956042408943, -0.03204222768545151, 0.004662605002522469, -0.014420741237699986, 0.02799711935222149, 0.011109710671007633, -0.012268511578440666, -0.007830695249140263, -0.004402275197207928, -0.0035064422991126776, 0.0002466663427185267, 0.004042495507746935, -0.03397413343191147, 0.028541039675474167, -0.008085163310170174, 0.05969997122883797, 0.051711905747652054, 0.033247582614421844, -0.041110388934612274, -0.029293866828083992, 0.07104818522930145, 0.02762744389474392, -0.0015050770016387105, -0.010650012642145157, 0.03415679559111595, 0.03364546597003937, 0.03189597278833389, 0.02495376020669937, -0.055402182042598724, 0.05476684868335724, -0.033066242933273315, 0.035704899579286575, -0.049127884209156036, 0.004639957100152969, 0.06877382099628448, -0.04577244445681572, 0.0444147065281868, -0.0003665622207336128, -0.041419148445129395, 0.014379234053194523, 0.026164419949054718, -0.02508813887834549, -0.005787698086351156, -0.02587113529443741, 0.04665123671293259, 0.01417281199246645, 0.022850196808576584, -0.04343023896217346, 0.035926952958106995, 0.0036875884979963303, 0.03980818763375282, 0.000601876643486321, 0.08551708608865738, 0.024812282994389534, 0.0029899519868195057, -0.009272010996937752, -0.04899860545992851, -0.004331354517489672, -0.03237394988536835, -0.01694289781153202, 0.013086823746562004, -0.003956233151257038, 0.04035428911447525, -0.08397158980369568, -0.0426151305437088, 0.014487055130302906, 0.00043377914698794484, 0.023466642946004868, -0.00537156593054533, -0.022094128653407097, -0.014401610009372234, -0.013131409883499146, 0.014090515673160553, 0.008023268543183804, -0.058067306876182556, -0.03205011039972305, 0.004571802914142609, -0.009411133825778961, 0.03609756752848625, -0.013744966126978397, -0.05858434736728668, 0.024235235527157784, 0.042035359889268875, -0.0499783493578434, 0.0015968263614922762, 0.028548089787364006, 0.05615880712866783, -0.07470064610242844, -0.03979076072573662, -0.017392169684171677, -0.031030647456645966, -0.06455617398023605, -0.05123961344361305, 0.01887141540646553, -0.04044531658291817, -0.04864615574479103, 0.03552805632352829, 0.009571284055709839, -0.020738976076245308, 0.00833441037684679, 0.020442645996809006, -0.024747073650360107, 0.04752187058329582, 0.0581418015062809, -0.03270003944635391, 0.03554512560367584, 0.005634462460875511, -0.046819910407066345, -0.013466902077198029, -0.01151872519403696, 0.06546418368816376, -0.0009844428859651089, 0.06257003545761108, -0.018721211701631546, 0.01186930388212204, 0.029949845746159554, -0.0035155867226421833, 0.07761223614215851, -0.005678082816302776, 0.04191294685006142, -0.04761066287755966, -0.018830209970474243, 0.010189677588641644, -0.0023272887337952852, 0.0040237922221422195, -0.006000160705298185, -0.028134997934103012, 0.0016634223284199834, -0.0013476088643074036, -0.0793846845626831, -0.04942794144153595, 0.056413937360048294, 0.01406456995755434, 0.0699445903301239, -0.0004701817233581096, -0.05611741542816162, -0.0020159638952463865, -0.005881754215806723, 0.010891054756939411, -0.045864082872867584, -0.012324297800660133, 0.000050245340389665216, 0.013226713985204697, -0.027559489011764526, -0.046660780906677246, -0.06624921411275864, -0.009583576582372189, 0.04588521644473076, 0.011943873018026352, 0.05848603695631027, -0.03480177000164986, -0.025369837880134583, -0.03440852090716362, -0.00655176118016243, -0.03526785224676132, -0.028184667229652405, 0.045310862362384796, 0.05668167397379875, 0.048540107905864716, -0.00831852201372385, -0.02773675136268139, -0.053646378219127655, 0.015264765359461308, -0.025709383189678192, -0.0209951288998127, -0.003468545852228999, -0.05174766853451729, -0.04247739911079407, 0.014524057507514954, 0.05505653843283653, 0.04999080300331116, -0.05295518785715103, -0.024392729625105858, 0.04017530381679535, 0.023395242169499397, -0.004304482601583004, 0.017830243334174156, 0.03749516233801842, -0.06594762951135635, 0.00654061883687973, -0.02208119072020054, -0.03401289880275726, 0.014407023787498474, 0.017850415781140327, -0.018411831930279732, -0.03708120062947273, -0.035630106925964355, -0.025818265974521637 ]
<p>I read what is <a href="http://en.wikipedia.org/wiki/Computational_science" rel="nofollow">computational science</a> in Wikipedia but the explanation and understanding are not very clear. </p> <p>So, I could you please give a simple example computational science project and what all basic skills a person should have?</p> <p>Also, </p> <ol> <li>Does computational science involves programming?</li> <li>How different are computational science and computational materials science?</li> <li>I am from Electrical and Computer Science (basically programming) background. I was assigned a computational materials science project. So, is it in my scope?</li> </ol> <p>Probably, the prof assigned based on what individual subjects I studied (Engineering Math, Engineering Physics, Engineering Chemistry, Probability, Programming).</p>
g5424
[ 0.05346021428704262, 0.030849618837237358, 0.028921501711010933, 0.012417943216860294, 0.03339780122041702, -0.029408294707536697, -0.05289042368531227, 0.02471349388360977, -0.004714696668088436, -0.03337600827217102, -0.012599378824234009, 0.02760896645486355, 0.028852663934230804, -0.011608963832259178, -0.022905267775058746, 0.0606003999710083, 0.005283437203615904, 0.004211358726024628, 0.020055001601576805, -0.0069321137852966785, 0.017430787906050682, -0.0013108219718560576, 0.05668410286307335, -0.07386408746242523, -0.06419683247804642, 0.046977560967206955, -0.007105487864464521, -0.02519133687019348, -0.0539025142788887, 0.009802490472793579, -0.055826492607593536, 0.007551899645477533, 0.005310051143169403, -0.04517398402094841, -0.021633664146065712, -0.02014448679983616, -0.016739577054977417, -0.060327403247356415, 0.053729522973299026, -0.009431756101548672, -0.048960380256175995, 0.006015116814523935, 0.019186127930879593, -0.001910160412080586, -0.010205057449638844, -0.00481143593788147, -0.01998177170753479, -0.05951859802007675, 0.037776973098516464, 0.004606030415743589, 0.043101102113723755, 0.024833781644701958, 0.01738213747739792, 0.024935945868492126, 0.016560805961489677, -0.04115057364106178, -0.01347954012453556, -0.017556961625814438, 0.1034768745303154, -0.07902294397354126, 0.017026061192154884, 0.04951883479952812, -0.05508957430720329, 0.006556373089551926, -0.022456500679254532, 0.0077370647341012955, 0.044239167124032974, 0.026387829333543777, 0.05167852342128754, 0.04030372574925423, -0.019048728048801422, -0.013593115843832493, -0.021798644214868546, -0.030429402366280556, -0.02422606386244297, 0.021174710243940353, -0.014449144713580608, -0.026026729494333267, 0.035393521189689636, 0.0418839231133461, 0.024434082210063934, 0.004233180079609156, -0.02346685901284218, 0.04164191335439682, -0.0022562157828360796, -0.04755660519003868, -0.13480904698371887, -0.034137122333049774, -0.0060012927278876305, -0.004875882063060999, -0.03016943670809269, 0.052295077592134476, 0.018204422667622566, 0.01283399946987629, 0.017002929002046585, 0.01818029209971428, -0.0529535710811615, -0.02757798321545124, 0.04473673924803734, 0.01614619791507721, -0.01472622063010931, -0.050635382533073425, 0.00578496465459466, -0.03627105802297592, 0.009668526239693165, 0.046776287257671356, 0.001364633091725409, 0.032057616859674454, -0.08741442114114761, 0.02708396688103676, -0.024573123082518578, -0.008183284662663937, -0.10033760964870453, 0.010045994073152542, -0.020748890936374664, 0.02511567808687687, 0.027128033339977264, -0.020304810255765915, 0.05553469806909561, 0.03480275720357895, -0.026255423203110695, -0.010782378725707531, 0.07077918946743011, -0.0022307331673800945, 0.011392339132726192, -0.003599420189857483, 0.027850914746522903, 0.0053530228324234486, -0.0027091135270893574, -0.04867913946509361, 0.020001783967018127, -0.015590893104672432, -0.03509853035211563, 0.026551946997642517, -0.020138630643486977, 0.01394727360457182, -0.02211456373333931, 0.010200283490121365, 0.0686211884021759, 0.016395526006817818, -0.008198677562177181, 0.008164143189787865, -0.04397473856806755, -0.038149673491716385, -0.012731511145830154, 0.006784140132367611, -0.04235221445560455, 0.06505070626735687, 0.0026220236904919147, -0.005004707723855972, 0.030104314908385277, 0.048971064388751984, 0.027777552604675293, -0.04500316083431244, 0.03773827850818634, 0.018803659826517105, -0.01827136240899563, -0.006028164643794298, 0.0032140242401510477, -0.01724066026508808, 0.07026631385087967, 0.025308851152658463, -0.011849590577185154, 0.08377210795879364, -0.04105240851640701, -0.0024482340086251497, -0.023133063688874245, -0.048967331647872925, 0.02605011686682701, -0.00912535935640335, 0.0045476690866053104, -0.014661220833659172, -0.007876223884522915, 0.03194855898618698, 0.03216884285211563, 0.00944986566901207, 0.05178464204072952, -0.00003901147283613682, 0.09136178344488144, -0.005491499323397875, -0.04888523742556572, 0.031978607177734375, -0.046306759119033813, 0.04468957334756851, -0.05889594554901123, -0.005340727511793375, 0.040697723627090454, 0.06463952362537384, -0.07830113917589188, 0.04661743715405464, -0.08125214278697968, -0.023181989789009094, -0.02798011340200901, -0.026425186544656754, -0.0037410033401101828, -0.048747919499874115, -0.036060839891433716, 0.0021785295102745295, -0.007637970615178347, -0.0868135616183281, 0.02787010744214058, 0.018070239573717117, -0.024419540539383888, 0.03264424949884415, 0.03602708876132965, 0.03300546854734421, -0.014768265187740326, 0.00042406897409819067, -0.013851760886609554, 0.011776916682720184, 0.03796941041946411, 0.020975347608327866, 0.02933577075600624, 0.01568027399480343, -0.040382131934165955, -0.01766255870461464, -0.09089789539575577, -0.04492327943444252, -0.04541401565074921, 0.027884317561984062, 0.0022440862376242876, -0.009973970241844654, 0.01643107831478119, 0.024065375328063965, 0.022921545431017876, 0.03006604127585888, 0.00385064329020679, 0.031702034175395966, 0.007542817387729883, -0.011681053787469864, 0.003243908751755953, -0.012169956229627132, -0.03536570817232132, -0.024679012596607208, 0.06422604620456696, 0.05374336242675781, 0.00000133372054733627, -0.02013329043984413, -0.002556024119257927, 0.01983203925192356, -0.014691879041492939, -0.0022841286845505238, 0.016672305762767792, -0.00797862745821476, 0.01218628790229559, -0.054408978670835495, 0.06003081426024437, -0.001517229015007615, -0.020964013412594795, 0.014175504446029663, 0.0118753332644701, -0.021270953118801117, -0.03187552094459534, 0.06831001490354538, -0.01941746100783348, -0.017474455758929253, 0.001774669042788446, 0.011479100212454796, -0.009603876620531082, 0.01109593827277422, 0.036826241761446, -0.06353713572025299, -0.006464844103902578, -0.013742418959736824, -0.015597661957144737, -0.010110384784638882, -0.05029004067182541, -0.028245912864804268, -0.005736676510423422, -0.0020409838762134314, 0.017329279333353043, 0.014810778200626373, -0.018933774903416634, -0.027410002425312996, -0.05687825381755829, -0.027707677334547043, 0.02278900519013405, 0.028068281710147858, 0.025786511600017548, -0.019962476566433907, -0.0021746535785496235, -0.07599876075983047, -0.03964592516422272, 0.061459608376026154, -0.020204540342092514, 0.024196695536375046, 0.006902569904923439, 0.012301575392484665, -0.038203731179237366, -0.0011692977277562022, -0.013506310991942883, -0.04047054424881935, 0.0006738046649843454, -0.015373406000435352, 0.017015479505062103, -0.0028819788713008165, 0.04067254811525345, 0.002590406918898225, -0.017521953210234642, 0.06642228364944458, -0.06432271748781204, -0.033285822719335556, 0.03745429962873459, 0.0022284386213868856, 0.004210818558931351, 0.011676223017275333, 0.020556559786200523, -0.013333448208868504, -0.05343346297740936, -0.020472055301070213, 0.03242330253124237, 0.022159915417432785, 0.06282030045986176, 0.04999544844031334, -0.0382327064871788, 0.021764477714896202, -0.03414411470293999, 0.029748287051916122, -0.02574104070663452, -0.05685962364077568, 0.008200339041650295, -0.04138157144188881, 0.049136947840452194, -0.0006492355023510754, 0.05304725468158722, 0.09197378158569336, 0.02737552858889103, -0.046125635504722595, -0.022314021363854408, 0.01497606374323368, 0.034329548478126526, -0.01018097996711731, -0.06215061619877815, -0.045137014240026474, -0.037547964602708817, -0.10498741269111633, 0.010567404329776764, -0.032605383545160294, 0.024230821058154106, -0.03029840998351574, 0.019594669342041016, -0.011477022431790829, 0.006342124659568071, -0.010581523180007935, 0.03298945352435112, 0.05290190130472183, 0.037742868065834045, 0.022221572697162628, 0.027165917679667473, -0.027897031977772713, 0.052533477544784546, 0.004537804983556271, 0.017027925699949265, 0.005188155919313431, -0.0182793028652668, -0.023284567520022392, -0.00959717109799385, 0.01051544863730669, 0.001979667227715254, 0.043752383440732956, 0.005769232288002968, -0.014386489987373352, -0.011981968767940998, 0.007392417639493942, -0.024423036724328995, 0.00374511512927711, 0.061489831656217575, 0.060301657766103745, 0.011895828880369663, -0.022245103493332863, 0.017115414142608643, -0.02942819707095623, 0.02967895194888115, 0.0012114389101043344, 0.04435545951128006, 0.003689691424369812, -0.010963977314531803, 0.014595291577279568, 0.008109877817332745, -0.022174540907144547, 0.008405053988099098, 0.033343762159347534, -0.012133652344346046, -0.09376654773950577, 0.0062451292760670185, -0.04103299602866173, -0.028197476640343666, 0.029323237016797066, -0.007143930997699499, -0.01275599468499422, 0.021746311336755753, -0.05823617801070213, -0.024227213114500046, 0.013640113174915314, 0.017168093472719193, -0.05323581025004387, -0.035695191472768784, 0.04545588418841362, -0.0018841681303456426, 0.022813059389591217, -0.05293811485171318, 0.05733208358287811, 0.004823039751499891, 0.03234967216849327, 0.029287751764059067, 0.012306593358516693, -0.0032782533671706915, 0.018105631694197655, -0.06966555863618851, 0.0019653229974210262, 0.0036601084284484386, -0.032384928315877914, -0.020735055208206177, 0.014786731451749802, 0.014011203311383724, -0.009932155720889568, -0.03949591517448425, -0.012878521345555782, -0.0341520719230175, 0.025907762348651886, 0.012099512852728367, -0.016976462677121162, -0.001079887617379427, 0.011916383169591427, 0.01872640661895275, 0.0432390533387661, -0.03429064527153969, -0.01917256973683834, 0.013540174812078476, -0.011716707609593868, 0.04835551232099533, 0.06044883280992508, -0.0039401003159582615, -0.004029631614685059, 0.006097719538956881, 0.01618427038192749, 0.06265676766633987, 0.06789789348840714, -0.031019438058137894, -0.007518203463405371, -0.01847984828054905, 0.006351640913635492, -0.025773607194423676, 0.037551864981651306, 0.023876149207353592, -0.024051202461123466, -0.06932302564382553, 0.0035633116494864225, -0.04587866738438606, 0.021417660638689995, 0.019873034209012985, 0.022199707105755806, -0.03622618317604065, -0.00039833056507632136, -0.014526440761983395, -0.024577440693974495, 0.014409003779292107, -0.0448899045586586, 0.013464527204632759, 0.04862557724118233, -0.016330627724528313, -0.0383678674697876, 0.00964534841477871, -0.005827363580465317, -0.024155162274837494, 0.009284477680921555, 0.055354587733745575, -0.08063693344593048, -0.02724648453295231, -0.0075654382817447186, -0.025041770190000534, -0.006484740413725376, 0.044784825295209885, -0.009249210357666016, 0.0206927303224802, -0.024649567902088165, 0.004452208522707224, -0.055306244641542435, -0.03997095301747322, 0.02401626668870449, 0.009455768391489983, 0.023171493783593178, 0.06280457973480225, -0.022043297067284584, 0.019767282530665398, 0.011214938014745712, -0.042340345680713654, 0.05719514936208725, -0.014010573737323284, 0.03215531259775162, 0.0514148585498333, -0.014581355266273022, 0.05746350437402725, 0.0010467161191627383, -0.04466303810477257, -0.03869706392288208, -0.015597492456436157, 0.002414281014353037, 0.02040840871632099, -0.0026609802152961493, -0.0027687475085258484, 0.0002789899881463498, -0.025512518361210823, -0.011957500129938126, -0.01095504965633154, 0.059180088341236115, -0.003258566837757826, -0.06303831934928894, 0.011357801035046577, 0.020955072715878487, 0.01768442615866661, 0.03277530521154404, 0.0003623147204052657, -0.007196578662842512, -0.036935463547706604, 0.007428918033838272, -0.028511788696050644, -0.017037732526659966, -0.08404196053743362, -0.05279124528169632, -0.030210381373763084, -0.010012136772274971, -0.016063880175352097, 0.056468091905117035, 0.008801541291177273, -0.06614816933870316, -0.01920616254210472, -0.0411200188100338, 0.026216838508844376, 0.06585883349180222, -0.012001353316009045, 0.02190271206200123, 0.0023794970475137234, 0.03906689211726189, 0.012278606183826923, -0.015616499818861485, -0.012550432235002518, -0.017436755821108818, 0.03429943695664406, 0.04834263026714325, 0.03724149614572525, 0.08771917968988419, 0.04283863306045532, 0.03761514648795128, -0.06966938078403473, 0.002852638717740774, 0.08557458221912384, 0.004339145962148905, 0.08664248138666153, -0.12913887202739716, -0.022585010156035423, -0.020572755485773087, 0.09663558751344681, -0.0010525101097300649, 0.010315454564988613, 0.05921022593975067, -0.017513038590550423, -0.06975342333316803, -0.004712868016213179, -0.039378974586725235, -0.009956387802958488, -0.054635196924209595, -0.014555713161826134, -0.05461062863469124, 0.06304755806922913, -0.0003681530652102083, -0.05726540461182594, -0.040728259831666946, 0.04364572465419769, 0.04307357221841812, -0.04767657071352005, -0.06826142966747284, -0.05685918778181076, 0.0014229363296180964, 0.028916003182530403, 0.02781028114259243, -0.017511023208498955, -0.0029096140060573816, -0.018325310200452805, -0.025714335963129997, 0.06711842864751816, 0.006772253662347794, 0.031884122639894485, -0.003882133634760976, 0.0013076585019007325, 0.06756636500358582, 0.04913022741675377, -0.0351862907409668, 0.026846809312701225, -0.028955016285181046, -0.04128185287117958, 0.005943531170487404, 0.0014112112112343311, 0.02290276437997818, -0.032691873610019684, -0.017698097974061966, 0.047736115753650665, 0.008470854721963406, 0.024579843506217003, 0.04061546176671982, 0.003384691197425127, 0.0430198572576046, 0.023053407669067383, 0.05424071103334427, -0.01569744013249874, 0.057620469480752945, 0.028680749237537384, -0.022290484979748726, -0.03380749374628067, -0.032168444246053696, -0.024881888180971146, 0.059376608580350876, 0.01846088282763958, -0.0042965710163116455, -0.01747445948421955, -0.05601353198289871, -0.04018070921301842, -0.034127891063690186, 0.058612752705812454, 0.004766842816025019, 0.06168832629919052, -0.028006477281451225, -0.009533855132758617, -0.026838958263397217, -0.0028849062509834766, 0.0718475729227066, -0.05327786132693291, 0.113795205950737, 0.0687187984585762, -0.03875748813152313, -0.04287831857800484, -0.022558586671948433, 0.014175177551805973, 0.12438992410898209, 0.003071113023906946, -0.0372537262737751, -0.07046599686145782, -0.007989668287336826, 0.01650114730000496, 0.01760450005531311, 0.011983204632997513, -0.026153722777962685, 0.02179894968867302, 0.01688983477652073, -0.00740032596513629, -0.06257864832878113, 0.018411384895443916, -0.009256218560039997, -0.03046487830579281, 0.013816220685839653, 0.006302265916019678, 0.008738751523196697, -0.0072501664981245995, -0.0337330661714077, -0.06546986848115921, 0.023645326495170593, -0.008996832184493542, 0.00941634550690651, 0.028594590723514557, -0.021365124732255936, -0.014120204374194145, 0.027435336261987686, -0.025451187044382095, -0.0411289818584919, 0.007374474313110113, 0.0678785964846611, 0.04491686075925827, -0.029331836849451065, -0.05371534451842308, 0.004385912325233221, -0.043238889425992966, -0.009254422038793564, 0.012005765922367573, 0.05232614278793335, 0.006349838338792324, -0.003947384189814329, 0.006865731440484524, -0.0138980932533741, 0.026573868468403816, -0.0492025688290596, 0.03457064926624298, 0.00023483982658945024, -0.008492879569530487, 0.03125438839197159, -0.021550672128796577, -0.0019786045886576176, 0.0014682586770504713, 0.056969888508319855, 0.010967743583023548, -0.03328631445765495, -0.010065536014735699, -0.008956988342106342, 0.011216528713703156, -0.10433298349380493, 0.04543832689523697, -0.006623909808695316, 0.05544165521860123, -0.027517355978488922, 0.05486647039651871, 0.022912677377462387, 0.01962696947157383, -0.03670433163642883, 0.028489865362644196, -0.03436011075973511, -0.03857574611902237, -0.005466172005981207, -0.05583043023943901, -0.0005635877605527639, -0.035180337727069855, -0.027693631127476692, -0.027617519721388817, 0.006093599833548069, 0.037630729377269745, -0.008011426776647568, -0.013236251659691334, 0.013550756499171257, 0.044932395219802856, -0.0034247534349560738, -0.02789822220802307, 0.047181498259305954, -0.02367379516363144, -0.06208246201276779, 0.0420323945581913, 0.015873651951551437, -0.011261017993092537, 0.05430558696389198, -0.002772374777123332, 0.018416253849864006, 0.00019575537589844316, 0.04287676885724068, 0.004380126483738422, -0.025203561410307884, -0.032152872532606125, -0.044671207666397095, 0.019673841074109077, 0.014412709511816502, 0.016047902405261993, 0.006585557945072651, -0.02837982587516308, 0.04065129533410072, -0.014463156461715698, 0.07401962578296661, -0.020918481051921844, -0.035778846591711044, -0.00350126507692039, -0.07368467003107071, -0.06283392012119293, 0.05514014512300491, 0.03166218474507332, -0.04547996073961258, -0.03869810700416565, 0.02221876196563244, 0.007367448415607214, 0.04575570672750473, 0.03299502655863762, -0.03429970517754555, -0.007337895222008228, 0.03129225969314575, 0.048471640795469284, -0.00626789266243577, -0.013631676323711872, 0.021520966663956642, -0.005918537732213736, -0.023400338366627693, -0.05723632872104645, 0.03826123848557472, -0.05076352506875992, 0.06597645580768585 ]
<p>Do you know why in the quantization of SU(2) Yang Mills Gauge Theory, it is always chosen the Weyl (temporal) gauge to derive the Hamiltonian?</p> <p>Is it possible to fix another gauge?</p>
g5425
[ 0.024926111102104187, -0.04085082188248634, -0.039705608040094376, -0.0244927816092968, 0.039403632283210754, -0.02317454293370247, 0.037121690809726715, 0.03802372142672539, -0.03490861877799034, 0.014378598891198635, 0.02920520305633545, 0.022311747074127197, -0.00002530203892092686, 0.06291290372610092, 0.019796252250671387, 0.02132761850953102, 0.10502268373966217, 0.004613974131643772, 0.03450765460729599, -0.04214094206690788, -0.06482992321252823, 0.018694957718253136, 0.04423147812485695, -0.08890485763549805, 0.0076900445856153965, -0.01508411206305027, 0.06308802962303162, 0.011412056162953377, 0.01619509980082512, 0.0549246110022068, -0.0016263395082205534, 0.008952081203460693, 0.04721047356724739, -0.07247186452150345, -0.01259384024888277, -0.030665287747979164, 0.035182952880859375, 0.007059634197503328, 0.017956890165805817, -0.011168998666107655, 0.026309704408049583, 0.0034915818832814693, -0.0020592445507645607, -0.019339831545948982, -0.05511824041604996, -0.026802565902471542, 0.003397594206035137, 0.019718701019883156, -0.008664583787322044, -0.02432367019355297, 0.04857750982046127, 0.03223910927772522, 0.05113401263952255, -0.06248020753264427, 0.06241302192211151, 0.024578357115387917, 0.016764841973781586, 0.015524933114647865, 0.03530632704496384, 0.07202649861574173, -0.009366940706968307, 0.04457579553127289, 0.04691101983189583, 0.05221676453948021, -0.0023877755738794804, 0.017236096784472466, -0.03876902535557747, -0.05300174653530121, 0.005411177407950163, -0.0024009253829717636, -0.005656222812831402, -0.058992404490709305, 0.013388154096901417, 0.046781811863183975, 0.04886457324028015, 0.05899366736412048, -0.0038864780217409134, 0.02645956538617611, -0.011497980915009975, -0.017423642799258232, -0.043908197432756424, -0.036210089921951294, -0.011228335089981556, -0.060361530631780624, 0.03951731696724892, -0.02715298719704151, 0.02028600126504898, 0.04380146786570549, -0.034884922206401825, 0.008596135303378105, -0.040914859622716904, -0.012444294057786465, 0.08191324770450592, 0.03748002275824547, -0.027430066838860512, 0.02414231188595295, -0.019871320575475693, 0.07290317118167877, -0.037105049937963486, 0.05073978751897812, -0.0712430402636528, 0.003467240370810032, 0.030249666422605515, -0.019219668582081795, 0.03711257874965668, 0.008619450032711029, 0.058484163135290146, -0.02906465344130993, 0.008140556514263153, -0.028994599357247353, -0.049414075911045074, 0.015358985401690006, 0.02288063056766987, 0.025953250005841255, -0.04648509621620178, -0.0005624429904855788, 0.020492978394031525, 0.033778414130210876, -0.03863818943500519, 0.02692900039255619, -0.019723601639270782, -0.08482031524181366, -0.04628770798444748, 0.020188650116324425, -0.014166200533509254, 0.01251332275569439, -0.07458579540252686, 0.013758444227278233, 0.06674260646104813, 0.011421900242567062, 0.008220324292778969, -0.0003377728571649641, -0.030479207634925842, 0.02750823274254799, 0.031565602868795395, -0.005124730058014393, 0.02001250721514225, -0.01619710959494114, 0.007648569997400045, 0.11572885513305664, -0.017725056037306786, -0.04187784716486931, -0.00511085195466876, -0.025880036875605583, 0.0026366314850747585, 0.05953149124979973, 0.0236178208142519, 0.01804438605904579, -0.013275419361889362, 0.00284641794860363, 0.000029341108529479243, 0.01636093109846115, 0.02714165486395359, 0.02411564253270626, 0.022166864946484566, -0.0441882386803627, 0.05469916760921478, 0.026279933750629425, 0.03231299668550491, -0.004727860447019339, 0.07600563764572144, -0.01358065940439701, 0.06405629962682724, -0.011612189933657646, -0.006801144685596228, -0.0035359191242605448, -0.022048193961381912, 0.004024263005703688, -0.00793145690113306, -0.039867062121629715, 0.006985978689044714, -0.011423238553106785, -0.05010080337524414, 0.0014668962685391307, 0.07178084552288055, 0.08677180856466293, -0.011175175197422504, 0.027048837393522263, -0.023279797285795212, 0.022259043529629707, -0.011828577145934105, 0.021115250885486603, -0.017346564680337906, -0.07460208982229233, -0.01335025392472744, 0.015459490939974785, -0.03233936429023743, 0.01993456669151783, -0.024049285799264908, -0.013244908303022385, 0.012869314290583134, -0.0025498592294752598, -0.0059701791033148766, 0.01705254055559635, -0.05172968655824661, 0.029414108023047447, 0.02488097734749317, -0.03234465792775154, -0.030809905380010605, -0.007053399924188852, -0.003927875775843859, 0.03671792149543762, 0.0026191810611635447, -0.0576072633266449, -0.02336784638464451, -0.03231241554021835, 0.03142830356955528, -0.004948181100189686, -0.01899673603475094, -0.008980575948953629, 0.03856098651885986, 0.047673549503088, 0.043661050498485565, 0.020476333796977997, -0.07972151786088943, -0.01994013600051403, 0.01312665268778801, 0.023015037178993225, -0.03477029874920845, -0.00912497192621231, -0.014401271939277649, 0.04005911573767662, 0.09409699589014053, 0.0026830832939594984, -0.028392823413014412, -0.0101703442633152, -0.013465930707752705, -0.021909840404987335, -0.06107397377490997, -0.0032073387410491705, -0.02317018434405327, -0.049245741218328476, -0.024948889389634132, -0.01258231420069933, 0.011125002056360245, 0.027633847668766975, -0.01661393977701664, -0.025237608700990677, 0.005530135706067085, -0.023845192044973373, -0.018979255110025406, 0.03480697423219681, 0.013635070994496346, 0.0016391162062063813, 0.05541399493813515, 0.0022977706976234913, 0.0231933631002903, 0.0018222799990326166, -0.0008899873355403543, 0.05389101803302765, 0.05315599963068962, 0.025122955441474915, -0.04327794536948204, -0.04901806265115738, -0.02035515569150448, -0.06001805514097214, 0.08381229639053345, -0.005421872716397047, -0.05323846638202667, -0.009365410543978214, -0.006963446736335754, -0.018263978883624077, 0.05708177015185356, 0.01589958369731903, -0.034637562930583954, 0.0050913430750370026, 0.03561943396925926, -0.004033992066979408, -0.037931930273771286, -0.05811392515897751, -0.06212158501148224, 0.030029403045773506, 0.017437472939491272, 0.02003847062587738, 0.015117820352315903, -0.01369430311024189, 0.018938960507512093, 0.003678484819829464, 0.003957797307521105, -0.019941534847021103, -0.02124267816543579, 0.04040573909878731, 0.003575375536456704, 0.048185620456933975, 0.013689037412405014, -0.04397379234433174, -0.06627354025840759, -0.06545405089855194, 0.04917366802692413, -0.002526259748265147, -0.011348782107234001, 0.009907502681016922, 0.013245034962892532, 0.045065492391586304, -0.00017294075223617256, -0.011159754358232021, 0.014458585530519485, 0.014789807610213757, -0.019301995635032654, 0.055939819663763046, 0.02340647019445896, 0.04281553626060486, -0.044409338384866714, -0.028465155512094498, 0.05977971851825714, 0.014098274521529675, -0.027172008529305458, 0.028371261432766914, 0.008022516965866089, -0.04887585714459419, 0.02232460305094719, 0.05437425151467323, 0.005889214109629393, -0.03437013179063797, -0.053536269813776016, 0.008098901249468327, -0.02847158908843994, -0.07204719632863998, -0.04133260250091553, 0.02220393903553486, -0.01687082089483738, 0.02484297566115856, 0.04218301549553871, -0.0018986179493367672, 0.0010484056547284126, 0.033470407128334045, -0.04726278781890869, -0.02457760088145733, 0.01287380512803793, -0.007326730061322451, 0.0008988695335574448, -0.10743458569049835, -0.04114405810832977, 0.00833819154649973, 0.006204942241311073, -0.04064270481467247, -0.039032358676195145, -0.03279081732034683, 0.009889080189168453, 0.02080082893371582, -0.01381700113415718, -0.019396470859646797, -0.00639883428812027, 0.04924268648028374, -0.03193172439932823, -0.022744910791516304, -0.0035313155967742205, 0.0186843853443861, 0.019030818715691566, -0.02502026967704296, -0.0007992886821739376, -0.012808479368686676, -0.033412765711545944, 0.011796155944466591, -0.00549661461263895, 0.015405353158712387, 0.008165860548615456, 0.07380027323961258, -0.017048539593815804, -0.0708797499537468, 0.017164206132292747, -0.004352705553174019, -0.02186479978263378, 0.04829592630267143, -0.0038494905456900597, 0.013163337484002113, -0.014551511965692043, 0.010045847855508327, 0.03782571852207184, -0.00738865090534091, 0.014178864657878876, -0.018884891644120216, -0.0009803847642615438, -0.007089067716151476, 0.07750941812992096, -0.020585279911756516, 0.01548747718334198, 0.012845614925026894, 0.006508315913379192, 0.03379136323928833, 0.001365077681839466, 0.017843613401055336, 0.009532365016639233, 0.016147242859005928, 0.019061528146266937, 0.007037484552711248, -0.04400940611958504, 0.026391230523586273, -0.010229906998574734, -0.0807914286851883, -0.05891580507159233, 0.005099685862660408, 0.005964664742350578, -0.04152431711554527, 0.0034248761367052794, 0.018618198111653328, 0.04531615972518921, 0.00795827992260456, 0.01941555179655552, -0.05765918269753456, -0.026165587827563286, -0.009278499521315098, -0.017853576689958572, -0.02828402630984783, -0.0050396970473229885, 0.05886627733707428, 0.04012654349207878, -0.01057598926126957, 0.025997968390583992, 0.006409956607967615, -0.10535944253206253, -0.02837473899126053, 0.04070182517170906, -0.0897170826792717, -0.05392957851290703, -0.05627236142754555, 0.006921438034623861, -0.03765830397605896, 0.016825441271066666, 0.022484343498945236, 0.06352312117815018, 0.050122786313295364, 0.008915254846215248, -0.028379956260323524, -0.012971756979823112, 0.07058080285787582, 0.018372531980276108, -0.043656229972839355, 0.022486062720417976, -0.03167947381734848, 0.07660646736621857, -0.01529975887387991, -0.01891169138252735, 0.014564583078026772, -0.06763483583927155, 0.012964305467903614, -0.00537980068475008, 0.02144779823720455, -0.07742572575807571, 0.052520982921123505, 0.10237152129411697, -0.018890105187892914, -0.012007875367999077, -0.006483276374638081, -0.03911247104406357, 0.009711062535643578, -0.0027733007445931435, -0.056655727326869965, -0.013894272968173027, -0.004257502034306526, -0.03681197762489319, -0.0009696774068288505, -0.0356723852455616, 0.0010528629645705223, 0.011873784475028515, -0.03901137039065361, -0.024033473804593086, -0.0023131065536290407, 0.0017561521381139755, 0.08815386891365051, -0.08368189632892609, -0.026769354939460754, -0.011484666727483273, 0.025294313207268715, -0.011956783942878246, -0.05237358808517456, -0.09427931904792786, 0.046041339635849, -0.05437314882874489, -0.04381939396262169, -0.035421863198280334, 0.016967831179499626, 0.06389565020799637, 0.006003473419696093, 0.0023009239230304956, -0.04173378646373749, -0.0029132936615496874, -0.023588668555021286, 0.04978860169649124, -0.024588288739323616, -0.005802875850349665, -0.00209609093144536, 0.03504079580307007, 0.017367633059620857, -0.039696380496025085, 0.009115156717598438, 0.0019216875080019236, -0.034854382276535034, 0.0035821024794131517, -0.04756181314587593, 0.000785066862590611, -0.001100725494325161, 0.06217622384428978, 0.01993411034345627, 0.03060150146484375, 0.02265818789601326, 0.005883004050701857, 0.027165817096829414, 0.01805819384753704, -0.04364407807588577, -0.020434660837054253, 0.05811173841357231, -0.021929729729890823, 0.012515304610133171, 0.0017143399454653263, 0.026383141055703163, 0.05747756361961365, 0.015928976237773895, -0.04068360477685928, 0.017038965597748756, -0.033268820494413376, -0.08237054944038391, -0.015785550698637962, 0.059610288590192795, 0.13020461797714233, -0.010943165980279446, 0.03073514625430107, -0.01683962531387806, 0.005455781705677509, -0.08755579590797424, 0.02479737624526024, -0.006837948225438595, 0.018440626561641693, -0.06719336658716202, -0.03799962252378464, 0.07502525299787521, -0.04315980523824692, -0.06697749346494675, 0.008682086132466793, -0.01863733120262623, 0.04733686521649361, -0.0003725613350979984, 0.04626282677054405, 0.026537803933024406, 0.030970243737101555, 0.007264473009854555, 0.011170689016580582, -0.054113488644361496, -0.054079700261354446, 0.0078758979216218, -0.009530589915812016, -0.0491236075758934, 0.06712357699871063, 0.02202530950307846, 0.05984823778271675, -0.01448784489184618, -0.01727028749883175, 0.03289937973022461, -0.043013207614421844, -0.03429792821407318, -0.048143766820430756, 0.02005710080265999, -0.02581731230020523, -0.015664055943489075, -0.05794990435242653, 0.011728713288903236, 0.05043964833021164, -0.029825838282704353, -0.03714202344417572, 0.017982883378863335, -0.024573026224970818, -0.014220727607607841, 0.03148931637406349, 0.019842198118567467, 0.007737133651971817, 0.03075471520423889, 0.04530801251530647, 0.02382700704038143, 0.05232473090291023, 0.028342779725790024, 0.016165077686309814, 0.06515161693096161, 0.014740553684532642, 0.03410089761018753, 0.031130077317357063, 0.006948960013687611, -0.0004353281401563436, 0.003544895676895976, 0.00893197301775217, -0.011921781115233898, -0.05052850767970085, -0.03879805654287338, 0.01665564253926277, -0.07803375273942947, 0.023586945608258247, 0.049746640026569366, 0.038016289472579956, 0.004799082409590483, 0.02292793057858944, 0.033808741718530655, 0.01672469638288021, 0.024175798520445824, -0.005583911668509245, -0.0693136528134346, -0.0264473557472229, 0.06279443204402924, 0.024361994117498398, -0.00533347437158227, -0.026984820142388344, 0.009671543724834919, 0.049733903259038925, 0.023330753669142723, 0.02768230251967907, -0.0045552365481853485, -0.005989305209368467, 0.10335810482501984, -0.027977177873253822, -0.04514581710100174, 0.05208027735352516, -0.01422029733657837, 0.02696484886109829, -0.028020566329360008, -0.0005993886734358966, -0.03042609803378582, -0.01367621123790741, -0.05346280336380005, -0.0012811659835278988, 0.03696452081203461, -0.010842620395123959, -0.00147390051279217, 0.089459627866745, -0.020956389605998993, -0.0013694906374439597, -0.024212045595049858, 0.033325742930173874, 0.022667955607175827, -0.00006519343151012436, 0.007694339379668236, 0.01274840161204338, -0.02203557640314102, -0.007880373857915401, 0.03211114555597305, -0.06027737632393837, 0.022758562117815018, -0.0633808970451355, 0.0004438225005287677, -0.026780376210808754, -0.023901553824543953, 0.006707379594445229, -0.023283662274479866, -0.0038031404837965965, 0.053090307861566544, 0.06451726704835892, -0.003254304639995098, -0.031518928706645966, 0.01296202652156353, 0.03895361348986626, -0.02281820774078369, -0.08292321860790253, 0.04280911758542061, -0.011947717517614365, 0.050519607961177826, -0.02768481709063053, 0.03349505364894867, 0.01338089071214199, 0.031886838376522064, -0.058843184262514114, 0.01892644353210926, 0.0015986330108717084, -0.004820855800062418, 0.03659247234463692, -0.048474203795194626, 0.02037140540778637, 0.004812305793166161, 0.02540270984172821, 0.038149889558553696, 0.000036195353459334, -0.03356236219406128, 0.0477442741394043, -0.04053248092532158, -0.01918822154402733, -0.06973398476839066, -0.008080078288912773, -0.035910528153181076, -0.00040323182474821806, -0.01807841844856739, -0.04285461828112602, 0.08014131337404251, -0.028328565880656242, -0.032300736755132675, -0.019688135012984276, 0.010004987008869648, 0.03371017426252365, -0.01748526282608509, -0.042174141854047775, 0.0017178308917209506, 0.03402597829699516, -0.01263431366533041, -0.009760880842804909, 0.00415183836594224, 0.029253611341118813, -0.02308029867708683, -0.017367316409945488, 0.03521374613046646, -0.019042834639549255, 0.007280381396412849, 0.004595269449055195, -0.003120975336059928, -0.01755114644765854, 0.0014308997197076678, 0.04861927404999733, -0.03390643745660782, -0.06619110703468323, -0.016125092282891273, 0.0004439165932126343, 0.007705573458224535, -0.00032190323690883815, -0.006475348956882954, -0.08464732021093369, 0.007211149670183659, -0.02348603866994381, 0.02094011753797531, -0.005022837780416012, 0.03742138668894768, 0.006252831779420376, -0.01754014939069748, -0.057647544890642166, -0.00023971698828972876, 0.004142690449953079, 0.015062885358929634, -0.013469668105244637, -0.04828289896249771, -0.03930448740720749, 0.003880195552483201, 0.029999297112226486, 0.004477823618799448, 0.028701160103082657, -0.048767466098070145, 0.016865214332938194, 0.01448000967502594, -0.005437564570456743, 0.04145035520195961, -0.016322128474712372, -0.005020508076995611, -0.016749076545238495, 0.09112951159477234, -0.09000304341316223, -0.0406266525387764, -0.018401293084025383, -0.0018719332292675972, -0.02057473547756672, -0.049839671701192856, 0.044076014310121536, 0.015162884257733822, 0.03681376203894615, 0.0019096434116363525, -0.018817607313394547, -0.0045359632931649685, 0.049728069454431534, -0.016695810481905937, 0.01774928718805313, 0.015285748057067394, -0.04803311824798584, 0.025830743834376335, -0.008757316507399082, -0.0779280737042427, 0.02063169702887535, -0.04916716739535332, 0.024454697966575623, 0.010191883891820908, -0.019781408831477165, -0.04670412838459015, -0.006020698230713606, -0.020171651616692543, 0.03159600496292114, -0.021428246051073074, -0.0018845596350729465, -0.02323251962661743 ]
<p>What will be the tensor product of two doublets $$ (x_1,x_2) ~\text{and}~ (y_1,y_2)? $$ I am very much confused in determining this.</p>
g5426
[ -0.019156834110617638, 0.026811417192220688, -0.023565975949168205, 0.04128020256757736, 0.06283946335315704, -0.04311802610754967, 0.06024540588259697, 0.0201274324208498, -0.013066121377050877, 0.017969125881791115, -0.07657191902399063, 0.05016016587615013, -0.0037738673854619265, -0.07174716889858246, 0.0020750199910253286, -0.0400826670229435, 0.03891100734472275, -0.002483830088749528, 0.024784287437796593, -0.03278286010026932, -0.0801674947142601, 0.0254332534968853, -0.013780801557004452, -0.05803387984633446, 0.03579344227910042, -0.03590676188468933, -0.016986355185508728, 0.10889847576618195, -0.06993290036916733, 0.014455186203122139, 0.058832041919231415, 0.014631098136305809, 0.022353406995534897, -0.0311137568205595, 0.03772687911987305, -0.001978136133402586, 0.044002432376146317, -0.005430217366665602, 0.028600264340639114, -0.007179476786404848, 0.033216770738363266, -0.0157583300024271, 0.03133275732398033, -0.061867304146289825, -0.014699607156217098, -0.030184675008058548, -0.014399653300642967, 0.012829086743295193, -0.031079508364200592, -0.006275988649576902, 0.04390491545200348, -0.0002684679930098355, 0.032704394310712814, 0.00764543516561389, -0.0036833800841122866, 0.014608502388000488, -0.0007655582739971578, -0.08423277735710144, 0.04518932104110718, -0.005199119448661804, -0.051831651479005814, 0.025793690234422684, -0.017468662932515144, 0.011650335043668747, 0.04122814163565636, 0.004902889020740986, -0.0015833048382773995, -0.01506969053298235, 0.02572733722627163, 0.0002103860315401107, 0.02144336700439453, -0.005804010201245546, 0.050847675651311874, 0.04295523092150688, -0.0010343297617509961, -0.06528089940547943, 0.042600467801094055, 0.04207570478320122, 0.05551416799426079, 0.05071906000375748, 0.03288703039288521, -0.0029914400074630976, 0.045647092163562775, 0.08007205277681351, 0.02779422327876091, 0.014112475328147411, -0.024053094908595085, 0.006353683769702911, -0.07773720473051071, 0.047240737825632095, -0.026245849207043648, -0.005324594210833311, 0.024412499740719795, 0.051749274134635925, 0.00930009875446558, -0.015212676487863064, -0.05606508255004883, -0.02973463013768196, 0.030232802033424377, 0.02065451629459858, 0.006441780366003513, 0.05080679804086685, 0.06553900241851807, -0.02984599769115448, 0.017867982387542725, 0.020283591002225876, 0.061983391642570496, -0.02643376775085926, -0.07178645581007004, -0.06140470504760742, -0.05678935348987579, 0.07733151316642761, 0.007112730760127306, -0.0616445317864418, -0.013340207748115063, 0.006766801234334707, -0.00632292777299881, -0.018877409398555756, 0.04526929184794426, 0.007076556794345379, 0.010922587476670742, -0.051340341567993164, -0.01699947565793991, 0.07940738648176193, 0.03232790529727936, -0.02191811054944992, -0.04345908761024475, 0.05736574903130531, 0.029175661504268646, -0.010307051241397858, -0.021434787660837173, 0.02020706981420517, 0.07823655009269714, -0.03189577907323837, -0.03009532019495964, 0.04625522345304489, -0.007005959749221802, 0.01741507463157177, 0.015621908940374851, -0.06921917200088501, -0.03538784012198448, -0.004990406800061464, -0.026616187766194344, 0.0207173153758049, -0.04313850402832031, -0.052502743899822235, 0.051471274346113205, -0.03587011620402336, -0.006766698323190212, -0.056200478225946426, 0.04993363469839096, 0.07577677071094513, 0.016209471970796585, 0.007038454059511423, 0.018777944147586823, -0.006783859338611364, 0.0689387321472168, -0.04445541277527809, 0.025624677538871765, -0.02523190528154373, 0.05930234119296074, 0.01702801324427128, 0.05073602870106697, -0.003621200565248728, -0.05470755323767662, -0.05491812154650688, 0.01020573265850544, -0.054549362510442734, -0.010529328137636185, -0.031016064807772636, 0.010912914760410786, -0.00929485633969307, 0.002396679250523448, 0.002833944745361805, 0.050482891499996185, 0.0038135938812047243, -0.04687204957008362, 0.051144104450941086, 0.008402539417147636, 0.03617250174283981, -0.08127383142709732, -0.004263614770025015, -0.0028278788086026907, 0.02350621111690998, -0.030126502737402916, -0.03501129895448685, -0.06727293133735657, -0.005060465540736914, -0.0638376772403717, 0.044210273772478104, -0.009401459246873856, 0.01990954950451851, 0.0020761520136147738, 0.028513124212622643, 0.030683450400829315, 0.013742823153734207, 0.040364619344472885, 0.034122392535209656, 0.009333309717476368, 0.041614752262830734, -0.057665709406137466, -0.03153476119041443, -0.013269447721540928, -0.015962712466716766, -0.08164536207914352, 0.01612408645451069, -0.005992004182189703, -0.05629066750407219, -0.006086957640945911, 0.00826561450958252, -0.03760311380028725, -0.017550436779856682, -0.022589799016714096, 0.0023631916847079992, 0.031905096024274826, -0.04671012610197067, -0.00882747769355774, -0.018145889043807983, -0.05707932636141777, -0.012304251082241535, 0.021013470366597176, 0.039612866938114166, 0.08763527870178223, -0.01727985590696335, -0.015367464162409306, 0.05635115131735802, -0.0117253502830863, -0.008218631148338318, -0.0021469928324222565, 0.03286192938685417, -0.03395985811948776, -0.01125823613256216, -0.0005871587200090289, -0.05783582478761673, 0.028669655323028564, -0.04759426787495613, -0.04692689701914787, 0.021991867572069168, 0.03271454945206642, 0.05405592545866966, 0.017016077414155006, 0.03766419366002083, 0.031469084322452545, 0.05496758595108986, 0.034326814115047455, 0.029635583981871605, 0.0509050115942955, -0.008797282353043556, 0.011568518355488777, 0.027070753276348114, -0.05056256800889969, 0.009011371061205864, -0.0506499819457531, 0.04481574892997742, -0.032248374074697495, 0.0026446033734828234, 0.02454349957406521, -0.022647909820079803, -0.05687379837036133, -0.0021815113723278046, 0.001421871711499989, 0.010463406331837177, 0.002740303985774517, 0.01607975922524929, -0.053268007934093475, -0.020375043153762817, 0.055133555084466934, 0.008307745680212975, 0.04811001569032669, -0.016503969207406044, -0.028446221724152565, 0.02450425922870636, -0.013959233649075031, 0.028695065528154373, -0.04245606064796448, -0.004493702203035355, -0.01825200952589512, -0.056943267583847046, -0.04045399650931358, 0.016580801457166672, 0.006596350111067295, 0.029788868501782417, 0.046536486595869064, 0.04120013117790222, 0.027205606922507286, 0.00444316491484642, -0.03971734642982483, 0.0749044269323349, 0.031054643914103508, 0.04354009032249451, 0.023699533194303513, 0.04516284167766571, 0.00984034314751625, -0.03420499712228775, 0.006990913767367601, -0.04702949896454811, -0.004898511804640293, -0.04666781798005104, -0.018007792532444, 0.02081046998500824, 0.06634949892759323, 0.019600840285420418, 0.06337904930114746, -0.014441009610891342, 0.02493627741932869, -0.05348413810133934, 0.007106897886842489, -0.02590005472302437, -0.01387843769043684, -0.024847332388162613, -0.01836819387972355, 0.022497355937957764, 0.08239062875509262, -0.03565358370542526, 0.007540103979408741, -0.00020763371139764786, -0.00026646567857824266, -0.009201853536069393, -0.008020021952688694, 0.002722113626077771, -0.025673288851976395, 0.013285190798342228, 0.035966966301202774, 0.0665612742304802, -0.0061610690318048, -0.029320383444428444, -0.02014816366136074, 0.07568135112524033, -0.02853279933333397, -0.039575740694999695, -0.04271436110138893, 0.007809493690729141, -0.008924578316509724, -0.02394776977598667, -0.004804268013685942, -0.01501056645065546, -0.022401288151741028, 0.04035365581512451, 0.013744447380304337, 0.003774705808609724, 0.07003528624773026, 0.04977380856871605, 0.012610262259840965, -0.04557345435023308, 0.00030233393772505224, -0.019801786169409752, -0.09012316167354584, 0.005432422272861004, 0.032247886061668396, 0.0025271365884691477, -0.006608877796679735, -0.03785508871078491, 0.03476322442293167, -0.01894446089863777, -0.0006873806705698371, 0.01648406870663166, 0.03604794666171074, 0.006302554160356522, -0.03718125447630882, -0.03337341919541359, 0.05061403289437294, -0.04257803410291672, 0.015743089839816093, -0.02351491153240204, 0.04746827483177185, -0.0263470858335495, -0.029405537992715836, 0.07559192925691605, -0.01740811951458454, 0.03850371390581131, 0.019144544377923012, 0.03839321434497833, 0.002046466339379549, 0.01915632002055645, -0.05288442596793175, -0.023840103298425674, 0.0014929771423339844, -0.04494393989443779, 0.042500872164964676, -0.05769674479961395, -0.007819811813533306, 0.02433149144053459, -0.006778618786484003, 0.03012913465499878, 0.019880058243870735, -0.0010944369714707136, -0.02114219404757023, -0.0036048523616045713, 0.0854959487915039, -0.06638062745332718, -0.024624092504382133, 0.0368095263838768, -0.05838368833065033, 0.0032730887178331614, -0.023635560646653175, -0.04027055203914642, 0.037787601351737976, 0.025135759264230728, -0.06252598017454147, -0.021214047446846962, 0.014154777862131596, 0.018067453056573868, -0.04041464999318123, -0.06508654356002808, 0.008316644467413425, -0.0008391717565245926, 0.002674985211342573, -0.045289456844329834, 0.07658302038908005, 0.01972040720283985, -0.004722981713712215, 0.008336192928254604, 0.0367499403655529, -0.0037109628319740295, 0.02820204384624958, 0.024256234988570213, -0.011537744663655758, -0.03737557306885719, -0.030645383521914482, -0.03282548114657402, 0.010012461803853512, -0.007756372448056936, -0.029911087825894356, -0.015298728831112385, 0.011346042156219482, 0.03975114971399307, 0.003244672669097781, -0.002247101627290249, 0.02048289217054844, -0.01238260418176651, 0.03235352784395218, -0.020718704909086227, -0.025950537994503975, 0.028703466057777405, -0.051419369876384735, 0.007487626280635595, -0.015905775129795074, -0.0097381342202425, -0.024080928415060043, -0.004103700630366802, 0.0685344859957695, 0.021623020991683006, -0.03497858718037605, 0.007229809183627367, 0.03749578446149826, 0.017210789024829865, -0.016166502609848976, -0.023497024551033974, 0.02263658493757248, -0.05732225999236107, -0.059553708881139755, 0.02735023759305477, 0.07200421392917633, -0.04475736990571022, 0.061306606978178024, 0.04614248499274254, -0.005582216661423445, 0.004041423089802265, -0.005898979026824236, 0.016741741448640823, -0.01684664562344551, -0.047133758664131165, 0.07358541339635849, -0.0032908443827182055, 0.001671180478297174, -0.01135969441384077, -0.09675110876560211, -0.0054054586216807365, -0.029694506898522377, -0.013666839338839054, -0.03677515685558319, 0.010046891868114471, -0.03756703808903694, -0.02660405822098255, 0.040269918739795685, -0.009992118924856186, -0.07262149453163147, 0.00928577035665512, 0.01848377287387848, 0.02923876978456974, -0.010298510082066059, 0.022987769916653633, -0.008640286512672901, 0.007365082390606403, 0.07911217212677002, 0.019828129559755325, 0.04084528237581253, 0.007008669897913933, 0.03229319676756859, -0.03275377303361893, -0.038074057549238205, 0.008306330069899559, 0.022124560549855232, 0.0653538629412651, -0.05967576429247856, 0.02610551193356514, -0.010771266184747219, -0.05068443343043327, 0.0016350497025996447, 0.013305045664310455, -0.030624067410826683, 0.04056363180279732, 0.040140874683856964, 0.09416420757770538, -0.00566612696275115, -0.009395706467330456, 0.04888617619872093, -0.020544013008475304, -0.04582171142101288, 0.027221249416470528, 0.0007614608621224761, 0.015635529533028603, -0.0071322182193398476, 0.04976963996887207, 0.0033133653923869133, -0.023164529353380203, 0.005853749345988035, 0.0425606369972229, -0.04125846549868584, -0.011565924622118473, 0.03510779142379761, -0.037521544843912125, 0.018134431913495064, -0.0008300335030071437, 0.0033003422431647778, 0.02044244110584259, -0.0038428823463618755, -0.058050885796546936, 0.022513022646307945, 0.06462769955396652, -0.043510135263204575, -0.00293606030754745, -0.029672471806406975, -0.05493619665503502, 0.04278313368558884, -0.016427358612418175, 0.013036845251917839, -0.06764435768127441, 0.0020771464332938194, 0.04836522042751312, -0.015007052570581436, -0.02265818417072296, -0.042048193514347076, 0.014589612372219563, -0.007869250141084194, -0.009522625245153904, -0.056821368634700775, -0.008913833647966385, -0.014811699278652668, -0.03148887678980827, -0.0025678493548184633, -0.05722858011722565, 0.013540166430175304, -0.05731883645057678, 0.014845489524304867, -0.010850826278328896, 0.024009795859456062, -0.039577387273311615, 0.02617899514734745, 0.03136299178004265, 0.01102110743522644, 0.050718482583761215, -0.0337831936776638, -0.00047357153380289674, 0.01666889525949955, 0.020568160340189934, 0.023453665897250175, 0.0023341639898717403, 0.028951410204172134, 0.0026016507763415575, 0.02425296977162361, 0.037798985838890076, 0.02095470204949379, -0.006156106013804674, -0.0006060776649974287, 0.047102831304073334, -0.027819933369755745, 0.003263660706579685, -0.021495740860700607, -0.019740574061870575, 0.005515933968126774, 0.06061607971787453, -0.012606889940798283, -0.009847074747085571, -0.027401909232139587, 0.022604458034038544, -0.01189398393034935, -0.06137198582291603, 0.003514750162139535, 0.04633013531565666, 0.021966062486171722, 0.012171724811196327, -0.04380960762500763, -0.035407472401857376, -0.03846258297562599, -0.008134736679494381, -0.009136723354458809, 0.05123118683695793, 0.021116608753800392, -0.05658285319805145, -0.033386074006557465, -0.009844104759395123, 0.07522863149642944, -0.0018781510880216956, 0.017082303762435913, 0.047823816537857056, 0.023905711248517036, -0.0001161264517577365, -0.03868633508682251, -0.015973860397934914, -0.02521076239645481, -0.008599289692938328, -0.05917820334434509, 0.02842484600841999, -0.0218906681984663, -0.04837598279118538, -0.04186706244945526, 0.019538378342986107, -0.018476489931344986, -0.0008734689326956868, 0.07833170890808105, -0.06334860622882843, -0.06523020565509796, -0.026901256293058395, 0.027836158871650696, 0.044843800365924835, 0.014520199969410896, 0.026040036231279373, 0.016852933913469315, 0.025665132328867912, -0.015474810265004635, -0.04780243709683418, -0.02002943679690361, 0.02841079607605934, -0.005089603364467621, -0.002207056852057576, -0.037285856902599335, 0.08099240064620972, 0.04810544475913048, 0.04789265990257263, -0.0030103002209216356, 0.04130662605166435, 0.020490091294050217, -0.014150931499898434, 0.003912626300007105, 0.07360439002513885, 0.0668061152100563, -0.013333836570382118, -0.11475255340337753, -0.040152568370103836, -0.02348855696618557, 0.02199605107307434, -0.02364296466112137, 0.007268156856298447, -0.001529133878648281, -0.002327685011550784, 0.0036248662509024143, -0.03288192301988602, 0.00404184777289629, -0.006426317151635885, -0.03787408396601677, -0.014444984495639801, -0.09377481043338776, 0.020854422822594643, -0.011617562733590603, 0.01504461094737053, 0.03989388048648834, -0.015405343845486641, -0.009050266817212105, -0.04518860578536987, -0.07000332325696945, 0.03500327840447426, -0.018432654440402985, -0.000886387366335839, 0.01320034358650446, -0.004213851410895586, -0.010241292417049408, -0.03316889703273773, 0.020821601152420044, -0.04849473759531975, -0.08919960260391235, -0.009993452578783035, -0.054235439747571945, -0.03651309385895729, -0.06492555141448975, -0.005566128063946962, 0.004782828036695719, -0.021296881139278412, -0.00724715506657958, 0.03011311963200569, 0.07110493630170822, -0.013208392076194286, -0.0027521185111254454, -0.03096887469291687, -0.03862163797020912, -0.00112988764885813, -0.00443856418132782, 0.04155721887946129, -0.006650717929005623, 0.008056235499680042, -0.0032752114348113537, 0.047164756804704666, -0.08706656843423843, 0.032897189259529114, -0.008917630650103092, 0.005352444015443325, 0.03258141130208969, -0.017712406814098358, 0.05923570320010185, -0.08258017152547836, -0.0023719819728285074, 0.03696359694004059, -0.034309886395931244, 0.01606648787856102, 0.01642899587750435, -0.0033276062458753586, -0.045976102352142334, 0.0127864433452487, 0.03541659191250801, -0.011262780986726284, 0.015812618657946587, 0.03210730850696564, 0.006248718127608299, -0.040878720581531525, -0.029505861923098564, -0.04159483313560486, 0.03125368431210518, 0.04113524779677391, 0.013361482881009579, 0.05207677558064461, -0.013798660598695278, 0.003712786128744483, -0.021893540397286415, 0.032565560191869736, 0.0028753262013196945, 0.03984431177377701, 0.025810403749346733, -0.040769271552562714, 0.022455018013715744, 0.0056609055027365685, -0.035604655742645264, -0.08078791201114655, -0.003634555032476783, 0.02840252034366131, -0.0759287178516388, 0.012847425416111946, -0.005794145166873932, 0.062082089483737946, 0.021355412900447845, -0.04945800453424454, 0.01788954809308052, -0.010512923821806908, -0.025937726721167564, 0.06961219012737274, 0.013959678821265697, -0.009878641925752163, -0.04659416899085045, 0.009270365349948406, -0.005676641594618559, -0.005411136895418167, -0.008055382408201694, 0.05774431303143501, -0.026338404044508934, 0.01571369357407093, -0.029875406995415688, 0.02816210500895977, -0.03856842964887619, 0.026644885540008545 ]
<p>I'm contemplating particle-hole symmetry, and as an example I am looking at either an electron moving along a hypothetical lattice of hydrogen ions, or a hole moving along a hypothetical lattice of helium atoms. </p> <p>According to some lecture notes I found, the hopping integral I get when I treat this in a tight-binding ansatz is positive for holes and negative for electrons, and now I want to see why this is so. </p> <p>For electrons, I can understand the result: The atomic wavefunctions are just the 1s hydrogen wavefunctions, and they are positive everywhere, so the matrix element with the kinetic energy operator gives something negative. </p> <p>Now, for holes I am not sure how I would have to proceed. Can I just say that the relevant Hamiltonian for holes is the negative of the Hamiltonian for electrons because, after all, a hole with energy $E$ would be an electron with energy $-E$ missing?</p> <p>Of, if that's wrong, how would I come to the conclusion that the hopping integral for electrons is negative and for holes it's positive?</p>
g5427
[ -0.01809384860098362, 0.02492602914571762, -0.02300136536359787, -0.037981290370225906, -0.008305237628519535, 0.004331585951149464, 0.038744475692510605, 0.018659384921193123, -0.006790037266910076, 0.019237972795963287, 0.005777386482805014, 0.048152610659599304, -0.004324659239500761, 0.04080762714147568, -0.01467909011989832, -0.036967456340789795, 0.047159112989902496, 0.05627802759408951, 0.009570842608809471, 0.022105520591139793, 0.018792875111103058, 0.04172834753990173, -0.022874217480421066, 0.015213207341730595, 0.011282752268016338, -0.01015651784837246, 0.009545433335006237, -0.06920576095581055, 0.020236484706401825, 0.01138236466795206, 0.01714378595352173, -0.046935100108385086, 0.03686664626002312, -0.03230661153793335, -0.028407491743564606, 0.02067415602505207, 0.07639054208993912, 0.021367283537983894, 0.010877844877541065, 0.0035559390671551228, -0.018896637484431267, -0.07608853280544281, -0.048907455056905746, -0.030118286609649658, 0.016319572925567627, -0.03387373313307762, 0.03000793233513832, 0.007146275136619806, 0.01045229658484459, 0.008390065282583237, 0.017278535291552544, 0.0744197890162468, -0.004768447484821081, -0.013574604876339436, 0.02660449407994747, 0.03791220486164093, -0.012542292475700378, 0.03149266541004181, 0.07393497228622437, 0.0485803447663784, 0.029290057718753815, -0.009463627822697163, 0.001617803587578237, -0.002070332644507289, 0.07375685125589371, 0.03168105706572533, -0.06505917757749557, -0.00900132767856121, -0.10099225491285324, 0.018580427393317223, -0.028804313391447067, -0.02971474640071392, -0.007013451308012009, -0.016486896201968193, -0.030959952622652054, 0.01944682002067566, 0.022161992266774178, -0.009824252687394619, 0.02183883637189865, -0.03321824222803116, -0.06881953775882721, 0.002416089177131653, 0.039618585258722305, -0.036409106105566025, 0.03421029821038246, 0.010353073477745056, 0.06019277125597, -0.03237496316432953, -0.03720207139849663, -0.023537706583738327, 0.032275110483169556, 0.02481548674404621, 0.06923412531614304, 0.04415144771337509, -0.024080291390419006, 0.04871506989002228, -0.034407418221235275, 0.0331319123506546, -0.05731578543782234, 0.021296294406056404, 0.0019383491016924381, -0.00958724319934845, 0.013010939583182335, -0.04289880394935608, -0.03498508781194687, -0.026037640869617462, -0.045730866491794586, -0.006620444823056459, 0.079706110060215, 0.03089885599911213, 0.023573502898216248, -0.027540549635887146, -0.03552871197462082, -0.01877002790570259, -0.00962374173104763, 0.017373448237776756, 0.06743178516626358, -0.03675149008631706, 0.001694168196991086, 0.04637658968567848, 0.0043549248948693275, 0.037158723920583725, 0.004551236983388662, 0.0705522671341896, 0.004409627988934517, -0.0010889990953728557, -0.051865387707948685, -0.003976571839302778, 0.0001384926727041602, -0.0030905217863619328, -0.005798943340778351, -0.005497873295098543, 0.012688162736594677, 0.03261162340641022, -0.017046533524990082, -0.004511734005063772, -0.02159026265144348, 0.029263243079185486, 0.00007314745016628876, 0.021194318309426308, -0.018158506602048874, -0.025341294705867767, 0.009566075168550014, 0.010445494204759598, -0.013181346468627453, -0.006623801309615374, 0.004703665152192116, -0.0519474633038044, 0.053415536880493164, -0.00885719247162342, 0.0016567662823945284, 0.06177915632724762, -0.01294276025146246, 0.002426732564345002, 0.0589432492852211, -0.03406485170125961, 0.06122900918126106, -0.03497423231601715, 0.034844331443309784, -0.010731400921940804, 0.04673159867525101, -0.02490728534758091, 0.0733787938952446, 0.04150635749101639, -0.032872579991817474, -0.012146534398198128, -0.011794054880738258, 0.0014201172161847353, 0.045332565903663635, 0.019353743642568588, -0.009646621532738209, 0.016585802659392357, 0.027991194278001785, -0.030727257952094078, 0.012302805669605732, 0.06925851851701736, -0.036476653069257736, -0.024145178496837616, -0.010683738626539707, 0.03376943618059158, 0.0295251477509737, -0.04885084554553032, 0.03433867171406746, 0.015167312696576118, 0.0537479966878891, 0.038533229380846024, -0.03020913153886795, 0.02886742725968361, -0.039045300334692, -0.024738654494285583, 0.07650294154882431, -0.025446033105254173, 0.05563504993915558, 0.010445796884596348, -0.03865371271967888, -0.02405814453959465, -0.0013211542973294854, -0.028288958594202995, -0.012798353098332882, -0.023626424372196198, -0.0567304827272892, 0.08643615245819092, 0.05994363874197006, -0.001365893753245473, 0.07466048002243042, -0.03326760604977608, 0.007171985227614641, 0.012939732521772385, -0.004538981709629297, -0.004974603187292814, 0.011179858818650246, -0.010170092806220055, -0.030549371615052223, 0.058097802102565765, 0.03147703409194946, -0.020151006057858467, -0.01191626489162445, -0.016763528808951378, -0.02543032541871071, -0.05904126167297363, -0.06533116847276688, -0.06567100435495377, -0.013428532518446445, -0.00448461202904582, -0.045153647661209106, 0.049272242933511734, -0.00993769709020853, -0.020163599401712418, -0.04617871716618538, 0.00029117558733560145, -0.08009045571088791, 0.025946345180273056, -0.04641018435359001, -0.03444802016019821, 0.005046873819082975, 0.02049204707145691, 0.015720102936029434, 0.025359682738780975, 0.011668600142002106, 0.027750583365559578, -0.04699335992336273, 0.008728520944714546, -0.0371573381125927, -0.00320423929952085, 0.004488979000598192, -0.040545787662267685, -0.011530105024576187, -0.02299482561647892, -0.06445048004388809, 0.028043366968631744, -0.008067167364060879, 0.021650414913892746, -0.08187485486268997, 0.016726942732930183, -0.01461325865238905, -0.06089388206601143, 0.023248497396707535, -0.010442597791552544, 0.01049742940813303, 0.016745802015066147, 0.014297878369688988, -0.035066764801740646, 0.021160107105970383, 0.023250002413988113, 0.020814688876271248, -0.06055905669927597, -0.004329042509198189, -0.02948213368654251, 0.003127585630863905, -0.026113172993063927, 0.024793313816189766, 0.10102497786283493, 0.02903836965560913, -0.02243899740278721, 0.05618812516331673, -0.07516934722661972, -0.006064009852707386, -0.015269332565367222, 0.04181091487407684, -0.025575051084160805, -0.04418748617172241, -0.005439459811896086, -0.01856119930744171, -0.05364105477929115, -0.029655821621418, -0.05484945699572563, 0.03107648901641369, 0.042528487741947174, -0.02139217220246792, 0.05987406149506569, 0.022263532504439354, 0.021335136145353317, 0.008320664055645466, 0.0488288551568985, 0.023478960618376732, -0.009342045523226261, 0.04317360743880272, -0.10496632009744644, -0.03127416968345642, 0.032149381935596466, -0.029794076457619667, -0.010596534237265587, -0.02882308140397072, 0.0013742714654654264, 0.11071702092885971, 0.03301839530467987, 0.0010579832596704364, 0.009358312003314495, -0.03131627291440964, -0.031066955998539925, -0.0382818728685379, 0.005101097282022238, 0.06051557883620262, -0.0213289987295866, -0.010971966199576855, 0.035897355526685715, -0.10268980264663696, -0.0063709975220263, 0.02384626492857933, -0.054227378219366074, -0.041892822831869125, -0.002126050181686878, -0.0045599606819450855, 0.016184426844120026, 0.047965701669454575, 0.023214619606733322, -0.012658006511628628, -0.05628387629985809, 0.017961444333195686, -0.0040398635901510715, -0.001471249619498849, -0.018242573365569115, -0.012594698928296566, 0.02516559511423111, -0.038002073764801025, -0.047713879495859146, 0.017974501475691795, -0.002774556167423725, 0.015943503007292747, 0.02414887212216854, -0.05523094907402992, -0.022207768633961678, -0.020288551226258278, 0.026772882789373398, -0.013525888323783875, -0.0381019301712513, -0.043710857629776, 0.041204165667295456, 0.02475929632782936, -0.029327644035220146, -0.012607844546437263, 0.0022304116282612085, 0.034557413309812546, 0.021020855754613876, -0.011622837744653225, 0.0032539793755859137, 0.04557457193732262, 0.03642454743385315, -0.03248405084013939, 0.06188764423131943, -0.03830518573522568, -0.038988109678030014, 0.010341615416109562, 0.012284409254789352, -0.02113543264567852, -0.029265383258461952, -0.04040392115712166, 0.04075324907898903, 0.004208428785204887, -0.08192010968923569, -0.01377810537815094, -0.016779590398073196, 0.013646726496517658, -0.05554915964603424, 0.020043130964040756, -0.007014787290245295, -0.019594412297010422, 0.0169652309268713, -0.060773033648729324, -0.028589662164449692, -0.046998944133520126, 0.019196955487132072, 0.037112414836883545, 0.05763436481356621, 0.05940190702676773, 0.02110852673649788, -0.0370962992310524, -0.010967246256768703, -0.02271675318479538, -0.038409583270549774, -0.009194508194923401, 0.02132439985871315, -0.0002013661287492141, 0.005708014592528343, 0.008116512559354305, -0.013277283869683743, -0.016966016963124275, -0.07027725130319595, -0.03861356899142265, 0.08128771185874939, -0.012233960442245007, -0.014740584418177605, 0.008985172025859356, -0.03822778910398483, 0.04053361713886261, 0.0007659568218514323, 0.04092156141996384, 0.033649712800979614, 0.0010917240288108587, -0.04282305762171745, -0.04218301549553871, -0.022386254742741585, 0.03441842272877693, -0.03278353810310364, -0.045911215245723724, -0.01457410678267479, -0.007509918417781591, -0.06827101111412048, 0.013565276749432087, -0.0007180793327279389, 0.03620590642094612, 0.07684113085269928, 0.005020834505558014, -0.02591063641011715, -0.019719010218977928, 0.07822581380605698, 0.0076737431809306145, 0.025167254731059074, -0.0029110244940966368, -0.030370201915502548, -0.04043940454721451, 0.009222534485161304, 0.011064129881560802, -0.0355774387717247, -0.05605514720082283, 0.008495737798511982, -0.08212582767009735, 0.044985078275203705, -0.02968420833349228, 0.060352686792612076, 0.024571307003498077, 0.04355326667428017, -0.02082916349172592, 0.025530926883220673, -0.01636979542672634, -0.01570902019739151, -0.07261354476213455, -0.03362145274877548, -0.04839377477765083, -0.05386664718389511, -0.000719026371371001, 0.004001366440206766, 0.0075826202519237995, -0.009172309190034866, -0.014968426898121834, -0.02818966470658779, -0.07761158049106598, 0.06483253836631775, 0.015243902802467346, 0.03800947964191437, -0.034190982580184937, 0.024848638102412224, -0.006731153931468725, 0.0432470478117466, 0.03398405760526657, 0.004287043120712042, -0.03071640618145466, 0.022276850417256355, -0.025165988132357597, 0.031099796295166016, 0.04329359158873558, 0.04118702933192253, -0.009037993848323822, 0.039850637316703796, 0.030880657956004143, -0.03286931663751602, 0.009329442866146564, -0.03299006447196007, -0.01987028867006302, -0.02968169003725052, -0.05361161753535271, -0.02540382370352745, 0.06936948001384735, 0.020181719213724136, -0.062016136944293976, -0.001212805393151939, -0.008863842114806175, 0.04771198332309723, -0.041074030101299286, 0.04120773822069168, 0.041008319705724716, 0.012055699713528156, 0.028649069368839264, -0.0027401200495660305, 0.02506536804139614, -0.03212413191795349, -0.005500593222677708, 0.01806962862610817, -0.027797745540738106, 0.008593767881393433, -0.02859937958419323, -0.07953592389822006, -0.020306451246142387, -0.011865789070725441, 0.04696281999349594, 0.04655076935887337, 0.12663906812667847, -0.02420746348798275, 0.0013307371409609914, -0.1093626320362091, -0.004016875755041838, 0.004889426287263632, -0.007141311652958393, -0.01794292964041233, -0.006175134796649218, -0.0012509622611105442, -0.03522717207670212, 0.004417486023157835, -0.051235128194093704, 0.032067157328128815, 0.021243033930659294, 0.06110388785600662, 0.04638851433992386, -0.07744795083999634, 0.015314420685172081, 0.02043815515935421, -0.014245834201574326, -0.031409844756126404, -0.03145471587777138, 0.03379727900028229, 0.05821216106414795, 0.00039648241363465786, 0.02497849240899086, 0.02894294634461403, 0.007640015799552202, -0.026766233146190643, -0.008565693162381649, 0.02250325307250023, -0.01807735674083233, 0.011267514899373055, -0.018183035776019096, -0.011132609099149704, 0.038972821086645126, 0.054130736738443375, -0.06325443089008331, -0.054422881454229355, -0.046614646911621094, 0.02582516148686409, -0.010287852957844734, -0.042957086116075516, -0.07114984840154648, 0.013323714025318623, -0.0559912770986557, -0.031780291348695755, -0.0038702283054590225, 0.017231395468115807, 0.04557323083281517, -0.018269088119268417, -0.001459144172258675, -0.02800934575498104, 0.0652720257639885, -0.023359451442956924, 0.02222440205514431, -0.02477164939045906, 0.07858607172966003, 0.07092220336198807, -0.03823542594909668, -0.019185863435268402, -0.009642351418733597, 0.03268364444375038, -0.03238123282790184, 0.006160912103950977, 0.03102421574294567, 0.01809471845626831, -0.002017839578911662, 0.049671418964862823, 0.0003889552899636328, -0.007475315593183041, -0.00975156668573618, 0.04676581546664238, 0.03556983172893524, -0.010270564816892147, 0.02304255962371826, -0.01616896316409111, -0.022346505895256996, 0.025040028616786003, -0.02296150103211403, -0.023984750732779503, 0.05079885572195053, -0.008838244713842869, -0.017849193885922432, 0.07237110286951065, 0.037508223205804825, 0.00049536646110937, 0.03534573316574097, -0.021558908745646477, -0.0502755343914032, -0.09270414710044861, -0.021855665370821953, 0.046314507722854614, 0.07331063598394394, -0.03427988290786743, -0.0028977985493838787, 0.023754678666591644, 0.012296043336391449, 0.04482130706310272, 0.0034453412517905235, 0.029943279922008514, -0.054247427731752396, 0.0347830094397068, -0.01849319040775299, 0.05641266331076622, 0.026071900501847267, 0.009215477854013443, 0.031752195209264755, -0.057805661112070084, 0.007368811406195164, 0.02449283003807068, -0.006834626197814941, -0.02061450481414795, -0.001443627174012363, 0.019094662740826607, -0.08695785701274872, -0.013914142735302448, 0.06814006716012955, 0.053076811134815216, -0.0572216622531414, 0.00710006570443511, -0.010568859055638313, -0.026934772729873657, -0.008548583835363388, 0.04732033610343933, -0.028715183958411217, 0.0579850971698761, -0.0002935605589300394, 0.02878786064684391, -0.09893611073493958, 0.0066857291385531425, 0.0008592939702793956, 0.057519473135471344, -0.01612992212176323, 0.03767713904380798, 0.0730985552072525, -0.0030861827544867992, -0.03758270666003227, -0.012801695615053177, 0.03726814687252045, -0.026504242792725563, -0.033027030527591705, 0.040970463305711746, 0.007454901002347469, -0.005798010155558586, -0.058329470455646515, -0.0044717625714838505, 0.03991756960749626, -0.010990922339260578, 0.02945159561932087, 0.011277790181338787, 0.012473995797336102, -0.014404023997485638, -0.005632591433823109, -0.004570721182972193, 0.002390773966908455, -0.008698612451553345, 0.004031324293464422, 0.02332095429301262, -0.0390327051281929, 0.022904541343450546, 0.004940979182720184, 0.013087577186524868, -0.011035680770874023, 0.000986002734862268, -0.0153317516669631, 0.04299210384488106, -0.0014720564940944314, -0.019822636619210243, -0.019648035988211632, 0.08916868269443512, -0.044257525354623795, -0.03513190895318985, 0.02574472688138485, 0.024864893406629562, -0.002673109993338585, 0.02442142739892006, -0.04714035987854004, -0.04636767879128456, -0.07998690009117126, -0.038439877331256866, -0.03126605972647667, -0.011325540021061897, 0.014610538259148598, -0.0344555601477623, 0.010408081114292145, -0.039470791816711426, -0.03190139681100845, 0.030397865921258926, 0.08504892885684967, 0.02998289465904236, -0.016248390078544617, 0.0325775220990181, -0.0031577316112816334, -0.017005784437060356, 0.018452467396855354, 0.014050297439098358, 0.023619849234819412, 0.0020944280549883842, 0.020548967644572258, -0.07191187888383865, -0.025430845096707344, -0.0013596052303910255, 0.05349777266383171, 0.08730930089950562, -0.0006677111377939582, 0.04325633868575096, 0.07105803489685059, 0.008590594865381718, 0.007251195143908262, 0.0011585729662328959, 0.006881324574351311, -0.004118328448385, 0.042980603873729706, -0.012910788878798485, -0.008456481620669365, 0.0006612942088395357, 0.03945188596844673, 0.006375370547175407, -0.031158756464719772, 0.019500399008393288, -0.0034967355895787477, 0.016781074926257133, -0.07875271141529083, 0.02481384202837944, -0.031153244897723198, 0.01848657801747322, -0.02141682431101799, 0.010748079977929592, -0.02171451598405838, -0.04606040194630623, 0.002267700619995594, 0.045994263142347336, -0.011829857714474201, -0.0642702654004097, -0.004169924184679985, -0.018363062292337418, -0.02091563120484352, 0.0010363809997215867, -0.04525017365813255, 0.01264078076928854, 0.10406912118196487, -0.001999682281166315, 0.0042517781257629395, 0.007381875533610582, -0.018916135653853416, 0.0392940379679203, 0.0015902320155873895, -0.02878333255648613, -0.006923809181898832, -0.0341474749147892, -0.019640246406197548, 0.0003285910643171519, 0.01078912615776062, 0.02889387123286724, -0.014503451995551586, -0.02211054600775242, -0.022638272494077682, -0.06314601004123688, 0.01032034307718277, -0.0033589156810194254 ]
<p>Could you please suggest the software, where I can load my 3D model and see how it behave on various conditions (speed - preferably including supersonic, temperature, pressure)?</p> <p>Both free &amp; commercial variants are interesting.</p>
g5428
[ 0.04612993076443672, 0.007884512655436993, 0.008255097083747387, -0.0007003486971370876, -0.02779296226799488, 0.02197064645588398, 0.02658471278846264, -0.028196310624480247, -0.05666419491171837, -0.002780677517876029, 0.04771212115883827, 0.00019351267837919295, 0.033161014318466187, -0.01625536009669304, 0.002575387479737401, 0.016309397295117378, 0.037517890334129333, -0.059442609548568726, -0.02684720605611801, 0.011869322508573532, 0.05703892931342125, 0.01534267421811819, 0.014915848150849342, -0.02241072617471218, -0.0015827646711841226, 0.019764341413974762, -0.05598746985197067, -0.02939792536199093, -0.022186575457453728, 0.01112863328307867, 0.019299974665045738, -0.0210246704518795, -0.041951991617679596, -0.043403469026088715, -0.03708171471953392, -0.025712162256240845, -0.025083744898438454, 0.02704690396785736, -0.022241391241550446, -0.003977187443524599, 0.039148274809122086, -0.034056924283504486, -0.009342626668512821, 0.0214738380163908, 0.0024518121499568224, -0.012333680875599384, -0.028435710817575455, -0.010129052214324474, -0.03979109972715378, -0.0008225358324125409, 0.05141825973987579, 0.028252096846699715, 0.03744564950466156, -0.014671243727207184, 0.0406058095395565, -0.0024148677475750446, -0.021013397723436356, 0.03793385252356529, -0.004956589546054602, -0.05283696576952934, -0.06485293805599213, 0.028685083612799644, 0.028993092477321625, -0.02418678253889084, -0.006504164543002844, -0.01431012898683548, 0.00906037725508213, -0.07283386588096619, 0.00927319098263979, 0.002027020091190934, 0.018016822636127472, 0.01738639362156391, -0.00400815112516284, 0.017048221081495285, -0.017911558970808983, -0.037386324256658554, -0.023388555273413658, -0.05298976972699165, -0.0049852775409817696, -0.014480034820735455, -0.018142255023121834, 0.05278868228197098, -0.03262404724955559, -0.04211638495326042, 0.04118724539875984, -0.02953162044286728, 0.0025158687494695187, -0.005249375477433205, 0.024033263325691223, -0.05731533467769623, -0.024388454854488373, 0.049292393028736115, 0.021793417632579803, 0.0034403048921376467, 0.01806379109621048, -0.019174935296177864, -0.0628773495554924, 0.09250830858945847, 0.038295961916446686, 0.026418574154376984, -0.0013811843236908317, -0.048301175236701965, 0.03278755024075508, 0.02290363982319832, -0.06141883134841919, -0.020686110481619835, -0.03569354861974716, -0.021662835031747818, 0.022098230198025703, -0.06614334136247635, 0.014565219171345234, -0.04288310185074806, -0.01638162136077881, 0.03691919520497322, 0.01808813214302063, -0.046993501484394073, -0.04621649533510208, -0.03921152278780937, -0.02763392962515354, 0.032450251281261444, 0.02254442498087883, -0.0329773910343647, 0.011034750379621983, 0.047271065413951874, 0.02332296408712864, -0.009485552087426186, -0.013713621534407139, -0.01683204248547554, -0.09880784898996353, 0.011327587999403477, 0.03518662601709366, -0.01377902366220951, -0.019471747800707817, 0.03313940390944481, -0.02453978918492794, 0.060288187116384506, -0.052352242171764374, 0.03694402799010277, -0.047225628048181534, -0.0044026137329638, -0.007177719380706549, -0.024778207764029503, 0.013864931650459766, 0.0343530997633934, 0.005899359937757254, -0.04241655394434929, -0.01229146309196949, 0.013543938286602497, -0.00674918619915843, -0.022946178913116455, 0.03935971111059189, -0.035881299525499344, 0.004628542345017195, 0.030235297977924347, -0.01883935183286667, -0.02024325355887413, -0.004085200373083353, 0.01797902025282383, 0.043021444231271744, 0.004777663387358189, -0.02501090243458748, 0.010882122442126274, -0.01576378010213375, 0.03958078473806381, -0.05142997205257416, 0.02000943012535572, 0.01476879883557558, -0.07015193998813629, 0.026462234556674957, 0.04034305363893509, -0.06284584105014801, 0.011409555561840534, 0.010760413482785225, 0.015922334045171738, 0.019815834239125252, -0.08662688732147217, 0.045187365263700485, -0.009484096430242062, 0.02328908070921898, -0.022587070241570473, 0.005265864543616772, 0.009472405537962914, -0.013418220914900303, -0.017076194286346436, -0.0217732023447752, 0.02078995853662491, 0.024744171649217606, 0.019086355343461037, -0.03384622558951378, 0.006073209457099438, 0.02493935078382492, -0.041550468653440475, -0.01480324286967516, -0.0010969938011839986, -0.017772456631064415, -0.0359562486410141, 0.031258758157491684, -0.0032942567486315966, -0.016546102240681648, 0.04752270504832268, 0.00010387121437815949, 0.047993823885917664, 0.07632007449865341, -1.651245469247442e-7, -0.02604714408516884, -0.01412791945040226, 0.03612937033176422, -0.019593648612499237, -0.0025147900450974703, 0.018108779564499855, -0.052238624542951584, 0.06380786001682281, 0.005917413160204887, 0.04373228922486305, 0.06781869381666183, 0.03157958760857582, -0.016732648015022278, -0.02372739091515541, -0.006051978096365929, 0.005472284276038408, 0.07403244078159332, -0.036535751074552536, 0.031283631920814514, -0.01686878688633442, -0.0025784869212657213, -0.04702100157737732, -0.01269122026860714, 0.029933318495750427, 0.11631615459918976, -0.002935511525720358, 0.015972448512911797, -0.07590480893850327, 0.008104618638753891, -0.041225314140319824, 0.08802936226129532, 0.02707446739077568, 0.002618531696498394, -0.006895389407873154, 0.01077713817358017, 0.028293080627918243, 0.008195368573069572, 0.025341952219605446, -0.03822588920593262, -0.02693077363073826, 0.005143978167325258, -0.03817051276564598, -0.01587086170911789, 0.02808084338903427, 0.06291703134775162, 0.015355267561972141, 0.0016960581997409463, -0.05660289153456688, -0.023609431460499763, -0.021195443347096443, -0.016360532492399216, 0.01680574007332325, -0.014846582897007465, -0.03921325504779816, -0.006300462409853935, 0.002334080869331956, -0.04474039748311043, 0.048841800540685654, -0.012696434743702412, 0.010439079254865646, 0.008712900802493095, 0.05175425484776497, 0.004998097661882639, 0.005732014309614897, -0.022110870108008385, 0.018490402027964592, 0.03853491321206093, 0.017264897003769875, 0.009147622622549534, 0.019044822081923485, -0.04114825651049614, 0.03557625785470009, -0.007499717175960541, -0.02307720109820366, 0.0011508871102705598, -0.028568079695105553, -0.024940943345427513, -0.06513122469186783, 0.050041940063238144, -0.0008397899800911546, 0.04982933774590492, -0.015832606703042984, -0.020626038312911987, 0.01467860583215952, 0.00989502016454935, 0.00083741988055408, -0.012558545917272568, 0.0431678406894207, -0.048183031380176544, 0.012348463758826256, -0.10072879493236542, 0.028587812557816505, 0.008686068467795849, -0.006273836828768253, 0.03143586218357086, 0.008751751855015755, 0.0340418666601181, -0.031125951558351517, 0.06862751394510269, 0.0716472938656807, -0.07307761907577515, 0.0030413649510592222, -0.0148323280736804, 0.03302406892180443, 0.023294325917959213, -0.01931578852236271, -0.014862910844385624, -0.04210645705461502, -0.0011909547029063106, 0.03531220555305481, 0.0008250594837591052, -0.0032864073291420937, -0.036077890545129776, -0.020711002871394157, 0.015042273327708244, 0.012089797295629978, -0.015996987000107765, -0.03115222416818142, 0.010233311913907528, 0.0017689124215394258, -0.013329043053090572, 0.10645865648984909, 0.08218994736671448, -0.006540974602103233, 0.0030203047208487988, 0.00948853138834238, 0.024895042181015015, 0.045488882809877396, 0.0311093982309103, -0.013321626000106335, -0.014759553596377373, 0.010721101425588131, -0.011159397661685944, 0.0053403000347316265, 0.043800558894872665, -0.03416357561945915, 0.04589133337140083, 0.019675014540553093, 0.036626413464546204, -0.0014059600653126836, -0.08318279683589935, -0.08816836029291153, -0.02707824297249317, 0.01261503342539072, 0.04897451028227806, -0.042769644409418106, 0.031037934124469757, 0.05912065878510475, 0.02166762575507164, -0.0253070667386055, 0.03509845212101936, 0.012769193388521671, 0.03532840684056282, -0.052141956984996796, -0.054531317204236984, 0.0458487942814827, -0.03255726024508476, 0.01335385162383318, 0.009522125124931335, 0.008215735666453838, -0.040159329771995544, 0.0060390387661755085, 0.0014167234767228365, 0.04024697095155716, 0.010054881684482098, -0.0495000034570694, 0.030765950679779053, -0.0006415096577256918, 0.02399204857647419, -0.0007813720731064677, 0.009102343581616879, 0.05918596312403679, -0.008040497079491615, 0.002767641795799136, 0.007856791839003563, 0.0058394731022417545, 0.0511610247194767, 0.017523296177387238, 0.039144888520240784, 0.044680774211883545, 0.003448497736826539, -0.03209428861737251, 0.039626214653253555, 0.03211488947272301, -0.09419959783554077, -0.023036932572722435, 0.03910538926720619, -0.07431592047214508, -0.06579489260911942, 0.0625496357679367, 0.026704462245106697, -0.00781564973294735, 0.015773994848132133, -0.04284718260169029, -0.043438561260700226, -0.02385910414159298, 0.006538371089845896, -0.034434106200933456, -0.0363251194357872, 0.052110809832811356, -0.06297554075717926, -0.09292291849851608, -0.03859466314315796, -0.027086099609732628, -0.039176248013973236, 0.019586291164159775, -0.0391087681055069, -0.04807876795530319, 0.04340429604053497, 0.0014710561372339725, 0.06155231595039368, -0.021670710295438766, -0.008840418420732021, -0.0034090690314769745, 0.031985506415367126, 0.008275162428617477, 0.0037583999801427126, -0.010778916999697685, 0.052380047738552094, -0.048144079744815826, 0.03339020535349846, 0.02050602063536644, 0.061870377510786057, 0.07127436250448227, -0.08483456820249557, 0.011398478411138058, 0.016744568943977356, -0.08386394381523132, -0.03246717154979706, 0.050140004605054855, -0.027701253071427345, 0.06488966196775436, 0.02166137658059597, -0.012668058276176453, -0.045511145144701004, -0.058720361441373825, -0.05102994665503502, 0.04854077473282814, 0.02622896432876587, -0.09423602372407913, -0.03378479555249214, 0.09124312549829483, 0.004880493972450495, -0.012308488599956036, -0.0605643168091774, -0.031950149685144424, 0.0013949081767350435, -0.033570315688848495, -0.039281632751226425, 0.10411275178194046, -0.015872124582529068, 0.018590232357382774, 0.06185050681233406, 0.00858919508755207, 0.035742614418268204, -0.02167057804763317, -0.03977290540933609, 0.05273563042283058, -0.0300299059599638, -0.007395295891910791, -0.02396477200090885, -0.0010331061203032732, -0.05795646086335182, -0.012710673734545708, -0.018707139417529106, 0.003967254422605038, 0.03587833791971207, -0.062303535640239716, 0.03496401011943817, 0.03607362508773804, -0.0010710370261222124, -0.0023015239275991917, -0.0179439727216959, -0.05632312223315239, 0.03569852188229561, -0.02183452993631363, 0.06618669629096985, 0.04805983975529671, 0.027338150888681412, 0.026357941329479218, -0.004416037816554308, -0.0752885639667511, 0.0004430594271980226, 0.013323955237865448, -0.04591723904013634, 0.008337379433214664, 0.06682854145765305, 0.034701235592365265, 0.00382608431391418, -0.022542539983987808, -0.03954640403389931, 0.0456722192466259, 0.030774295330047607, -0.023123105987906456, 0.000614168297033757, -0.0036507872864603996, -0.033789586275815964, -0.031143860891461372, 0.024002933874726295, -0.020319825038313866, -0.011488711461424828, 0.0524568073451519, 0.06302747875452042, 0.014537310227751732, -0.02725241333246231, 0.052330903708934784, 0.006805244833230972, -0.021271971985697746, 0.01729421503841877, 0.0003825509629677981, -0.008323317393660545, -0.02614150568842888, 0.07694841176271439, 0.0034186337143182755, 0.00907081924378872, -0.052212491631507874, 0.04188099130988121, -0.05493585020303726, 0.09851031750440598, 0.04339948296546936, -0.06156733259558678, 0.024596435949206352, 0.001164132496342063, -0.04874967783689499, 0.051663659512996674, -0.03021809458732605, -0.048542171716690063, -0.016988173127174377, 0.00528851430863142, -0.019139360636472702, -0.014297851361334324, -0.020853480324149132, -0.04595738649368286, 0.016717130318284035, 0.0658775046467781, -0.06278841942548752, 0.039135489612817764, -0.01998422108590603, 0.038007888942956924, 0.015215998515486717, 0.0031848277430981398, 0.0116724306717515, 0.012396575883030891, 0.09358897805213928, 0.07921823859214783, -0.062081389129161835, 0.025994259864091873, -0.018142661079764366, 0.028394434601068497, 0.015063108876347542, 0.0619831308722496, 0.006963244639337063, -0.035462480038404465, 0.02965572662651539, -0.04585916921496391, 0.025595812126994133, -0.014906685799360275, 0.012396606616675854, 0.053103506565093994, -0.0067000617273151875, -0.004512461833655834, 0.005891392473131418, -0.010711992159485817, 0.0413937084376812, 0.019810102880001068, 0.07081110030412674, -0.0531352274119854, -0.0476100780069828, 0.0033193216659128666, -0.05557577311992645, 0.05202556774020195, -0.044681210070848465, 0.0705408900976181, -0.016903730109333992, 0.025452954694628716, -0.021923314779996872, 0.017855847254395485, -0.020598534494638443, 0.03467373177409172, 0.03761593997478485, 0.01572870835661888, 0.008128464221954346, -0.004436245653778315, 0.0036035114899277687, -0.05624467879533768, 0.007370558101683855, -0.0110118193551898, -0.0047601135447621346, 0.01609436422586441, -0.017605841159820557, 0.011668712832033634, -0.01062415074557066, -0.03339080885052681, 0.04693226516246796, 0.03427563235163689, 0.005163877736777067, -0.03853233903646469, -0.02169741690158844, -0.010163913480937481, -0.08537322282791138, -0.03625589981675148, -0.021682361140847206, 0.014595916494727135, 0.009667521342635155, -0.019405227154493332, -0.002056163502857089, -0.05545626953244209, 0.01807565800845623, -0.043948300182819366, 0.049576535820961, -0.024524468928575516, -0.049769554287195206, 0.05759471654891968, -0.036179929971694946, 0.07695246487855911, -0.04556240513920784, 0.011903342790901661, 0.02339499071240425, 0.05282866582274437, -0.041499532759189606, -0.031146656721830368, -0.0483466275036335, -0.02824653871357441, 0.0634320080280304, 0.02163224294781685, 0.014639654196798801, 0.074458047747612, -0.000044715259718941525, 0.00293978420086205, 0.006663493346422911, -0.015997976064682007, 0.025076815858483315, 0.02366812899708748, -0.005214603152126074, 0.09244158118963242, 0.04127657413482666, 0.02730962075293064, 0.0318787582218647, -0.0001585407298989594, -0.005365132354199886, -0.011277942918241024, -0.016711782664060593, 0.029444096609950066, -0.02317582629621029, -0.026616711169481277, 0.02546900138258934, -0.02410629577934742, -0.004910400602966547, 0.01447863969951868, -0.01860327459871769, 0.00040326829184778035, 0.013496502302587032, -0.010411215014755726, 0.007049019448459148, -0.01797928288578987, 0.000939984864089638, -0.05461200326681137, -0.04200305417180061, -0.02339787594974041, -0.006814411375671625, -0.010635262355208397, 0.03709268942475319, -0.0374842993915081, 0.014126939699053764, 0.03106101043522358, -0.006977811921387911, -0.0704740509390831, 0.032776325941085815, -0.09093484282493591, -0.0027354636695235968, -0.03591148555278778, -0.009775955229997635, -0.030076460912823677, -0.014657181687653065, -0.055095374584198, 0.0010335788829252124, 0.05706832930445671, 0.03927022963762283, -0.012958406470716, 0.031217528507113457, -0.0011175103718414903, -0.00788919162005186, 0.02263689786195755, -0.030080150812864304, 0.005927318707108498, -0.006565480958670378, -0.01284109242260456, 0.07226080447435379, 0.05992148444056511, -0.03569583222270012, -0.06043999269604683, -0.03780704364180565, -0.006757068447768688, -0.000786151154898107, 0.04573732241988182, 0.011466676369309425, 0.02055450715124607, 0.040622860193252563, -0.05166803300380707, 0.03912045806646347, -0.028426937758922577, 0.003915166947990656, 0.046509578824043274, -0.03207241743803024, -0.027903614565730095, -0.03362955152988434, 0.005580070894211531, -0.0006569510442204773, 0.06323482096195221, 0.002340750303119421, -0.04889288917183876, 0.0015950283268466592, 0.013669408857822418, -0.04069435968995094, -0.03870270401239395, -0.01135893166065216, 0.03391873836517334, 0.01566227525472641, -0.011686470359563828, -0.016052594408392906, 0.08442967385053635, -0.0013594906777143478, -0.11201096326112747, 0.029989143833518028, 0.004521001596003771, -0.004474005661904812, 0.017370563000440598, 0.009586728177964687, -0.037397876381874084, 0.002462836680933833, -0.020111938938498497, 0.015097400173544884, 0.016284426674246788, -0.016974419355392456, -0.03371760621666908, 0.045042987912893295, 0.013227695599198341, -0.006695447489619255, 0.020712751895189285, 0.02436019480228424, 0.005784375127404928, -0.02017066441476345, 0.02303246408700943, 0.044441524893045425, -0.015800606459379196, -0.05190446972846985, 0.028984837234020233, -0.016424959525465965, 0.023374266922473907, -0.0684417337179184, -0.0733395367860794, -0.0032520657405257225, 0.03044307976961136, 0.0018676712643355131, 0.020155517384409904, -0.0032657121773809195, -0.0045745656825602055, -0.027634141966700554, -0.0028688085731118917, -0.0025165947154164314, -0.013884023763239384, -0.02455732226371765, 0.018868589773774147, 0.03580566123127937 ]
<p>A physical quantity can be represented by the following form:</p> <p>$A = a_1\sigma_1 + a_2\sigma_2 + a_3\sigma_3$ where $\sigma$ matrices are Pauli matrices. Also suppose that there is $B = b_1\Sigma_1 + b_2\Sigma_2 + b_3\Sigma_3$.</p> <p>A. I read that $a_1,a_2,a_3$ are direction vectors, and when the sum of A's representing real quantity and B's is zero, as each quantity can only be 1 or -1, probability $AB$ being 1 or -1 depend on the value of $-a_1b_1 - a_2b_2 - a_3b_3$. </p> <p>The question would be: isn't $a_1,a_2.., b_1,b_2,..$ only direction vectors? If so, how can probability of finding $AB$ being 1 change? I do get this mathematically, but I am unable to picture the situation with $a,b$ being direction vectors.</p> <p>B. I read that when the sum of A's representing real quantity and B's is zero, determining a value on one direction of $A$ set the value of the whole $A$. Is this true? Can anyone explain this?</p>
g5429
[ -0.01965651847422123, -0.004001555498689413, -0.024890083819627762, -0.001201843610033393, 0.026392407715320587, -0.006651917938143015, 0.048162125051021576, 0.020812857896089554, -0.06582320481538773, -0.0022126915864646435, 0.003751055570319295, 0.010494960471987724, 0.054531436413526535, -0.013257546350359917, -0.008683593012392521, -0.012755936942994595, 0.047029152512550354, -0.01355735957622528, 0.01784709095954895, 0.027168722823262215, -0.037140022963285446, -0.026769738644361496, -0.029453696683049202, -0.023294536396861076, 0.011390316300094128, -0.12257067114114761, -0.02273014932870865, -0.006856847554445267, -0.022688986733555794, -0.02491900511085987, -0.02874710224568844, 0.054776158183813095, 0.05895864963531494, -0.037552110850811005, -0.02802707441151142, -0.05653524026274681, 0.051374565809965134, 0.031606439501047134, 0.01580308936536312, 0.025633471086621284, -0.019584016874432564, -0.03920445591211319, 0.0287505891174078, -0.0371796116232872, -0.058130692690610886, -0.022730862721800804, 0.002933834446594119, 0.012204011902213097, 0.02917351759970188, 0.019033029675483704, 0.02043556608259678, -0.029979057610034943, 0.007465108763426542, -0.002930092392489314, -0.022869164124131203, 0.023695820942521095, 0.03587786853313446, -0.00235101580619812, 0.038960617035627365, 0.05673336237668991, 0.06835440546274185, -0.03364970535039902, -0.026021260768175125, -0.021601222455501556, 0.06317934393882751, -0.019882965832948685, -0.03978944197297096, 0.013132967986166477, -0.03910709545016289, 0.038988009095191956, 0.004863109439611435, 0.013942951336503029, 0.03404973819851875, -0.052938126027584076, 0.00688193179666996, -0.031207963824272156, 0.005448914598673582, 0.014789553359150887, 0.05117456242442131, 0.05006393790245056, 0.007375262677669525, 0.0021326751448214054, 0.061916958540678024, 0.024865835905075073, 0.04350120201706886, 0.03965502977371216, 0.03469179570674896, 0.047764286398887634, -0.0420953594148159, 0.013993019238114357, -0.021374445408582687, 0.013715284876525402, 0.0015236387262120843, 0.04475812613964081, -0.019485974684357643, -0.05409136787056923, -0.04326260834932327, 0.06089678034186363, -0.020791741088032722, 0.006988431327044964, 0.031495850533246994, 0.08766639977693558, 0.06016939505934715, -0.012179065495729446, -0.07134904712438583, 0.03611103445291519, 0.010438057594001293, 0.038098812103271484, -0.033980391919612885, -0.011715049855411053, -0.0660448670387268, -0.01349907461553812, -0.034428492188453674, -0.020722758024930954, -0.022755470126867294, 0.040009766817092896, 0.06680574268102646, -0.0033313948661088943, 0.0043162149377167225, 0.01684509590268135, 0.019097423180937767, -0.03425079956650734, 0.07640737295150757, 0.05003231391310692, -0.018042240291833878, 0.025945130735635757, -0.07802875339984894, 0.08095172047615051, 0.08697903901338577, -0.03594765067100525, 0.026472117751836777, -0.028233807533979416, 0.025927063077688217, 0.0007102341623976827, 0.010202022269368172, 0.006973614450544119, -0.03356385603547096, 0.07419418543577194, 0.03130103275179863, 0.02206721343100071, -0.0304653849452734, -0.026626035571098328, -0.029901163652539253, 0.010750026442110538, 0.023401977494359016, -0.022630002349615097, -0.009058746509253979, -0.0270540714263916, 0.048969145864248276, -0.007359145674854517, 0.034124523401260376, 0.0887419655919075, -0.05117914080619812, -0.05130661651492119, -0.00602018041536212, 0.031102057546377182, 0.015811733901500702, 0.0038856344763189554, -0.029657812789082527, -0.032628025859594345, 0.06029320880770683, -0.0015746824210509658, -0.0035577493254095316, -0.002316234400495887, -0.029222799465060234, -0.016380686312913895, 0.011836486868560314, -0.039617665112018585, 0.02881218120455742, 0.02494937740266323, 0.029145609587430954, -0.011240772902965546, -0.028877614066004753, 0.012803767807781696, 0.02091001160442829, 0.06349527835845947, 0.005402611568570137, 0.036774955689907074, 0.046525824815034866, 0.01958060823380947, -0.020999355241656303, -0.008793729357421398, 0.008305618539452553, -0.0006930359522812068, 0.030485589057207108, -0.03388145565986633, -0.013295038603246212, 0.09750086814165115, -0.06839942187070847, 0.006812367122620344, -0.04243254289031029, 0.01127906609326601, -0.023191018030047417, 0.00022293702932074666, 0.017365779727697372, -0.01508931815624237, 0.017620710656046867, -0.006019751075655222, -0.026620304211974144, 0.05247430503368378, 0.025866979733109474, 0.03687359392642975, 0.016478849574923515, 0.009301606565713882, -0.00037354862433858216, 0.029575450345873833, 0.03108201175928116, -0.0033478932455182076, -0.04952462390065193, 0.018525928258895874, 0.010243372060358524, 0.018498850986361504, 0.020126264542341232, -0.005386343225836754, 0.008255003951489925, -0.038761839270591736, 0.06783992052078247, 0.010755029506981373, -0.004753156565129757, -0.010191204957664013, 0.0043205260299146175, -0.05171471834182739, 0.020306872203946114, 0.06303365528583527, -0.03632960468530655, 0.07581295818090439, 0.02546919882297516, -0.06447474658489227, 0.015473329462110996, 0.03128174692392349, -0.04267672076821327, 0.009816540405154228, -0.023044362664222717, 0.06526468694210052, 0.03029131330549717, -0.0029220201540738344, 0.00843009166419506, 0.005448971875011921, 0.06352142244577408, 0.03556971624493599, -0.009689114056527615, -0.07585133612155914, 0.023982519283890724, 0.07646030187606812, 0.05434790253639221, -0.07977960258722305, -0.010369719937443733, -0.019411001354455948, -0.04236561805009842, 0.0513717383146286, -0.06627563387155533, -0.06463871151208878, -0.050271544605493546, 0.020464790984988213, -0.003325504483655095, -0.005446539726108313, -0.01587572507560253, -0.002961323596537113, -0.01008619274944067, 0.03684019669890404, -0.022242000326514244, -0.026757730171084404, 0.08837203681468964, 0.06287826597690582, 0.01884980872273445, -0.021405702456831932, -0.02683981880545616, 0.0008673311676830053, 0.015129070729017258, 0.04787313938140869, -0.013687580823898315, 0.02018636278808117, 0.04363081976771355, 0.001430606935173273, -0.010522383265197277, 0.03898394852876663, 0.0007379180169664323, 0.007361377589404583, -0.0074242400005459785, 0.030901620164513588, -0.022074423730373383, 0.05098193883895874, -0.035061199218034744, -0.03537695109844208, 0.025236746296286583, -0.03927521035075188, 0.018223445862531662, -0.008535302244126797, 0.007866857573390007, 0.04100174829363823, -0.012644439935684204, 0.060073088854551315, 0.04734455421566963, -0.09402426332235336, 0.013729950413107872, -0.004754454828798771, 0.0027325961273163557, -0.057530518621206284, 0.02265424095094204, 0.03991178423166275, -0.021806858479976654, 0.04414725676178932, 0.014149090275168419, -0.03684394061565399, 0.07803895324468613, 0.05650217831134796, -0.07318797707557678, 0.02326136827468872, 0.017571721225976944, -0.028448637574911118, 0.006503512617200613, 0.0378776490688324, -0.00374414911493659, -0.058556050062179565, -0.04441944509744644, 0.0120518384501338, 0.004201049450784922, 0.004280303604900837, -0.0017766730161383748, -0.03796279430389404, -0.00991425383836031, -0.017675261944532394, -0.015649840235710144, -0.0026372538413852453, 0.019167734310030937, -0.010766066610813141, -0.019306546077132225, 0.027844969183206558, -0.015858210623264313, 0.016814185306429863, 0.03191818669438362, -0.0016910904087126255, 0.0417197048664093, -0.014180359430611134, -0.07494837790727615, -0.026567362248897552, -0.01549896877259016, -0.033644188195466995, 0.02860504575073719, -0.0042668976821005344, -0.02536955662071705, -0.024374008178710938, 0.0022592702880501747, -0.0014846102567389607, 0.03210771083831787, -0.01581750251352787, 0.0005945697193965316, 0.03911671042442322, 0.073588065803051, 0.006609001662582159, -0.0026764373760670424, -0.02673095278441906, -0.00654303003102541, 0.015080520883202553, 0.012108181603252888, 0.05856067314743996, -0.028529686853289604, 0.0330214761197567, -0.0021410968620330095, -0.002894424134865403, -0.00824873149394989, -0.06064390018582344, -0.03423531726002693, 0.006038011983036995, 0.08209576457738876, -0.012520872987806797, 0.009487236849963665, -0.002898147562518716, 0.021258100867271423, 0.0305956844240427, 0.04112447798252106, 0.009047306142747402, -0.013091452419757843, 0.05527930334210396, -0.0012917628046125174, -0.03886590152978897, -0.04208727553486824, -0.01633649878203869, -0.029535746201872826, 0.03645333647727966, 0.018888212740421295, 0.0013082892401143909, 0.02248452603816986, 0.016343431547284126, 0.01022733561694622, -0.0015367037849500775, -0.06528656929731369, 0.0020485681015998125, -0.02067805640399456, -0.025054307654500008, 0.014042590744793415, -0.01212388277053833, -0.026435721665620804, -0.022001933306455612, -0.02142854779958725, -0.02244006283581257, -0.023790299892425537, -0.03749499469995499, -0.05231274291872978, 0.022272475063800812, -0.031465575098991394, -0.005869115702807903, 0.03439963981509209, -0.035436466336250305, 0.08482713997364044, 0.0029355839360505342, 0.01334060076624155, 0.03427654132246971, 0.004816174041479826, 0.016889235004782677, -0.006531293969601393, -0.03390868753194809, 0.008754117414355278, -0.08249234408140182, 0.030139656737446785, 0.062463484704494476, -0.003762456588447094, 0.021986711770296097, 0.04969736561179161, -0.014100247994065285, 0.053528137505054474, -0.0255719106644392, -0.021994180977344513, -0.02764013782143593, -0.0020373761653900146, 0.026887010782957077, 0.018815917894244194, 0.01614566519856453, 0.0816364735364914, 0.0022559063509106636, -0.010899082757532597, 0.036087896674871445, 0.011242165230214596, -0.011169174686074257, -0.059360139071941376, -0.018307127058506012, -0.05557499825954437, 0.030111823230981827, 0.0097729517146945, 0.021345963701605797, 0.03299211338162422, 0.04071247950196266, 0.022331848740577698, -0.02699173055589199, -0.005593044683337212, -0.008348850533366203, -0.02532937563955784, -0.05126696825027466, 0.02601516619324684, -0.03464766591787338, -0.06519869714975357, 0.018415575847029686, -0.015276755206286907, -0.11001543700695038, 0.03137193247675896, 0.021481655538082123, -0.019331341609358788, 0.053191300481557846, 0.05288640037178993, 0.04521767422556877, -0.018494749441742897, -0.057592373341321945, -0.01955859549343586, 0.021488934755325317, -0.03667247295379639, -0.006309655494987965, -0.04964710772037506, -0.0056203207932412624, -0.044073279947042465, -0.010872266255319118, -0.0028690313920378685, 0.049743883311748505, 0.022569695487618446, 0.016958752647042274, -0.0158443171530962, -0.049792129546403885, -0.05121748149394989, -0.02237621694803238, -0.053441356867551804, -0.022853104397654533, -0.026054931804537773, 0.015945149585604668, 0.058110304176807404, 0.0411706380546093, 0.0033921583089977503, 0.0028790405485779047, -0.015486003831028938, -0.07617075741291046, 0.01437163632363081, -0.040692493319511414, 0.07011044025421143, 0.02183881215751171, 0.06580999493598938, 0.0065633514896035194, -0.08226653933525085, -0.031239131465554237, -0.016902796924114227, 0.004851787816733122, -0.020706500858068466, -0.0030064487364143133, -0.026907948777079582, 0.008853070437908173, 0.004919894505292177, -0.029157491400837898, -0.03412482142448425, 0.01765514351427555, 0.012737361714243889, -0.027798490598797798, -0.017644301056861877, 0.031226489692926407, -0.016873715445399284, 0.031009318307042122, -0.013020290061831474, -0.03371113911271095, 0.008850758895277977, -0.04602896049618721, -0.012271203100681305, 0.046562690287828445, -0.03259885311126709, 0.043669648468494415, 0.012128658592700958, -0.01281428150832653, 0.010320001281797886, -0.03015325590968132, -0.0027277835179120302, -0.034331344068050385, -0.05999007076025009, -0.08185169100761414, 0.030840786173939705, 0.059919603168964386, -0.002494016895070672, 0.011098709888756275, -0.028333157300949097, -0.019792873412370682, -0.060826003551483154, -0.01355029921978712, 0.032624050974845886, 0.023528702557086945, 0.054503925144672394, 0.005181672051548958, 0.024050571024417877, -0.06033945083618164, -0.028689023107290268, 0.05192803591489792, -0.003844225313514471, -0.02179035171866417, -0.018632542341947556, -0.012832967564463615, -0.026191452518105507, -0.04759102314710617, -0.03659197315573692, 0.026221863925457, -0.05919916182756424, -0.04658040404319763, 0.017445312812924385, -0.0068943193182349205, -0.060651663690805435, 0.01663302816450596, -0.0053148427978158, -0.009158973582088947, 0.032059937715530396, 0.0029788301326334476, -0.03662760555744171, -0.05361884832382202, -0.008801480755209923, -0.02281329408288002, -0.010631203651428223, -0.03112378530204296, 0.0037913562264293432, 0.08874659985303879, -0.02632567659020424, -0.011525673791766167, -0.013817334547638893, 0.011142910458147526, 0.01831677369773388, -0.005223101004958153, -0.07431250065565109, -0.07087327539920807, -0.04409457743167877, 0.03605766221880913, 0.01590067148208618, 0.0009698371286503971, 0.024768656119704247, 0.002798710484057665, -0.020470093935728073, 0.009714532643556595, -0.044570453464984894, -0.015418902039527893, 0.05094699189066887, 0.019853714853525162, -0.03744324669241905, 0.00011559105769265443, -0.01938972994685173, -0.04760108143091202, -0.04729164391756058, -0.019156528636813164, -0.011021483689546585, 0.03978915140032768, -0.036685094237327576, -0.026861390098929405, 0.00965571403503418, -0.005504414904862642, -0.020040391013026237, -0.0020874259062111378, 0.012102394364774227, 0.02446490153670311, -0.043314129114151, -0.004459786228835583, 0.02321597933769226, 0.037975821644067764, -0.0057570054195821285, 0.024094222113490105, -0.035607993602752686, 0.07251052558422089, 0.04367389157414436, -0.002573467558249831, -0.01852872408926487, 0.012168454006314278, -0.021339450031518936, 0.031055305153131485, 0.0074073695577681065, -0.005260813049972057, 0.030454738065600395, -0.031704727560281754, 0.08290550112724304, 0.040290962904691696, -0.025806380435824394, -0.0003034284454770386, 0.0756903812289238, 0.06258836388587952, -0.002403608290478587, -0.03844787925481796, -0.04408293962478638, 0.06380517780780792, 0.017424706369638443, -0.0011536722304299474, -0.051101017743349075, 0.043370041996240616, 0.04323884844779968, 0.09009774029254913, -0.0155861247330904, -0.012228420935571194, 0.02840595692396164, 0.024665698409080505, -0.02178942784667015, -0.013123060576617718, 0.0019227254670113325, -0.012340331450104713, -0.0697387158870697, -0.006187032908201218, 0.03088783286511898, 0.009351908229291439, 0.0012624413939192891, 0.002198893576860428, -0.049010712653398514, 0.0022852174006402493, 0.0290627870708704, -0.002168702892959118, 0.02790870890021324, -0.08830869942903519, -0.015971364453434944, -0.016881991177797318, 0.0004581663233693689, 0.01059792097657919, -0.005972706247121096, 0.06232443451881409, 0.020245881751179695, -0.006551101338118315, -0.009116183035075665, -0.011660175397992134, -0.008432649075984955, -0.014310626313090324, -0.060460954904556274, 0.05736261233687401, 0.019352059811353683, 0.01664104498922825, -0.013145853765308857, 0.05351347103714943, -0.048859886825084686, -0.03391260281205177, 0.06486303359270096, 0.022546933963894844, -0.0033730335999280214, -0.002459837356582284, -0.026867052540183067, 0.03147907555103302, 0.012174834497272968, 0.026739388704299927, -0.03716171532869339, 0.018717851489782333, 0.05420004576444626, -0.05565611273050308, 0.07652847468852997, 0.007312513887882233, -0.04376654699444771, -0.05643560737371445, 0.0014712007250636816, 0.06598486751317978, -0.04391412064433098, 0.020272674039006233, 0.01017450075596571, 0.007043768651783466, 0.022497281432151794, 0.02992972731590271, -0.054861776530742645, -0.01766449213027954, 0.06396083533763885, 0.022133728489279747, 0.009886907413601875, -0.038684457540512085, -0.06638840585947037, 0.00004845955845667049, -0.00741231394931674, 0.008784220553934574, -0.010134267620742321, -0.06676026433706284, -0.04638107120990753, 0.02322404645383358, 0.008809635415673256, -0.0032784780487418175, -0.004392098169773817, 0.016140390187501907, -0.03294362500309944, -0.020328601822257042, -0.04630647599697113, 0.007690064143389463, -0.02536376193165779, 0.006670873146504164, 0.03611624613404274, 0.03601183369755745, -0.046609457582235336, -0.0009815782541409135, -0.08634768426418304, 0.07025256007909775, 0.03852580487728119, 0.002128573600202799, -0.0008315225131809711, -0.06322812288999557, -0.04858303442597389, -0.008367005735635757, -0.04494599625468254, -0.01796417124569416, 0.01505226455628872, 0.02222897857427597, -0.05516331270337105, -0.005946659483015537, -0.07528004050254822, 0.07730337232351303, 0.05375903099775314, -0.04060325026512146, -0.09935031086206436, 0.0030509873759001493, -0.043329864740371704, 0.07940260320901871, 0.014801585115492344, 0.01849771849811077, 0.008112955838441849, -0.01727680116891861, 0.0041465917602181435, -0.061037808656692505, 0.0026773104909807444, -0.026612699031829834, -0.031493231654167175, 0.02585642598569393, -0.01707395724952221, -0.04488896206021309, -0.057384032756090164, 0.03962891548871994 ]
<blockquote> <p><strong>Question:</strong> The maximum range of projectile is $R$ and the maximum height attained by the particle is <em>H</em>. </p> <p>If the area covered by the particle between its path and horizontal line is $A$, then $A$ =</p> <ol> <li><p>$\frac{2}{5}$</p></li> <li><p>$\frac{2}{3}$</p></li> <li><p>$\frac{4}{5}$</p></li> <li><p>$\frac{1}{3}$</p></li> </ol> </blockquote> <p>I know the formula for maximum range $R$ and maximum height $H$</p> <p>$R=\frac{U^2}{g}$, $U$ is initial veocity and $g$ is acceleration due to gravity </p> <p>$$H=\frac{U^2 \sin^2\theta}{2g}$$</p> <p>I can't find the way to realte this formula with the question.</p>
g5430
[ 0.07089799642562866, 0.041662611067295074, 0.0037063350901007652, 0.029854267835617065, 0.012581066228449345, 0.04146180301904678, -0.019470298662781715, -0.0035310008097440004, -0.0798499807715416, -0.0075179110281169415, -0.04465050250291824, 0.04473003372550011, 0.06888491660356522, 0.021652735769748688, -0.03457576036453247, -0.00801425613462925, 0.08402212709188461, -0.027750294655561447, -0.03727563098073006, -0.03192116692662239, -0.020722249522805214, -0.0044004051014781, -0.006055206060409546, -0.03878156095743179, -0.015188140794634819, -0.02920575812458992, 0.06594454497098923, -0.014072325080633163, -0.06703398376703262, 0.04001166671514511, 0.0020801012869924307, -0.02949650213122368, 0.0018836031667888165, -0.038650840520858765, 0.008330599404871464, -0.038869164884090424, 0.0438757948577404, 0.0196377020329237, 0.027004122734069824, -0.02301076054573059, 0.0386408194899559, -0.03272853419184685, 0.08392224460840225, -0.027879731729626656, 0.004860294982790947, -0.01697652041912079, -0.01195848174393177, -0.008989973925054073, -0.0036769635044038296, -0.05258616805076599, -0.10651525110006332, 0.012424363754689693, -0.019305529072880745, -0.0681266039609909, 0.0023949937894940376, 0.03951607272028923, -0.0252948310226202, -0.03132735937833786, 0.03361964598298073, 0.028274212032556534, -0.010803064331412315, -0.025222938507795334, -0.010650095529854298, -0.03441953659057617, 0.06493537873029709, -0.02152317576110363, -0.034527212381362915, 0.015806907787919044, -0.04034551978111267, 0.0024347989819943905, 0.04957067593932152, -0.05995645001530647, -0.0011363971279934049, -0.05514536052942276, -0.07183121889829636, -0.033624257892370224, -0.04407431557774544, 0.01951483078300953, 0.01883895881474018, 0.021412091329693794, -0.01118724886327982, 0.022781988605856895, -0.011661066673696041, -0.0666370615363121, -0.0047449106350541115, 0.02384393848478794, 0.044078849256038666, 0.01674116589128971, -0.03469453006982803, 0.026897955685853958, -0.012648656032979488, 0.01703181490302086, 0.03018082305788994, 0.01109896507114172, -0.02693856693804264, 0.01086749043315649, -0.0337543860077858, 0.03817501291632652, 0.012938403524458408, -0.030680878087878227, 0.06773500889539719, -0.028899626806378365, 0.05625254288315773, -0.02523675374686718, -0.0001784982596291229, 0.0067313783802092075, 0.09657826274633408, 0.0029687241185456514, 0.047161441296339035, -0.05801243707537651, -0.0029740482568740845, -0.08512440323829651, -0.03025495633482933, -0.10462739318609238, -0.02952485904097557, -0.014410947449505329, 0.07211828976869583, 0.026939356699585915, -0.0070293257012963295, 0.07086197286844254, 0.013522992841899395, 0.04344900697469711, 0.007464401889592409, 0.06417064368724823, -0.03156523406505585, -0.019429204985499382, -0.020844830200076103, 0.010596523061394691, 0.01648883894085884, -0.04207831621170044, 0.005077714566141367, -0.030035406351089478, 0.0017458336660638452, -0.011118685826659203, -0.010868411511182785, -0.012145539745688438, 0.05564429238438606, 0.05582807958126068, -0.024309713393449783, -0.01331527903676033, -0.029246218502521515, -0.028866944834589958, 0.009887256659567356, 0.024708757176995277, -0.02342621237039566, 0.001765384920872748, -0.01419861987233162, -0.005437811836600304, -0.027015604078769684, -0.010884162969887257, -0.0025537176989018917, 0.07096391916275024, -0.014607817865908146, -0.025968661531805992, 0.05654097720980644, -0.011585594154894352, 0.04486856982111931, 0.03768645599484444, 0.013653740286827087, 0.001699252286925912, 0.009307699277997017, 0.019655410200357437, 0.013704713433980942, 0.008176157251000404, -0.09140380471944809, 0.03651443123817444, -0.03629344329237938, -0.030894996598362923, 0.03449421375989914, -0.06302161514759064, -0.03735551983118057, 0.0008625449263490736, 0.061644673347473145, 0.009404377080500126, -0.012489551678299904, -0.006754570174962282, 0.039910659193992615, -0.07984756678342819, 0.0002607791102491319, 0.048852428793907166, 0.016965854912996292, -0.05690350756049156, 0.019303275272250175, 0.03945635259151459, -0.025228574872016907, -0.005150904413312674, 0.05459718406200409, -0.008570829406380653, -0.027668654918670654, -0.024612074717879295, -0.045234035700559616, 0.007748648524284363, 0.03378525376319885, -0.011608270928263664, -0.02114785835146904, 0.03237041458487511, 0.0925353392958641, -0.058077652007341385, -0.0350593626499176, -0.017039554193615913, 0.012425938621163368, 0.06628410518169403, 0.028000136837363243, 0.0017768751131370664, 0.009933252818882465, 0.0022163281682878733, 0.0064871832728385925, -0.009886308573186398, -0.029702764004468918, 0.055893104523420334, -0.02525682933628559, 0.011936740018427372, -0.024089155718684196, 0.06294330209493637, 0.02649213932454586, -0.04658164829015732, 0.000841288361698389, 0.034602656960487366, -0.012032709084451199, 0.031422946602106094, -0.04591305926442146, 0.03256038948893547, -0.011416086927056313, -0.0058142757043242455, -0.004190887324512005, 0.022184262052178383, 0.025058573111891747, -0.04713054373860359, 0.018506741151213646, -0.004505874589085579, -0.040143273770809174, 0.01791236735880375, 0.011829718947410583, -0.0656595528125763, 0.06588180363178253, 0.006155512761324644, -0.018886195495724678, -0.002260871697217226, 0.03025457262992859, -0.0012891137739643455, 0.005107524339109659, -0.04130527377128601, -0.016300013288855553, -0.05964747071266174, 0.03730762004852295, -0.04141039401292801, 0.009861716069281101, 0.005667086690664291, -0.029105251654982567, 0.0005453928024508059, -0.012072570621967316, 0.00888791587203741, -0.014073595404624939, 0.00819491222500801, -0.0043842000886797905, -0.034001655876636505, -0.0545617938041687, -0.004686584696173668, -0.01207062229514122, -0.04741674289107323, -0.02464744634926319, -0.05370772257447243, -0.026830213144421577, 0.007074274122714996, -0.08938473463058472, 0.06480003893375397, -0.05737783759832382, -0.0208671186119318, 0.001705882023088634, -0.0026081702671945095, -0.013156818225979805, 0.07244063913822174, 0.04594828560948372, 0.07678684592247009, -0.060362331569194794, -0.022354021668434143, 0.0013769970973953605, 0.007890106178820133, 0.04998769611120224, 0.024846341460943222, 0.004371255170553923, -0.02717888168990612, -0.023233609274029732, 0.028872977942228317, 0.045574869960546494, -0.03670162707567215, -0.004920023027807474, 0.018999001011252403, -0.02781570702791214, 0.03186648339033127, 0.025520777329802513, -0.031932100653648376, 0.028722388669848442, 0.05113879591226578, -0.03032480552792549, 0.08261706680059433, 0.0058180904015898705, 0.005113694351166487, 0.046054042875766754, 0.02009640447795391, -0.0054635051637887955, -0.0439121313393116, -0.027701592072844505, -0.024501917883753777, 0.0069235325790941715, 0.036446914076805115, 0.024707602337002754, -0.047708842903375626, -0.023493966087698936, 0.020748788490891457, -0.030738523229956627, 0.05155154690146446, 0.012027462013065815, -0.010932582430541515, -0.022399043664336205, -0.03918981924653053, -0.009342271834611893, -0.0016462779603898525, -0.009033236652612686, -0.020139070227742195, -0.02263900823891163, -0.07808694988489151, -0.031597260385751724, 0.0008898948435671628, -0.03421349078416824, 0.013328216038644314, -0.021226702257990837, 0.06242740899324417, -0.04874415695667267, -0.0028305568266659975, 0.016349827870726585, 0.01876373216509819, 0.06825363636016846, 0.004841257818043232, -0.01359407790005207, -0.06679859012365341, 0.015710320323705673, 0.03511839359998703, 0.05635760352015495, -0.009834430180490017, -0.03996719792485237, -0.015928195789456367, -0.0021278199274092913, -0.0032218554988503456, -0.0006151429261080921, 0.013288803398609161, -0.005919203627854586, 0.03734070435166359, 0.041571035981178284, -0.0020247905049473047, 0.007978109642863274, 0.0001373953273287043, -0.01878930628299713, 0.006342039909213781, 0.04141121730208397, 0.03311953693628311, 0.024036377668380737, 0.029129402711987495, 0.007316600997000933, -0.004027486313134432, 0.009583857841789722, -0.011019594967365265, 0.028237275779247284, 0.04476676508784294, -0.027683664113283157, -0.011096978560090065, 0.009842411614954472, 0.01255065482109785, -0.020268918946385384, 0.01940833404660225, 0.014260463416576385, -0.06120815500617027, 0.02272334322333336, 0.013626886531710625, -0.019243445247411728, -0.015218781307339668, -0.03200182318687439, -0.047335635870695114, -0.051878638565540314, 0.018075594678521156, 0.018634170293807983, 0.007861226797103882, 0.027165135368704796, 0.04898742213845253, 0.00016029301332309842, 0.03771752864122391, -0.01665818691253662, -0.034378789365291595, 0.06401238590478897, -0.04803046956658363, 0.003147606970742345, -0.05237260088324547, -0.04284921661019325, 0.04812410846352577, -0.01168584730476141, -0.027488024905323982, 0.05711326375603676, 0.0757625550031662, -0.059107955545186996, 0.029162907972931862, 0.016097914427518845, -0.03253655880689621, 0.031344927847385406, 0.01292541902512312, -0.049226172268390656, -0.07694739103317261, 0.062448520213365555, -0.014153216034173965, -0.01730963960289955, 0.00004003114372608252, 0.018682600930333138, -0.02112528495490551, -0.05455084517598152, -0.04350847750902176, 0.018293704837560654, -0.06371410191059113, 0.021254966035485268, 0.030909106135368347, -0.062343645840883255, -0.03142011538147926, 0.045476190745830536, 0.009424185380339622, 0.00023865314142312855, -0.060169681906700134, 0.06384545564651489, 0.023333685472607613, -0.019125910475850105, -0.0304612647742033, 0.0204045157879591, 0.045521676540374756, -0.0017871574964374304, 0.0066464729607105255, -0.009895281866192818, 0.02360445261001587, -0.053632158786058426, 0.04583792760968208, -0.027017109096050262, -0.05693194270133972, 0.014344106428325176, 0.017239777371287346, 0.025277042761445045, 0.007019765209406614, 0.020510049536824226, 0.03174315392971039, 0.002579232444986701, 0.04481176659464836, -0.017492596060037613, -0.010468457825481892, -0.019866731017827988, 0.016883691772818565, 0.03522401675581932, -0.021008988842368126, 0.01777898333966732, -0.011757530272006989, 0.0036646591033786535, -0.0638657882809639, -0.018770497292280197, 0.02305041439831257, 0.052519358694553375, 0.01743057556450367, 0.0035837232135236263, 0.005699271336197853, 0.008863802999258041, -0.0076157995499670506, 0.050124164670705795, -0.023232564330101013, -0.09231095761060715, -0.015304828062653542, -0.016346093267202377, -0.012984939850866795, -0.019824834540486336, 0.041168585419654846, 0.022383425384759903, 0.012017813511192799, -0.038003213703632355, 0.00212386273778975, -0.04935595393180847, 0.06970309466123581, 0.02630910649895668, -0.057022836059331894, -0.017814218997955322, -0.0591730959713459, -0.06124436482787132, 0.04024384543299675, 0.0024095799308270216, 0.03432244434952736, -0.05516940355300903, -0.018893834203481674, 0.015803193673491478, -0.014665456488728523, -0.043379392474889755, 0.026006972417235374, -0.03962046280503273, -0.018099481239914894, 0.013752475380897522, -0.06200632452964783, 0.019471298903226852, 0.03712260723114014, 0.00865880772471428, 0.014812176115810871, -0.0017244269838556647, -0.02763105370104313, 0.05958821624517441, 0.03552039712667465, -0.045918695628643036, 0.049795474857091904, 0.0640990287065506, 0.013802689500153065, 0.02540716715157032, 0.0009062173776328564, 0.039529070258140564, 0.020062750205397606, 0.04827487841248512, -0.0480659082531929, -0.022631026804447174, -0.03682350739836693, 0.025707105174660683, 0.09443683922290802, -0.04286091402173042, -0.028967415913939476, 0.07832328975200653, -0.040852513164281845, 0.06975554674863815, 0.01728539541363716, 0.031350456178188324, 0.0076793767511844635, -0.03133189678192139, -0.019144533202052116, 0.03133184090256691, 0.06684030592441559, 0.024170231074094772, -0.014425933361053467, -0.05903118476271629, -0.01620417647063732, -0.05329195410013199, -0.012062613852322102, 0.0009610357810743153, 0.021895695477724075, -0.0029908684082329273, -0.057930316776037216, -0.05029291287064552, -0.044383712112903595, 0.0063583729788661, 0.03303557261824608, -0.02396441623568535, 0.021465975791215897, -0.09571576118469238, -0.00047186081064864993, 0.059220779687166214, 0.0019033343996852636, -0.003885382553562522, -0.011723915114998817, -0.009794090874493122, -0.03135165944695473, 0.027075953781604767, 0.03236384689807892, 0.038726989179849625, -0.02109607495367527, -0.028067339211702347, -0.011050524190068245, 0.02402406744658947, -0.04464109614491463, -0.035957857966423035, 0.03071831539273262, 0.005113207269459963, -0.018228918313980103, -0.0011870047310367227, 0.011949459090828896, 0.06844823807477951, -0.028366459533572197, 0.01427576132118702, 0.024231690913438797, 0.0182975884526968, 0.07882094383239746, 0.0749276876449585, 0.03550378978252411, 0.008265305310487747, 0.003434073878452182, -0.008967580273747444, 0.037065085023641586, -0.07271047681570053, 0.009378011338412762, 0.027615783736109734, -0.025298764929175377, -0.038424231112003326, 0.012849865481257439, -0.01491664256900549, 0.0642336755990982, 0.03407605364918709, -0.04924548789858818, -0.026158692315220833, -0.018221799284219742, -0.001247100648470223, 0.0065232571214437485, -0.01185817364603281, -0.02150377444922924, 0.0173349492251873, -0.036840882152318954, -0.03774538263678551, 0.029067998751997948, 0.06812456995248795, 0.05679107457399368, 0.003138964297249913, 0.01616302877664566, 0.052854057401418686, -0.008253890089690685, -0.01898004300892353, 0.004130003973841667, -0.006885985843837261, -0.02102179266512394, 0.04132986068725586, 0.03604305908083916, 0.08613254874944687, 0.06239471584558487, -0.05729614198207855, -0.025505568832159042, 0.06496535986661911, -0.017945915460586548, -0.0055717299692332745, -0.010868466459214687, -0.002884198911488056, 0.02665363997220993, -0.01091376505792141, -0.07850643992424011, 0.043605122715234756, -0.006231995765119791, 0.018135761842131615, -0.000735243724193424, 0.04251623526215553, -0.026179926469922066, 0.06624897569417953, -0.03062407672405243, 0.04266514629125595, 0.01911603845655918, -0.0315399095416069, 0.051144517958164215, -0.007490810938179493, 0.05397713929414749, -0.012453201226890087, 0.050866369158029556, -0.01803707517683506, 0.03558493033051491, -0.02633536607027054, -0.01163394097238779, -0.04302089288830757, -0.024943847209215164, 0.04757123813033104, -0.00030128390062600374, -0.04293942078948021, -0.015856802463531494, 0.010048785246908665, -0.01912781223654747, -0.057582393288612366, 0.00024445619783364236, -0.032264236360788345, -0.01804283820092678, 0.01080088410526514, -0.0004906866233795881, -0.008296062238514423, -0.027597179636359215, -0.031385794281959534, -0.027286307886242867, 0.043910443782806396, -0.017716627568006516, 0.016972852870821953, 0.04493192955851555, 0.008351517841219902, -0.010516601614654064, -0.027192432433366776, -0.026905858889222145, 0.0067926133051514626, -0.046518273651599884, -0.03688373416662216, -0.009211481548845768, 0.027112150564789772, -0.012005687691271305, -0.043982069939374924, 0.0066593424417078495, -0.03968866541981697, 0.020159726962447166, -0.008679536171257496, -0.026561038568615913, -0.013301878236234188, -0.04900122433900833, 0.02949364110827446, -0.00006176249735290185, -0.015724625438451767, -0.0062804496847093105, 0.0744711384177208, -0.0017147654434666038, -0.018322762101888657, 0.0075560095719993114, 0.04307818412780762, -0.04500304535031319, -0.016590971499681473, 0.0012256904738023877, -0.0430571511387825, 0.07053051888942719, 0.035113390535116196, -0.043122489005327225, 0.03611871600151062, -0.02052147686481476, 0.000852754688821733, -0.006321646273136139, 0.014809468761086464, 0.004808534402400255, -0.014983125030994415, 0.04900534451007843, -0.06156934052705765, -0.01369502767920494, 0.006440389901399612, 0.08291111886501312, 0.011997068300843239, -0.03303593024611473, -0.02242438681423664, 0.019950659945607185, 0.027373403310775757, 0.07765232026576996, 0.002594962017610669, -0.027776436880230904, -0.01080406829714775, -0.026837879791855812, -0.018688559532165527, -0.07802274823188782, -0.022641507908701897, -0.015465764328837395, -0.006245613098144531, -0.017291860654950142, 0.040893491357564926, -0.015547054819762707, 0.028392957523465157, -0.02623685449361801, -0.023656589910387993, 0.03764106333255768, -0.0305746141821146, 0.005036725662648678, -0.002303259912878275, -0.010530462488532066, 0.03712892904877663, 0.08154626190662384, -0.028565432876348495, -0.004663089755922556, -0.023015612736344337, -0.022650107741355896, -0.009237655438482761, 0.012830344960093498, 0.014248888939619064, 0.04186861962080002, 0.039479225873947144, -0.021716495975852013, 0.05877692252397537, 0.06594596803188324, -0.06743454188108444, 0.09726293385028839, 0.054452069103717804, -0.08186142146587372, 0.018185680732131004, 0.01507987268269062, 0.012162353843450546, -0.01846357062458992, -0.00947936438024044, -0.05251206457614899, 0.014337246306240559, -0.043305955827236176, 0.059940680861473083, -0.044150445610284805, -0.015061508864164352, 0.004596326500177383 ]
<p>My nephew is 3 and weighs around 30 pounds I am guessing. However, I would like to weigh him at home. I have kitchen scales, one flat one that goes up 1kg and one that looks like this picture that goes up to 5kg. <img src="http://i.stack.imgur.com/u3rsam.jpg" alt="enter image description here"></p> <p>What is a safe and practical way I can weigh my nephew at home?</p>
g5431
[ 0.07831283658742905, 0.06742919236421585, 0.006625328212976456, -0.08604951947927475, 0.036095697432756424, 0.018544163554906845, -0.08059106022119522, -0.049610503017902374, -0.03374585509300232, -0.02111309953033924, -0.06324257701635361, -0.017045937478542328, -0.002706066705286503, 0.04031849652528763, -0.034704580903053284, 0.026945393532514572, -0.03030524030327797, -0.007251948118209839, 0.05728863924741745, 0.022502079606056213, -0.006018674932420254, -0.0004986084531992674, 0.007959364913403988, -0.03017536550760269, -0.03629530966281891, -0.032271113246679306, -0.027461666613817215, 0.07017498463392258, -0.020757727324962616, 0.026782875880599022, -0.03618235886096954, 0.0037466920912265778, -0.010585140436887741, -0.008328337222337723, 0.020605871453881264, -0.0432785227894783, 0.05546678602695465, 0.031148109585046768, 0.01552149374037981, -0.051946576684713364, -0.03925296664237976, 0.06680256873369217, -0.011266661807894707, 0.01934218965470791, -0.011068153195083141, 0.029789838939905167, -0.018732832744717598, 0.03780094161629677, -0.01065072137862444, -0.007065676152706146, -0.04217032343149185, -0.03357422351837158, -0.0072534033097326756, -0.01814858615398407, 0.0017358020413666964, -0.07667136937379837, -0.0025844015181064606, -0.0691513791680336, 0.0009824316948652267, 0.04533766210079193, 0.022902386263012886, -0.038055602461099625, -0.04797704890370369, -0.03101516142487526, 0.03975709155201912, 0.12001291662454605, 0.009608224965631962, 0.01353541947901249, -0.011433767154812813, 0.052593473345041275, 0.007580014411360025, -0.0387236662209034, 0.07360383123159409, -0.005872498266398907, -0.019534818828105927, -0.021495165303349495, 0.01643276773393154, 0.0001478597114328295, 0.02230878360569477, -0.002727207727730274, -0.04856756329536438, 0.09632334113121033, 0.034572385251522064, 0.005754576530307531, -0.07824800908565521, -0.04220952093601227, 0.024770893156528473, -0.018794994801282883, -0.061965301632881165, -0.06964612752199173, -0.021683214232325554, -0.053127046674489975, 0.016406962648034096, 0.012627460062503815, -0.020320799201726913, 0.012000675313174725, -0.0025086388923227787, 0.06467518955469131, 0.0313616581261158, -0.007219936233013868, -0.012547745369374752, -0.0321793407201767, -0.01582534983754158, -0.05617332458496094, -0.08025716245174408, -0.01985340192914009, 0.07979311794042587, -0.01589827425777912, 0.004297242965549231, -0.011050334200263023, -0.018029101192951202, -0.03775126859545708, -0.004584362264722586, -0.061343155801296234, 0.041956909000873566, -0.026558876037597656, 0.0383211113512516, -0.013881884515285492, -0.009377057664096355, -0.04646514728665352, 0.021549416705965996, -0.03171499818563461, 0.04865073785185814, 0.00844314694404602, -0.051977768540382385, 0.030973339453339577, -0.02919902466237545, 0.014827780425548553, -0.0010023334762081504, -0.06547631323337555, 0.04743843153119087, 0.033448636531829834, -0.06480675935745239, 0.011163768358528614, 0.05099375173449516, 0.005741629283875227, 0.006476309150457382, 0.006603812798857689, -0.026697931811213493, -0.011913326568901539, -0.014497867785394192, -0.019517678767442703, -0.013381660915911198, 0.03169435262680054, 0.07937388867139816, -0.039814338088035583, 0.041829634457826614, 0.016090121120214462, 0.04570779949426651, -0.01772516407072544, 0.02528258040547371, 0.006961909122765064, -0.01585896871984005, 0.020364733412861824, -0.03635949268937111, -0.03189392387866974, 0.022100800648331642, 0.03835133835673332, 0.07404689490795135, -0.006256096996366978, 0.030876638367772102, -0.03401131182909012, 0.013004143722355366, -0.007034727837890387, -0.01187900360673666, 0.018104195594787598, 0.011861555278301239, 0.022289056330919266, 0.04289940744638443, -0.0392225980758667, -0.03865065798163414, 0.0030982305761426687, 0.025294676423072815, -0.06913139671087265, 0.025058327242732048, -0.06757870316505432, -0.007963293232023716, 0.03036201186478138, 0.03005254827439785, -0.06083177775144577, -0.045989058911800385, -0.013552308082580566, 0.017758488655090332, -0.05087629705667496, 0.006627445109188557, 0.006581489462405443, 0.02777218259871006, -0.03924359753727913, 0.007748722098767757, 0.03322996944189072, 0.058273062109947205, -0.027819154784083366, 0.014841662719845772, 0.04311755672097206, -0.023218393325805664, -0.01218701247125864, 0.01351120788604021, 0.039557650685310364, -0.00085999391740188, -0.04461102560162544, 0.04035152494907379, -0.03477438911795616, -0.003828897140920162, 0.002303455723449588, 0.028976861387491226, 0.03668912500143051, 0.020032035186886787, -0.03661724179983139, 0.020321937277913094, -0.05064718797802925, -0.05633539706468582, 0.027571849524974823, -0.04164908826351166, 0.025941474363207817, 0.027882976457476616, 0.09238669276237488, -0.0017853004392236471, 0.02358756586909294, -0.06405312567949295, -0.0537104457616806, -0.030707834288477898, 0.021909045055508614, 0.02376849576830864, 0.014360404573380947, 0.0553753599524498, -0.006080830469727516, -0.01098110992461443, -0.02295951172709465, -0.01809021644294262, 0.01490752212703228, -0.002809957368299365, -0.015734901651740074, 0.012529321014881134, -0.009511234238743782, 0.049053288996219635, 0.022237049415707588, 0.01704956777393818, -0.021858830004930496, -0.026623867452144623, 0.01359901949763298, 0.06273829191923141, -0.013957303017377853, 0.09593701362609863, -0.027514372020959854, 0.011525258421897888, -0.07743188738822937, 0.012602380476891994, 0.008708965964615345, -0.0031648054718971252, -0.04242955893278122, -0.009189238771796227, 0.035110607743263245, -0.030688799917697906, -0.02899979241192341, -0.03352867811918259, 0.02941240556538105, -0.016652170568704605, 0.007227546069771051, 0.008812732994556427, 0.02835073694586754, 0.022514833137392998, -0.0022964344825595617, -0.031105007976293564, 0.03912871703505516, -0.01651063561439514, -0.0371432900428772, -0.0401134267449379, -0.010737557895481586, -0.012141023762524128, 0.03210741654038429, -0.014541609212756157, -0.02186005935072899, 0.00496874051168561, 0.02926488220691681, -0.015666944906115532, -0.048056576400995255, 0.022901833057403564, -0.016899004578590393, 0.05682970955967903, 0.002758089220151305, 0.021598095074295998, 0.05715697631239891, 0.00638994574546814, -0.051761187613010406, 0.005581763107329607, 0.040529973804950714, -0.029364150017499924, -0.06471170485019684, -0.02353198081254959, -0.019721338525414467, -0.01407615840435028, 0.035346224904060364, 0.008009258657693863, -0.012993832118809223, -0.02220391295850277, 0.011869516223669052, 0.03644513711333275, -0.03814071789383888, -0.0015150803374126554, -0.03776233270764351, -0.0064286901615560055, -0.006352204363793135, 0.04357418045401573, 0.028666706755757332, 0.020611820742487907, 0.003385825315490365, -0.002495135646313429, 0.04580335319042206, 0.08927040547132492, -0.04200167953968048, -0.003225957741960883, 0.0032364565413445234, -0.03880060464143753, 0.06875552982091904, -0.001105849165469408, -0.047148991376161575, 0.0051246643997728825, -0.011023266240954399, 0.020831527188420296, -0.033825647085905075, 0.0115567147731781, 0.0469013974070549, -0.06907887011766434, 0.02642962336540222, -0.035274438560009, 0.0322306752204895, -0.007551978342235088, 0.05857408419251442, -0.006972272880375385, 0.011353284120559692, 0.021707260981202126, 0.053814731538295746, 0.005308125633746386, 0.013737194240093231, -0.09738393872976303, -0.023462796583771706, -0.013300466351211071, -0.034712981432676315, -0.008274395950138569, 0.002954492811113596, 0.001491692615672946, 0.003643065458163619, 0.011000030674040318, -0.0671771913766861, -0.028809266164898872, -0.026544222608208656, -0.025405140593647957, -0.06671702116727829, -0.0317801870405674, -0.03630949929356575, -0.026809247210621834, 0.011759834364056587, -0.005175863392651081, -0.043840330094099045, 0.021168215200304985, 0.003967505879700184, -0.045750949531793594, 0.027249060571193695, 0.00043545165681280196, -0.010394244454801083, -0.04425051808357239, 0.013347902335226536, -0.036545008420944214, -0.059691257774829865, -0.019745228812098503, -0.0002851007448043674, -0.0326557457447052, 0.02842898480594158, 0.009626292623579502, 0.07644253969192505, 0.0049237716011703014, -0.02193991094827652, 0.012211820110678673, -0.07185262441635132, 0.03174035623669624, 0.020088601857423782, 0.047328222543001175, 0.005414973013103008, 0.022381307557225227, 0.050577204674482346, -0.048098374158144, 0.034077487885951996, 0.01906350627541542, -0.07094644755125046, -0.0323675312101841, 0.024849819019436836, -0.054750099778175354, 0.025835273787379265, 0.06537973880767822, -0.002506938064470887, 0.006772217806428671, -0.03162504360079765, -0.045515626668930054, 0.009122002869844437, 0.021755162626504898, 0.030375581234693527, -0.010029609315097332, 0.0016932577127590775, -0.008077139966189861, 0.048847656697034836, -0.011575894430279732, 0.02893444523215294, -0.0014835381880402565, 0.013528169132769108, -0.041831258684396744, 0.02474149689078331, 0.0468137264251709, -0.02754107303917408, -0.0035872990265488625, -0.011985470540821552, -0.010868030600249767, 0.02962140366435051, 0.09638381749391556, 0.022969158366322517, 0.013968059793114662, -0.010556158609688282, 0.018863623961806297, -0.01948057860136032, 0.014299925416707993, 0.03242683410644531, -0.019738581031560898, 0.0015550288371741772, -0.08106023073196411, -0.0383220911026001, -0.05288957431912422, 0.043032556772232056, 0.04181293398141861, -0.011078639887273312, 0.043492190539836884, 0.08749701827764511, 0.015463804826140404, -0.02786611206829548, 0.033833909779787064, 0.006864514667540789, 0.03708910569548607, 0.027337098494172096, 0.04747512564063072, -0.022442646324634552, -0.05472078546881676, -0.03144138678908348, -0.00145919609349221, 0.0914897620677948, -0.044037677347660065, 0.05250553414225578, -0.09777140617370605, -0.023229049518704414, -0.04822419211268425, 0.015457824803888798, 0.03968857228755951, -0.006697258446365595, -0.032658401876688004, 0.048806559294462204, -0.04135290905833244, -0.03874097764492035, -0.019824746996164322, 0.0070199863985180855, -0.014492377638816833, -0.023082293570041656, 0.009889751672744751, -0.017716892063617706, 0.0021332877222448587, -0.019151706248521805, 0.03262664005160332, -0.02386298216879368, 0.005111901089549065, -0.04225553199648857, -0.0824216678738594, -0.013112164102494717, 0.04451373964548111, -0.006148155778646469, -0.014714875258505344, 0.005161508452147245, 0.0134821068495512, 0.022642293944954872, 0.0007929647108539939, 0.01566898450255394, 0.03398605063557625, 0.019821330904960632, -0.04180566966533661, 0.003849593922495842, -0.00912813562899828, 0.03711136057972908, -0.0003246513952035457, 0.024066397920250893, -0.021915432065725327, 0.025611670687794685, -0.010069887153804302, 0.00677519990131259, 0.028348399326205254, 0.0053818984888494015, 0.029451826587319374, 0.03823807090520859, 0.016332339495420456, 0.008442460559308529, -0.0380939319729805, 0.05062345415353775, -0.04125848412513733, -0.009340403601527214, 0.06362359970808029, -0.08264622092247009, 0.06290951371192932, -0.019044000655412674, -0.028208158910274506, -0.0011402091477066278, 0.009579978883266449, -0.01859232410788536, -0.011860745958983898, -0.0176224485039711, 0.03466685116291046, 0.06170940771698952, 0.043291445821523666, -0.02921249344944954, -0.007512296549975872, -0.03349960595369339, 0.03094393014907837, 0.011793287470936775, 0.02538665384054184, 0.0975651666522026, 0.010189238935709, 0.056395865976810455, 0.04041421785950661, -0.020325379446148872, -0.00432169996201992, -0.03001328557729721, -0.04634886607527733, 0.02291163057088852, -0.04875098168849945, -0.01899794302880764, -0.0058064707554876804, -0.02344275452196598, 0.012141666375100613, -0.02109633944928646, 0.018926968798041344, -0.022011438384652138, -0.03308725729584694, 0.019771870225667953, 0.0031091999262571335, 0.03605854511260986, -0.015693413093686104, -0.028615470975637436, 0.04221078380942345, 0.013598226942121983, -0.009700499475002289, 0.025572406128048897, -0.058013930916786194, -0.009146597236394882, 0.03414925932884216, -0.005559263750910759, 0.008241510950028896, 0.040648140013217926, 0.05421235039830208, 0.025698106735944748, 0.019477149471640587, 0.007395763881504536, 0.016078505665063858, 0.0264892578125, 0.04864901676774025, -0.016193170100450516, -0.01936792954802513, -0.042306363582611084, 0.01705392450094223, -0.012804020196199417, 0.012892122380435467, -0.04500983655452728, 0.005859930533915758, -0.018467653542757034, -0.013883008621633053, -0.03696855157613754, -0.039087291806936264, 0.05293690040707588, -0.027296394109725952, -0.054047659039497375, 0.02377651073038578, 0.008601490408182144, 0.020144939422607422, 0.003150473115965724, -0.05433173105120659, 0.006269610486924648, 0.0439121276140213, -0.005653383210301399, -0.03822394460439682, 0.08163894712924957, -0.021618854254484177, -0.017453379929065704, -0.0688416138291359, 0.03554866462945938, 0.0023089346941560507, -0.03649665042757988, 0.001605316298082471, -0.03704594075679779, 0.026175208389759064, 0.0035807390231639147, -0.054433342069387436, -0.000041097864595940337, -0.01624979078769684, -0.029951564967632294, -0.02425529435276985, 0.0756719633936882, 0.03073839843273163, 0.05404043197631836, -0.017368687316775322, 0.04134780913591385, 0.03295831382274628, -0.06901253014802933, -0.06549645960330963, 0.040096260607242584, 0.05160718783736229, -0.021930132061243057, 0.029146067798137665, 0.0010564828990027308, -0.0024222899228334427, -0.02571878395974636, -0.0023731214459985495, -0.027157699689269066, 0.0011195216793566942, -0.027620255947113037, -0.013856427744030952, -0.020283112302422523, -0.022991934791207314, 0.007804553490132093, 0.04446520283818245, -0.04807109385728836, 0.005424599163234234, -0.011689629405736923, 0.022424381226301193, 0.0017775546293705702, 0.041410841047763824, 0.06548519432544708, 0.0034911842085421085, 0.02471254952251911, -0.0007211106712929904, 0.017575286328792572, 0.07350996136665344, 0.04412423446774483, 0.0023188269697129726, 0.042447783052921295, -0.004604497458785772, 0.025773974135518074, -0.00042722461512312293, 0.07878239452838898, -0.03349137306213379, 0.09188356250524521, 0.06108639016747475, 0.04454551637172699, -0.002203574636951089, -0.052313655614852905, -0.023300830274820328, -0.016548728570342064, -0.02705235965549946, 0.0001785280037438497, 0.007079759147018194, -0.08318210393190384, 0.003264319384470582, 0.01769939251244068, -0.005885981488972902, -0.0447528101503849, 0.002951540518552065, 0.04296785220503807, 0.010459870100021362, -0.030738193541765213, 0.04002944752573967, -0.053520385175943375, 0.053838878870010376, -0.02813248336315155, -0.026835577562451363, 0.05086028203368187, -0.08715420961380005, -0.010639330372214317, -0.05322553217411041, -0.02760026976466179, -0.030596941709518433, -0.09029683470726013, 0.020247099921107292, -0.005310198292136192, 0.0353497676551342, -0.0057808528654277325, -0.028494825586676598, -0.012943344190716743, 0.049037590622901917, 0.014113751240074635, -0.02297339402139187, 0.009449420496821404, -0.005290339235216379, 0.03519638627767563, 0.03441648930311203, 0.0109117291867733, 0.0323212631046772, -0.000050146307330578566, 0.009800800122320652, -0.02389935590326786, 0.03264818340539932, -0.020023543387651443, 0.041164420545101166, -0.006581906694918871, -0.041406821459531784, 0.0014551886124536395, 0.0367252454161644, -0.0024904869496822357, 0.07910098135471344, 0.005827323999255896, 0.04192575439810753, -0.04874793440103531, 0.010475990362465382, 0.0032815500162541866, -0.03893045336008072, 0.04287690296769142, -0.030876901000738144, -0.0757322758436203, -0.05462938919663429, -0.028334705159068108, -0.01062503457069397, 0.039594657719135284, 0.05143005773425102, -0.010207599960267544, -0.03827301040291786, 0.01174469105899334, 0.013411642983555794, -0.015873637050390244, -0.06062059849500656, -0.0015500899171456695, 0.04937359318137169, 0.029046084731817245, 0.0016210710164159536, -0.011469364166259766, -0.021841753274202347, -0.021121831610798836, 0.04239538311958313, -0.023661315441131592, -0.014120961539447308, -0.008604367263615131, -0.04309264197945595, 0.05840304493904114, -0.019933078438043594, 0.09208812564611435, 0.05228602886199951, 0.06533114612102509, -0.01643764041364193, -0.017363417893648148, 0.009444006718695164, 0.05065888166427612, 0.02054375596344471, 0.02682117372751236, -0.04082880914211273, 0.023123634979128838, 0.046543095260858536, 0.024277949705719948, 0.00019986930419690907, -0.019147446379065514, -0.0008426987333223224, -0.033463116735219955, 0.08183562010526657, 0.010296434164047241, -0.03073824942111969, 0.007082846015691757, 0.002487394493073225, -0.046059075742959976, -0.027396589517593384, -0.06602749973535538, -0.03693697229027748, -0.03690051659941673, 0.024632075801491737, -0.018999990075826645, 0.01025215070694685, 0.05963744968175888, -0.03767918050289154, -0.06208010017871857, -0.03864038735628128, 0.0007559646037407219 ]
<p>The textbook explanation is that, at <a href="http://en.wikipedia.org/wiki/Brewster%27s_angle" rel="nofollow">Brewster's angle</a>, the electric dipoles excited by the incident light can't reradiate to the reflection direction since it's aligned with the dipole moments.</p> <p>Is there a deeper understanding of the microscopic physics picture? For example, is there an actual calculation of these electric dipoles induced by the near field?</p>
g5432
[ -0.05076504498720169, 0.0648430809378624, -0.026287512853741646, 0.009163705632090569, 0.030593015253543854, 0.04541194438934326, 0.08278605341911316, 0.03223707154393196, -0.017136935144662857, 0.012385310605168343, -0.04660293087363243, 0.010038047097623348, 0.032919179648160934, -0.02141331136226654, -0.012090422213077545, -0.0004129848093725741, 0.062401529401540756, 0.032957129180431366, 0.016870206221938133, 0.031046340242028236, -0.01324459258466959, -0.015364959836006165, -0.08054554462432861, -0.04914082586765289, -0.020489146932959557, 0.02791152521967888, 0.005410979967564344, -0.002635762793943286, -0.0013328740606084466, -0.03512214496731758, -0.01740376092493534, -0.03403947502374649, 0.053395748138427734, -0.012827602215111256, 0.026981407776474953, -0.050983548164367676, -0.06358549743890762, 0.027969365939497948, 0.007704335730522871, 0.013711418956518173, 0.01119748130440712, -0.0013195557985454798, -0.05581871047616005, -0.0057272291742265224, -0.03767194598913193, 0.015312142670154572, -0.023147305473685265, -0.034503575414419174, -0.015972383320331573, 0.008604471571743488, -0.02323748916387558, 0.03534537926316261, 0.10809828341007233, 0.02398967370390892, 0.044234033674001694, 0.03151235729455948, -0.008723720908164978, -0.018510734662413597, 0.0709160789847374, 0.018866855651140213, 0.001702062669210136, 0.0250940453261137, -0.0012788152089342475, 0.0693497285246849, 0.04766577109694481, -0.03682387247681618, -0.04681216925382614, -0.04806021600961685, -0.01902039721608162, -0.00692138634622097, -0.017907846719026566, -0.02243475243449211, -0.07903464883565903, 0.0038724811747670174, -0.03687875717878342, 0.004431729204952717, 0.029095569625496864, 0.0020636487752199173, 0.01862603984773159, 0.03349609673023224, -0.019949212670326233, 0.0071722581051290035, -0.00048369247815571725, -0.02214120328426361, 0.09129834920167923, -0.032407913357019424, -0.015842534601688385, -0.013395708985626698, 0.002202011179178953, -0.0625992864370346, 0.02401050552725792, 0.010574913583695889, 0.018230367451906204, -0.009996750392019749, -0.03666853532195091, -0.042763471603393555, 0.005416548810899258, 0.00801454484462738, -0.010435212403535843, 0.005052227061241865, -0.07456900924444199, 0.04730011895298958, 0.04466892033815384, 0.0378635935485363, 0.02796422876417637, -0.02224045619368553, 0.009428931400179863, -0.02789924480021, -0.020237110555171967, 0.07002490758895874, -0.04056273028254509, -0.06102823093533516, -0.009932169690728188, 0.025491926819086075, -0.0517427921295166, -0.0022217666264623404, 0.04557520151138306, -0.06972436606884003, 0.009517720900475979, 0.11579419672489166, 0.06625880300998688, 0.04605935141444206, -0.046905193477869034, 0.03325783088803291, -0.018983477726578712, 0.01617518626153469, 0.010692927055060863, -0.01987352967262268, 0.01784304901957512, -0.03237326815724373, 0.001503466279245913, -0.03127233311533928, -0.004791686311364174, 0.029321962967514992, 0.03656737506389618, 0.019390219822525978, 0.03072856180369854, 0.0005109325284138322, -0.03201267495751381, 0.023309115320444107, 0.04163704067468643, 0.0005731685669161379, 0.011471930891275406, -0.03696564957499504, 0.0372982881963253, 0.014247256331145763, -0.03134051337838173, 0.0007018308388069272, 0.0892295092344284, 0.03697488084435463, 0.0033911752980202436, 0.022328805178403854, 0.00732110720127821, -0.03565267100930214, -0.03109552524983883, -0.01472389418631792, 0.022554047405719757, -0.07553019374608994, 0.005501567851752043, 0.0650651827454567, 0.03945617377758026, -0.030885402113199234, -0.008415687829256058, 0.034138716757297516, -0.06454343348741531, 0.014009781181812286, -0.0023808444384485483, -0.08364317566156387, 0.02754504606127739, -0.05630979314446449, -0.016740120947360992, -0.029735952615737915, 0.07884770631790161, 0.04330870509147644, -0.02528463676571846, 0.09743129462003708, -0.018826594576239586, -0.008666462264955044, 0.027647996321320534, 0.07662034034729004, -0.028884759172797203, 0.04771443456411362, 0.04147878661751747, 0.0337841734290123, 0.01880135014653206, -0.025314273312687874, -0.05412529781460762, 0.0320313461124897, 0.0017020488157868385, -0.03376723825931549, 0.0034944000653922558, 0.01573607698082924, -0.018436558544635773, 0.04246371611952782, -0.009380818344652653, 0.0015867454931139946, 0.004625583533197641, -0.035863932222127914, -0.005720522254705429, 0.03841829672455788, -0.03650705888867378, 0.04756731539964676, 0.04718775674700737, 0.03042779304087162, 0.009508498013019562, 0.035984933376312256, -0.003841160098090768, 0.005930868908762932, -0.02220013365149498, -0.014543652534484863, -0.0004992660833522677, 0.018882310017943382, -0.008311163634061813, 0.02494375966489315, -0.014951705001294613, 0.0023027744609862566, -0.0540277399122715, -0.016215713694691658, -0.00037315115332603455, 0.0014368585543707013, -0.023901645094156265, 0.036376215517520905, 0.0074768937192857265, 0.013215825892984867, -0.016054075211286545, -0.015697065740823746, -0.01515819039195776, 0.006531169172376394, 0.0011587843764573336, -0.016417067497968674, -0.12057123333215714, -0.02535988576710224, -0.0013108794810250401, 0.01831480860710144, 0.03417054936289787, 0.05050841346383095, -0.03362013027071953, 0.013437855988740921, 0.018066493794322014, -0.03123270720243454, 0.0039327568374574184, -0.02625461295247078, -0.02810039557516575, 0.03742798790335655, -0.03391234576702118, -0.017425308004021645, 0.06652332842350006, -0.009056203998625278, 0.005395652260631323, 0.018731391057372093, 0.06411456316709518, -0.023166226223111153, 0.0233902670443058, 0.011344398371875286, -0.032565969973802567, 0.03379753977060318, -0.03601360321044922, 0.02598908729851246, -0.049438588321208954, -0.02936406619846821, -0.04612372815608978, 0.002936143195256591, 0.04738843813538551, -0.0016460822662338614, -0.0064719561487436295, -0.004822939168661833, -0.009231251664459705, 0.018995242193341255, 0.001749762217514217, -0.008169222623109818, -0.08097502589225769, 0.08262351900339127, 0.015897726640105247, -0.007548375520855188, 0.024225052446126938, -0.02338477224111557, 0.0161883644759655, -0.0313381627202034, -0.000033288066333625466, -0.015233921818435192, -0.05847838521003723, -0.014468774199485779, 0.002133946865797043, -0.045508287847042084, 0.029551098123192787, -0.04013650864362717, -0.058201879262924194, -0.03995782509446144, 0.009897908195853233, -0.02422594279050827, -0.019307276234030724, -0.03240761533379555, 0.05848319083452225, -0.005815420299768448, -0.0202004574239254, -0.002401060191914439, 0.12611272931098938, -0.0014069272438064218, -0.043862245976924896, 0.05559774115681648, -0.00765201635658741, 0.0006301808753050864, -0.023940060287714005, -0.00965751800686121, 0.026769287884235382, 0.05751753970980644, 0.017946908250451088, -0.0895623117685318, -0.0302137341350317, 0.038481343537569046, -0.014307339675724506, -0.0009792257333174348, 0.01909738779067993, 0.016741205006837845, -0.04848062992095947, 0.01990949548780918, -0.014877893961966038, 0.014035006053745747, 0.038813766092061996, 0.049250900745391846, -0.01107828039675951, 0.04451844468712807, 0.0055798115208745, -0.024801630526781082, 0.008378129452466965, 0.011253800243139267, -0.03368173539638519, 0.03874794766306877, -0.010072275064885616, -0.03437541797757149, 0.03536190092563629, -0.013031487353146076, -0.0297379270195961, -0.008431775495409966, -0.01703939586877823, -0.04911315068602562, -0.05080319195985794, 0.05057745426893234, 0.014959430322051048, 0.01833599992096424, 0.04127545282244682, -0.033246446400880814, -0.09917490184307098, -0.03320265933871269, 0.009258954785764217, 0.029482077807188034, -0.014367806725203991, -0.018869636580348015, 0.031405068933963776, -0.002383509883657098, 0.0544019490480423, 0.03317338600754738, -0.02997600845992565, 0.02460312470793724, -0.024181487038731575, -0.002233087085187435, -0.0015901064034551382, 0.01403836254030466, 0.0324116013944149, 0.02111979015171528, 0.0433635488152504, -0.02185829170048237, -0.013165094889700413, -0.038102589547634125, -0.02884172834455967, -0.01528196595609188, -0.04081764072179794, 0.013722105883061886, 0.003002756740897894, -0.03688951954245567, -0.10101649910211563, -0.019404811784625053, -0.040419138967990875, 0.025144511833786964, -0.03143806755542755, -0.02281363494694233, -0.012136644683778286, -0.000776351778768003, -0.07599391043186188, 0.013493333011865616, -0.029647640883922577, 0.06513374298810959, 0.013848761096596718, -0.019680989906191826, 0.022127652540802956, 0.015063806436955929, -0.05448082089424133, -0.035285841673612595, -0.017432136461138725, 0.04517892375588417, -0.0034762697760015726, 0.0004263548762537539, -0.022880377247929573, 0.01618773303925991, 0.009063003584742546, -0.08275828510522842, 0.004306703805923462, -0.023939302191138268, -0.01766803301870823, 0.014176888391375542, 0.10840065777301788, 0.032889507710933685, -0.016818851232528687, -0.002696027746424079, -0.011397751979529858, 0.01984398625791073, 0.026997633278369904, 0.032894160598516464, -0.028179554268717766, 0.009402574971318245, -0.03743808716535568, 0.0070786611177027225, -0.027650214731693268, -0.05014166608452797, 0.04529518634080887, 0.03296821191906929, 0.016718877479434013, -0.027401696890592575, 0.006726330146193504, 0.0025359592400491238, 0.013434074819087982, -0.018385954201221466, 0.03476082161068916, -0.029712384566664696, 0.006613158620893955, 0.03348515182733536, -0.021851688623428345, 0.0013363990001380444, 0.01139063760638237, -0.04539778456091881, 0.015472978353500366, -0.017836418002843857, -0.02372516505420208, -0.016121020540595055, -0.04468058794736862, 0.05368965119123459, -0.01870211400091648, 0.07676101475954056, 0.05540396645665169, 0.06005168706178665, 0.10382016748189926, -0.023810885846614838, 0.051694873720407486, -0.0036981457378715277, 0.051235053688287735, 0.07285305112600327, -0.06921274960041046, -0.008857759647071362, 0.03835833817720413, -0.018057655543088913, -0.022143661975860596, -0.028977397829294205, -0.017818646505475044, -0.0577399879693985, 0.024193212389945984, -0.05260716751217842, -0.07832425087690353, 0.02315671183168888, 0.0017779867630451918, 0.03660525754094124, -0.025876551866531372, -0.019061140716075897, 0.005304500460624695, -0.008152262307703495, 0.07181146740913391, -0.02226068824529648, 0.000622523482888937, -0.041833292692899704, -0.028334982693195343, -0.058497846126556396, -0.0046463459730148315, 0.009186114184558392, 0.02333291620016098, -0.02653050608932972, 0.0608106330037117, 0.0025294607039541006, -0.031021051108837128, -0.023861084133386612, -0.012484047561883926, -0.04299292340874672, 0.03501158580183983, -0.031590789556503296, 0.056844234466552734, 0.011584586463868618, -0.022148748859763145, -0.02553296461701393, -0.007629638537764549, 0.06673376262187958, -0.02153618447482586, -0.05030883848667145, 0.00801414716988802, -0.04120134934782982, -0.04402170330286026, -0.0635017678141594, -0.022277653217315674, 0.027916988357901573, 0.04091334342956543, 0.02360239066183567, -0.016812046989798546, 0.04308673366904259, -0.01625058613717556, -0.017640547826886177, -0.009559759870171547, 0.05193474143743515, 0.002252796897664666, 0.04792509973049164, 0.07802949845790863, -0.03126397356390953, 0.008597241714596748, 0.015411414206027985, -0.05825832113623619, -0.036069806665182114, 0.0353371761739254, 0.08398405462503433, 0.028715750202536583, -0.026884131133556366, -0.014117802493274212, 0.0544557124376297, -0.0529196634888649, -0.027136996388435364, -0.004050279036164284, -0.007644567172974348, -0.03511441498994827, -0.02970856986939907, -0.00036433187779039145, -0.05361006408929825, -0.01608153246343136, 0.03516232594847679, 0.025522928684949875, 0.022753579542040825, -0.03295065462589264, 0.02008848823606968, 0.07995569705963135, 0.046508174389600754, 0.07580766826868057, -0.05341465026140213, 0.04501955211162567, -0.06158844381570816, 0.014247685670852661, -0.016603464260697365, 0.028273409232497215, 0.038142066448926926, 0.08254709094762802, 0.021010451018810272, 0.056856099516153336, -0.026028336957097054, -0.034714922308921814, 0.0003215793985873461, 0.012042460963129997, -0.0030872775241732597, -0.010776298120617867, 0.01726776920258999, -0.0018340670503675938, -0.007887453772127628, 0.008158461190760136, 0.023250257596373558, -0.04672868549823761, -0.010071583092212677, 0.008568348363041878, -0.04128223657608032, 0.07428649067878723, 0.0371520072221756, 0.020040718838572502, 0.0367620550096035, 0.012080675922334194, 0.004202216863632202, -0.017975835129618645, -0.0307836402207613, 0.0402856208384037, -0.04754212871193886, 0.001182827865704894, -0.04995424672961235, 0.0023568428587168455, -0.02348378673195839, 0.006143919192254543, 0.03842860087752342, 0.006094897165894508, -0.008167801424860954, -0.027425888925790787, 0.04446529597043991, 0.04408619925379753, -0.022436896339058876, 0.03046870231628418, -0.0136758703738451, -0.021504266187548637, -0.009407052770256996, -0.07599710673093796, 0.009046189486980438, 0.09685731679201126, -0.0286372322589159, -0.015069386921823025, -0.006935387849807739, -0.038709934800863266, -0.028835901990532875, -0.02447458542883396, -0.07070097327232361, 0.02706013433635235, 0.006503156386315823, 0.022375665605068207, 0.010106628760695457, 0.02008688822388649, 0.0027027989272028208, 0.0023650317452847958, 0.03621484711766243, 0.03676718473434448, -0.024865787476301193, -0.015161481685936451, 0.005424147937446833, -0.0015088103245943785, 0.01802958734333515, 0.004822288174182177, 0.01024909969419241, -0.018057944253087044, 0.0051671830005943775, 0.007002908270806074, -0.054645780473947525, -0.07976920902729034, 0.0038945083506405354, -0.05598358064889908, 0.026875918731093407, -0.04284472018480301, -0.08278095722198486, -0.015336769632995129, -0.027274152263998985, -0.03873296454548836, 0.06352900713682175, -0.017468756064772606, 0.036746226251125336, 0.02463172748684883, 0.02154339663684368, 0.042357850819826126, 0.036526791751384735, -0.06931217759847641, 0.05536630377173424, 0.09104511141777039, 0.04519841820001602, -0.009700972586870193, -0.008888253010809422, 0.03989125415682793, 0.032558608800172806, -0.005645181983709335, 0.021771376952528954, 0.053071826696395874, -0.02009851485490799, -0.019389720633625984, -0.0017474850174039602, -0.04543963447213173, 0.012956256046891212, -0.000790163001511246, 0.0257391519844532, 0.024085452780127525, -0.06662694364786148, -0.0071482970379292965, -0.0035995100624859333, -0.017107060179114342, -0.0010456076124683022, -0.036313656717538834, 0.000983089325018227, 0.02175830490887165, 0.0024048658087849617, -0.016522901132702827, -0.006809855345636606, 0.004829607903957367, -0.03695174306631088, 0.009806782938539982, -0.015556483529508114, 0.034918732941150665, -0.06367897987365723, 0.017362063750624657, -0.01014196127653122, -0.03818044438958168, -0.06729985773563385, 0.005393459461629391, 0.014045653864741325, -0.058541830629110336, 0.02755771204829216, -0.026149773970246315, 0.017540279775857925, 0.0016247709281742573, -0.010800749063491821, 0.02278728410601616, 0.08252456039190292, 0.017443306744098663, -0.009672974236309528, -0.06722493469715118, -0.01682230830192566, -0.03680792078375816, -0.010093826800584793, -0.015556205064058304, -0.06014285236597061, -0.014527902938425541, -0.003760113613680005, -0.0057863518595695496, 0.013937507756054401, 0.020698241889476776, -0.002541698981076479, 0.03853239864110947, 0.008449864573776722, 0.002190402476117015, -0.01172948069870472, 0.0018413560464978218, -0.05276292562484741, 0.026492949575185776, -0.015494248829782009, -0.012481686659157276, -0.025827091187238693, 0.022564850747585297, 0.010367636568844318, -0.019733905792236328, 0.06765232980251312, 0.018436690792441368, 0.018321819603443146, 0.06610071659088135, 0.03547336161136627, 0.012261013500392437, 0.027742303907871246, -0.004051956348121166, 0.07090707123279572, -0.03806125745177269, -0.006179343443363905, -0.02376001700758934, 0.0371357686817646, -0.008571409620344639, 0.03503768891096115, 0.004124263767153025, -0.0534311980009079, -0.012092987075448036, 0.028954245150089264, 0.019094202667474747, -0.0018945694901049137, -0.010581154376268387, 0.03412777557969093, -0.017916826531291008, -0.019335731863975525, -0.02975557930767536, 0.03118983283638954, 0.014951598830521107, -0.05965935438871384, 0.010134078562259674, 0.013167086988687515, 0.02018061652779579, -0.006981649901717901, -0.02070268616080284, -0.06487571448087692, -0.054562758654356, -0.024710271507501602, -0.04740648716688156, 0.029446717351675034, 0.0720040574669838, 0.03310089930891991, -0.02087179198861122, 0.004777940921485424, -0.016649998724460602, -0.022473201155662537, 0.09435752779245377, -0.029475653544068336, -0.023067159578204155, 0.023565609008073807, 0.03808114677667618, -0.056053511798381805, -0.016692405566573143, -0.016739586368203163, 0.007507722359150648, -0.027223367244005203, -0.0006691695307381451, -0.043456126004457474, -0.049338724464178085, -0.025644324719905853 ]
<p>Antimatter and matter particles annihilate. But does <a href="http://en.wikipedia.org/wiki/Dark_energy" rel="nofollow">dark energy</a> annihilate energy?</p> <p>We consider energy to be photons, and such, correct? So when we say energy, we're actually talking about some bosons, right? </p> <p>So photons and anti-photons would annihilate, gluons and anti-gluons.</p> <p>I am not sure if anti-bosons are hypothesized so please forgive. I am amateur to this.</p>
g5433
[ 0.04747806861996651, 0.024389728903770447, 0.03686864301562309, -0.025339575484395027, 0.07085511833429337, 0.011288098059594631, -0.050892408937215805, 0.0495181605219841, -0.0662611648440361, -0.003877002280205488, 0.03488007187843323, 0.011631189845502377, -0.027145925909280777, -0.06327656656503677, -0.03791974112391472, 0.020230060443282127, 0.018163572996854782, 0.024111922830343246, 0.029117971658706665, 0.02819746360182762, -0.010247688740491867, -0.04194733127951622, 0.01385052315890789, -0.047360893338918686, -0.02024981379508972, -0.01689925231039524, -0.018545232713222504, -0.05507814884185791, -0.019120842218399048, 0.001991638680920005, 0.022623954340815544, 0.002113423077389598, 0.047217655926942825, -0.04415977746248245, 0.04119548574090004, -0.05348619446158409, 0.08735540509223938, 0.0038287402130663395, 0.0022045497316867113, -0.010694928467273712, 0.004478097427636385, -0.009520100429654121, 0.014748604968190193, 0.004466966260224581, 0.011991968378424644, 0.03012336604297161, -0.0187055803835392, 0.02106582187116146, -0.011028775945305824, -0.0458160899579525, 0.02601012773811817, 0.016877563670277596, 0.07852248102426529, 0.040539320558309555, -0.015780305489897728, -0.04189340025186539, -0.0018790890462696552, -0.04730340093374252, 0.07510195672512054, 0.013379042968153954, -0.022449953481554985, 0.010945694521069527, -0.022733427584171295, 0.011096799746155739, 0.033045001327991486, -0.04618983715772629, 0.005637276917695999, -0.004176286049187183, 0.03333895280957222, 0.006793854292482138, 0.06256137788295746, 0.008743087761104107, -0.009277607314288616, -0.029454438015818596, 0.05860431492328644, -0.03179221972823143, 0.015192573890089989, -0.05043406039476395, -0.006348044145852327, -0.016809655353426933, -0.05455943942070007, -0.03360874578356743, 0.08119615167379379, -0.018898770213127136, 0.08308128267526627, -0.052548497915267944, -0.042156197130680084, -0.02275894768536091, 0.01578585058450699, 0.033277418464422226, 0.0117186876013875, 0.01714380830526352, 0.08849998563528061, -0.026175275444984436, -0.007095091510564089, 0.043878644704818726, 0.010071953758597374, 0.049884967505931854, -0.05445782095193863, -0.02355664223432541, -0.04965643584728241, 0.0052406033501029015, 0.009490938857197762, -0.012381676584482193, 0.09181460738182068, -0.05042394995689392, 0.014628908596932888, -0.06594602763652802, 0.03681924194097519, 0.051316700875759125, -0.04833126813173294, 0.018797563388943672, -0.04987656697630882, -0.010733969509601593, 0.0034005087800323963, 0.011366793885827065, 0.06550604104995728, -0.06378836184740067, 0.01697477325797081, 0.06962361186742783, 0.0011597046395763755, 0.0658055916428566, -0.01231906097382307, -0.001993120415136218, -0.053233131766319275, -0.014245409518480301, 0.02394901216030121, 0.029318533837795258, -0.020703040063381195, -0.04053542762994766, 0.07566627860069275, -0.03434479236602783, -0.027785323560237885, 0.04810918867588043, 0.03696442395448685, 0.08608951419591904, 0.011744532734155655, 0.006536735687404871, -0.03631315007805824, -0.017736710608005524, 0.03301507607102394, 0.01254927646368742, -0.02013579197227955, 0.0539962537586689, -0.07314040511846542, 0.023114606738090515, -0.05788208916783333, -0.004373171832412481, -0.02805810049176216, 0.11637387424707413, 0.058980733156204224, 0.03230861574411392, 0.02639329805970192, -0.08126844465732574, 0.023227054625749588, -0.0044549391604959965, 0.011198621243238449, -0.01249297522008419, -0.06686320155858994, 0.02460358291864395, 0.021133100613951683, -0.0024472728837281466, 0.048421334475278854, 0.01451047696173191, -0.03649018332362175, 0.01871282421052456, -0.002900477731600404, -0.0330142043530941, 0.0208683293312788, -0.007033528760075569, -0.021293126046657562, 0.03075423091650009, -0.0033639222383499146, 0.03444666042923927, 0.047927334904670715, 0.06358496099710464, 0.008469812572002411, 0.015331252478063107, -0.06128687411546707, -0.03844054788351059, 0.011726241558790207, 0.0343504473567009, 0.037680380046367645, -0.03692135214805603, 0.052032675594091415, -0.026679499074816704, -0.04245405271649361, 0.020166531205177307, 0.01145410817116499, 0.02095818519592285, -0.0018779400270432234, 0.020410580560564995, 0.01803377829492092, 0.014083759859204292, 0.07856641709804535, -0.035348933190107346, -0.019965220242738724, 0.01341012679040432, 0.013637762516736984, 0.04747386649250984, -0.02878192439675331, -0.023549865931272507, -0.050381168723106384, -0.028474600985646248, 0.06438320130109787, 0.012960802763700485, 0.012574613094329834, -0.009637746028602123, 0.06399155408143997, -0.007227672263979912, 0.025859998539090157, -0.014013360254466534, 0.015717342495918274, 0.007368424907326698, -0.0461389496922493, 0.024215534329414368, -0.034941673278808594, -0.003876329865306616, -0.018338428810238838, -0.009354114532470703, -0.04282379895448685, -0.01767439767718315, 0.0006979299942031503, -0.029531504958868027, 0.019588995724916458, 0.05013912171125412, -0.046804219484329224, -0.0660874992609024, -0.01695231720805168, -0.024992262944579124, -0.002948084846138954, 0.005223001353442669, 0.0028526035603135824, -0.03884225711226463, 0.06814964860677719, 0.006190661806613207, -0.0166617464274168, -0.037327840924263, 0.041041649878025055, 0.0706208199262619, -0.02832084894180298, -0.030881017446517944, 0.005208259914070368, 0.017593566328287125, 0.012935472652316093, -0.06719014793634415, 0.02423120103776455, -0.048213984817266464, -0.02985595166683197, 0.001630085869692266, 0.037161484360694885, -0.006575404200702906, -0.034892331808805466, 0.04079313203692436, 0.04425610974431038, -0.013634156435728073, -0.026857206597924232, 0.03522738069295883, -0.09900173544883728, 0.005917654372751713, 0.0566210113465786, -0.03262196481227875, -0.02341817319393158, -0.003521494334563613, -0.03348565101623535, -0.014631099067628384, 0.006963375024497509, 0.0038400492630898952, -0.007907535880804062, 0.05492908135056496, -0.003771326271817088, 0.02294038236141205, 0.0013812814140692353, -0.026579206809401512, 0.04431789368391037, 0.04318813234567642, -0.004390660207718611, -0.004634665325284004, 0.054425373673439026, -0.033552441745996475, -0.04328125715255737, 0.0712071880698204, -0.08595776557922363, -0.010606834664940834, 0.0298721082508564, -0.047806572169065475, -0.0257713720202446, -0.03205207735300064, -0.07887830585241318, -0.0634414330124855, -0.006495154462754726, -0.002205651020631194, 0.05129185691475868, -0.0055643972009420395, -0.04348994418978691, -0.003465348156169057, 0.030500564724206924, -0.023623956367373466, -0.041018273681402206, 0.043902549892663956, -0.028823036700487137, -0.0318564847111702, -0.046950746327638626, -0.037817295640707016, 0.001741916174069047, 0.021599747240543365, -0.08051125705242157, -0.014803440310060978, -0.01637575589120388, 0.0021733047906309366, -0.03917895630002022, 0.08594556897878647, 0.01074232067912817, 0.05489123985171318, 0.004057332873344421, 0.015382103621959686, -0.017176460474729538, -0.0010672928765416145, 0.04095816984772682, -0.013258952647447586, 0.00978801865130663, 0.0442766435444355, 0.035301826894283295, -0.05231606960296631, 0.034806959331035614, 0.014749106019735336, -0.0524149090051651, -0.019389059394598007, -0.08635471016168594, 0.002225792035460472, 0.011749348603188992, -0.030767979100346565, -0.05368472635746002, 0.04379281774163246, -0.047999702394008636, 0.02775418944656849, -0.0017741168849170208, 0.02237030491232872, 0.04312240704894066, 0.10043228417634964, 0.02114834450185299, -0.005021394696086645, -0.02956378273665905, 0.04560057818889618, -0.032002441585063934, 0.08732365071773529, -0.002909580012783408, -0.044260527938604355, 0.024926433339715004, -0.0258786641061306, -0.0011599472491070628, 0.012108897790312767, 0.08526209741830826, -0.04184279963374138, -0.03871208429336548, -0.014846318401396275, 0.053850676864385605, 0.03857843950390816, 0.04921490326523781, -0.038622643798589706, 0.007479607127606869, 0.00667257234454155, 0.09301814436912537, 0.017753195017576218, -0.02407316118478775, -0.0016392177203670144, -0.059446632862091064, -0.008572923019528389, 0.009999396279454231, -0.053736645728349686, 0.04355386272072792, 0.0015438137343153358, -0.001096472144126892, 0.014756729826331139, -0.005966188386082649, 0.02885691449046135, 0.032536931335926056, 0.047486335039138794, -0.003463587025180459, -0.02371469885110855, 0.007619318086653948, 0.04219045862555504, 0.05318747088313103, 0.037755176424980164, -0.03535626828670502, -0.0061532314866781235, -0.026083309203386307, -0.024437315762043, -0.04205649718642235, -0.00198337621986866, 0.01311100460588932, -0.002032289979979396, -0.03322602063417435, 0.003501895582303405, -0.02187950909137726, -0.03205203264951706, 0.018341755494475365, -0.03559629246592522, -0.0026140499394387007, 0.022788450121879578, -0.004129163455218077, 0.02145363949239254, 0.014797020703554153, -0.03345094248652458, 0.07064133137464523, 0.05560200288891792, 0.02632135897874832, -0.06499018520116806, -0.016315339133143425, -0.010873210616409779, 0.022175868973135948, 0.023613139986991882, -0.014850787818431854, -0.052834901958703995, 0.014396170154213905, -0.009238621219992638, -0.015929002314805984, -0.008809429593384266, 0.0013369624502956867, -0.01033803354948759, 0.025402188301086426, 0.008639734238386154, -0.0022114734165370464, -0.02468721568584442, -0.07569663971662521, 0.08458216488361359, 0.04090350121259689, -0.025382500141859055, -0.02750416286289692, 0.005339099559932947, 0.0512232668697834, -0.030908996239304543, 0.003045284189283848, 0.022223379462957382, -0.007398810237646103, -0.006740147713571787, 0.014064310118556023, 0.01985812745988369, 0.06284400075674057, -0.032414499670267105, 0.08665745705366135, -0.0062043615616858006, 0.08801465481519699, -0.05081990361213684, 0.03266480192542076, 0.059004995971918106, -0.006469865329563618, -0.03623048961162567, -0.02234327606856823, -0.02897682972252369, 0.02045428939163685, 0.024231506511569023, -0.013638177886605263, -0.030022146180272102, -0.0026578903198242188, 0.018689051270484924, -0.0032091201283037663, 0.013392860069870949, -0.03266981616616249, 0.06611324101686478, -0.06228183954954147, -0.018670542165637016, 0.03175686299800873, 0.04332498461008072, 0.03800573572516441, -0.02176639623939991, -0.013108224608004093, -0.02042892947793007, -0.04962993040680885, -0.019220637157559395, 0.017662711441516876, 0.0035571372136473656, -0.008464562706649303, 0.011645876802504063, -0.009681700728833675, -0.09230168163776398, -0.02430851012468338, -0.020702911540865898, -0.018497876822948456, 0.015973657369613647, 0.0015774358762428164, -0.004382022190839052, 0.0413532480597496, -0.05259682610630989, -0.07742514461278915, 0.07814449816942215, -0.06707897037267685, 0.053045570850372314, -0.004726116079837084, -0.00852163229137659, -0.07339579612016678, 0.012341061607003212, 0.004829717334359884, -0.052323002368211746, 0.02856476604938507, 0.02828134037554264, -0.029795335605740547, 0.009680246002972126, -0.034399449825286865, 0.029242318123579025, -0.015523320063948631, -0.027170008048415184, -0.00915373396128416, -0.053591493517160416, 0.008461236953735352, 0.06029803305864334, 0.014540040865540504, -0.019508222118020058, 0.010663502849638462, -0.049557216465473175, -0.03607386723160744, 0.005505943205207586, 0.014389527030289173, 0.07722006738185883, -0.012096275575459003, 0.017608579248189926, -0.005002692807465792, 0.07365897297859192, 0.029435113072395325, -0.05663743615150452, -0.005131150130182505, 0.032542113214731216, -0.011723640374839306, -0.020202377811074257, 0.025652777403593063, -0.01951218768954277, -0.03669407591223717, -0.01941056363284588, 0.025519708171486855, 0.04689708352088928, 0.017475008964538574, 0.006799399387091398, 0.00036132094101049006, -0.006984942127019167, -0.01581517979502678, -0.004427597392350435, -0.03674326464533806, 0.002811160869896412, 0.008196952752768993, -0.011351937428116798, 0.006385184824466705, 0.020856617018580437, 0.019758159294724464, 0.0735311210155487, -0.056377071887254715, -0.0010278690606355667, -0.03334232047200203, -0.02645293064415455, 0.00922742672264576, -0.06333880871534348, -0.009414251893758774, -0.010730603709816933, 0.052270207554101944, -0.009477446787059307, -0.009235428646206856, 0.025019975379109383, 0.010478529147803783, -0.013074174523353577, -0.0218335147947073, -0.03518816456198692, -0.0351233035326004, 0.030724359676241875, -0.02239689603447914, 0.01923116110265255, 0.052953336387872696, -0.032194286584854126, -0.016810186207294464, -0.07783331722021103, -0.01920715719461441, -0.015223393216729164, 0.02832517959177494, 0.03818512707948685, -0.0073762135580182076, -0.032965827733278275, 0.011803136207163334, -0.026230551302433014, 0.05483182519674301, -0.0196648258715868, -0.06972872465848923, -0.00858286488801241, 0.06918810307979584, 0.008102498948574066, 0.023525653406977654, -0.018014056608080864, 0.0030822164844721556, 0.018961364403367043, -0.04899564012885094, 0.04959343001246452, 0.03686918318271637, -0.004803118761628866, 0.003994536120444536, -0.01715433970093727, -0.03334837034344673, 0.014535732567310333, -0.05785203352570534, -0.035995595157146454, 0.013711598701775074, -0.02544800564646721, -0.0250399112701416, 0.014508851803839207, -0.024409987032413483, -0.02429872937500477, 0.009095611050724983, 0.004526293370872736, 0.07016824185848236, 0.07692573219537735, -0.031010877341032028, 0.0538431741297245, 0.002212697407230735, 0.037213124334812164, -0.026083622127771378, 0.03523237258195877, -0.005531520117074251, 0.043482281267642975, 0.01345866546034813, -0.06511230766773224, -0.0490790493786335, 0.0002704722573980689, 0.005277878604829311, 0.03317401185631752, 0.06068936362862587, -0.03280075266957283, 0.0075125317089259624, 0.0008105721208266914, 0.07274804264307022, 0.07331331074237823, -0.024169867858290672, 0.10625426471233368, 0.055403780192136765, 0.013501538895070553, -0.04042486473917961, -0.04422177001833916, 0.043331798166036606, 0.008434927091002464, -0.04420563206076622, -0.015383034944534302, -0.022816840559244156, -0.00010632110934238881, 0.007259859703481197, 0.003017798298969865, 0.06287535279989243, -0.0021190845873206854, 0.07953649759292603, -0.004182623699307442, -0.009355777874588966, 0.03569262847304344, 0.03023746982216835, -0.04195777699351311, 0.012194332666695118, -0.010121084749698639, -0.05274263769388199, -0.021975314244627953, 0.011305245570838451, -0.035203732550144196, -0.029446778818964958, -0.00650012819096446, -0.06263396143913269, -0.03234100714325905, 0.008981829509139061, -0.030770540237426758, 0.02255363203585148, -0.02648933231830597, -0.02654222771525383, -0.03116573393344879, -0.00014042732072994113, -0.006487787701189518, 0.060540638864040375, -0.004598371218889952, -0.007101876195520163, 0.00035929211298935115, -0.05404600873589516, -0.015160449780523777, -0.04234883561730385, -0.0028223604895174503, -0.03443389758467674, -0.03264785185456276, -0.015468180179595947, 0.02274944633245468, 0.031530559062957764, 0.00339690875262022, 0.029509736225008965, -0.011621329002082348, 0.0016124526737257838, -0.026087267324328423, 0.015322933904826641, 0.03776289522647858, 0.012201910838484764, -0.016964931041002274, -0.03308037295937538, -0.01709757186472416, 0.0031123682856559753, -0.013932608999311924, 0.01202138140797615, -0.0448044054210186, -0.018891477957367897, -0.023136863484978676, 0.03782034292817116, 0.049672093242406845, -0.0010759519645944238, -0.060627248138189316, -0.028814304620027542, 0.017946461215615273, -0.003968329168856144, -0.003288715612143278, -0.057926639914512634, 0.03263070806860924, -0.004478595219552517, -0.0021069988142699003, -0.03340241685509682, -0.025345616042613983, 0.01526803057640791, 0.026489565148949623, 0.03925639018416405, 0.03247199207544327, 0.027221975848078728, -0.02544545941054821, 0.019977547228336334, -0.029509617015719414, 0.029793886467814445, -0.02375343069434166, -0.007174953818321228, -0.013767962343990803, -0.04120594635605812, 0.02830514684319496, 0.025946376845240593, 0.013906870037317276, 0.004653864074498415, 0.015296944417059422, 0.01780792698264122, -0.026050040498375893, -0.05174628272652626, 0.009448799304664135, -0.02940528653562069, -0.06213618069887161, 0.0036033031065016985, -0.01706775091588497, 0.018096812069416046, -0.0017822780646383762, 0.017720285803079605, 0.005349429789930582, -0.018176352605223656, -0.07794564217329025, -0.035189978778362274, -0.008619067259132862, -0.02305719442665577, -0.056583210825920105, 0.004750844091176987, 0.03710411116480827, 0.004585028160363436, -0.030552396550774574, -0.005493802018463612, 0.026754027232527733, 0.011245007626712322, 0.03822135180234909, 0.05182809755206108, -0.048352643847465515, 0.02878156118094921, -0.0041318004950881, -0.03944404423236847, -0.0015730689046904445, 0.01000142376869917, -0.030912399291992188, -0.008326232433319092, -0.027291858568787575, 0.007836398668587208, -0.02656490169465542, -0.010752798989415169, -0.02069777622818947 ]
<p>Why does Mother Nature allow bound states in arbitrarily weak attractive potential in 2D but not in 3D?</p> <p>See, for example, this article: <a href="http://scitation.aip.org/content/aip/journal/jmp/44/2/10.1063/1.1532538" rel="nofollow">http://scitation.aip.org/content/aip/journal/jmp/44/2/10.1063/1.1532538</a></p>
g5434
[ 0.0467492900788784, 0.042078688740730286, 0.009164874441921711, 0.0047719646245241165, 0.0015520347515121102, 0.09141505509614944, 0.012662936933338642, -0.010330329649150372, -0.021800970658659935, -0.05152590200304985, 0.0022861624602228403, -0.025914136320352554, 0.07295230031013489, 0.02990585006773472, -0.006431948859244585, 0.02634090930223465, 0.02501828409731388, 0.013260097242891788, 0.052196990698575974, -0.00641446840018034, -0.07022182643413544, 0.01635162904858589, -0.031382396817207336, 0.003897233633324504, 0.016856035217642784, 0.04131893068552017, 0.0424475222826004, -0.06048249080777168, -0.033064182847738266, 0.020039953291416168, 0.02727631665766239, 0.024359822273254395, 0.010703211650252342, -0.028678951784968376, -0.0008164840401150286, 0.014401537366211414, 0.03475038707256317, -0.024880681186914444, -0.028708960860967636, 0.013763717375695705, -0.02967848628759384, -0.05674983933568001, 0.01711340621113777, 0.002934338292106986, -0.06091158092021942, -0.015509289689362049, 0.0384497307240963, 0.027171200141310692, 0.00663988059386611, -0.07390673458576202, -0.018453530967235565, 0.06469108909368515, 0.08623608201742172, -0.03239467367529869, 0.07878678292036057, -0.02486545406281948, -0.036728810518980026, 0.016531268134713173, 0.018959971144795418, 0.0051474724896252155, -0.02095639705657959, 0.02009524591267109, 0.01147526130080223, 0.026616336777806282, 0.06086147204041481, -0.03256789594888687, -0.09181851893663406, 0.001965827774256468, 0.01581050083041191, -0.001011230400763452, -0.009966866113245487, -0.022149747237563133, -0.07199560105800629, -0.08632958680391312, 0.02310633286833763, 0.019860250875353813, 0.016973916441202164, -0.01752842776477337, -0.032405074685811996, -0.007443613838404417, -0.027202460914850235, -0.009074761532247066, -0.02587166242301464, 0.030904240906238556, 0.08296132832765579, -0.0027061505243182182, 0.038486454635858536, -0.020632803440093994, -0.022267865017056465, 0.037064481526613235, -0.07905087620019913, 0.023199500516057014, 0.04111403226852417, -0.004279831890016794, -0.053231336176395416, -0.036207277327775955, -0.014215190894901752, 0.012450055219233036, -0.009585208259522915, 0.017930367961525917, -0.02212424762547016, -0.003110620193183422, -0.0050156451761722565, 0.05990978330373764, -0.01698903739452362, 0.011238095350563526, 0.03829517960548401, -0.0007951552979648113, -0.018324214965105057, -0.01575026847422123, 0.010118064470589161, 0.003928629215806723, -0.02038358710706234, -0.017428100109100342, -0.0371883250772953, 0.03536238148808479, 0.0502353236079216, -0.022486217319965363, 0.03862727805972099, 0.05279755964875221, 0.058351702988147736, 0.056697435677051544, 0.015233602374792099, 0.053232286125421524, 0.05282297730445862, -0.00883583165705204, -0.03980044648051262, 0.019188227131962776, 0.02041523903608322, -0.03923816233873367, 0.00910418201237917, -0.02606462873518467, 0.012640057131648064, -0.026960531249642372, -0.03665013983845711, 0.01781356893479824, -0.039561547338962555, -0.03928053751587868, -0.023776555433869362, -0.005036938935518265, -0.10227558016777039, -0.031217988580465317, 0.023874493315815926, 0.004046327900141478, -0.05509594455361366, 0.035183168947696686, 0.03662954270839691, 0.006792508065700531, 0.0005069034523330629, 0.03544045239686966, 0.0018507695058360696, 0.04443327710032463, 0.02635999396443367, -0.03555255010724068, -0.005713234189897776, -0.013042718172073364, 0.06994955241680145, 0.03064003773033619, -0.011050071567296982, -0.011520973406732082, 0.05402833968400955, 0.07317934930324554, -0.08675962686538696, -0.016124706715345383, -0.023888282477855682, 0.023388730362057686, 0.0097434027120471, -0.05997862294316292, -0.07040463387966156, -0.026350757107138634, -0.008870875462889671, 0.01941833086311817, -0.014987114816904068, 0.06595060229301453, -0.023236382752656937, 0.006752500310540199, -0.005978544242680073, -0.06336839497089386, 0.06932537257671356, -0.031033944338560104, -0.034729763865470886, 0.01885956898331642, -0.06318600475788116, -0.018164178356528282, 0.033339641988277435, -0.03789867088198662, -0.00758882611989975, 0.04477637633681297, -0.012282740324735641, -0.027520563453435898, -0.027970610186457634, 0.03168513998389244, -0.02243049256503582, 0.049834955483675, -0.02013087458908558, -0.040281444787979126, 0.0683068111538887, -0.023401418700814247, -0.019693825393915176, -0.013922247104346752, -0.04232041910290718, 0.015105565078556538, -0.0063108596950769424, -0.0447591096162796, 0.0286117997020483, 0.0017324407817795873, 0.015086031518876553, 0.042427632957696915, 0.05556802079081535, 0.0022193731274455786, -0.04508710652589798, 0.06682084500789642, -0.045911967754364014, -0.042789850383996964, 0.021127324551343918, -0.06896872818470001, 0.017112672328948975, 0.04473263770341873, -0.06847153604030609, 0.012781466357409954, -0.008573627099394798, -0.06904918700456619, 0.012553641572594643, 0.012129505164921284, -0.004892558790743351, 0.007513330318033695, -0.07584542036056519, 0.029092513024806976, 0.02109694667160511, -0.012796226888895035, -0.058793529868125916, -0.0316331684589386, -0.004807587713003159, 0.035216834396123886, 0.011539360508322716, 0.05611049383878708, -0.01047851424664259, -0.009646980091929436, -0.029130375012755394, -0.05237051472067833, 0.03318826109170914, 0.024775445461273193, -0.0057077654637396336, 0.03018796257674694, 0.058142565190792084, -0.02924351580440998, 0.03494745492935181, 0.023201243951916695, 0.026401197537779808, 0.07776860147714615, 0.03228212520480156, -0.0481436662375927, -0.01264125294983387, 0.008868802338838577, -0.008846897631883621, 0.02991015836596489, -0.015532417222857475, 0.015300407074391842, 0.010640745982527733, -0.05126916244626045, -0.003869204316288233, 0.00003281011595390737, -0.005335158668458462, -0.05349745973944664, -0.032141681760549545, -0.0011396297486498952, -0.04440433904528618, -0.06536242365837097, -0.07526282966136932, 0.02248820662498474, -0.02308749593794346, 0.04141543433070183, 0.000555887003429234, -0.011221515014767647, -0.01435042917728424, 0.018265152350068092, -0.018271226435899734, 0.0004909010021947324, 0.004774245899170637, 0.021578598767518997, -0.04778267443180084, -0.033246565610170364, -0.00006201914948178455, -0.006483159027993679, 0.03852817416191101, -0.018342526629567146, -0.027401108294725418, -0.023598240688443184, -0.02380305342376232, 0.03129521384835243, 0.019589807838201523, 0.019259711727499962, 0.00697055459022522, -0.018037311732769012, -0.03331600874662399, -0.036876481026411057, -0.06730066984891891, -0.016069702804088593, -0.03806673735380173, 0.05399351194500923, 0.02116207219660282, 0.05810074135661125, 0.035578880459070206, 0.031132159754633904, -0.027831071987748146, -0.004075187724083662, -0.02279042638838291, 0.0006730366731062531, -0.01652083359658718, 0.033410318195819855, 0.018893122673034668, 0.013705410063266754, -0.004409567452967167, -0.012491186149418354, -0.00241404608823359, -0.0034361183643341064, -0.060037415474653244, -0.003909524530172348, -0.012784305959939957, -0.09134817123413086, 0.018708912655711174, 0.0016038503963500261, -0.01912194862961769, 0.011089695617556572, 0.027273157611489296, -0.009954558685421944, -0.052383486181497574, -0.07590733468532562, -0.05841217190027237, -0.003561745397746563, 0.04650172218680382, 0.02064545825123787, 0.01030929759144783, -0.0035073761828243732, -0.08365131169557571, -0.055119287222623825, -0.05784139037132263, 0.01606561243534088, 0.024658186361193657, -0.06228156387805939, -0.046119384467601776, -0.024355461820960045, -0.026395970955491066, -0.02053620107471943, 0.008344498462975025, 0.02593240886926651, -0.03361187502741814, 0.02146049216389656, 0.00255782064050436, -0.02284746617078781, -0.004020415246486664, 0.01723596267402172, 0.020985400304198265, 0.020270561799407005, -0.013372027315199375, 0.026820151135325432, -0.011019492521882057, -0.012646989896893501, -0.01502680592238903, 0.0400768481194973, -0.021833984181284904, 0.0006013577221892774, 0.005927154328674078, -0.0328613817691803, 0.008815906010568142, 0.019577715545892715, -0.024053344503045082, 0.05226884037256241, 0.07354049384593964, -0.01547924429178238, 0.02269614487886429, -0.0003148989053443074, 0.00009173557918984443, 0.04226548224687576, 0.08181353658437729, 0.019171366468071938, 0.012566429562866688, 0.015540948137640953, -0.010650098323822021, -0.029298199340701103, 0.036585573107004166, 0.00867294892668724, 0.0422658696770668, 0.02541912905871868, 0.03777347132563591, 0.003416839288547635, -0.04461883753538132, -0.001324790413491428, -0.057720255106687546, -0.029859239235520363, 0.01247484888881445, 0.023038078099489212, -0.030923910439014435, 0.007471056655049324, 0.023800062015652657, 0.012885138392448425, 0.025349000468850136, -0.02397170476615429, -0.03153344616293907, 0.06157838553190231, -0.054937563836574554, 0.011368896812200546, -0.08629569411277771, -0.041801441460847855, -0.024957917630672455, -0.056999821215867996, -0.0020168565679341555, 0.06740737706422806, -0.06314344704151154, -0.04281539469957352, 0.017989862710237503, 0.02053738385438919, 0.01750849559903145, -0.031428102403879166, 0.021814392879605293, -0.07259424030780792, -0.010888668708503246, -0.04928470402956009, 0.01198003999888897, -0.011127042584121227, 0.013838453218340874, 0.06299523264169693, -0.005534384865313768, 0.025901680812239647, 0.036189738661050797, 0.06730181723833084, 0.017836257815361023, -0.0305623821914196, 0.019196756184101105, 0.03200579807162285, 0.00541129382327199, 0.005522332154214382, -0.04312462732195854, -0.022748202085494995, -0.012214493937790394, 0.008576253429055214, -0.07313758879899979, 0.029457937926054, 0.04526444524526596, 0.0053642019629478455, 0.044578686356544495, 0.02727627567946911, 0.03317426145076752, -0.0035040711518377066, -0.0185958631336689, 0.03128824010491371, -0.015220195055007935, 0.01982644572854042, -0.003337249858304858, -0.03150948882102966, -0.03655310347676277, -0.018284950405359268, 0.01974749006330967, -0.020917441695928574, 0.040551070123910904, -0.006462386343628168, -0.07123922556638718, 0.030725622549653053, 0.005884389393031597, 0.02101738192141056, 0.03651047125458717, -0.009942933917045593, -0.05523870512843132, -0.02290920354425907, 0.01218718197196722, 0.002534199506044388, -0.021583229303359985, 0.03139572590589523, -0.03894558176398277, -0.03410303220152855, 0.016358913853764534, 0.02607748657464981, 0.00582536868751049, 0.06854955852031708, 0.007602897938340902, -0.020727382972836494, 0.05953693762421608, -0.03896830603480339, 0.002940408419817686, -0.07151611149311066, -0.012695418670773506, -0.011548162437975407, 0.05409849435091019, 0.01478245947510004, 0.010176886804401875, 0.042728450149297714, -0.04154170677065849, -0.003802528139203787, -0.08951009809970856, -0.03794383630156517, 0.03377395123243332, -0.006511821411550045, -0.04639466851949692, 0.0014358205953612924, -0.004727671388536692, -0.005160607863217592, -0.0025413688272237778, 0.030876532196998596, -0.012087583541870117, 0.01423442643135786, -0.08742114901542664, -0.042719315737485886, -0.004878446459770203, 0.025464272126555443, -0.020550107583403587, 0.054982513189315796, 0.061980098485946655, -0.05796127766370773, 0.04763110727071762, -0.0216453205794096, -0.023430513218045235, -0.05168384313583374, 0.010018163360655308, 0.03419889137148857, 0.025643331930041313, -0.03582305833697319, -0.020691649988293648, 0.008210644125938416, -0.023949839174747467, -0.044228214770555496, 0.03289825841784477, 0.02248167060315609, 0.025335760787129402, -0.11104898154735565, 0.03146340325474739, -0.011003261432051659, -0.053912755101919174, -0.011155237443745136, 0.038135383278131485, 0.06784088164567947, -0.022796088829636574, 0.022182337939739227, 0.02385939471423626, 0.007184350863099098, 0.06098218634724617, -0.052185699343681335, -0.021065013483166695, -0.012713773176074028, 0.005113814026117325, -0.0033856562804430723, 0.019477128982543945, -0.01634521409869194, -0.03364963456988335, 0.06401931494474411, -0.02300616167485714, -0.025643261149525642, 0.017991799861192703, -0.03904973715543747, 0.031786657869815826, -0.0034505079966038465, 0.01085200160741806, -0.02877049706876278, -0.06627234071493149, 0.008051849901676178, 0.02675681747496128, 0.009453443810343742, -0.03624130040407181, -0.0052992128767073154, -0.02094958908855915, -0.014815774746239185, -0.010422185063362122, 0.10311488807201385, 0.04578277841210365, 0.0012891287915408611, 0.0016192945186048746, -0.02584167756140232, 0.012439491227269173, 0.02007925882935524, 0.03800620138645172, 0.03837025910615921, -0.010859196074306965, -0.02315993420779705, 0.053410809487104416, 0.009030147455632687, 0.0007893320871517062, 0.04130527749657631, -0.05116107687354088, -0.033891431987285614, -0.013321439735591412, -0.0009713054751046002, 0.005713903810828924, 0.05248797684907913, 0.055539488792419434, -0.021560322493314743, 0.04623384401202202, 0.00766373984515667, 0.006786534562706947, -0.0034102010540664196, 0.016715364530682564, -0.05702316761016846, -0.03993917256593704, 0.008851341903209686, 0.010328875854611397, -0.021884463727474213, 0.026409143581986427, -0.028565984219312668, -0.02904641442000866, 0.06133955344557762, -0.08369551599025726, -0.0056447056122124195, 0.0365828275680542, -0.004872328136116266, 0.011755171231925488, 0.014015533961355686, 0.020618747919797897, 0.06005624309182167, -0.009415081702172756, 0.02513110265135765, -0.003483485197648406, 0.06699629127979279, -0.059386901557445526, 0.02505652979016304, -0.02555975317955017, -0.02832164615392685, 0.0011273162672296166, -0.06517185270786285, 0.03278806805610657, 0.011787782423198223, -0.01837448962032795, -0.010944786481559277, -0.033383455127477646, -0.00564386835321784, 0.10587264597415924, 0.005253605544567108, 0.04538857564330101, 0.03663253411650658, -0.0728871077299118, -0.0028512519784271717, 0.028704555705189705, 0.043557118624448776, 0.013930391520261765, -0.0006721611716784537, 0.034772537648677826, 0.03130284696817398, 0.012258755974471569, -0.043568205088377, -0.06903763115406036, -0.045229822397232056, 0.04017030820250511, -0.032398831099271774, -0.036444514989852905, 0.04102523997426033, 0.06753579527139664, -0.015872351825237274, 0.0022532923612743616, 0.010698387399315834, 0.018052011728286743, -0.008460178039968014, -0.026850055903196335, 0.003058953443542123, 0.09488289803266525, 0.026347091421484947, -0.008625054731965065, -0.03224264457821846, -0.057940974831581116, 0.004527590703219175, -0.03464851900935173, -0.019179221242666245, 0.014948876574635506, -0.029755648225545883, -0.03519617021083832, 0.03927016630768776, -0.007594128139317036, 0.050363585352897644, 0.04114430397748947, -0.04663768783211708, 0.03743723779916763, -0.029045822098851204, -0.00032978522358462214, -0.023689784109592438, 0.019844338297843933, -0.03351069614291191, -0.01365791168063879, 0.05891773849725723, 0.0026172783691436052, 0.023193098604679108, 0.05102594196796417, 0.0263581071048975, 0.09308347851037979, -0.03309127688407898, 0.0727488324046135, 0.030832510441541672, 0.025988927111029625, 0.02432975545525551, -0.0834016352891922, -0.018082965165376663, -0.04354872182011604, 0.03122318908572197, 0.003764351364225149, 0.02990787848830223, 0.04797143489122391, 0.01923741027712822, 0.038221199065446854, -0.0003752904594875872, -0.06621380150318146, 0.010263457894325256, 0.039475683122873306, 0.012941031716763973, 0.010250318795442581, -0.0020383174996823072, -0.016320493072271347, -0.06073811650276184, 0.012579256668686867, -0.020453911274671555, 0.06371276080608368, -0.023668188601732254, 0.006995838135480881, 0.019951000809669495, -0.017862431704998016, -0.02968217246234417, -0.02192746102809906, 0.07127966731786728, 0.022890036925673485, 0.010663558728992939, 0.04548532888293266, 0.04275944456458092, -0.00011719111353158951, 0.02079133130609989, 0.07009627670049667, 0.005709964316338301, -0.028679149225354195, -0.0005597586277872324, 0.0036955683026462793, 0.01769416034221649, -0.011592588387429714, -0.023973895236849785, 0.040436722338199615, -0.011433814652264118, 0.0018538321601226926, 0.021498845890164375, -0.03534053638577461, -0.03115300089120865, 0.005053727887570858, -0.007103979121893644, -0.060502637177705765, -0.009507148526608944, -0.018995806574821472, 0.02957741543650627, -0.0019637495279312134, -0.021643318235874176, -0.047228582203388214, -0.025575650855898857, 0.011297827586531639, -0.06434445083141327, 0.07830361276865005, -0.006221456453204155, -0.0567740835249424, 0.08384725451469421, 0.0403432659804821, -0.011862724088132381, -0.008454610593616962, -0.050896622240543365, -0.028263872489333153, -0.0021137178409844637, 0.05395011231303215, -0.009148307144641876, 0.037609826773405075, 0.019621366634964943, 0.012523975223302841, 0.010265063494443893, 0.06265682727098465, -0.013822084292769432, -0.007145408075302839, -0.01164628379046917, 0.03990279510617256, -0.000989102991297841, -0.031912244856357574, 0.034857127815485 ]
<p>There are lots of models of gravity mediated SUSY breaking with various spectra as well as various general gauge mediation models. Are there any "smoking gun" experimental singnatures that could definitely distinguish between the two scenarios? Would this be possible to do at the LHC or would we need an ILC-type machine to do that?</p>
g5435
[ -0.01726333424448967, 0.024521278217434883, -0.005241947248578072, -0.02173071727156639, 0.006342602428048849, -0.027490736916661263, -0.047914598137140274, 0.04401618242263794, -0.016986049711704254, -0.021909574046730995, 0.046115223318338394, -0.002283354289829731, 0.03669806569814682, 0.04435121268033981, 0.03144370764493942, 0.008370742201805115, 0.02442215383052826, -0.029341842979192734, 0.020624063909053802, -0.02208140306174755, -0.011966975405812263, -0.039291441440582275, 0.006829068996012211, -0.07369271665811539, -0.07869222015142441, -0.03979521244764328, 0.03729430213570595, 0.013887244276702404, -0.0021476573310792446, 0.002376610180363059, -0.00902611669152975, -0.04888273775577545, -0.00010173368355026469, -0.040474116802215576, -0.07414749264717102, -0.0316106453537941, 0.02173548936843872, 0.01189974881708622, -0.01715650036931038, -0.0062242834828794, 0.006126074586063623, -0.011778394691646099, 0.01254207082092762, -0.01837538555264473, -0.001410794910043478, 0.01861586794257164, 0.05761206895112991, 0.013207502663135529, 0.009392243809998035, -0.0014596563996747136, 0.005513797048479319, -0.03251446783542633, 0.03676709905266762, 0.027608398348093033, -0.008297598920762539, -0.017139475792646408, -0.004436102695763111, 0.005811681039631367, 0.026562174782156944, 0.011923977173864841, -0.01981361024081707, 0.019130723550915718, 0.01860722340643406, -0.022910568863153458, 0.03287450224161148, 0.058630503714084625, -0.04287264123558998, -0.07584096491336823, -0.0053424108773469925, -0.043458446860313416, 0.014759034849703312, 0.03362983837723732, 0.033962737768888474, -0.003923418931663036, 0.0067054652608931065, 0.02127280831336975, 0.0038069328293204308, 0.007103547919541597, -0.0474095344543457, 0.01724659651517868, -0.0340440571308136, -0.030643824487924576, -0.0022749050986021757, -0.018554411828517914, 0.00023877959756646305, -0.0441509410738945, -0.017044944688677788, 0.06754587590694427, 0.01905023492872715, 0.0032122170086950064, -0.01597721315920353, 0.019734468311071396, 0.016395753249526024, -0.045021902769804, -0.004643997177481651, 0.04612014442682266, 0.019199175760149956, 0.07047377526760101, -0.07447745651006699, -0.010211033746600151, -0.03447025641798973, 0.05231810733675957, 0.025926515460014343, 0.04131258279085159, -0.040763843804597855, -0.017591318115592003, 0.055432405322790146, -0.039005346596241, 0.04338005557656288, -0.006605863571166992, -0.014873829670250416, 0.02732689678668976, -0.02919788658618927, 0.030073510482907295, 0.015157620422542095, -0.08701509237289429, 0.01327524147927761, -0.010491318069398403, -0.039085503667593, 0.0010332680540159345, -0.013743586838245392, -0.008118625730276108, -0.04283227398991585, -0.0008430189336650074, -0.024879055097699165, 0.019948579370975494, -0.04148394986987114, 0.011438081972301006, 0.021340863779187202, -0.027287688106298447, 0.05772434175014496, -0.02932986430823803, -0.028853798285126686, 0.029607517644762993, 0.022352105006575584, 0.019515400752425194, 0.0560777522623539, -0.027525736019015312, -0.00501402048394084, -0.02796085551381111, 0.0035694094840437174, -0.029005620628595352, -0.033119913190603256, -0.0011698121670633554, 0.0027521755546331406, -0.00001735870864649769, -0.0013916176976636052, 0.022123578935861588, -0.06370113044977188, -0.0014828162966296077, 0.0019252336351200938, 0.07446081936359406, 0.05644911900162697, -0.02953849732875824, 0.012287506833672523, 0.0008471126202493906, -0.0033408813178539276, -0.010416432283818722, 0.00799678172916174, -0.053328607231378555, -0.02372080273926258, -0.02390412800014019, 0.00588298961520195, -0.029180731624364853, -0.04259101301431656, 0.009721595793962479, -0.006575108040124178, 0.008632225915789604, 0.06520677357912064, -0.03318408131599426, -0.09501262754201889, -0.03754011541604996, -0.006033719051629305, 0.05431042239069939, 0.0498904213309288, 0.07198647409677505, -0.01471848413348198, -0.014611447229981422, -0.029235320165753365, 0.018915867432951927, 0.036605674773454666, -0.04794856905937195, -0.03219808638095856, -0.057152509689331055, 0.03355182707309723, -0.035498980432748795, 0.006945569533854723, 0.0019933755975216627, 0.06531629711389542, 0.02272222749888897, -0.04979630187153816, 0.0036181658506393433, -0.01237234566360712, 0.020465945824980736, -0.052018776535987854, -0.020482344552874565, 0.044816095381975174, -0.006253323517739773, -0.005350681487470865, 0.019789163023233414, -0.05972088873386383, 0.017819762229919434, 0.0176105760037899, -0.03958854079246521, -0.05311567708849907, -0.018528206273913383, -0.01482290867716074, -0.03367023542523384, -0.00904851034283638, -0.032542988657951355, 0.02396303229033947, -0.01654544286429882, 0.0253395214676857, -0.06563457101583481, -0.02291123941540718, -0.03679576516151428, 0.0347839817404747, 0.07594791054725647, 0.00023052917094901204, 0.0808907225728035, -0.032792989164590836, -0.015135486610233784, 0.028910111635923386, 0.027949241921305656, 0.017644871026277542, -0.017114687711000443, -0.021429086104035378, 0.01372490730136633, -0.02779870480298996, -0.04217924177646637, 0.0285556148737669, 0.047827642410993576, 0.04682573303580284, -0.018796076998114586, 0.013912220485508442, 0.014988454058766365, 0.04315315932035446, -0.023166624829173088, -0.003963696304708719, -0.02082829549908638, 0.06615854799747467, -0.02224033884704113, -0.005868407431989908, -0.009191004559397697, 0.05284982547163963, -0.021097591146826744, -0.01661841757595539, 0.012254494242370129, -0.04075261950492859, -0.025331301614642143, -0.016279933974146843, -0.004604347050189972, -0.05570732057094574, -0.014075947925448418, -0.054323550313711166, -0.0472373329102993, 0.06671953946352005, 0.04982767626643181, -0.08007513731718063, 0.03552257642149925, 0.013335252180695534, -0.023097077384591103, -0.0018756691133603454, 0.021185841411352158, -0.032867394387722015, -0.05616002902388573, 0.018385371193289757, -0.0846487507224083, -0.05255528911948204, 0.02662813849747181, -0.06379007548093796, -0.0672474354505539, 0.052129946649074554, -0.0028225001879036427, 0.026626192033290863, 0.05967462807893753, -0.036853816360235214, -0.02723015286028385, 0.016615841537714005, -0.049419429153203964, -0.006811623461544514, -0.03827875852584839, -0.007374072913080454, -0.008534356020390987, 0.05209021270275116, -0.0023784327786415815, -0.01387265045195818, 0.004731151275336742, -0.056723013520240784, 0.052818674594163895, -0.03730623051524162, -0.038375239819288254, -0.00011998382251476869, 0.014526697807013988, -0.06280215829610825, 0.004185674712061882, -0.02679385244846344, -0.027525849640369415, 0.006431668531149626, 0.009697184897959232, 0.013726248405873775, -0.015922699123620987, 0.024704666808247566, 0.05718802288174629, -0.049942344427108765, -0.05651288852095604, -0.05257263779640198, 0.00373174250125885, 0.1008344441652298, -0.07585206627845764, -0.016469093039631844, 0.00040741273551248014, 0.015169578604400158, 0.08727685362100601, 0.04008223116397858, -0.04447001963853836, 0.03597597777843475, 0.04110966995358467, 0.012201173231005669, -0.03790360316634178, 0.005228534806519747, 0.014070606790482998, 0.006341265514492989, -0.05731583386659622, -0.04152386263012886, 0.06465448439121246, 0.01962050423026085, -0.01935134455561638, -0.08343667536973953, 0.011841514147818089, 0.005051139742136002, 0.02392292395234108, 0.027620721608400345, 0.04011959210038185, -0.04379934445023537, 0.04822711646556854, -0.004929688759148121, 0.018941208720207214, 0.04131912440061569, 0.035568322986364365, -0.017949841916561127, -0.011387978680431843, 0.013851992785930634, 0.03709203004837036, 0.03156889230012894, 0.018325654789805412, -0.018633108586072922, 0.0008629467920400202, 0.04635317251086235, -0.0467110276222229, 0.03975721076130867, -0.023622801527380943, 0.021552912890911102, -0.03367774933576584, 0.03808978572487831, -0.04184100031852722, 0.0721304640173912, 0.0314863882958889, 0.013006582856178284, -0.010661783628165722, 0.020080434158444405, 0.012557837180793285, 0.029543021693825722, 0.019877824932336807, -0.017850236967206, 0.07489205151796341, -0.004486771300435066, 0.01878223940730095, 0.0010723554296419024, 0.022970329970121384, 0.0223349891602993, 0.06824396550655365, -0.022737789899110794, -0.011276278644800186, 0.04510531947016716, -0.008796046487987041, 0.06251901388168335, -0.02101653255522251, 0.005755639169365168, 0.0332527682185173, 0.02851099520921707, 0.0482952706515789, 0.03851708769798279, -0.013790068216621876, 0.0050979722291231155, -0.02158930152654648, -0.0009481266606599092, 0.0006515986169688404, -0.03554153069853783, 0.004579851403832436, 0.030179759487509727, 0.011999601498246193, -0.06498360633850098, -0.00911649875342846, -0.01914200931787491, 0.031790006905794144, -0.0299324132502079, -0.05807711184024811, 0.0067765433341264725, 0.016855526715517044, 0.028125125914812088, 0.035356175154447556, 0.02374873124063015, -0.05069372057914734, -0.019087355583906174, -0.038121260702610016, 0.029959898442029953, -0.0031495187431573868, 0.005163639318197966, 0.04588891193270683, 0.04637916758656502, -0.012136920355260372, 0.00012916236300952733, -0.0648636519908905, 0.0068772886879742146, -0.07391361892223358, -0.022970164194703102, 0.021626319736242294, 0.06077200174331665, 0.02427331544458866, 0.02502043917775154, 0.07149453461170197, 0.034697018563747406, -0.003664260497316718, -0.01636837050318718, 0.0040679192170500755, -0.020034169778227806, -0.0000527685260749422, -0.012588188983500004, -0.016477501019835472, 0.06018851697444916, -0.040415044873952866, -0.027119942009449005, -0.006499976385384798, -0.025411637499928474, 0.023465074598789215, -0.06901940703392029, -0.05393576622009277, -0.059337832033634186, 0.02345632202923298, 0.0958729162812233, -0.015897009521722794, 0.055423907935619354, -0.01853962428867817, 0.05895012244582176, 0.05066884681582451, 0.017768006771802902, -0.023285357281565666, -0.0367581807076931, 0.053353406488895416, -0.00993063859641552, 0.012956932187080383, -0.06381554901599884, 0.0515989288687706, -0.06710463017225266, 0.017029253765940666, 0.03103829175233841, 0.08481456339359283, 0.025485116988420486, -0.02196449786424637, 0.0024793455377221107, -0.03574543818831444, 0.050010744482278824, -0.02105015330016613, -0.0064078643918037415, 0.019051561132073402, -0.10416565835475922, 0.009066839702427387, -0.01845342107117176, 0.01750478893518448, -0.01587691530585289, -0.03409779444336891, 0.006529598031193018, 0.017100021243095398, -0.009841332212090492, -0.01819581724703312, -0.020986096933484077, -0.045476291328668594, -0.009820237755775452, -0.03853029012680054, -0.020735202357172966, -0.023451315239071846, 0.02224518358707428, -0.02880924753844738, -0.016015829518437386, 0.03574226051568985, -0.07395388185977936, -0.026572762057185173, -0.03223294019699097, 0.014487805776298046, -0.008370931260287762, 0.036338090896606445, -0.004733886569738388, -0.01299075223505497, -0.013131795451045036, 0.029533473774790764, -0.006703113205730915, -0.046258535236120224, -0.01972021721303463, 0.0038404620718210936, 0.044088102877140045, 0.01644035056233406, 0.063198983669281, -0.011996771208941936, -0.03483355790376663, 0.018732581287622452, 0.05256543308496475, 0.030672268941998482, -0.041429080069065094, 0.04488281160593033, -0.03216888755559921, -0.018448257818818092, -0.015795070677995682, 0.005939518101513386, 0.021999863907694817, 0.005545623134821653, 0.019760962575674057, 0.04652264341711998, 0.029319744557142258, -0.08768017590045929, 0.004956397693604231, -0.03567415848374367, 0.007452037185430527, 0.05435531586408615, 0.0498337484896183, 0.04972401261329651, 0.003872903063893318, 0.010323405265808105, 0.03800392150878906, -0.0740305483341217, 0.0920373871922493, -0.009979362599551678, 0.04487341642379761, 0.06459035724401474, 0.10081914067268372, -0.013367724604904652, 0.01714301109313965, 0.02546636201441288, -0.0641552209854126, -0.03422442823648453, -0.02208070270717144, -0.033867426216602325, 0.0167824849486351, -0.028044188395142555, 0.02704644948244095, -0.06929513067007065, 0.008050781674683094, 0.04178774356842041, 0.02376355230808258, -0.05315326899290085, -0.04584793746471405, 0.008656519465148449, 0.054781630635261536, 0.0409218892455101, 0.013718372210860252, 0.013361185789108276, -0.00001561212593514938, -0.07819603383541107, 0.00943734496831894, 0.0033006176818162203, -0.012512491084635258, 0.022043250501155853, 0.0566357783973217, 0.03034774772822857, -0.011311504058539867, 0.011581115424633026, -0.009194515645503998, -0.08335231989622116, 0.06459257751703262, -0.02150147035717964, 0.006531770806759596, 0.007689002901315689, 0.0016148770228028297, 0.003367313416674733, -0.030315877869725227, -0.04351427033543587, 0.04791634902358055, 0.03427896276116371, 0.036263249814510345, 0.013445110060274601, 0.039551395922899246, 0.0448550283908844, 0.02363438531756401, -0.014206727035343647, -0.01101846992969513, 0.038217317312955856, -0.0301718320697546, 0.05287729203701019, 0.03232930600643158, 0.02606877312064171, -0.019591091200709343, -0.06056971848011017, 0.014919815585017204, 0.015314152464270592, -0.05189002305269241, 0.03030964359641075, -0.016726547852158546, -0.043358758091926575, -0.048434384167194366, 0.04780031740665436, 0.040657103061676025, 0.018216051161289215, -0.011938872747123241, -0.006703102961182594, 0.014863443560898304, 0.0480593740940094, -0.01774330623447895, 0.023857440799474716, 0.03325812891125679, 0.020347055047750473, -0.026691030710935593, -0.018224520608782768, 0.017626237124204636, -0.04048231989145279, -0.028182001784443855, 0.03024623915553093, -0.0314311720430851, -0.043967485427856445, -0.03277743235230446, 0.023132819682359695, 0.033393342047929764, -0.00709668081253767, 0.005138997919857502, -0.019680850207805634, -0.039288900792598724, 0.002688780426979065, -0.007477361708879471, 0.03750103712081909, 0.02568952366709709, 0.007855433970689774, 0.008258082903921604, 0.028324270620942116, 0.07602215558290482, -0.011190926656126976, -0.02035721391439438, 0.02485397830605507, 0.010182103142142296, -0.01107900682836771, 0.039154477417469025, 0.03791952133178711, 0.0435703881084919, 0.0076197171583771706, 0.049679018557071686, 0.019258955493569374, 0.03971589729189873, 0.04369935393333435, 0.00364893046207726, 0.0018283809768036008, -0.03184203431010246, -0.01650231145322323, -0.03143059462308884, -0.05135323479771614, -0.03680713474750519, -0.020317034795880318, -0.06601713597774506, -0.029696617275476456, -0.04354595020413399, -0.024400869384407997, 0.030033454298973083, -0.032437216490507126, -0.018342044204473495, -0.004345760215073824, 0.020064543932676315, -0.05051296204328537, -0.005569830536842346, -0.0036661799531430006, -0.04916062578558922, 0.0013331810478121042, 0.01394690852612257, -0.015524814836680889, -0.03749561682343483, -0.0661541149020195, -0.05654962733387947, 0.014009970240294933, -0.033415745943784714, -0.10422413051128387, -0.03709787502884865, 0.05364742502570152, 0.010614129714667797, -0.039141424000263214, 0.05067238211631775, 0.02200278639793396, 0.013772490434348583, 0.068886399269104, 0.015171937644481659, 0.04233406111598015, 0.0662073940038681, 0.04567283019423485, -0.07064423710107803, -0.014621187932789326, 0.004232876468449831, 0.011065448634326458, -0.016076328232884407, 0.02028549648821354, -0.03621278703212738, -0.02435905486345291, -0.05909469723701477, 0.06392388790845871, -0.011796437203884125, 0.0792914479970932, -0.03328996151685715, 0.00862783845514059, -0.009477301500737667, -0.009786764159798622, -0.0032634837552905083, -0.0006439943099394441, -0.03383881598711014, -0.03509100526571274, -0.010411059483885765, -0.04919668659567833, -0.02191498689353466, 0.11974532157182693, 0.02063954807817936, 0.06984302401542664, 0.03904498741030693, -0.019015349447727203, -0.042235083878040314, -0.022499719634652138, 0.09893904626369476, 0.08357719331979752, -0.015336781740188599, -0.016215471550822258, 0.003986778203397989, 0.0047420598566532135, -0.012388921342790127, -0.02837005816400051, -0.02800104394555092, -0.01238712202757597, 0.014946121722459793, -0.01036999374628067, 0.019435636699199677, -0.01080881617963314, 0.004548715893179178, -0.0739421620965004, -0.017323041334748268, 0.029210997745394707, 0.0012627094984054565, -0.013779479078948498, -0.02403249405324459, 0.031483426690101624, -0.05860679969191551, 0.014149176888167858, 0.010499672032892704, -0.02313610166311264, 0.04891575500369072, 0.035804495215415955, -0.01218425389379263, -0.004050015471875668, -0.0274786539375782, -0.002716469345614314, 0.05285072326660156, -0.012030484154820442, 0.0031849644146859646, 0.03181888535618782, 0.007795129436999559, -0.04122859239578247, -0.05506350100040436, -0.0033647825475782156, -0.03957455977797508, -0.021548544988036156, -0.025902677327394485, -0.019565507769584656, 0.039341479539871216, 0.031189223751425743, -0.002203895477578044, -0.005382406059652567, 0.037313252687454224, 0.042392875999212265 ]
<p>The phenomenon of high temperature superconductivity has been known for decades, particularly layered cuprate superconductors. We know the precise lattice structure of the materials. We know the band theory of electrons and how electronic orbitals mix. But yet, theoreticians still haven't solved high Tc superconductivity yet. What is the obstacle to solving it? What are we missing?</p>
g5436
[ 0.00018226706015411764, 0.09380373358726501, 0.019658813253045082, 0.05511860176920891, 0.0065630218014121056, 0.01964845508337021, 0.017155742272734642, 0.04830608144402504, 0.006976712960749865, -0.03442906588315964, -0.041408952325582504, -0.006259405054152012, -0.015153393149375916, -0.019692763686180115, -0.00022053015709389, 0.005292749032378197, 0.007916854694485664, 0.00008413071191171184, 0.043823737651109695, 0.018926434218883514, -0.02240082435309887, -0.0034606510307639837, 0.05792255327105522, -0.021330920979380608, -0.09303969144821167, 0.02082126773893833, -0.02930525131523609, -0.039696790277957916, 0.05384485796093941, 0.007500924170017242, 0.036810409277677536, -0.04675082489848137, 0.029757719486951828, 0.010105133056640625, 0.013420789502561092, -0.014200730249285698, 0.04352612420916557, 0.0010042705107480288, 0.0250798799097538, 0.04017746075987816, -0.017768248915672302, -0.025316966697573662, -0.02519277296960354, -0.05875689163804054, -0.024118933826684952, 0.01161027979105711, 0.006854249630123377, -0.022251779213547707, -0.014206023886799812, -0.0027924065943807364, 0.006724691018462181, 0.041784610599279404, 0.04059796780347824, -0.004801057279109955, -0.024690043181180954, -0.03151853382587433, 0.03120114654302597, 0.008960735984146595, 0.056560639292001724, -0.04456435889005661, 0.013233279809355736, 0.051761239767074585, -0.0021659021731466055, 0.03524036332964897, 0.07096284627914429, 0.026421215385198593, -0.03217450901865959, 0.014652470126748085, -0.015516234561800957, -0.02694409340620041, 0.04005195200443268, -0.05140417441725731, 0.001986003713682294, 0.023739043623209, -0.03585575148463249, -0.018883485347032547, 0.006163610145449638, -0.0027106422930955887, 0.04146870970726013, -0.027859602123498917, 0.016228633001446724, -0.02778223156929016, 0.02311689965426922, 0.026021357625722885, -0.005837227683514357, -0.03144534304738045, 0.005160985980182886, -0.00044955487828701735, -0.03679921478033066, 0.1054350808262825, 0.006894232705235481, -0.033187732100486755, 0.017433639615774155, -0.01761052943766117, 0.015345497988164425, 0.006164765451103449, 0.03400949761271477, 0.017804592847824097, -0.008387602865695953, -0.02970699593424797, -0.0644931048154831, -0.016594482585787773, 0.03622758015990257, 0.04936620593070984, 0.0023499829694628716, 0.010310683399438858, 0.012164154089987278, 0.012263592332601547, -0.00437366496771574, 0.07830914855003357, -0.03025858663022518, 0.06800808012485504, 0.03227260708808899, 0.010841882787644863, -0.012714062817394733, 0.10670936852693558, 0.003572884714230895, 0.019677115604281425, -0.0395827554166317, -0.007249714806675911, 0.01669425331056118, 0.03790668770670891, -0.03125686198472977, 0.03206757828593254, 0.027954695746302605, 0.0070127747021615505, -0.0089629627764225, -0.010011727921664715, 0.02287377417087555, 0.0036761597730219364, 0.013080023229122162, 0.044861748814582825, 0.023619893938302994, 0.02827303856611252, 0.030571801587939262, 0.0453471764922142, 0.0016371043166145682, -0.030100202187895775, 0.042567770928144455, -0.02996298111975193, -0.05759415403008461, -0.019062776118516922, -0.0006594037404283881, 0.046826619654893875, 0.019125107675790787, -0.009233498945832253, -0.029277203604578972, 0.011991674080491066, -0.017024120315909386, -0.026070550084114075, -0.00954878143966198, 0.054184675216674805, 0.008480079472064972, -0.04527423158288002, -0.037044964730739594, -0.02173992432653904, 0.07867824286222458, -0.025671841576695442, 0.008668526075780392, 0.0008460478857159615, 0.0037714175414294004, 0.027901457622647285, -0.06313015520572662, -0.0035808098036795855, 0.020126763731241226, 0.01118447259068489, -0.08403502404689789, 0.04148230701684952, -0.06014722213149071, 0.06009892746806145, -0.061257943511009216, 0.03304425999522209, 0.030376939103007317, 0.0888715386390686, 0.0023983940482139587, 0.0357910618185997, -0.011083187535405159, 0.005335234571248293, 0.0011005410924553871, 0.004550552926957607, 0.039429180324077606, 0.01987980306148529, 0.0036013401113450527, 0.01048227958381176, 0.03305970877408981, -0.010211191140115261, -0.040862999856472015, -0.010515042580664158, 0.06604218482971191, 0.055179718881845474, -0.02772648073732853, -0.026133164763450623, -0.0009055754635483027, -0.029804253950715065, 0.021627942100167274, -0.006191552616655827, 0.03940686956048012, -0.007316443603485823, -0.02427605725824833, -0.049642905592918396, -0.006790999323129654, -0.049666550010442734, 0.010390485636889935, -0.013523939996957779, -0.007024826016277075, 0.023382339626550674, -0.05130594223737717, -0.0008823613170534372, 0.031010814011096954, -0.005826129578053951, -0.058954108506441116, -0.021609533578157425, -0.018112512305378914, 0.03301950916647911, -0.01909603178501129, 0.015218405984342098, -0.001072210492566228, -0.057732291519641876, -0.035161636769771576, -0.05655233934521675, 0.012477537617087364, -0.0495443269610405, 0.010431036353111267, 0.028311310335993767, -0.03949422761797905, -0.034288253635168076, -0.02873862162232399, 0.016411736607551575, -0.016256969422101974, -0.039593204855918884, -0.025838708505034447, 0.05988788977265358, -0.04004491865634918, -0.05615661293268204, 0.013991385698318481, 0.015114407986402512, -0.010966535657644272, -0.023513901978731155, -0.024815570563077927, 0.04720557481050491, 0.015882816165685654, -0.006793828681111336, -0.02565879002213478, -0.02706708014011383, 0.011915110982954502, -0.0463644340634346, -0.011318755336105824, 0.03309193626046181, -0.03509660065174103, -0.002071802271530032, 0.01948792301118374, -0.020026007667183876, -0.017693867906928062, -0.0033899263944476843, -0.030617285519838333, -0.022263748571276665, 0.010255352593958378, 0.05701524019241333, -0.01705946959555149, -0.07435018569231033, 0.024694344028830528, 0.035718802362680435, -0.01073840819299221, -0.030640549957752228, -0.02824382297694683, -0.011562707833945751, -0.03824977949261665, -0.012135430239140987, -0.0562266930937767, -0.048897672444581985, -0.04433995485305786, 0.09185149520635605, 0.0010502805234864354, -0.04180461913347244, -0.01550387218594551, -0.061787236481904984, -0.021958721801638603, 0.04629712179303169, -0.008729417808353901, -0.015137266367673874, 0.016483614221215248, -0.04863682761788368, -0.0033083020243793726, 0.006626835558563471, 0.0023798453621566296, 0.011811346746981144, 0.018945546820759773, 0.006713973358273506, 0.07964937388896942, -0.01114726159721613, 0.05039592832326889, -0.03644529730081558, 0.037344690412282944, 0.05444905534386635, -0.024087561294436455, -0.004951676819473505, 0.07604619115591049, 0.008625742979347706, -0.04562365263700485, 0.045470599085092545, -0.035779744386672974, 0.030856415629386902, 0.04978327080607414, 0.017627963796257973, 0.042180340737104416, -0.008411454036831856, 0.04872546344995499, -0.024497361853718758, -0.03675951808691025, -0.04158854857087135, 0.04581596329808235, 0.07942632585763931, 0.014302537776529789, -0.04241499677300453, 0.01299457997083664, 0.0015538475709035993, -0.024378031492233276, 0.058366719633340836, 0.05141868442296982, -0.01744941435754299, -0.0062820459716022015, -0.02239188179373741, -0.03365233540534973, -0.009037045761942863, -0.056687675416469574, 0.028587840497493744, -0.08718279004096985, -0.0405987873673439, -0.05813081935048103, 0.010100691579282284, 0.06584913283586502, 0.0030730434227734804, -0.024786049500107765, -0.015527059324085712, -0.00007107957208063453, -0.05370154604315758, 0.04376843944191933, 0.024583322927355766, 0.05525453761219978, 0.003933983389288187, -0.012579809874296188, -0.04337477684020996, -0.04769867658615112, 0.011825649067759514, 0.013973163440823555, -0.005458845756947994, -0.06731665879487991, 0.03378908336162567, 0.03841495141386986, 0.008623327128589153, 0.04168996587395668, 0.056937724351882935, 0.03384038433432579, -0.015822758898139, -0.05915248021483421, 0.013694419525563717, -0.01063163299113512, 0.029001910239458084, -0.007039084564894438, -0.009785723872482777, 0.010772309266030788, 0.01676052249968052, 0.04203648120164871, 0.013992121443152428, -0.04949832707643509, -0.05534753203392029, 0.031474266201257706, 0.03540363535284996, 0.02981235459446907, -0.016554370522499084, 0.012882301583886147, -0.01115270797163248, -0.026450224220752716, 0.000604674278292805, 0.0880315825343132, -0.05236472189426422, -0.08741786330938339, 0.032660506665706635, 0.05757949501276016, 0.014958212152123451, 0.036280661821365356, 0.025952760130167007, -0.02957836166024208, -0.06304485350847244, 0.01340296771377325, 0.013734415173530579, -0.06627850979566574, 0.010361791588366032, -0.07800903916358948, -0.021962624043226242, -0.008339631371200085, 0.020586030557751656, -0.0682731345295906, -0.016972456127405167, -0.05937519297003746, -0.07453174889087677, -0.019121048972010612, 0.0019037320744246244, 0.06267520785331726, -0.10557620227336884, 0.031259749084711075, -0.0583832822740078, 0.008505275472998619, -0.04293755814433098, 0.008001078851521015, 0.03681687265634537, 0.02440120466053486, 0.016766024753451347, 0.04562506079673767, -0.019430149346590042, -0.00558094959706068, 0.017957529053092003, 0.021823612973093987, -0.05220087990164757, 0.025539640337228775, -0.0706598237156868, -0.048503488302230835, 0.019811315461993217, 0.047252122312784195, 0.0030364515259861946, -0.006467917468398809, 0.03620533645153046, 0.008014187216758728, 0.0030213098507374525, 0.010999330319464207, 0.012299402616918087, -0.053258880972862244, -0.02677859365940094, -0.01694486290216446, 0.004579873755574226, 0.053520072251558304, 0.01891344226896763, -0.044196415692567825, -0.02563285082578659, -0.009401170536875725, -0.04042460396885872, 0.0019626105204224586, 0.01571515016257763, -0.05293281376361847, 0.042690861970186234, 0.016332300379872322, 0.017134178429841995, -0.021409213542938232, 0.005511499010026455, -0.044881485402584076, -0.023766234517097473, -0.021100226789712906, 0.03098984807729721, -0.016382062807679176, 0.0037577971816062927, 0.01798906922340393, -0.030571255832910538, -0.02667400985956192, 0.05630699172616005, -0.06953985244035721, -0.06716830283403397, -0.005276536103338003, -0.015730496495962143, -0.022049298509955406, 0.04951347038149834, -0.011632143519818783, -0.04194602742791176, 0.02723083086311817, -0.016607316210865974, 0.041979383677244186, -0.049754198640584946, 0.049829017370939255, -0.04015286639332771, 0.01302386075258255, -0.004994521848857403, -0.021078849211335182, 0.05759328231215477, 0.04509593918919563, 0.0680098608136177, -0.011418544687330723, -0.05083729326725006, -0.037112582474946976, -0.000179939903318882, 0.004351948853582144, 0.009901254437863827, 0.019657619297504425, 0.06676827371120453, 0.0252077579498291, 0.04738753288984299, 0.010679674334824085, 0.006393560208380222, -0.07876026630401611, 0.050038911402225494, 0.023805759847164154, -0.05418148636817932, 0.018545791506767273, 0.015731170773506165, 0.004772681277245283, -0.006990356836467981, -0.004267905373126268, -0.08613227307796478, 0.0525747612118721, 0.051701415330171585, 0.011063258163630962, 0.024735767394304276, -0.010139450430870056, -0.01519889198243618, 0.03078530728816986, 0.003089828882366419, 0.041883621364831924, 0.03152843192219734, 0.04724080115556717, -0.015103297308087349, 0.05591817945241928, -0.04975445196032524, -0.009639918804168701, 0.005991166923195124, -0.024020319804549217, 0.042994383722543716, -0.04595823585987091, 0.03878570720553398, -0.021625690162181854, -0.041922006756067276, 0.008007043972611427, 0.02279050461947918, -0.05460519716143608, 0.0004773206019308418, -0.01777615211904049, -0.01957857981324196, 0.03424865007400513, -0.009710652753710747, -0.027259444817900658, -0.046957217156887054, 0.004758449736982584, -0.015748074278235435, 0.018860822543501854, 0.01779363304376602, 0.007311046589165926, -0.0058843521401286125, -0.02560580149292946, 0.06696347892284393, 0.037840988487005234, -0.02886081673204899, -0.017575275152921677, 0.0706118792295456, 0.014489199966192245, 0.058977749198675156, -0.005676294211298227, 0.04219409078359604, 0.03517487272620201, -0.06072497367858887, -0.03128308802843094, 0.004267911426723003, 0.023029005154967308, 0.013687330298125744, -0.027276424691081047, 0.03198809549212456, -0.03292257711291313, -0.017652831971645355, 0.04886128380894661, -0.026908250525593758, 0.02041034959256649, -0.05129272863268852, -0.01919936016201973, 0.014796744100749493, 0.015660902485251427, -0.01416216790676117, 0.04977165535092354, 0.005890437867492437, 0.06561790406703949, 0.021478552371263504, -0.04419804364442825, 0.0062136161141097546, 0.04920433834195137, -0.013256129808723927, -0.04472328722476959, 0.03753719851374626, -0.01870652474462986, -0.03048185631632805, -0.013779223896563053, 0.041757725179195404, -0.02021143212914467, 0.03531178832054138, -0.0028831742238253355, -0.009291657246649265, 0.004391799680888653, 0.027867140248417854, -0.023244936019182205, 0.02118658646941185, -0.057010721415281296, 0.054586563259363174, -0.031674109399318695, -0.019160280004143715, 0.004924936220049858, 0.008110642433166504, -0.053853727877140045, 0.0019611006136983633, 0.02781246416270733, -0.023982372134923935, 0.04152502492070198, -0.02361988089978695, -0.00017182805459015071, 0.05076627805829048, -0.04026458039879799, 0.0026288903318345547, 0.05275537818670273, 0.021295668557286263, -0.01221755612641573, 0.059618428349494934, 0.05989959090948105, 0.03431782126426697, 0.05520555004477501, 0.010809818282723427, -0.011718093417584896, -0.0017023470718413591, 0.01632009632885456, 0.02020310051739216, -0.02511134184896946, -0.029249800369143486, -0.03585982695221901, -0.05480004847049713, 0.004026760347187519, 0.08363479375839233, -0.028481807559728622, -0.04672111198306084, 0.010625611059367657, -0.016590356826782227, -0.02391725219786167, -0.00860596727579832, 0.013193679973483086, -0.021569915115833282, 0.006986731197685003, 0.026120709255337715, 0.10248173028230667, 0.015359747223556042, 0.01995721273124218, -0.06376516819000244, 0.04599842429161072, 0.06862499564886093, 0.03443574532866478, 0.002362004714086652, -0.054453376680612564, -0.028416708111763, -0.08396872878074646, 0.013414203189313412, -0.031617242842912674, -0.027413390576839447, -0.012873535975813866, 0.012499435804784298, 0.007472437806427479, -0.019139792770147324, 0.024307856336236, -0.00985032506287098, -0.06954305619001389, 0.022773386910557747, 0.018600864335894585, -0.0386795811355114, -0.04305243864655495, 0.002409671898931265, -0.0014366644900292158, -0.052382808178663254, -0.03452857956290245, 0.027150580659508705, 0.011389215476810932, 0.018916316330432892, -0.01670626364648342, 0.00030302454251796007, 0.0340217761695385, 0.10148590058088303, 0.007397185079753399, 0.0540383979678154, 0.05202949047088623, -0.0483657643198967, 0.012856894172728062, -0.09706354141235352, -0.028700560331344604, -0.011007762514054775, 0.009187966585159302, -0.0337049700319767, 0.009278859943151474, -0.04152298346161842, -0.06554538756608963, -0.016867035999894142, -0.018115811049938202, -0.005963762756437063, -0.07203735411167145, 0.04757793992757797, 0.011023600585758686, 0.02659117430448532, 0.0230353232473135, 0.004035900812596083, -0.0353337824344635, 0.000655277690384537, -0.08215561509132385, 0.014706096611917019, 0.0294719859957695, 0.018339665606617928, -0.014540503732860088, -0.004769034683704376, 0.030965793877840042, 0.02367422543466091, 0.002631805371493101, -0.01870449259877205, 0.023652207106351852, 0.014222217723727226, -0.01340179331600666, -0.036266814917325974, 0.018923912197351456, -0.035019244998693466, 0.04175762087106705, 0.006015635095536709, -0.003423720132559538, -0.03457808494567871, -0.04952649027109146, 0.04325581341981888, -0.031183265149593353, 0.07469180971384048, 0.048259761184453964, -0.06032966449856758, 0.017305903136730194, 0.016398604959249496, -0.06039271131157875, -0.018165579065680504, 0.041666507720947266, -0.0021735550835728645, -0.00820133090019226, -0.020361032336950302, 0.029292406514286995, -0.01557990349829197, -0.0051398868672549725, -0.03938047215342522, 0.019156180322170258, -0.021898776292800903, 0.020090045407414436, 0.01195602212101221, 0.06378789991140366, 0.07074713706970215, -0.009869759902358055, 0.03968752548098564, -0.03843357041478157, 0.03804146870970726, 0.03864624351263046, 0.03262563794851303, 0.015636363998055458, -0.025941448286175728, -0.011437534354627132, -0.008858371526002884, -0.009996907785534859, -0.04718679189682007, -0.09765408933162689, -0.011327037587761879, -0.06700926274061203, -0.024212852120399475, 0.007189667318016291, 0.015344656072556973, -0.025062493979930878, -0.04227510094642639, -0.06143617630004883, 0.016631709411740303, -0.04207368940114975, -0.02748570404946804, 0.028641128912568092, -0.013900762423872948, 0.031251370906829834, -0.011516370810568333, -0.014640760608017445, 0.02342815138399601, 0.048634614795446396, 0.015419566072523594, 0.07083683460950851, 0.026075677946209908, -0.03243505582213402, -0.0841732993721962 ]
<p>When computing the first order perturbative corrections to string theory over a curved background, we find the background has to be Ricci-flat if the dilaton is constant and we have no fluxes. Such is the case for Calabi-Yau compactifications. However, to fourth order in perturbation theory, we find nonzero contributions to the beta function. But this can be resolved by perturbative modifications to the background metric which cancels the beta function order by order in perturbation theory.</p> <p>Does this procedure work for a generic time-varying background which is Ricci-flat to first order in perturbation theory? If not, does that tell us we can't apply first quantized string theory to such backgrounds?</p>
g5437
[ 0.05332208052277565, -0.06210861727595329, 0.0038926969282329082, -0.04729190096259117, 0.05464675650000572, -0.0025754801463335752, 0.028920631855726242, -0.009900709614157677, -0.03690551593899727, 0.007417676504701376, -0.02212400548160076, 0.04202961549162865, 0.02359102852642536, 0.050089459866285324, -0.016786037012934685, 0.017129695042967796, 0.031315289437770844, 0.0897175520658493, -0.0278015173971653, -0.05474042892456055, -0.001734505407512188, 0.011291226372122765, 0.028261698782444, -0.0195644311606884, 0.0015565073117613792, 0.01096542738378048, 0.0019083203515037894, -0.009657088667154312, -0.0673767700791359, 0.011112825945019722, 0.0437810979783535, 0.04526716098189354, 0.04853060469031334, 0.0034382077865302563, 0.012012983672320843, 0.07460784167051315, 0.08020241558551788, -0.005319091957062483, 0.04768184572458267, 0.02791135199368, -0.019013211131095886, -0.018569789826869965, 0.05080359801650047, -0.002687386004254222, -0.006866297218948603, -0.006279645953327417, -0.03215887397527695, -0.00000766266202845145, 0.01601330004632473, 0.08739368617534637, -0.00527030136436224, 0.03495844826102257, 0.0872868075966835, -0.05480823293328285, -0.01591125875711441, 0.046208705753088, 0.05015232041478157, -0.043940022587776184, 0.05335653945803642, 0.0464186891913414, -0.011044543236494064, 0.00618626456707716, 0.016625484451651573, -0.023307356983423233, -0.013213268481194973, -0.06389305740594864, -0.003819995326921344, -0.007861028425395489, -0.055104389786720276, 0.017115507274866104, 0.011446250602602959, 0.01698259823024273, -0.027072347700595856, -0.02481698803603649, -0.007260746788233519, 0.04757425934076309, 0.0012920201988890767, -0.05329669639468193, -0.04947517812252045, -0.048232585191726685, -0.027228424325585365, -0.02517806738615036, 0.01925157755613327, 0.018209796398878098, 0.09991134703159332, -0.05525803565979004, 0.030954964458942413, 0.0736284852027893, -0.018259096890687943, 0.00006532846600748599, 0.017592912539839745, -0.009660339914262295, -0.013302554376423359, -0.03839683160185814, 0.06287168711423874, 0.014529542066156864, -0.007419167552143335, -0.02333790808916092, 0.01199103333055973, -0.0662953183054924, -0.0008876920328475535, 0.09337817132472992, 0.01147742010653019, 0.05991746485233307, 0.003051174571737647, 0.025326460599899292, 0.024599477648735046, -0.020130982622504234, 0.052081573754549026, -0.03195694833993912, -0.004165749531239271, -0.0109630785882473, 0.045882485806941986, -0.0652492567896843, -0.05645374581217766, -0.031858429312705994, 0.013480443507432938, -0.019248079508543015, -0.05902527645230293, 0.038446806371212006, -0.06306583434343338, 0.04553624242544174, -0.0019308419432491064, -0.004518942907452583, -0.044738154858350754, 0.022584471851587296, -0.08409995585680008, 0.0018227671971544623, 0.07779569178819656, -0.017875997349619865, 0.013582836836576462, -0.0073339324444532394, 0.04627179354429245, 0.058457836508750916, 0.014643150381743908, 0.018837446346879005, -0.02009807527065277, -0.016918495297431946, -0.004368533845990896, -0.007834705524146557, -0.03180485591292381, -0.03753548115491867, 0.05630020797252655, 0.0007579404045827687, 0.00390894478186965, -0.02303803525865078, 0.015657447278499603, -0.010842133313417435, 0.0053322878666222095, -0.00278908247128129, 0.017775528132915497, 0.05049338564276695, 0.031949013471603394, 0.01781792938709259, 0.0400422066450119, 0.02460622787475586, 0.02711818739771843, -0.009169960394501686, 0.03161197900772095, 0.013643053360283375, 0.007366907317191362, 0.018407342955470085, 0.08643428236246109, -0.055570945143699646, -0.03356172516942024, 0.019138114526867867, -0.04973628371953964, -0.002864326350390911, 0.0005004100385122001, -0.01376204565167427, -0.04891715198755264, -0.008931899443268776, 0.008836813271045685, 0.01759183593094349, -0.046801671385765076, 0.049015793949365616, -0.036821383982896805, 0.0053086369298398495, -0.00005706246156478301, 0.004697014112025499, 0.01317343208938837, -0.026639793068170547, -0.04356490448117256, 0.010206173174083233, 0.039495255798101425, 0.03670176491141319, -0.08179358392953873, -0.0008825344266369939, 0.017428476363420486, -0.07071021944284439, -0.027990242466330528, -0.0973253846168518, 0.038845717906951904, 0.028726687654852867, 0.029055021703243256, -0.019726336002349854, 0.019927218556404114, -0.012103710323572159, -0.01900709792971611, 0.01825800910592079, -0.010169049724936485, 0.08415494859218597, 0.04251996800303459, -0.047404710203409195, 0.0069595579989254475, 0.00655330391600728, 0.0032701347954571247, 0.027229079976677895, 0.024590926244854927, -0.06062263622879982, -0.0011275545693933964, -0.017022516578435898, 0.046274151653051376, 0.03568383678793907, -0.058361608535051346, 0.012692835181951523, 0.004366388078778982, 0.05494576320052147, -0.010802360251545906, 0.05738934502005577, 0.0036676295567303896, -0.007121920119971037, 0.036806073039770126, 0.01668144203722477, -0.021597405895590782, 0.005373730789870024, 0.04284019023180008, -0.007544863503426313, -0.011084849946200848, 0.029345542192459106, -0.0638027936220169, -0.01580812968313694, -0.03739587590098381, 0.004320912528783083, 0.030293330550193787, -0.01384048257023096, -0.006875531282275915, -0.019000550732016563, 0.04278837516903877, 0.008287458680570126, -0.04723682999610901, 0.0003347830497659743, -0.025172824040055275, 0.018789978697896004, 0.017036575824022293, -0.01021014153957367, 0.016613153740763664, 0.017151786014437675, -0.061888836324214935, -0.04504247382283211, 0.0015920894220471382, -0.02859247475862503, -0.040568724274635315, 0.0649321898818016, 0.045148707926273346, -0.06626247614622116, 0.019740577787160873, -0.006857920438051224, -0.045824795961380005, -0.06042097508907318, 0.04349231719970703, -0.0010208740131929517, 0.05130482092499733, 0.0476054884493351, -0.07288838177919388, 0.04323187842965126, -0.007851745001971722, -0.02962898649275303, -0.0006672667805105448, 0.00011725560034392402, 0.049380216747522354, 0.06859374791383743, 0.023643551394343376, 0.03647148609161377, -0.03199625760316849, 0.016748476773500443, 0.0073923892341554165, 0.023732757195830345, -0.05094398558139801, 0.0016498997574672103, -0.004469846375286579, -0.04936022683978081, -0.05518830940127373, -0.0467122346162796, -0.033160500228405, -0.018590517342090607, 0.004201180301606655, -0.04395390301942825, 0.0016654415521770716, 0.0030073709785938263, -0.005752254743129015, 0.06831136345863342, 0.03237990662455559, 0.025159340351819992, 0.02066047117114067, -0.022800879552960396, 0.03255743533372879, -0.037488214671611786, 0.002214644569903612, 0.08204106986522675, 0.001386597752571106, 0.007733117323368788, 0.0008172348025254905, 0.011767474003136158, 0.0007180941174738109, -0.02480127662420273, -0.014691691845655441, -0.030947474762797356, 0.0587741956114769, -0.0021868525072932243, -0.01229284331202507, -0.00201327889226377, 0.05056202411651611, 0.023320188745856285, 0.05735551938414574, 0.029506949707865715, 0.031053686514496803, -0.051977939903736115, 0.032679080963134766, 0.008448388427495956, -0.03200912848114967, 0.04680269956588745, -0.016027135774493217, 0.014582612551748753, 0.00032146068406291306, 0.07634689658880234, -0.02959633059799671, 0.018395720049738884, -0.026389431208372116, 0.006549309007823467, 0.05911356955766678, -0.03862270340323448, 0.0048560407012701035, -0.01537640206515789, -0.02420002967119217, -0.0346776507794857, 0.0022989786230027676, 0.01647329330444336, 0.0004211149935144931, 0.008604218252003193, -0.07685022056102753, -0.0014772877329960465, 0.02061833068728447, 0.026468848809599876, 0.03922627493739128, 0.04788584262132645, 0.024975746870040894, -0.011005653999745846, -0.07396858930587769, 0.031637996435165405, 0.061711303889751434, -0.06907611340284348, -0.03004867024719715, 0.004933658987283707, 0.02641431987285614, 0.07636414468288422, 0.06334645301103592, 0.09531246870756149, -0.029399162158370018, -0.03325634077191353, -0.0015984881902113557, -0.011934751644730568, -0.0010286894394084811, 0.011328852735459805, 0.019210252910852432, -0.009345813654363155, -0.013018017634749413, -0.01848459057509899, -0.05253977328538895, 0.007528046611696482, 0.03747241944074631, 0.03410032391548157, -0.007995055057108402, 0.007081653922796249, -0.011685879901051521, 0.031496960669755936, 0.022222667932510376, 0.04733506217598915, -0.026765579357743263, 0.0032610450871288776, 0.0366557277739048, -0.004793872591108084, 0.015452309511601925, 0.013315238058567047, -0.03772028908133507, 0.06964673101902008, -0.053622640669345856, -0.04431026056408882, -0.020450659096240997, -0.07177499681711197, -0.055471040308475494, -0.006956187542527914, -0.025905875489115715, -0.038732051849365234, -0.0007167169242165983, -0.05916791781783104, 0.026563016697764397, -0.016650337725877762, 0.027755143120884895, 0.013721581548452377, 0.006625542417168617, 0.031572312116622925, 0.06355834007263184, -0.058889131993055344, 0.003645677585154772, -0.005598091520369053, -0.015639595687389374, 0.010655142366886139, -0.01985790580511093, -0.02438204549252987, 0.0019312903750687838, 0.006120836362242699, -0.029684998095035553, -0.06313680112361908, 0.076346255838871, -0.072538360953331, -0.004332426469773054, -0.05815114080905914, 0.015612466260790825, -0.024578869342803955, 0.013186405412852764, -0.0002823247923515737, -0.024069499224424362, -0.044259801506996155, 0.014703329652547836, 0.09271177649497986, 0.013896145857870579, -0.038859426975250244, 0.013584038242697716, -0.01645510084927082, 0.0207416582852602, 0.02358190156519413, 0.049152109771966934, 0.01131472922861576, -0.06995271146297455, 0.03206704929471016, -0.03694302961230278, 0.03142288327217102, 0.003525008447468281, -0.024573050439357758, 0.06999020278453827, 0.01857518032193184, -0.02263646386563778, -0.04016248509287834, -0.05696776881814003, 0.02318699285387993, -0.03682156652212143, -0.015847353264689445, 0.04211953654885292, 0.007798675913363695, -0.04355369508266449, 0.003172231838107109, -0.050857994705438614, 0.040129803121089935, 0.008952328003942966, -0.03396279364824295, 0.009707730263471603, -0.0010351667879149318, 0.06020006164908409, 0.03325824439525604, -0.01391440536826849, 0.013044260442256927, -0.011225498281419277, 0.037757646292448044, -0.022303510457277298, -0.00837731920182705, 0.02172663062810898, 0.035888995975255966, -0.01695696823298931, 0.027060916647315025, -0.00982815120369196, 0.015655284747481346, 0.02783205173909664, -0.02875572443008423, -0.03907020017504692, 0.04575027897953987, -0.022749824449419975, -0.022863231599330902, -0.010061965323984623, -0.0289001502096653, -0.009119084104895592, -0.015667935833334923, 0.01676773838698864, -0.014675564132630825, 0.009771103039383888, 0.007582375779747963, -0.030318181961774826, -0.015472677536308765, -0.002274435944855213, -0.01764526031911373, -0.021286390721797943, 0.030326509848237038, 0.008029492571949959, -0.04816403239965439, 0.012778694741427898, 0.03764953464269638, 0.05322876572608948, -0.02372003346681595, -0.05143533647060394, -0.013025335967540741, -0.07327137887477875, 0.028403285890817642, 0.051876723766326904, 0.011841102503240108, -0.04164765030145645, 0.07624689489603043, 0.009382420219480991, -0.006558701861649752, 0.004658316727727652, 0.012171189300715923, -0.038258668035268784, 0.03663216158747673, -0.0540546216070652, -0.059007104486227036, -0.036581266671419144, -0.005202102940529585, -0.0062108952552080154, -0.008558177389204502, -0.048792168498039246, -0.026881560683250427, -0.012637755833566189, 0.009585986845195293, 0.005857669282704592, -0.003334315959364176, 0.05343620106577873, 0.05059441551566124, -0.027651391923427582, -0.04457971453666687, 0.015143166296184063, -0.009891994297504425, -0.07120735943317413, 0.0032092020846903324, 0.0039334907196462154, 0.004458497278392315, 0.01700514741241932, 0.03701343014836311, -0.005379500798881054, 0.0469868928194046, 0.017142968252301216, 0.02283882349729538, -0.028912216424942017, 0.05905879661440849, 0.05933235213160515, 0.01759442687034607, -0.046811431646347046, 0.004493572749197483, -0.05368158593773842, 0.03546668589115143, 0.003439984517171979, -0.060357119888067245, -0.02119027078151703, 0.004609239753335714, 0.01953599601984024, 0.02407144568860531, -0.058944642543792725, 0.029741015285253525, -0.01177656464278698, -0.051492322236299515, 0.01843550242483616, -0.016193967312574387, -0.0036206827498972416, -0.024116074666380882, 0.06640667468309402, -0.0008948970353230834, 0.01571701280772686, -0.01806873269379139, 0.02140197902917862, -0.03977474942803383, 0.024813072755932808, -0.034185539931058884, -0.012709535658359528, 0.020135125145316124, -0.0003253667091485113, 0.031136024743318558, 0.01382740680128336, -0.014498963952064514, -0.05660970136523247, -0.08061513304710388, -0.06373672187328339, -0.0013022085186094046, -0.03407158702611923, 0.07452341914176941, 0.02206130139529705, -0.032678984105587006, -0.049927305430173874, 0.0021048833150416613, -0.03278909996151924, 0.004919334314763546, 0.039090514183044434, 0.0014527089660987258, -0.02485320158302784, -0.03612595051527023, -0.022367263212800026, -0.013266091234982014, -0.024581393226981163, 0.06551004946231842, -0.015714148059487343, -0.0067941490560770035, -0.07791644334793091, 0.06684412807226181, 0.026970451697707176, -0.014201744459569454, 0.02288234233856201, 0.024511678144335747, 0.04792839661240578, -0.021530602127313614, 0.04686514288187027, 0.05434942990541458, -0.009535451419651508, -0.011621403507888317, 0.05566713586449623, 0.002631224226206541, 0.000505443022120744, 0.030392471700906754, -0.043650198727846146, -0.0746471956372261, -0.03197965770959854, 0.019601741805672646, 0.05721354857087135, -0.07820006459951401, 0.054598428308963776, -0.015357056632637978, 0.03352399915456772, 0.0010558905778452754, -0.030264446511864662, 0.023948512971401215, 0.00596107030287385, -0.008812871761620045, 0.002725775819271803, -0.024981101974844933, -0.0018979242304340005, -0.019579609856009483, -0.02705344185233116, 0.02527778595685959, 0.015105455182492733, 0.02690107375383377, -0.006602160166949034, -0.002400086261332035, -0.06946668773889542, -0.0049206288531422615, -0.0715995579957962, 0.016638481989502907, 0.053275518119335175, -0.06218946352601051, -0.04604778438806534, 0.009966940619051456, 0.04609779268503189, 0.0017859921790659428, -0.036941513419151306, 0.022335847839713097, 0.01791061833500862, 0.0482899434864521, 0.022953910753130913, -0.007265420630574226, -0.044135984033346176, -0.03687059134244919, -0.005243687424808741, 0.02348247356712818, 0.03934941813349724, -0.023922987282276154, -0.04134441539645195, -0.014531026594340801, 0.00483866548165679, 0.00019903824431821704, 0.025250405073165894, 0.026971939951181412, 0.0140512241050601, -0.03815425559878349, 0.022297507151961327, 0.04083869606256485, -0.03897202014923096, 0.008536613546311855, -0.030511481687426567, 0.040801551192998886, 0.06940800696611404, -0.019678357988595963, -0.022610554471611977, 0.018440766260027885, -0.019788462668657303, 0.03963911905884743, 0.05031263083219528, -0.01100139319896698, 0.003669131314381957, -0.006175005342811346, -0.05021800100803375, 0.023958170786499977, -0.041606783866882324, 0.017191991209983826, -0.03714033216238022, -0.029057536274194717, 0.037980254739522934, 0.04341050237417221, -0.06783595681190491, -0.026666490361094475, 0.045303136110305786, -0.0013864916982129216, -0.0156862735748291, -0.03183374181389809, 0.012832988053560257, 0.00041673818486742675, 0.018281392753124237, -0.06106579676270485, -0.02863982692360878, -0.08150769770145416, 0.03451085090637207, -0.04941931739449501, -0.01935892179608345, -0.028029223904013634, -0.06477736681699753, 0.04074220359325409, -0.07223724573850632, 0.032508619129657745, -0.04208981990814209, 0.06294242292642593, 0.006932414602488279, 0.02061450108885765, -0.09849316626787186, 0.023659110069274902, -0.032423436641693115, 0.004531845450401306, -0.001478177378885448, -0.005205520428717136, -0.0021460698917508125, -0.043108318001031876, -0.0017645445186644793, -0.017441660165786743, -0.05859019234776497, -0.08201245963573456, 0.004412532784044743, 0.03583439812064171, -0.0062368097715079784, 0.012963834218680859, -0.05348953604698181, 0.0214993953704834, 0.01274933759123087, 0.04828237369656563, -0.05066068843007088, -0.06000148132443428, 0.04889540374279022, -0.06881549209356308, -0.01723235659301281, -0.03565167263150215, -0.013343197293579578, 0.024299390614032745, 0.013053055852651596, 0.06020889803767204, 0.023648416623473167, 0.006200931966304779, -0.05050407722592354, -0.034663159400224686, 0.022285284474492073, 0.009518340229988098, 0.024678634479641914, 0.0158207006752491, 0.01624000258743763, 0.03693489357829094, -0.0075436788611114025, -0.024357551708817482, 0.05330205708742142, 0.0030989903025329113, -0.007021459750831127, -0.0046226573176681995, -0.02366800047457218, 0.011408818885684013, 0.01512923650443554, -0.04078599438071251, -0.026349429041147232, 0.018077373504638672 ]
<p>In the strong coupling limit of type IIA and heterotic E8 string theory, we get 11 dimensional M-theory in which we have no strings. Instead, we have M2 branes.</p> <p>Are there any other backgrounds in string theory which can't be described by first quantized string theory?</p>
g5438
[ 0.030830737203359604, 0.012897846288979053, 0.018921228125691414, -0.028842920437455177, 0.016192451119422913, 0.029073944315314293, -0.009551746770739555, -0.03752826899290085, 0.05649181082844734, -0.03625881299376488, -0.004525052849203348, 0.03755003586411476, -0.02216985635459423, 0.043956346809864044, 0.019835125654935837, 0.016004644334316254, 0.010492637753486633, 0.045270342379808426, 0.047440305352211, -0.034368619322776794, -0.03432292491197586, -0.004457416012883186, -0.03248662129044533, -0.0593235045671463, -0.03660569339990616, 0.035860590636730194, 0.007610974833369255, -0.0013413080014288425, -0.01968478225171566, 0.01350969448685646, 0.03654396906495094, -0.05389238893985748, 0.06750363111495972, -0.006603869143873453, 0.03323529288172722, 0.030417485162615776, -0.011726511642336845, 0.014891247265040874, -0.008138426579535007, 0.006593272555619478, -0.0031830300576984882, -0.0464942529797554, -0.00005946124656475149, -0.016083892434835434, -0.05530182644724846, -0.0026862649247050285, -0.014636503532528877, 0.04543808847665787, -0.0001652610080782324, 0.0014848823193460703, 0.049847207963466644, 0.048748258501291275, 0.09424911439418793, -0.06028984114527702, 0.03433229401707649, -0.009037291631102562, -0.007564582861959934, -0.048533592373132706, 0.021051114425063133, 0.026083113625645638, -0.024473421275615692, 0.052786245942115784, -0.00424082251265645, 0.04457106068730354, -0.003140774555504322, -0.007425361312925816, -0.03165103867650032, -0.01934991031885147, -0.0441724956035614, 0.02337001822888851, 0.06368383020162582, -0.044480305165052414, -0.03213294595479965, 0.0077973781153559685, 0.013643080368638039, 0.05791406333446503, -0.02062993124127388, -0.006506555248051882, 0.016634562984108925, 0.030626581981778145, -0.016349097713828087, 0.011218119412660599, -0.07663359493017197, -0.017824841663241386, 0.04149151220917702, -0.04241682216525078, 0.025738127529621124, 0.05743774026632309, -0.03852672129869461, 0.019611168652772903, 0.02861768566071987, -0.003333776257932186, -0.04653715714812279, -0.027524052187800407, 0.056346602737903595, 0.0014555543893948197, 0.016877392306923866, 0.04016320779919624, -0.039546456187963486, -0.06010731682181358, 0.04052914306521416, 0.02397511899471283, 0.018875086680054665, 0.013553326018154621, 0.04815150424838066, 0.007687131408601999, 0.028852220624685287, -0.012421585619449615, 0.014991354197263718, 0.049629002809524536, -0.015796083956956863, 0.04082059860229492, -0.07470913231372833, -0.06058356165885925, -0.06416451930999756, -0.002769952639937401, -0.02027408592402935, -0.0007859263569116592, -0.056279946118593216, 0.01346287690103054, 0.02562440000474453, -0.01409977488219738, 0.06794862449169159, 0.025912415236234665, -0.01261008158326149, -0.01133032888174057, -0.01122972834855318, -0.005300571676343679, 0.06620828062295914, -0.017835503444075584, 0.0101937809959054, -0.037776414304971695, 0.07300306111574173, 0.045451585203409195, 0.007999211549758911, 0.061459966003894806, -0.009153527207672596, -0.002607774455100298, -0.03521978110074997, 0.03232429921627045, -0.044396497309207916, -0.058811090886592865, 0.0010451988782733679, -0.028442997485399246, 0.017040163278579712, -0.015497087500989437, 0.0960158184170723, 0.009271970950067043, -0.01251070573925972, 0.06375814229249954, 0.0021563207264989614, 0.084957055747509, 0.052260562777519226, 0.04997580125927925, -0.024187210947275162, 0.004893838427960873, 0.04367539659142494, -0.022097062319517136, -0.016625991091132164, -0.01851697266101837, 0.027743469923734665, 0.02228396385908127, 0.004629749339073896, -0.019163334742188454, -0.0017799778142943978, -0.06771251559257507, -0.029181329533457756, 0.04618394747376442, 0.08040756732225418, 0.027141356840729713, -0.032466888427734375, 0.028698574751615524, 0.03504501283168793, 0.027876462787389755, -0.02646716870367527, 0.08144526928663254, -0.007716577500104904, 0.008503727614879608, -0.0036657105665653944, 0.06708039343357086, -0.003011909546330571, 0.0020201168954372406, -0.026133546605706215, -0.013997300527989864, -0.028415173292160034, 0.011670881882309914, -0.06910804659128189, 0.0258322861045599, 0.009600670076906681, -0.022401368245482445, -0.052863284945487976, -0.02565782517194748, 0.004365655593574047, 0.02431989461183548, -0.03193940222263336, -0.026356831192970276, -0.03199711814522743, -0.0026076624635607004, -0.007498758379369974, 0.00312136672437191, 0.06509073823690414, 0.07421119511127472, -0.006114421412348747, 0.0014918202068656683, -0.037119656801223755, 0.004117881413549185, -0.04531028866767883, -0.014522586949169636, 0.0023762406781315804, -0.00832569319754839, -0.031115902587771416, -0.021826688200235367, -0.015420367941260338, 0.028310880064964294, -0.0573393777012825, -0.004523731768131256, 0.0045516095124185085, 0.005010351072996855, 0.029365237802267075, 0.056745436042547226, 0.07941069453954697, -0.012784196995198727, 0.0745072141289711, -0.006871538236737251, 0.008473730646073818, 0.043620515614748, 0.02739286608994007, 0.036334630101919174, -0.021688787266612053, 0.006412187125533819, -0.02920229360461235, -0.023354751989245415, 0.016659455373883247, -0.0437614880502224, 0.006471345666795969, -0.04122012108564377, 0.0005611671367660165, 0.005529683083295822, -0.005827794317156076, 0.028943920508027077, 0.023228172212839127, 0.03367748484015465, -0.023623574525117874, 0.003385307500138879, -0.009002335369586945, -0.025914322584867477, 0.0037127339746803045, 0.030911803245544434, -0.00028000024030916393, 0.05655433237552643, -0.017137115821242332, -0.03975609317421913, -0.012970158830285072, 0.028740478679537773, 0.002379853744059801, -0.018778108060359955, 0.020827388390898705, -0.024509264156222343, -0.04956110939383507, -0.055475398898124695, 0.014447853900492191, -0.03420054912567139, 0.05299924314022064, 0.009081702679395676, -0.10795175284147263, 0.0015221008798107505, 0.01931254379451275, -0.03224989399313927, -0.020010830834507942, -0.038806796073913574, -0.09112649410963058, 0.052764978259801865, -0.03599580004811287, 0.0009437287226319313, 0.024220282211899757, 0.027768753468990326, -0.010953016579151154, 0.06392907351255417, -0.013465779833495617, -0.006083250045776367, -0.006225335877388716, 0.010380755178630352, 0.05124210566282272, -0.03570621460676193, -0.02951246313750744, -0.03707441687583923, 0.00022113477461971343, -0.002641487866640091, 0.011257397010922432, -0.007641491945832968, 0.011380966752767563, -0.02602103352546692, 0.059449754655361176, 0.034958887845277786, 0.03185451775789261, 0.020775601267814636, 0.014736714772880077, -0.016782358288764954, 0.003062207717448473, 0.0455830954015255, -0.0027372920885682106, 0.022976798936724663, 0.0017995248781517148, 0.020355988293886185, 0.040528181940317154, -0.0376150906085968, -0.013505002483725548, -0.08144781738519669, -0.012674921192228794, 0.010282354429364204, 0.007176036946475506, 0.04050029069185257, 0.05467480793595314, 0.01972619630396366, -0.008525474928319454, 0.030030926689505577, 0.05689593404531479, -0.012740290723741055, 0.03279854357242584, 0.0037561010103672743, -0.01754262112081051, 0.02778313308954239, 0.08244948089122772, 0.004087574314326048, -0.03565966337919235, 0.058901168406009674, -0.03905857726931572, 0.02833056077361107, -0.0752294510602951, 0.03663499653339386, -0.007165152113884687, -0.018785353749990463, -0.009738000109791756, 0.022328095510601997, -0.08932533115148544, -0.017952855676412582, -0.015400472097098827, -0.045538075268268585, 0.039785388857126236, -0.012858252972364426, -0.035231731832027435, 0.03944249451160431, 0.05599115416407585, -0.023408910259604454, -0.0019930226262658834, 0.0182042196393013, 0.007263285107910633, 0.0076570394448935986, 0.016110198572278023, 0.0056446087546646595, 0.0542566142976284, 0.023641714826226234, 0.011867577210068703, 0.011149415746331215, -0.006839888636022806, 0.112269826233387, 0.03598092123866081, 0.09091973304748535, 0.015756756067276, -0.07748839259147644, -0.033878669142723083, 0.016080835834145546, 0.04746660590171814, -0.049705132842063904, 0.026516085490584373, -0.022584687918424606, -0.043545812368392944, -0.07578779011964798, 0.017678551375865936, 0.02821434661746025, 0.07212595641613007, 0.0025235472712665796, 0.006972166709601879, -0.013801032677292824, 0.056459661573171616, -0.03561484068632126, 0.03251926600933075, -0.0073521193116903305, -0.04748351126909256, 0.030648186802864075, 0.049962788820266724, -0.007330848835408688, 0.022927500307559967, 0.03660046309232712, 0.02357858419418335, 0.037779636681079865, -0.0168018601834774, -0.015200342983007431, -0.08658164739608765, -0.026482854038476944, -0.014449111185967922, 0.032938044518232346, 0.004302415531128645, -0.06160086765885353, 0.007103148382157087, -0.02004431188106537, 0.07782494276762009, -0.03812819719314575, 0.046482812613248825, -0.03682641685009003, 0.0375032015144825, 0.03952363505959511, 0.0033579382579773664, -0.062094032764434814, -0.03096110187470913, -0.027321413159370422, -0.051246508955955505, 0.003973207902163267, 0.029507476836442947, -0.054645463824272156, 0.02288694679737091, -0.040565893054008484, -0.009583236649632454, -0.027241045609116554, 0.0204014889895916, -0.08941272646188736, -0.025072693824768066, -0.030021190643310547, -0.00011237220314797014, -0.029924746602773666, 0.017727965489029884, 0.055689770728349686, -0.027634387835860252, -0.04153500124812126, -0.02670459821820259, 0.015172542072832584, -0.008197639137506485, 0.0018165124347433448, -0.015776140615344048, -0.0047571430914103985, 0.027994967997074127, -0.01616424322128296, 0.007345710415393114, -0.015812303870916367, -0.024686498567461967, -0.00018174810975324363, -0.01576090045273304, 0.012353784404695034, 0.015140579082071781, 0.03085092268884182, 0.0034507981035858393, 0.02585699036717415, -0.019295230507850647, 0.008401875384151936, 0.004582688212394714, 0.012678219005465508, -0.0029342719353735447, 0.005797503050416708, -0.0364428348839283, -0.004314657766371965, -0.01697631925344467, -0.007081403397023678, -0.07612250000238419, 0.01585741527378559, -0.0043882941827178, -0.012280331924557686, -0.019755009561777115, 0.027132224291563034, 0.019128955900669098, 0.04293001443147659, -0.06988347321748734, 0.03952283412218094, 0.02630617469549179, 0.05242418870329857, -0.07144971191883087, -0.026770859956741333, -0.05603842809796333, 0.057736836373806, -0.05545271560549736, 0.022400829941034317, -0.004335680510848761, 0.027928274124860764, 0.017830651253461838, -0.04079444333910942, -0.01981303282082081, 0.03283063694834709, -0.057541508227586746, -0.030028091743588448, -0.05185085907578468, -0.03326614573597908, 0.047407615929841995, -0.0058520338498055935, -0.017298396676778793, 0.024017443880438805, 0.04723415523767471, 0.0068273707292973995, -0.01911316253244877, 0.045550089329481125, -0.07277250289916992, 0.019472256302833557, -0.04781103506684303, -0.023507049307227135, -0.04726908728480339, -0.026572760194540024, 0.008828642778098583, 0.059006545692682266, 0.014529888518154621, -0.011541989631950855, -0.016862651333212852, 0.009524928405880928, -0.025109287351369858, -0.052572041749954224, 0.01786613278090954, 0.04367610067129135, 0.019400672987103462, 0.01920747011899948, 0.02574063092470169, -0.019832909107208252, -0.020016387104988098, -0.012779789045453072, -0.03248586505651474, 0.019716842100024223, -0.07739034295082092, -0.02291759103536606, 0.02368537336587906, 0.023629695177078247, -0.0067718857899308205, 0.02564840205013752, -0.008647238835692406, -0.003331564599648118, -0.054878830909729004, -0.0017541080014780164, 0.07304883748292923, 0.015058672986924648, 0.05512207746505737, 0.041904330253601074, -0.02505667135119438, -0.016579972580075264, 0.00886926893144846, 0.049412257969379425, 0.024502703920006752, -0.034798212349414825, 0.0007261147839017212, 0.0039517926052212715, 0.054745741188526154, 0.021183358505368233, 0.0048125446774065495, 0.046072330325841904, -0.021852077916264534, 0.0048552039079368114, -0.011999093927443027, -0.00024330707674380392, -0.0021415208466351032, 0.026163306087255478, -0.015430995263159275, 0.025278858840465546, -0.040608979761600494, 0.014806152321398258, 0.02740524336695671, -0.07989639043807983, -0.05292316898703575, 0.0019431497203186154, -0.0022765924222767353, 0.015376284718513489, -0.05706630274653435, 0.015596309676766396, -0.0070325639098882675, -0.04151752591133118, 0.01606561802327633, 0.020641477778553963, -0.049266133457422256, -0.01735347881913185, 0.030575191602110863, 0.021563541144132614, -0.01894575171172619, -0.03184163570404053, -0.033347245305776596, -0.014765056781470776, 0.029995301738381386, -0.0149686885997653, -0.010827381163835526, 0.047773804515600204, 0.04107731208205223, 0.04178677499294281, 0.036409225314855576, -0.06046908348798752, 0.005534227937459946, -0.06795093417167664, -0.031334444880485535, -0.05258237570524216, -0.001689945813268423, 0.02884036675095558, 0.03237129747867584, -0.026310104876756668, -0.08388268947601318, -0.003044010140001774, -0.007818485610187054, 0.029596393927931786, 0.0049766311421990395, -0.013203692622482777, -0.04199697822332382, -0.01016547903418541, -0.030126241967082024, 0.013266963884234428, 0.024134967476129532, 0.01256419625133276, -0.03486623242497444, -0.023082392290234566, -0.021647535264492035, 0.03283664956688881, 0.06665723770856857, 0.011480155400931835, 0.0834462121129036, 0.04356878995895386, -0.026206307113170624, 0.0466042198240757, -0.02075275219976902, 0.009893983602523804, -0.010923056863248348, 0.0756574422121048, 0.05246267840266228, -0.03537271171808243, -0.03740999847650528, 0.045179806649684906, -0.0016589032020419836, -0.09805630147457123, 0.0002276505547342822, -0.040956251323223114, 0.005169338081032038, -0.016223246231675148, 0.025208579376339912, -0.046102169901132584, 0.003812396200373769, 0.012444403022527695, -0.0014097754610702395, 0.01929214596748352, -0.015456457622349262, 0.011567439883947372, 0.0025566916447132826, -0.03466679900884628, -0.002110074507072568, -0.016933836042881012, -0.0034457615111023188, 0.017059924080967903, -0.007432359270751476, 0.046330925077199936, -0.018263310194015503, 0.0042616440914571285, -0.04416109621524811, -0.05050932615995407, -0.0839180052280426, 0.027108825743198395, 0.026281872764229774, -0.013037103228271008, -0.0036077285185456276, 0.032554082572460175, 0.05857483297586441, 0.009808550588786602, -0.034950025379657745, -0.03689805418252945, -0.009226912632584572, 0.03385544195771217, -0.02911013923585415, -0.03562431409955025, -0.03970399498939514, -0.043753307312726974, 0.050632543861866, 0.0041215443052351475, 0.017488086596131325, -0.04575563967227936, -0.018520841374993324, 0.03129526227712631, -0.05907043069601059, -0.0791974738240242, 0.03721127286553383, 0.05258328467607498, -0.004176956135779619, -0.04113142564892769, -0.02384081669151783, 0.03929191455245018, -0.018087588250637054, -0.06143498793244362, -0.022462651133537292, 0.0034718394745141268, -0.037601251155138016, 0.016547460108995438, -0.005146168638020754, 0.029119674116373062, -0.020705537870526314, -0.03506171703338623, 0.029352813959121704, 0.0026452119927853346, 0.011761197820305824, -0.0003934872802346945, 0.01900721713900566, -0.024103762581944466, 0.04100419580936432, 0.019137710332870483, -0.04150216653943062, 0.013782770372927189, 0.10481531172990799, -0.03523430973291397, -0.033319491893053055, -0.008320457302033901, 0.04531063139438629, -0.01704230159521103, -0.11575797200202942, -0.006897253450006247, 0.03538540378212929, -0.001426327507942915, 0.00925547257065773, -0.0013295203680172563, -0.0433683879673481, 0.010095256380736828, 0.019512055441737175, -0.0369228795170784, -0.03023437038064003, -0.05475281924009323, -0.024032648652791977, -0.013238195329904556, -0.0294982697814703, 0.07457976043224335, -0.013109819032251835, 0.09973470866680145, 0.04450029134750366, -0.030775783583521843, -0.054650988429784775, -0.03371907398104668, 0.0012653362937271595, -0.03999791666865349, -0.01864386536180973, -0.052342403680086136, -0.02352513000369072, 0.055345866829156876, 0.004323044791817665, -0.01926010102033615, 0.0413900725543499, -0.050871822983026505, 0.011924964375793934, 0.026994457468390465, -0.059449829161167145, 0.022131694480776787, 0.033248379826545715, 0.006292770151048899, -0.09471818059682846, -0.041868068277835846, -0.03997000306844711, -0.012298324145376682, 0.02578822150826454, -0.04613150283694267, 0.013400194235146046, -0.012012045830488205, -0.02667958103120327, -0.03472772613167763, 0.02121037431061268, 0.07819493860006332, -0.03276858851313591, -0.06776969134807587, -0.022269608452916145, 0.028535494580864906, 0.04828999191522598, 0.022034192457795143, 0.023875271901488304, 0.0732148215174675, 0.04115957394242287, 0.02138381637632847, 0.007324349135160446, 0.034159593284130096, 0.005635539535433054, -0.02284804731607437, 0.01970010995864868, -0.04453670233488083, -0.017330648377537727, -0.005928312428295612, 0.02455933205783367, -0.008948401547968388, 0.015251146629452705, -0.009708907455205917 ]
<p>What are possible effects of electromagnetic pulse / EMP on superconductor-based devices/equimpent/transportation?</p> <p>Are they resilient or more sensitive to EMP?</p>
g5439
[ -0.005229236092418432, 0.009955573827028275, -0.013096850365400314, 0.05250142887234688, 0.042490389198064804, 0.061556294560432434, 0.008286137133836746, 0.04939078167080879, 0.01406767126172781, 0.015016423538327217, -0.09911280125379562, -0.005169309210032225, -0.04537947475910187, 0.019053950905799866, 0.012947027571499348, 0.010523753240704536, 0.10334724187850952, -0.03217482566833496, 0.03213493898510933, 0.058143261820077896, 0.0030498008709400892, -0.04736873134970665, -0.02003594860434532, -0.011392183601856232, -0.02564573660492897, 0.0418568029999733, 0.11797429621219635, -0.05867995694279671, -0.0039069764316082, -0.012747956439852715, -0.023924943059682846, -0.046282798051834106, 0.050343334674835205, -0.030782893300056458, -0.04336101561784744, -0.023902876302599907, -0.015413708984851837, 0.03163035586476326, 0.028942476958036423, 0.03185660019516945, 0.0014463772531598806, -0.04399580508470535, -0.01376518327742815, -0.06455369293689728, -0.0005239953752607107, 0.0012584038777276874, -0.006355194374918938, 0.004437190946191549, -0.03751782327890396, -0.009839111007750034, -0.02292112447321415, -0.045135751366615295, 0.05710156261920929, -0.0003926192584913224, 0.000611092138569802, -0.03070186823606491, 0.01578233763575554, 0.0032767660450190306, -0.04345808923244476, -0.0037070929538458586, -0.015382558107376099, 0.060843463987112045, -0.020091334357857704, -0.050260718911886215, 0.03047916106879711, 0.027159923687577248, -0.017534907907247543, -0.0005505296285264194, 0.0166347436606884, 0.0415029413998127, 0.025552179664373398, -0.016254043206572533, -0.09161294251680374, -0.010461048223078251, 0.04920927807688713, 0.028931042179465294, -0.02200808748602867, -0.00014736417506355792, 0.0032949813175946474, 0.0116690369322896, -0.035823896527290344, -0.020039118826389313, 0.04475751519203186, 0.031920257955789566, 0.04941391944885254, -0.040007006376981735, -0.02557099051773548, 0.017890481278300285, 0.00933152250945568, 0.002123235957697034, -0.001333857886493206, -0.05637088790535927, -0.0027533217798918486, 0.03468311205506325, 0.017963403835892677, 0.07914531975984573, 0.042948123067617416, -0.013689846731722355, 0.03428424894809723, -0.007230266463011503, -0.01202891580760479, -0.06352337449789047, -0.030945729464292526, 0.0266793891787529, -0.06783292442560196, -0.02141382172703743, -0.002404203172773123, 0.000014260169336921535, 0.026074331253767014, -0.014787339605391026, -0.002135206712409854, 0.03802689537405968, -0.06395717710256577, 0.019437633454799652, 0.03330579772591591, 0.028663787990808487, -0.01279799547046423, -0.06120360270142555, -0.0019998892676085234, 0.028495892882347107, 0.05024634301662445, 0.023088645190000534, -0.09501621872186661, 0.011968535371124744, 0.000764630560297519, 0.017642371356487274, -0.03658151999115944, 0.03633742779493332, 0.01683177426457405, 0.08018504083156586, -0.0011475048959255219, -0.03772216662764549, -0.04831903800368309, -0.030902042984962463, 0.006626533344388008, 0.02124094031751156, 0.029180552810430527, -0.027659839019179344, -0.028809214010834694, -0.014503367245197296, 0.02604898251593113, -0.02387075498700142, 0.016484219580888748, 0.03226067125797272, 0.005593090318143368, 0.028810063377022743, -0.06567887216806412, 0.018142670392990112, -0.020254913717508316, 0.02107197977602482, -0.01330358162522316, 0.015929007902741432, -0.022356778383255005, -0.03918818384408951, 0.017013726755976677, 0.01167495921254158, 0.012715858407318592, -0.03598715364933014, 0.008090779185295105, 0.03346722200512886, -0.03690258786082268, 0.00337057001888752, -0.008481825701892376, -0.011514373123645782, 0.05320493504405022, -0.04012984409928322, 0.031662728637456894, -0.01027713529765606, 0.05905622988939285, 0.05154362693428993, -0.0420045368373394, -0.05805984511971474, 0.04041511192917824, 0.07811148464679718, -0.009575680829584599, 0.010683340951800346, 0.04769342392683029, -0.05131947249174118, 0.03855302184820175, -0.07260666787624359, -0.005960558541119099, 0.0024865076411515474, -0.017709046602249146, -0.07378032058477402, 0.012150639668107033, -0.013666466809809208, -0.03551430627703667, 0.07734659314155579, -0.04748149216175079, -0.009959102608263493, -0.0856330469250679, -0.015453982166945934, -0.05556826665997505, 0.06541211158037186, -0.04044602811336517, -0.03603732958436012, -0.08021055907011032, 0.009639515541493893, -0.007379815448075533, 0.005339076742529869, 0.00841896515339613, 0.05127616599202156, 0.09098304808139801, -0.05475972965359688, -0.0004955336335115135, -0.004428868647664785, -0.06478651612997055, -0.011098754592239857, 0.006961418781429529, -0.07485602796077728, 0.0434713214635849, 0.032621849328279495, 0.06346020102500916, -0.010776981711387634, -0.04172578454017639, -0.021870838478207588, 0.008296456187963486, 0.001989717362448573, 0.012336271815001965, 0.0005182948079891503, 0.017239650711417198, -0.04774657264351845, 0.04417194798588753, -0.030114348977804184, -0.0421643890440464, -0.015098090283572674, -0.015949442982673645, 0.0158724132925272, 0.0475364550948143, -0.05698111653327942, -0.023617522791028023, 0.015681885182857513, -0.0016662704292684793, -0.0034932391718029976, 0.030101517215371132, 0.0023850840516388416, -0.005720664747059345, -0.05850718170404434, -0.00756240077316761, -0.030459051951766014, 0.04566213861107826, -0.027115317061543465, 0.018592828884720802, -0.04716753587126732, 0.05946893244981766, -0.08890106528997421, -0.002137579722329974, 0.029507236555218697, 0.04978428781032562, -0.019321290776133537, -0.011970283463597298, -0.018660003319382668, -0.001121318549849093, 0.02976829744875431, -0.0013801060849800706, -0.0344218872487545, 0.018786318600177765, 0.012144465930759907, -0.059321265667676926, -0.016231423243880272, -0.020955312997102737, -0.0020142439752817154, 0.004226223565638065, 0.014160733669996262, 0.018041325733065605, 0.039529792964458466, -0.01995300129055977, -0.022139767184853554, -0.025404758751392365, 0.03305840864777565, -0.015467103570699692, -0.005745996255427599, -0.03778153657913208, 0.051313597708940506, 0.07285843044519424, -0.029572028666734695, 0.039306674152612686, 0.027172140777111053, 0.00390798831358552, -0.06215505301952362, -0.03899739682674408, -0.0016677306266501546, -0.023861108347773552, -0.05320072919130325, 0.0026908251456916332, -0.01021265797317028, 0.004116952419281006, -0.05978185310959816, 0.01983414590358734, 0.016312267631292343, -0.03465721383690834, -0.05662061274051666, 0.04060833901166916, 0.058566864579916, -0.024030184373259544, -0.022358223795890808, -0.0016471896087750793, -0.05991410091519356, -0.010108431801199913, -0.012923681177198887, 0.048993341624736786, 0.05329291522502899, 0.01822110451757908, 0.010531798005104065, -0.009640398435294628, -0.004974591080099344, -0.01899081841111183, -0.04161359369754791, 0.06392817944288254, 0.019539035856723785, -0.01942315511405468, 0.06843816488981247, 0.025758756324648857, -0.022001147270202637, -0.032519809901714325, 0.04037202522158623, 0.062061384320259094, 0.01328524760901928, 0.020391350612044334, 0.010395561344921589, -0.016887566074728966, -0.03968016803264618, 0.02241642214357853, 0.011054395698010921, -0.0038777401205152273, 0.00436533335596323, 0.0787883773446083, 0.0015206373063847423, -0.011812331154942513, 0.025217296555638313, -0.025538470596075058, 0.014161319471895695, 0.014735577628016472, 0.014556553214788437, -0.06501539051532745, 0.036395587027072906, -0.007588933687657118, 0.06660724431276321, -0.020172523334622383, 0.0055002677254378796, 0.06638479977846146, -0.03468497470021248, -0.055865801870822906, -0.023328006267547607, 0.01630004681646824, 0.059781406074762344, 0.019569430500268936, -0.0284519512206316, 0.059576183557510376, -0.02552853152155876, 0.09661699086427689, 0.04307215288281441, 0.01812378130853176, 0.057545486837625504, -0.013559557497501373, -0.009853815659880638, -0.011779436841607094, 0.0175939928740263, -0.061093978583812714, -0.00678911991417408, -0.03419893980026245, 0.05436849966645241, 0.022729622200131416, 0.013401313684880733, -0.003460940206423402, -0.029047036543488503, 0.05172475427389145, 0.049062374979257584, 0.00017628309433348477, 0.005918500479310751, 0.0018788358429446816, 0.00041652252548374236, -0.045374054461717606, 0.03222755715250969, 0.024622522294521332, 0.021708156913518906, 0.040525276213884354, -0.010216667316854, -0.050664711743593216, 0.015017710626125336, 0.030281279236078262, -0.05608441308140755, -0.014148217625916004, -0.04833514988422394, -0.016778774559497833, -0.0198421161621809, 0.02860124781727791, 0.01835153065621853, -0.08872074633836746, 0.012027324177324772, -0.026549983769655228, 0.023891696706414223, -0.05795465409755707, -0.003362456103786826, 0.03161277249455452, -0.03209355100989342, 0.029688190668821335, -0.041936859488487244, 0.028824105858802795, -0.005451513919979334, 0.04585622623562813, 0.009355415590107441, 0.01110828947275877, 0.013542582280933857, -0.03463130444288254, -0.012773008085787296, -0.03446749970316887, -0.00015358440577983856, -0.03272894024848938, 0.006097374949604273, -0.029877785593271255, -0.05074302479624748, -0.048198260366916656, -0.04633881524205208, 0.014429661445319653, -0.017035219818353653, 0.045230284333229065, 0.0143535565584898, 0.051928624510765076, -0.028016725555062294, 0.008649195544421673, -0.032039936631917953, 0.06216241046786308, 0.009363732300698757, -0.05955386534333229, 0.0023989295586943626, 0.06662648916244507, -0.031550243496894836, 0.041849203407764435, 0.05190054327249527, -0.016580576077103615, 0.05406509339809418, -0.024992411956191063, 0.0005771804135292768, 0.049662236124277115, 0.009857641533017159, 0.041130997240543365, -0.016096381470561028, 0.05852773040533066, 0.014302929863333702, 0.05763654783368111, -0.03439779579639435, 0.008979305624961853, -0.025025060400366783, -0.00013673529610969126, 0.05859936773777008, -0.04218818619847298, -0.04295710101723671, 0.02696273848414421, -0.007156782783567905, -0.03580179065465927, 0.007302009034901857, 0.01859193481504917, -0.019452033564448357, -0.0010708103654906154, -0.01365592610090971, 0.05379838868975639, -0.029935073107481003, 0.05520974472165108, -0.03516194224357605, -0.01620502956211567, 0.03491491079330444, -0.007019766140729189, -0.005348430015146732, -0.034521330147981644, -0.015996066853404045, -0.031168732792139053, -0.01749689131975174, -0.03895999491214752, 0.06867356598377228, -0.03182164579629898, -0.02249300666153431, 0.06190861761569977, 0.07133470475673676, 0.03576580062508583, -0.022526131942868233, -0.00585628068074584, 0.013864409178495407, -0.015861472114920616, -0.046152208000421524, 0.02436674013733864, -0.03212183341383934, -0.005869477987289429, -0.013423931784927845, 0.012710913084447384, 0.01730247214436531, -0.04615730792284012, 0.08734538406133652, 0.015287264250218868, -0.01750132441520691, 0.02844233065843582, -0.01959807425737381, -0.00815344974398613, -0.026593731716275215, -0.016977692022919655, -0.07962014526128769, 0.0567687451839447, -0.008417801931500435, 0.005671744234859943, 0.009242549538612366, 0.030954789370298386, -0.01191163994371891, 0.011442945338785648, 0.04949434474110603, -0.009487531147897243, 0.012204338796436787, -0.02746395394206047, -0.015247909352183342, -0.010760623961687088, -0.0952451229095459, -0.0686756819486618, 0.0627862811088562, -0.04115564376115799, -0.008164845407009125, -0.005828894209116697, 0.02762383036315441, -0.07260125875473022, 0.004843267612159252, -0.02044389769434929, -0.02816854976117611, -0.022280117496848106, 0.01233793143182993, 0.0598301962018013, 0.05443529412150383, 0.03310936316847801, 0.022357795387506485, -0.04033520072698593, 0.019398825243115425, 0.05592338740825653, 0.009942729026079178, 0.06063345819711685, 0.009770925156772137, -0.0031071538105607033, -0.08925200998783112, -0.008285848423838615, 0.0077264923602342606, 0.0685269758105278, 0.02304975688457489, -0.045700810849666595, 0.03748615086078644, -0.01603642851114273, -0.056883733719587326, -0.01643800176680088, 0.06619343906641006, -0.006599590182304382, -0.017309309914708138, -0.05085577070713043, -0.006707499269396067, -0.03501865267753601, -0.03910340368747711, 0.02224070392549038, 0.024858856573700905, -0.0480973944067955, 0.025878814980387688, 0.04644129425287247, 0.06196453794836998, 0.0063805049285292625, -0.027123218402266502, -0.020438281819224358, -0.028230853378772736, 0.022740576416254044, 0.02229970134794712, 0.004373922944068909, 0.015527213923633099, 0.033340707421302795, -0.06347550451755524, -0.022247055545449257, -0.006248706951737404, -0.006909979972988367, 0.036697033792734146, -0.002590838121250272, 0.016493957489728928, 0.0008876809733919799, -0.07886058837175369, -0.020986434072256088, -0.016953120008111, -0.013007148168981075, -0.016587616875767708, 0.020280878990888596, 0.004659346304833889, -0.021485406905412674, 0.03975336626172066, -0.0015242391964420676, 0.00975617952644825, -0.044615499675273895, 0.020808087661862373, 0.016921278089284897, 0.0012407796457409859, 0.06409518420696259, 0.012546636164188385, -0.01551045011729002, -0.0018394500948488712, 0.06828074902296066, -0.007619259878993034, -0.05402857065200806, 0.01764526404440403, -0.05845816060900688, 0.02169538475573063, 0.041506025940179825, 0.07105927169322968, 0.012285072356462479, -0.003732615150511265, -0.04146391153335571, 0.018022723495960236, 0.02452007494866848, -0.01626885123550892, -0.002495128195732832, -0.04404246434569359, 0.02154913730919361, 0.042908925563097, 0.028752131387591362, -0.08345731347799301, -0.01091819629073143, 0.022913623601198196, -0.04843069985508919, -0.029787681996822357, 0.020299522206187248, -0.028821757063269615, -0.02333189733326435, 0.0529603473842144, -0.0057655274868011475, -0.0017361750360578299, -0.03116690181195736, 0.01906033232808113, -0.034816499799489975, -0.002798075322061777, 0.016872532665729523, -0.006401825696229935, 0.04586515203118324, 0.007246747147291899, -0.030536357313394547, 0.0289467666298151, 0.00255058822222054, 0.0009861481375992298, 0.01667746715247631, 0.04797665774822235, -0.006606084294617176, -0.04092467203736305, -0.01750706508755684, -0.048231590539216995, 0.039994899183511734, -0.002265392569825053, -0.014873016625642776, -0.0045083751901984215, -0.04904400184750557, 0.04375160112977028, 0.040301933884620667, 0.08774785697460175, -0.011457663029432297, 0.03367866948246956, -0.012761642225086689, 0.011248116381466389, 0.0013344401959329844, -0.029952410608530045, 0.00722771231085062, -0.005545560736209154, -0.00591628672555089, 0.0185936838388443, -0.008771265856921673, -0.02590964362025261, -0.017447704449295998, -0.06723342835903168, -0.023442836478352547, -0.016507934778928757, 0.034665558487176895, 0.018857644870877266, 0.004235055297613144, -0.009548351168632507, 0.00966434646397829, -0.031704239547252655, -0.04396665841341019, -0.0014690094394609332, -0.0009644581587053835, -0.021324580535292625, 0.01196092925965786, -0.06682813167572021, -0.02313133142888546, -0.0664452388882637, -0.05204126611351967, -0.017272906377911568, -0.0066594770178198814, -0.00683049950748682, 0.03903111815452576, -0.0036090051289647818, -0.0216823760420084, 0.051993079483509064, -0.05423905700445175, -0.005450890865176916, 0.024296630173921585, -0.03468120098114014, 0.035383082926273346, 0.027860764414072037, 0.06376215070486069, 0.05413617193698883, 0.005687300115823746, -0.031192436814308167, -0.04160007834434509, 0.04416115581989288, -0.00638217618688941, -0.045067861676216125, -0.03715486079454422, 0.024138757959008217, 0.019520634785294533, -0.006757055874913931, 0.033170923590660095, 0.021724561229348183, 0.01056502666324377, -0.039050862193107605, -0.000052484079787973315, 0.05143413692712784, 0.04164496436715126, 0.0918990820646286, 0.0033578630536794662, 0.0022898009046912193, -0.01788589172065258, 0.05392441898584366, 0.019646350294351578, 0.0042831324972212315, 0.01811305619776249, 0.04449979215860367, 0.009057104587554932, 0.05269502103328705, -0.007521473336964846, -0.0024029784835875034, 0.025906158611178398, -0.024154212325811386, 0.00899867806583643, 0.03371281176805496, 0.007575207389891148, -0.05715718865394592, 0.013892419636249542, -0.0021843945141881704, -0.028871992602944374, 0.015190462581813335, -0.026344655081629753, 0.02418673038482666, 0.021370774134993553, 0.055393196642398834, -0.06427119672298431, -0.009892633184790611, 0.010181398130953312, -0.05264973267912865, -0.07507415115833282, 0.061538565903902054, -0.052472710609436035, 0.02597680687904358, -0.0415390320122242, -0.009565409272909164, -0.022832440212368965, -0.017452925443649292, 0.01139124110341072, -0.015521842986345291, -0.09978694468736649, 0.06883645802736282, -0.0600886307656765, -0.005973254330456257, -0.03540167957544327, -0.02562512643635273, -0.01538290549069643, 0.018882468342781067, 0.047780588269233704, -0.011587441898882389, -0.01633230783045292, -0.035792794078588486, -0.03632870689034462, 0.022697564214468002, 0.024631233885884285, 0.026871895417571068 ]
<blockquote> <p><strong>Possible Duplicate:</strong><br> <a href="http://physics.stackexchange.com/questions/36131/friction-between-atoms-in-spring">Friction between atoms in spring</a> </p> </blockquote> <p>thanks john:when we apply a stress within elastic range of metal/spring,due to flow of atoms the particular void(defect) region getting filled by atoms &amp; get organised crystal structure in that region,when we released that force the atoms filled in void region doesnt return to its previous position right,due to this the spring could not obey the same in 1st&amp;2nd cycles,is my statement true? one more doubt, after few cycles, voids of springs are filled by atoms&amp; now the springs obey different from the spring with void right,if my statemnt true, then in books the oscillation decay of springs in constant rate(1/e) it should be false right..then the oscillation decay should be a variable depends on defects in spring material.... can u give some more papers for my reference?</p>
g193
[ 0.09363558888435364, 0.010176103562116623, -0.008752991445362568, 0.0066287764348089695, 0.01933462917804718, 0.017810877412557602, 0.04941368103027344, -0.012664683163166046, -0.004006136674433947, -0.0640837699174881, -0.004886324051767588, 0.07711368799209595, 0.0028006962966173887, -0.04000197350978851, -0.03389240801334381, -0.01263740099966526, 0.039834100753068924, -0.0015597487799823284, -0.014195813797414303, -0.003355711465701461, 0.01378561370074749, 0.042444922029972076, -0.040167611092329025, -0.03220115974545479, -0.0010399536695331335, 0.05216772481799126, 0.006930474191904068, -0.062035396695137024, -0.011217833496630192, -0.044516127556562424, 0.0950251966714859, -0.02180364914238453, 0.03430132195353508, -0.082771897315979, -0.06443628668785095, 0.009992789477109909, 0.04265643656253815, 0.0070475260727107525, -0.015009191818535328, -0.0029294209089130163, 0.027767235413193703, -0.04387199506163597, 0.025572381913661957, 0.008795483969151974, 0.005950036458671093, -0.02680681087076664, -0.02836611494421959, 0.012629307806491852, -0.02449231781065464, -0.009333305060863495, 0.044454075396060944, 0.024186385795474052, 0.025040211156010628, -0.03254835680127144, -0.00787664670497179, 0.0182004664093256, 0.03177041932940483, -0.06302385777235031, 0.09511938691139221, -0.014262738637626171, 0.0005196299753151834, -0.008529636077582836, 0.012121626175940037, 0.00888651330024004, 0.03574226051568985, -0.012974780052900314, -0.0055536008439958096, 0.01116415299475193, 0.03268926963210106, -0.015534652397036552, -0.00396440364420414, 0.016870127990841866, 0.001012587919831276, -0.018369823694229126, -0.04989229887723923, 0.07473339140415192, 0.026343848556280136, 0.0305988397449255, 0.026529479771852493, -0.0006011461955495179, -0.0366024486720562, 0.03097427263855934, -0.01259631011635065, 0.055008575320243835, 0.07640206068754196, 0.006960969418287277, -0.022553443908691406, 0.004561589565128088, 0.0015690081054344773, 0.0532907098531723, 0.017197653651237488, -0.04887472465634346, -0.01765243522822857, 0.007105827331542969, -0.05485124886035919, -0.010649391449987888, -0.012524663470685482, 0.10218258947134018, -0.010219044052064419, 0.012308095581829548, -0.03227237984538078, -0.0848846510052681, 0.019551292061805725, -0.03304141387343407, 0.019343985244631767, -0.03015538677573204, -0.01298454962670803, -0.00019326362235005945, -0.038654159754514694, 0.0525708943605423, 0.013141925446689129, 0.013362308964133263, -0.03149911388754845, -0.0036980698350816965, -0.015849769115447998, 0.004620861727744341, 0.038703788071870804, 0.021655099466443062, 0.00796862505376339, 0.024904794991016388, -0.02357328124344349, -0.013575942255556583, 0.04264071583747864, 0.046981193125247955, 0.018318751826882362, -0.020112624391913414, 0.06173880398273468, -0.0243394635617733, -0.024115944281220436, 0.005319384858012199, -0.03402216359972954, 0.040210552513599396, 0.019452307373285294, 0.02872159145772457, -0.05866061896085739, 0.03425933048129082, 0.05686991289258003, -0.006737385410815477, -0.012715188786387444, -0.01121099479496479, -0.004503815434873104, 0.01201795507222414, -0.01881098933517933, -0.04984063655138016, -0.023124588653445244, 0.04959355667233467, -0.030497480183839798, 0.00006380321428878233, -0.009234394878149033, -0.0068069035187363625, 0.006499757524579763, 0.026973024010658264, -0.05707721412181854, -0.029611140489578247, -0.036300454288721085, -0.030176598578691483, -0.017961697652935982, -0.009094911627471447, 0.003235860727727413, 0.06373802572488785, 0.003923073410987854, -0.018918899819254875, 0.04465274140238762, 0.03659704327583313, -0.03851736709475517, 0.03386174887418747, -0.03491686284542084, -0.021865902468562126, 0.028119435533881187, -0.02134230174124241, -0.06775148212909698, 0.005924081429839134, -0.007168564945459366, 0.04474405571818352, 0.02912510372698307, 0.0043542655184865, 0.04935919865965843, -0.034984663128852844, 0.07541980594396591, -0.004342203959822655, 0.013075956143438816, -0.013693436048924923, -0.03687053918838501, -0.04245946183800697, -0.017963213846087456, 0.04851924255490303, 0.031098606064915657, 0.016700981184840202, -0.050860509276390076, -0.019492922350764275, -0.035561803728342056, -0.0636940747499466, -0.0008835717453621328, 0.026578359305858612, -0.008067041635513306, -0.013717090710997581, 0.03166322410106659, -0.07552280277013779, -0.004817430395632982, 0.0355977788567543, 0.017602624371647835, 0.03496357426047325, 0.025757314637303352, -0.009565172716975212, -0.0044171460904181, -0.00792086124420166, -0.04763851687312126, -0.010585812851786613, 0.015202749520540237, 0.017678607255220413, 0.009428847581148148, 0.019835742190480232, 0.014732619747519493, 0.04770402982831001, -0.0116514191031456, -0.018215222284197807, 0.03756488487124443, -0.06480716913938522, 0.013911922462284565, 0.009738169610500336, 0.027089348062872887, 0.010123147629201412, 0.007674568798393011, -0.03376678749918938, -0.027404462918639183, -0.019860275089740753, -0.017202293500304222, -0.042414113879203796, -0.010591328144073486, -0.006193691398948431, -0.04070959985256195, 0.0128176836296916, 0.0065726409666240215, -0.039546940475702286, 0.04824506491422653, 0.02002681791782379, -0.004524915013462305, 0.04048553854227066, -0.02355022542178631, -0.045415692031383514, 0.020176174119114876, -0.0617731511592865, -0.07821480184793472, -0.06096493452787399, 0.018798796460032463, -0.0315176323056221, -0.006508536636829376, -0.005470992997288704, 0.02836526185274124, 0.04020240530371666, 0.06947337836027145, -0.03429418429732323, -0.028743963688611984, 0.03571533411741257, -0.003370059886947274, -0.01925143599510193, -0.04849949851632118, 0.03635188937187195, 0.010793504305183887, -0.09782692790031433, -0.013192710466682911, -0.011791562661528587, 0.06740007549524307, -0.015943823382258415, -0.02640141360461712, -0.023989379405975342, -0.019426357001066208, -0.029917331412434578, -0.019761115312576294, -0.013700776733458042, 0.006536849774420261, 0.040899280458688736, -0.01932692527770996, 0.10011903941631317, -0.019578706473112106, -0.002807417418807745, 0.008055092766880989, -0.0008110082126222551, -0.03593464940786362, -0.02466992288827896, -0.022619621828198433, 0.022850902751088142, -0.008089559152722359, -0.029420876875519753, -0.011546027846634388, 0.01651562936604023, -0.030322592705488205, -0.015818968415260315, -0.015117199160158634, 0.03970195725560188, 0.030178040266036987, 0.004374089650809765, 0.06176425889134407, 0.08779709041118622, -0.015124209225177765, 0.11803197860717773, 0.007220452185720205, -0.061386022716760635, -0.050994884222745895, 0.11429225653409958, 0.01464878860861063, -0.049669455736875534, -0.017251204699277878, -0.009832996875047684, -0.014333321712911129, 0.031119640916585922, 0.01821458525955677, 0.0037128992844372988, 0.04068167507648468, 0.010525865480303764, 0.010235757566988468, 0.03888397663831711, 0.027795366942882538, -0.061946265399456024, -0.10439170897006989, 0.026892082765698433, 0.00543596176430583, -0.0019402295583859086, 0.025149615481495857, -0.030258076265454292, -0.031421102583408356, -0.00601469399407506, 0.07417604327201843, -0.027356883510947227, -0.036377519369125366, 0.008211198262870312, -0.021376924589276314, 0.0029000351205468178, -0.05619152635335922, 0.006924552842974663, -0.017656467854976654, -0.008988717570900917, -0.05346198007464409, -0.04938273876905441, -0.003513712203130126, -0.06482205539941788, 0.00018255530449096113, 0.03227165341377258, 0.009877528063952923, 0.07027649879455566, -0.015436300076544285, -0.006341650616377592, 0.041493020951747894, 0.05337650328874588, 0.01693054847419262, 0.04222681000828743, -0.03710143640637398, 0.07783706486225128, -0.016401268541812897, -0.004753726068884134, 0.07075196504592896, 0.023127727210521698, -0.05975868180394173, 0.011313268914818764, 0.010517056100070477, 0.04360436648130417, 0.022335296496748924, -0.01033452246338129, -0.06746503710746765, -0.035586461424827576, 0.0021287957206368446, -0.09704016149044037, 0.016423450782895088, -0.007776958867907524, -0.04532165452837944, -0.005973997991532087, 0.06308936327695847, 0.07174429297447205, -0.02494240179657936, -0.03773682564496994, -0.03174631670117378, -0.09140390902757645, 0.008142152801156044, -0.022098686546087265, 0.08589497208595276, -0.02593553252518177, 0.013839720748364925, 0.10174202919006348, -0.031161634251475334, -0.00512775918468833, 0.039979465305805206, -0.017016850411891937, -0.021153366193175316, 0.0002090342459268868, -0.005281214136630297, -0.012715950608253479, 0.03863443806767464, -0.01896783523261547, -0.03807641565799713, -0.04609003663063049, -0.03350990265607834, 0.017973562702536583, -0.023396000266075134, 0.0601198710501194, 0.03771418705582619, -0.04018353298306465, 0.012879517860710621, 0.022450823336839676, 0.008553070947527885, -0.0008508939063176513, 0.007718361914157867, -0.018668971955776215, -0.06309805065393448, 0.05386617034673691, 0.01020458247512579, 0.02089204452931881, 0.02499878592789173, -0.04908592253923416, 0.02599268965423107, -0.01131665613502264, -0.0013520753709599376, -0.04715004190802574, -0.05143118277192116, -0.011135421693325043, 0.002900285180658102, -0.008122758008539677, 0.008411912247538567, 0.048742540180683136, 0.035946231335401535, 0.010813513770699501, 0.0050096334889531136, 0.12256307899951935, 0.008188562467694283, 0.036124587059020996, 0.0568891242146492, 0.015952343121170998, 0.009748080745339394, -0.02720804326236248, -0.006723692175000906, -0.09688936918973923, -0.015301726758480072, -0.003875864902511239, 0.029663680121302605, -0.009382995776832104, -0.053981129080057144, 0.0836859792470932, 0.001554498914629221, 0.03340137377381325, -0.0382080115377903, 0.035432010889053345, -0.013434750027954578, 0.03532705456018448, 0.04706243798136711, 0.04771625995635986, -0.0029182513244450092, 0.02681148238480091, -0.05834423005580902, 0.0014373945305123925, 0.0011035804636776447, -0.053648218512535095, -0.009035690687596798, -0.0014133240329101682, 0.024870701134204865, -0.025169629603624344, 0.002907720161601901, -0.02642574906349182, -0.01933516003191471, -0.015387075021862984, -0.06783505529165268, 0.008958184160292149, 0.0015364809660241008, -0.011836784891784191, 0.0246119424700737, 0.028066467493772507, -0.005753601435571909, -0.030088720843195915, -0.003985193558037281, -0.0352572426199913, -0.07003326714038849, 0.006493864115327597, 0.05896160006523132, -0.03377882391214371, 0.003979627043008804, 0.02408936806023121, 0.08000040054321289, -0.018769780173897743, 0.027324238792061806, -0.021962067112326622, 0.04668999835848808, -0.031650692224502563, -0.016546018421649933, -0.002645437838509679, 0.024281583726406097, 0.0096761304885149, -0.04395928978919983, -0.038548484444618225, -0.04378194734454155, -0.04727298393845558, 0.03096145950257778, -0.022061390802264214, 0.11849478632211685, 0.01994655653834343, 0.022687498480081558, -0.021848073229193687, -0.003327928716316819, 0.004897373728454113, 0.030056895688176155, 0.04108181223273277, -0.009249645285308361, -0.00902483705431223, -0.08181356638669968, -0.007845044136047363, -0.010478206910192966, -0.001648598350584507, 0.004223199095577002, 0.02576948143541813, 0.035051632672548294, 0.009360388852655888, -0.014143120497465134, -0.03596648573875427, 0.014642625115811825, 0.022735940292477608, -0.005404007155448198, 0.0367056205868721, 0.024769112467765808, 0.020315373316407204, -0.007564296945929527, 0.0017043992411345243, -0.054839447140693665, -0.04329904168844223, -0.0011152519145980477, 0.012592755258083344, 0.03199981525540352, -0.0019226670265197754, 0.03028535097837448, 0.013731654733419418, -0.01684316247701645, -0.003861150471493602, -0.024410588666796684, -0.0016771763330325484, 0.022843962535262108, -0.017486754804849625, -0.01235143281519413, -0.009963899850845337, 0.030386190861463547, -0.020017379894852638, 0.01591031439602375, -0.0271867997944355, -0.02202112041413784, 0.013279878534376621, 0.009450833313167095, -0.02234332635998726, 0.03049827367067337, 0.01636524125933647, -0.005003688391298056, 0.02558153308928013, -0.06155410781502724, 0.003456938313320279, 0.03543538972735405, -0.044228654354810715, -0.005302716046571732, 0.08057007193565369, -0.03954019770026207, 0.05853007733821869, -0.012866518460214138, 0.06413298100233078, 0.0328138992190361, -0.0537613146007061, 0.0031264720018953085, 0.018158195540308952, 0.04819369688630104, 0.01627335138618946, 0.02738284505903721, 0.01287868432700634, 0.10163862258195877, -0.015032529830932617, -0.02781771868467331, -0.01287850271910429, 0.08417428284883499, 0.07336418330669403, 0.036982130259275436, -0.011351365596055984, -0.03605031594634056, 0.015794333070516586, -0.03368813171982765, 0.020375078544020653, -0.08618412911891937, -0.09568650275468826, 0.03156290203332901, -0.004655960015952587, 0.013709594495594501, -0.007482545915991068, 0.003542352234944701, 0.03038487210869789, 0.00029295028070919216, 0.015358115546405315, -0.0041373553685843945, -0.021529335528612137, 0.03181105852127075, -0.045339036732912064, -0.03524406999349594, 0.01577899418771267, -0.004103449173271656, 0.031006185337901115, 0.01911812275648117, 0.0006902912282384932, 0.005033070687204599, -0.014255947433412075, -0.019656021147966385, 0.047968268394470215, 0.003503028769046068, 0.03923084959387779, 0.09872972220182419, -0.01823609136044979, 0.0008813791791908443, -0.016707424074411392, 0.006819333881139755, 0.001930045080371201, -0.017011333256959915, 0.041240524500608444, -0.026243645697832108, 0.03728947043418884, 0.02095918543636799, 0.019197551533579826, -0.012713403441011906, -0.008905354887247086, 0.06394670903682709, 0.027655787765979767, 0.026896359398961067, -0.046175483614206314, 0.026189662516117096, 0.03903116658329964, 0.0020721894688904285, -0.035915225744247437, -0.04309747740626335, 0.03781082108616829, -0.07318044453859329, -0.00916853453963995, 0.0034113996662199497, 0.00304667791351676, -0.021716002374887466, -0.009547858498990536, -0.05395513400435448, 0.009758122265338898, -0.05722520872950554, 0.05155319720506668, -0.046112820506095886, -0.01060204766690731, 0.039011381566524506, -0.016758328303694725, -0.03680183365941048, -0.01486209686845541, 0.037683092057704926, 0.04066278785467148, -0.02353738620877266, -0.003261963138356805, 0.06927070766687393, 0.007263743784278631, -0.04810313135385513, -0.005503172520548105, 0.023577312007546425, 0.004213477484881878, 0.01718737743794918, -0.016809634864330292, 0.03601636365056038, 0.023581653833389282, -0.06459968537092209, -0.027167629450559616, 0.027335749939084053, -0.056182585656642914, -0.09242960810661316, -0.009075012989342213, 0.03302367404103279, 0.03423858806490898, -0.007039796095341444, 0.026062652468681335, 0.03655454143881798, -0.02072705514729023, -0.009034531190991402, -0.008535974659025669, 0.01229687687009573, -0.030640505254268646, 0.03761523589491844, -0.015202132984995842, 0.029653454199433327, 0.023218052461743355, -0.023661525920033455, 0.028802264481782913, 0.04037654772400856, -0.001847055391408503, 0.0009009719942696393, -0.007667291443794966, -0.008467189967632294, -0.0045711505226790905, -0.02003832347691059, 0.054943520575761795, -0.03396804630756378, -0.013425192795693874, -0.023787567391991615, 0.015213718637824059, -0.008216137997806072, 0.03922020643949509, 0.011021985672414303, -0.018608490005135536, -0.004939861595630646, -0.0127556836232543, 0.032150235027074814, 0.00042769720312207937, -0.01762295700609684, -0.04499364644289017, -0.013058921322226524, -0.012296972796320915, -0.028822820633649826, 0.0675688162446022, 0.020991133525967598, 0.012047523632645607, -0.037217702716588974, 0.02241039089858532, -0.06432157754898071, -0.01094098575413227, 0.03572183847427368, -0.025351272895932198, 0.028113216161727905, -0.013724775053560734, 0.010325605049729347, -0.005255136173218489, 0.013487055897712708, -0.02226591482758522, 0.027827901765704155, 0.003358597634360194, -0.03146569803357124, -0.03847205638885498, -0.013184189796447754, -0.06635797768831253, -0.04771100729703903, -0.002116797724738717, 0.01142101176083088, -0.013663358055055141, 0.008503924123942852, -0.04570583999156952, -0.01317130122333765, -0.05014898255467415, 0.057962220162153244, 0.013426926918327808, -0.019138477742671967, 0.03192918375134468, 0.07139261066913605, -0.05123719945549965, -0.0533449687063694, 0.012651906348764896, 0.0004654946969822049, -0.01272166520357132, 0.03625427186489105, -0.025890180841088295, 0.021589159965515137, -0.0849243551492691, -0.047158293426036835, 0.08788608759641647, 0.007842719554901123, -0.07523692399263382, -0.029549675062298775, -0.032240383327007294, -0.01877584122121334, -0.007739074528217316, -0.012518306262791157, -0.06445514410734177, -0.019543670117855072, 0.04057750850915909, -0.022480390965938568, 0.0036271808203309774, -0.04510517045855522, 0.05463634803891182, -0.028223708271980286, -0.038148652762174606, 0.019158311188220978, -0.029535509645938873, 0.014045107178390026, 0.0076738689094781876 ]
<p>I can't find any numbers about table tennis. What accelerations occur during a forehand smash for example?</p> <p>Thanks in advance &amp; kind regards, Hans</p>
g5440
[ 0.0483710877597332, 0.0937529057264328, 0.0046455143019557, 0.052155133336782455, -0.00734303891658783, 0.019031787291169167, 0.07231790572404861, 0.02650262415409088, -0.0485670268535614, -0.029437169432640076, -0.0736626461148262, 0.0019632342737168074, 0.04861092567443848, 0.02368956431746483, 0.02636846899986267, -0.0009551865514367819, -0.04410590976476669, -0.023427005857229233, -0.02604806423187256, 0.05810684338212013, 0.002660587662830949, -0.04183066636323929, -0.05128061771392822, -0.05074240639805794, -0.010393274948000908, 0.07095750421285629, -0.06476937979459763, -0.0010475821327418089, -0.05431494861841202, -0.046341635286808014, 0.008947989903390408, 0.015196084976196289, 0.02375483699142933, -0.04441912844777107, -0.03609807789325714, 0.013300465419888496, 0.010439671576023102, -0.060150396078825, -0.04700124263763428, -0.03834991902112961, -0.04196055606007576, -0.047555387020111084, 0.010918761603534222, -0.0006986204534769058, -0.007499042898416519, 0.04339886084198952, -0.0019085091771557927, 0.017102763056755066, -0.005197108257561922, 0.021573010832071304, 0.010817552916705608, -0.029395364224910736, -0.0011419291840866208, 0.03859136998653412, -0.04910910874605179, 0.0327792726457119, 0.0339178629219532, 0.007933609187602997, 0.11071920394897461, 0.0815480649471283, -0.043994005769491196, -0.008739456534385681, 0.017684459686279297, -0.04389983043074608, 0.06985100358724594, 0.023045483976602554, 0.04879587143659592, -0.010464365594089031, 0.025609470903873444, -0.05447294935584068, 0.008285892195999622, -0.010012215003371239, 0.0014310848200693727, 0.011042498983442783, -0.05017291381955147, -0.003620455041527748, -0.02539188042283058, -0.019525956362485886, -0.05054227262735367, 0.043038178235292435, 0.025857027620077133, 0.03390747681260109, 0.029775366187095642, -0.08568453788757324, 0.03173395246267319, 0.0019728972110897303, -0.031787510961294174, 0.055841002613306046, -0.04588063061237335, 0.005323088727891445, 0.07155725359916687, 0.056148186326026917, 0.04715590924024582, -0.004496119450777769, -0.062184903770685196, -0.04250110685825348, -0.01221912819892168, 0.07698258757591248, -0.04239900782704353, -0.027046816423535347, -0.028373131528496742, 0.009802340529859066, 0.04337267950177193, -0.047427743673324585, 0.008552736602723598, 0.04286124184727669, 0.0002822321548592299, -0.05982343107461929, 0.03745802864432335, -0.001157961436547339, 0.05465741455554962, -0.01638041064143181, -0.01141267642378807, 0.03338710591197014, -0.0035649167839437723, -0.06304451823234558, 0.05765928700566292, 0.017313115298748016, -0.05864241346716881, 0.004406284540891647, 0.018462765961885452, 0.02336139976978302, -0.03275195509195328, 0.019608160480856895, 0.02120341919362545, 0.03192609176039696, -0.0026541000697761774, -0.02760944701731205, -0.052723050117492676, 0.009262919425964355, -0.007011855021119118, -0.017880139872431755, 0.01732398197054863, 0.02566772885620594, 0.049116719514131546, 0.013400389812886715, -0.0027866570744663477, 0.0488133430480957, 0.014288914389908314, 0.012438136152923107, 0.024326123297214508, -0.04873262718319893, -0.016597405076026917, -0.07881239056587219, 0.03626570478081703, -0.0026229913346469402, 0.06521377712488174, -0.0047536613419651985, -0.0017503915587440133, 0.04237334802746773, 0.06864011287689209, 0.00650222972035408, 0.027959691360592842, -0.014034911058843136, 0.029737170785665512, 0.013973912224173546, -0.016579678282141685, -0.0012440099380910397, 0.0012335667852312326, 0.040541838854551315, 0.029557175934314728, -0.038409557193517685, 0.0237214807420969, 0.04284651204943657, -0.028081804513931274, 0.0019392131362110376, -0.016628418117761612, -0.023398244753479958, -0.001028991537168622, 0.0005622606840915978, -0.08632759749889374, -0.07458294183015823, 0.053665995597839355, 0.005378132686018944, -0.046326518058776855, 0.02494843862950802, -0.018934428691864014, -0.0004967059940099716, 0.02011955715715885, 0.011358396150171757, -0.023039963096380234, -0.022674210369586945, 0.013202601112425327, -0.006882946938276291, 0.030060194432735443, -0.052887335419654846, -0.0007528135320171714, 0.04043792188167572, -0.02580711804330349, 0.03382018208503723, 0.014235853217542171, -0.06274546682834625, 0.011332336813211441, -0.0174893569201231, 0.010877914726734161, 0.0324469618499279, 0.043874189257621765, 0.024105578660964966, -0.06005328521132469, 0.0015617242315784097, -0.010546988807618618, 0.04110344126820564, 0.003058268455788493, -0.02221071720123291, 0.006947504356503487, 0.0491124764084816, 0.0031317914836108685, 0.015958011150360107, -0.04304245859384537, 0.009167851880192757, 0.00882464088499546, 0.02991236373782158, 0.04376029968261719, 0.0666816458106041, -0.008873560465872288, 0.02688496746122837, -0.024981331080198288, -0.017405172809958458, 0.043939653784036636, 0.0066675604321062565, 0.024529140442609787, -0.04302632063627243, -0.02724829502403736, 0.009638962335884571, -0.046270668506622314, 0.0029955666977912188, 0.02727607823908329, 0.03817526996135712, -0.015046820044517517, 0.018675606697797775, -0.019185934215784073, 0.038782138377428055, -0.04037795960903168, -0.05495763570070267, -0.03331191837787628, -0.02629132941365242, 0.006743573118001223, 0.017431655898690224, 0.044444773346185684, 0.0010237059323117137, 0.035793736577034, -0.03826533630490303, -0.03192080184817314, 0.04337673261761665, 0.003934705164283514, -0.03353770822286606, 0.0721583142876625, -0.019218822941184044, 0.00039302866207435727, -0.02137834019958973, -0.018224608153104782, -0.020318740978837013, 0.048612676560878754, 0.06186559051275253, -0.03572425618767738, 0.00811205618083477, -0.029460666701197624, 0.04374990612268448, -0.007970823906362057, -0.0015486369375139475, -0.01672484166920185, 0.05409368872642517, 0.020473595708608627, -0.007180258631706238, 0.0083173718303442, -0.04448837414383888, 0.014301121234893799, -0.011774918995797634, -0.04044773429632187, 0.013254770077764988, -0.04841085895895958, -0.009123406372964382, 0.003980182111263275, 0.058409225195646286, 0.028816504403948784, -0.028184155002236366, 0.014070258475840092, -0.0512034110724926, -0.026781797409057617, -0.019077645614743233, -0.03406994789838791, -0.016065973788499832, 0.00755653902888298, 0.016574474051594734, 0.009417691268026829, 0.02844993770122528, 0.01699363812804222, -0.05078199505805969, -0.0873100608587265, 0.013943500816822052, -0.04826688766479492, -0.044181425124406815, 0.0210853461176157, 0.01768825389444828, 0.0074934689328074455, 0.03962502256035805, 0.025981945917010307, -0.006692179013043642, 0.026205405592918396, -0.01111816056072712, -0.014386430382728577, -0.02947358600795269, -0.04763923957943916, 0.002500487258657813, -0.02346232533454895, 0.02017415128648281, 0.01738925278186798, -0.03184007108211517, 0.0031813308596611023, -0.027974838390946388, -0.01484474167227745, 0.025789139792323112, -0.014516167342662811, 0.06114460527896881, -0.07706880569458008, -0.01820049248635769, 0.05057332664728165, 0.06405912339687347, 0.03532795235514641, 0.017755942419171333, -0.01896997168660164, -0.12791289389133453, 0.022304434329271317, 0.022733796387910843, -0.009985304437577724, -0.03027459979057312, 0.00959869846701622, 0.004086053930222988, 0.0062616425566375256, -0.08608954399824142, 0.038015104830265045, -0.02141423523426056, 0.003863335121423006, -0.015855656936764717, -0.04236661270260811, 0.012648271396756172, -0.0023728013038635254, 0.07172555476427078, 0.054550886154174805, 0.04014802724123001, 0.03144316375255585, 0.03864208236336708, -0.007868701592087746, -0.04229746758937836, 0.014353997074067593, -0.03024040348827839, 0.042452894151210785, -0.028007809072732925, 0.059940844774246216, 0.010031639598309994, 0.03672328591346741, -0.04924258217215538, -0.0508275143802166, 0.016292279586195946, 0.033426590263843536, 0.029530279338359833, -0.008114256896078587, -0.01812908612191677, -0.0273726899176836, -0.03398608788847923, 0.01232646219432354, 0.024311410263180733, 0.0005662326002493501, -0.00434538209810853, -0.0426095686852932, 0.011056134477257729, -0.04627729579806328, 0.04866086691617966, -0.053322408348321915, 0.003202287945896387, -0.032379016280174255, -0.00715991435572505, 0.045473869889974594, -0.09013885259628296, -0.011305556632578373, -0.01948217861354351, -0.005842705722898245, 0.03892594575881958, 0.02393590845167637, 0.03280802443623543, 0.05164070054888725, 0.07805727422237396, -0.010766389779746532, 0.006253780797123909, -0.04246964678168297, 0.008968742564320564, -0.003508093301206827, 0.028878800570964813, -0.004561171866953373, -0.06289692968130112, 0.08661855012178421, -0.06003957986831665, -0.049593571573495865, 0.005192135460674763, 0.021997278556227684, -0.016902660951018333, -0.02775053307414055, 0.03982219845056534, -0.0008804094395600259, 0.07618260383605957, -0.007378638722002506, 0.02311151660978794, 0.025607848539948463, 0.002817448228597641, -0.015033179894089699, 0.084951251745224, 0.014800370670855045, 0.056047361344099045, 0.004918213933706284, 0.0015930978115648031, 0.001667924108915031, 0.016809459775686264, -0.03088703192770481, -0.09682942181825638, -0.024252718314528465, 0.008087104186415672, 0.02424238994717598, -0.007686133962124586, -0.0351681187748909, 0.008052455261349678, 0.06385181844234467, 0.021943578496575356, 0.020650548860430717, -0.02337607368826866, -0.02239212580025196, 0.004830065183341503, 0.03683995455503464, 0.008721566759049892, 0.0005486875306814909, 0.040286894887685776, 0.005426444578915834, 0.04304809123277664, 0.017020292580127716, 0.031183769926428795, -0.002349861664697528, 0.05201679468154907, 0.03248884901404381, 0.05829065665602684, 0.03356451913714409, -0.026339447125792503, 0.013110371306538582, 0.034149859100580215, 0.0031049984972923994, 0.015388251282274723, 0.0017633243696764112, 0.083282969892025, -0.01009720005095005, -0.05945657566189766, 0.010472503490746021, -0.011042963713407516, 0.04868457838892937, 0.034584417939186096, -0.04285692423582077, -0.012644012458622456, 0.014420323073863983, 0.004840833600610495, -0.02726537361741066, -0.020331017673015594, -0.025446031242609024, -0.036299433559179306, -0.02825193665921688, -0.00029513906338252127, -0.0475703701376915, -0.07263412326574326, -0.021471984684467316, 0.007225342094898224, -0.050337888300418854, -0.005664805416017771, -0.045203566551208496, 0.005322267767041922, 0.03844720125198364, -0.05796629190444946, -0.017459042370319366, -0.016544682905077934, 0.021129274740815163, 0.0024665272794663906, -0.04836937040090561, 0.01525658555328846, 0.02853086218237877, -0.006317885126918554, -0.012483146041631699, 0.03257089853286743, -0.07415535300970078, -0.07692667096853256, -0.041789859533309937, 0.0032042081002146006, -0.016321728006005287, -0.013363891281187534, 0.03575296700000763, 0.032693058252334595, 0.00854870118200779, 0.038749419152736664, -0.05590013787150383, 0.01730189099907875, -0.03262244910001755, 0.015805475413799286, -0.011200688779354095, -0.03561440110206604, 0.00852151308208704, -0.006385468877851963, -0.07720915228128433, -0.04489840194582939, 0.028599416837096214, -0.006535504013299942, 0.03890188783407211, 0.023624537512660027, 0.00707018980756402, -0.04774105176329613, 0.022463016211986542, 0.003077390370890498, 0.019775621592998505, 0.03150707855820656, 0.015082390047609806, -0.01389291137456894, -0.037608955055475235, 0.023850183933973312, 0.03625442460179329, -0.04429245367646217, -0.010639643296599388, -0.03357188403606415, 0.017743660137057304, -0.0043913195841014385, -0.03675909340381622, 0.01810111291706562, -0.024490701034665108, 0.031712278723716736, -0.02275685779750347, -0.017768098041415215, -0.015793954953551292, -0.03988860920071602, -0.025113549083471298, -0.05651045963168144, 0.0270224642008543, -0.021214503794908524, -0.04549434781074524, -0.05098565295338631, 0.03348536044359207, -0.046816036105155945, 0.011175615713000298, -0.009061268530786037, -0.13048744201660156, 0.06901437044143677, -0.02906070649623871, 0.015509647317230701, -0.038576558232307434, 0.023697588592767715, -0.004449381493031979, 0.022279053926467896, -0.013807309791445732, -0.01657198742032051, 0.02703789249062538, 0.014468695968389511, 0.0723237469792366, -0.020964568480849266, -0.04466714337468147, 0.03995983675122261, -0.001238394295796752, 0.0068762884475290775, -0.00996787752956152, -0.06501114368438721, 0.023757267743349075, 0.07224885374307632, 0.01865437626838684, 0.006808392703533173, 0.004302594810724258, -0.04015200957655907, -0.03191028907895088, -0.011289538815617561, 0.05586310848593712, -0.01637592539191246, -0.00919430237263441, -0.011911127716302872, 0.0365704707801342, 0.02169858105480671, 0.010976963676512241, -0.04670463502407074, 0.00031267371377907693, -0.003750923089683056, -0.040645990520715714, -0.04133494943380356, 0.027438053861260414, 0.022296838462352753, 0.02677498385310173, 0.005248833913356066, 0.0013823320623487234, 0.04991268366575241, 0.02389059215784073, 0.010841294191777706, -0.0016343824099749327, -0.02028624713420868, -0.018909482285380363, 0.044857125729322433, -0.023773904889822006, -0.02007920853793621, 0.004560958128422499, -0.062385305762290955, -0.020718080922961235, 0.09527881443500519, -0.009358675219118595, -0.005193368997424841, -0.0013782744063064456, 0.04754505679011345, 0.018903963267803192, -0.05062129721045494, 0.00040062295738607645, 0.006728188134729862, 0.010756388306617737, -0.02881458029150963, -0.015182236209511757, 0.0015827862080186605, -0.024502316489815712, 0.01356692798435688, -0.03185615316033363, 0.04015686735510826, -0.06371539831161499, -0.05435148626565933, 0.02751612849533558, -0.04457376152276993, 0.021219663321971893, -0.027931658551096916, 0.06227640062570572, -0.04236503690481186, -0.0043351794593036175, 0.016113875433802605, 0.004345006309449673, -0.019239643588662148, -0.043560683727264404, 0.05562844127416611, 0.004022220615297556, -0.06163835898041725, 0.0665581151843071, -0.01624661311507225, 0.010872140526771545, 0.07804033905267715, 0.007529506925493479, 0.020129475742578506, 0.010858774185180664, 0.014593805186450481, 0.0006701148813590407, 0.05289185792207718, 0.01727082021534443, 0.03183402493596077, 0.010913868434727192, -0.05764753371477127, -0.001259923679754138, 0.024229496717453003, -0.018535668030381203, -0.034720610827207565, -0.005919135175645351, -0.05224510282278061, -0.053129564970731735, -0.03671181946992874, -0.0484079048037529, 0.007404082454741001, 0.015266060829162598, 0.03764298930764198, 0.016491133719682693, 0.0025546594988554716, 0.0188624057918787, -0.06728486716747284, 0.008748529478907585, 0.0011414771433919668, -0.012246276251971722, -0.04933522641658783, 0.003508748486638069, -0.006046278402209282, 0.026460735127329826, 0.006281448062509298, 0.01786681078374386, 0.03708060458302498, 0.0287440475076437, 0.022583132609725, -0.06536410748958588, -0.0003620399802457541, 0.011449682526290417, 0.03320041298866272, 0.0030780374072492123, -0.008244435302913189, -0.03341987729072571, -0.026104489341378212, -0.027919882908463478, 0.038443125784397125, 0.04080922529101372, 0.03597625344991684, 0.0064726113341748714, 0.056615766137838364, 0.015039818361401558, -0.004124091472476721, 0.02205011434853077, -0.00014826346887275577, -0.00302814319729805, -0.004634521901607513, 0.03505246341228485, -0.0035252950619906187, 0.024828670546412468, -0.04575764015316963, -0.030969610437750816, 0.01860758475959301, -0.08684083819389343, 0.049977950751781464, 0.05379090830683708, 0.01048664003610611, -0.018328286707401276, 0.058016616851091385, -0.04429563879966736, 0.044399768114089966, -0.049820028245449066, -0.06531907618045807, 0.012466386891901493, 0.011651018634438515, 0.0001344892953056842, 0.031044114381074905, 0.01172829233109951, -0.00014315074076876044, 0.027233906090259552, 0.07088373601436615, -0.04242963716387749, -0.04993479326367378, 0.023243047297000885, 0.003529967274516821, -0.025930970907211304, 0.0077431402169167995, 0.06051883473992348, -0.0035323973279446363, -0.029529625549912453, -0.056771691888570786, -0.03975322097539902, 0.03444553539156914, -0.025415480136871338, 0.0836283415555954, -0.02310393936932087, -0.09146270900964737, -0.01147023867815733, 0.07409565150737762, -0.07043065130710602, 0.004857847932726145, -0.013299981132149696, 0.023607349023222923, -0.02241799794137478, -0.03715131804347038, -0.0005517569370567799, 0.036085352301597595, 0.018036123365163803, 0.06151527911424637, -0.006535389926284552, 0.005837263073772192, 0.012755035422742367, -0.047154247760772705, 0.04627831652760506, 0.012629910372197628, 0.09409324079751968, -0.027938157320022583, 0.0254498403519392, 0.056375183165073395, -0.04742281511425972, -0.009264280088245869, 0.0037693032063543797, -0.018862919881939888, -0.059644173830747604, -0.005988172255456448, -0.023233775049448013, 0.01313044410198927, 0.04078971967101097, 0.024939320981502533, -0.04093587398529053, -0.04003819078207016, -0.05262615531682968, -0.02189883217215538 ]
<p><img src="http://i.stack.imgur.com/Vl3a6.jpg" alt="Picture of gravity"></p> <p>We assume that the earth planet is a black hole. When a light beam is fired. The only way that even light can move is A and B which means this is impossible that light move on other ways C, D, E</p> <p>Isn't it true?</p>
g5441
[ 0.00202179909683764, 0.060027606785297394, 0.006708511151373386, 0.031541481614112854, 0.09188004583120346, 0.060706522315740585, 0.02926008775830269, 0.0049549429677426815, -0.019616344943642616, -0.07274793088436127, 0.021776990965008736, -0.006850695237517357, 0.017664670944213867, -0.026061860844492912, -0.02365778759121895, -0.01578775979578495, 0.049773238599300385, -0.031160522252321243, 0.053074534982442856, 0.013489717617630959, 0.041971202939748764, 0.005811770912259817, 0.031073814257979393, -0.06491509824991226, -0.008575966581702232, -0.03237174451351166, -0.0049507394433021545, -0.011640177108347416, -0.024139652028679848, -0.04419100657105446, 0.011300429701805115, -0.006424242164939642, 0.001447958522476256, -0.05003774166107178, -0.010514827445149422, -0.08013643324375153, 0.017994945868849754, 0.038339775055646896, 0.019191863015294075, -0.01114675309509039, -0.017453588545322418, 0.008134989999234676, -0.027609046548604965, 0.023824423551559448, 0.0640716478228569, -0.03995022177696228, 0.044546257704496384, 0.0007026937091723084, 0.019764894619584084, 0.01837811805307865, -0.017741261050105095, 0.017146166414022446, 0.040745146572589874, -0.05906868726015091, 0.037578508257865906, 0.048902589827775955, -0.03670411556959152, -0.008243066258728504, 0.04278077185153961, 0.050486017018556595, -0.033992551267147064, -0.060706544667482376, 0.055520541965961456, 0.022784771397709846, 0.007741844281554222, -0.03190147876739502, -0.07647769898176193, -0.018542923033237457, 0.0042962743900716305, -0.055487580597400665, 0.04484734311699867, -0.02401614934206009, -0.03228261321783066, -0.003974820487201214, -0.015821384266018867, 0.04482755437493324, -0.03251679241657257, 0.004672009963542223, -0.029104910790920258, 0.023763485252857208, -0.03536802902817726, -0.048295747488737106, -0.0074182311072945595, -0.026323430240154266, 0.08243633061647415, -0.029171956703066826, 0.0019445829093456268, -0.017060816287994385, -0.00896511971950531, 0.0010597293730825186, 0.05324632674455643, -0.004779718350619078, 0.07410873472690582, 0.09077838808298111, -0.03882075473666191, -0.004432880785316229, -0.031465478241443634, 0.060873132199048996, 0.0008125499589368701, -0.006770242005586624, -0.07731079310178757, 0.008567730896174908, -0.03900187090039253, 0.02890137955546379, 0.07943317294120789, -0.06924665719270706, 0.021321430802345276, -0.013718867674469948, -0.0052131181582808495, -0.014147019945085049, 0.009221640415489674, -0.0664466843008995, 0.003687563817948103, -0.057215120643377304, -0.04112735018134117, -0.007408980280160904, 0.07518155127763748, -0.03491995483636856, 0.045458320528268814, 0.03177183121442795, 0.02599043771624565, 0.025441575795412064, 0.014978115446865559, 0.04693093150854111, 0.005854518618434668, -0.037291109561920166, 0.0031023777555674314, -0.06827842444181442, 0.035644493997097015, -0.01924004778265953, -0.01499095931649208, 0.0288490429520607, -0.033622320741415024, 0.05976090580224991, 0.004263025708496571, 0.006296847015619278, 0.020730793476104736, 0.0010037953034043312, -0.048674650490283966, 0.013454371131956577, 0.010723228566348553, -0.01418150682002306, 0.034012649208307266, 0.016140161082148552, -0.03424676135182381, 0.058446548879146576, -0.016097940504550934, -0.0038034177850931883, 0.06282539665699005, 0.034819312393665314, -0.004427205305546522, 0.1464628130197525, 0.007759984582662582, 0.020043764263391495, 0.01903424970805645, -0.0074517372995615005, 0.10445879399776459, 0.046131595969200134, -0.05372719466686249, 0.0215600598603487, 0.03953224793076515, 0.015148762613534927, -0.015483762137591839, -0.0024853129871189594, -0.009915969334542751, 0.0019200260285288095, -0.02098608948290348, -0.03521266579627991, 0.03563391789793968, 0.004098041448742151, -0.05520956963300705, -0.02059587463736534, 0.024537676945328712, 0.02424166165292263, 0.05159766972064972, 0.035520173609256744, -0.012314925901591778, 0.0001747774367686361, -0.04588528349995613, -0.03604322671890259, 0.025235353037714958, 0.018816646188497543, -0.032295435667037964, -0.015786195173859596, -0.0008572209626436234, -0.03876029700040817, -0.031475480645895004, -0.009766784496605396, 0.027174124494194984, -0.008437473326921463, -0.05337437614798546, -0.01717936433851719, 0.04688827320933342, 0.012682342901825905, 0.01779780723154545, -0.04114418476819992, -0.03686556965112686, 0.007897290401160717, 0.03223442658782005, 0.0720188245177269, 0.023314721882343292, 0.022131511941552162, 0.021010760217905045, -0.009409978985786438, 0.014258740469813347, 0.004343252629041672, -0.032267116010189056, 0.03798850625753403, 0.008731884881854057, -0.0020027505233883858, 0.05394544452428818, -0.029545797035098076, 0.027201294898986816, 0.06500379741191864, -0.012003276497125626, 0.005993288476020098, -0.08801285177469254, 0.010522075928747654, -0.0013296038378030062, -0.005859325639903545, -0.07578843832015991, -0.01061172317713499, -0.013368183746933937, -0.014394901692867279, 0.006724693346768618, 0.024997752159833908, -0.08973520994186401, -0.021092897281050682, 0.03428347036242485, 0.017258042469620705, -0.0644119381904602, -0.020291713997721672, 0.00326337106525898, 0.005886062979698181, 0.05001047998666763, 0.02891005575656891, -0.020187729969620705, -0.01355931255966425, -0.02536509931087494, 0.05608167126774788, 0.0015811994671821594, -0.05233188718557358, -0.013132037594914436, -0.040045227855443954, 0.044970426708459854, -0.009677913039922714, 0.0038559166714549065, 0.051967862993478775, -0.027397630736231804, 0.051363054662942886, 0.048814333975315094, -0.05042191967368126, -0.026017477735877037, 0.0022030924446880817, 0.01417512260377407, -0.02122015319764614, 0.00027564397896640003, 0.04153221473097801, -0.05996788665652275, -0.02810148149728775, 0.004875498358160257, -0.016162602230906487, 0.044221460819244385, 0.026350047439336777, -0.03388040512800217, -0.011264895088970661, -0.05504291504621506, -0.03338184952735901, 0.004234242718666792, 0.023470692336559296, -0.06623943895101547, -0.007372495252639055, 0.04316196218132973, 0.008680209517478943, -0.02201571874320507, 0.03870377317070961, -0.005194426979869604, 0.020396150648593903, 0.03726976737380028, -0.009058449417352676, -0.020152589306235313, 0.02743394486606121, -0.05174918472766876, -0.048949021846055984, 0.07269880920648575, -0.02853565849363804, -0.031193505972623825, -0.015056603588163853, -0.011898983269929886, -0.04389486461877823, -0.008312583900988102, 0.01900203712284565, 0.03959362581372261, 0.03939537703990936, -0.03150157257914543, 0.010478244163095951, 0.007678705267608166, -0.03238668292760849, -0.03107829950749874, 0.055058788508176804, 0.003516047028824687, -0.013583340682089329, -0.031333986669778824, 0.010445197112858295, 0.018465593457221985, -0.009267223067581654, -0.01905972696840763, -0.05332234129309654, 0.03273078799247742, 0.03966232389211655, 0.024051303043961525, 0.05338190123438835, -0.04782750457525253, 0.07135999947786331, 0.010403943248093128, -0.0029962295666337013, -0.008216651156544685, 0.012149144895374775, 0.08371449261903763, 0.009223466739058495, -0.007956739515066147, -0.011598384007811546, -0.07327695935964584, -0.006061824969947338, 0.0334797203540802, 0.041098613291978836, -0.00026558077661320567, -0.021559609100222588, -0.0382600799202919, 0.0062689525075256824, -0.014485713094472885, 0.0370914563536644, -0.04522135481238365, 0.01202378049492836, 0.005711596459150314, 0.005703733768314123, 0.0005433637415990233, 0.02176603674888611, 0.07114841043949127, 0.056013643741607666, -0.007334920112043619, -0.04827387258410454, -0.04562654346227646, 0.06571652740240097, 0.004757705610245466, 0.030498821288347244, -0.0006097668083384633, -0.04634849727153778, -0.029209360480308533, -0.0024991047102957964, 0.034591931849718094, -0.047726619988679886, 0.0436401292681694, 0.02380210906267166, -0.008184839971363544, 0.06054166704416275, 0.047431427985429764, -0.012640861794352531, 0.036596376448869705, -0.00920995231717825, -0.030542682856321335, 0.009362069889903069, 0.03500647842884064, -0.003917290363460779, 0.02250458300113678, 0.0010937389452010393, -0.004258490167558193, -0.01108918059617281, 0.0032645699102431536, 0.013978070579469204, 0.04167577996850014, -0.025667523965239525, 0.03293567895889282, 0.03593364730477333, 0.0845346674323082, -0.06176373362541199, 0.03821922093629837, -0.031379420310258865, 0.004581839311867952, 0.014208628796041012, 0.03437700867652893, 0.023968789726495743, 0.04711462929844856, 0.010143396444618702, -0.012578126974403858, 0.014405656605958939, -0.008111829869449139, -0.06050843372941017, -0.020001130178570747, 0.0009139972389675677, 0.02528993785381317, -0.0187641941010952, -0.03204963356256485, -0.05976254492998123, 0.010954487137496471, 0.026097768917679787, 0.01494821347296238, 0.030139535665512085, -0.03081596828997135, -0.05308932065963745, 0.052093636244535446, 0.043687622994184494, 0.04178465157747269, -0.0564374104142189, -0.033969126641750336, -0.005953756161034107, -0.0011981271672993898, 0.005845621228218079, 0.0036322083324193954, -0.0023007190320640802, 0.04804716259241104, 0.011489774100482464, -0.04240608960390091, 0.028142957016825676, 0.04722656309604645, -0.01547528337687254, -0.024961484596133232, 0.022648748010396957, -0.021412396803498268, 0.0014663641341030598, 0.0270399060100317, 0.023729214444756508, 0.03950876370072365, -0.013239261694252491, 0.0629156306385994, 0.07399912923574448, 0.01547517254948616, 0.01692121848464012, -0.011292841285467148, 0.004468841478228569, -0.022128043696284294, -0.007572977803647518, -0.003934884909540415, 0.014700698666274548, -0.034102197736501694, 0.08726754039525986, 0.01609956845641136, 0.04041937366127968, 0.046216826885938644, 0.04640805721282959, 0.0658240094780922, 0.009561973623931408, 0.016355453059077263, 0.0012209139531478286, -0.026863619685173035, 0.08576660603284836, 0.01103788148611784, -0.032749976962804794, 0.025502152740955353, -0.0051654609851539135, 0.028540967032313347, -0.03627312183380127, -0.039240241050720215, -0.018898604437708855, -0.03059636987745762, -0.016014568507671356, -0.006320951506495476, 0.06634741276502609, -0.028623558580875397, 0.051619093865156174, -0.054800622165203094, -0.03575904294848442, 0.06723245978355408, 0.018636805936694145, 0.030677692964673042, -0.02563171274960041, -0.06693544238805771, -0.026279227808117867, -0.06210947036743164, -0.018873242661356926, -0.046672187745571136, 0.02993006445467472, -0.010798292234539986, 0.05847488343715668, -0.07212065905332565, 0.02200501039624214, -0.008680526167154312, 0.010227366350591183, -0.0061393254436552525, -0.02424122765660286, -0.045662131160497665, -0.08322396874427795, 0.008134107105433941, 0.0204346664249897, -0.0033747688867151737, -0.0071432520635426044, -0.019906960427761078, 0.035466406494379044, 0.0006916204001754522, 0.015080725774168968, -0.001353599363937974, 0.007477918639779091, -0.04971932992339134, -0.07027138769626617, -0.059141986072063446, 0.0001348244259133935, -0.04169851541519165, -0.0048482222482562065, 0.004789452068507671, 0.020770812407135963, -0.08277668803930283, -0.018683956936001778, 0.0007214324432425201, -0.04265522584319115, 0.01512797549366951, 0.023190978914499283, -0.010975316166877747, 0.02398833818733692, -0.04007422551512718, 0.033101290464401245, 0.018787965178489685, 0.0006106877117417753, -0.06430994719266891, 0.06204560026526451, 0.06099178269505501, -0.0893331989645958, 0.0009822602150961757, 0.021475011482834816, 0.003707083873450756, -0.05275745317339897, -0.004727690946310759, -0.021464204415678978, 0.005021236836910248, -0.0028225125279277563, 0.060870569199323654, 0.00809693057090044, -0.04752489924430847, -0.011786791495978832, 0.022163402289152145, 0.06565863639116287, 0.031725503504276276, -0.0015724946279078722, 0.021808069199323654, -0.0377868227660656, -0.0007775886915624142, -0.020599648356437683, 0.05023828521370888, -0.006067541427910328, 0.04183454439043999, -0.06134740263223648, 0.014355096034705639, -0.026440629735589027, -0.010087981820106506, 0.03010634332895279, 0.023244723677635193, 0.028292857110500336, -0.041015371680259705, -0.018739601597189903, 0.007377368863672018, -0.07524053752422333, -0.042000800371170044, 0.04009919986128807, -0.058800339698791504, 0.034755539149045944, 0.010080595500767231, 0.022536925971508026, -0.03847555071115494, -0.026454146951436996, -0.0460481159389019, -0.07317841053009033, 0.03126683458685875, 0.0420607328414917, 0.021542513743042946, -0.04716309905052185, 0.007091484032571316, -0.04038465395569801, 0.016538215801119804, -0.004916474223136902, 0.02085399255156517, 0.0314764529466629, -0.04545919597148895, -0.0046513816341757774, -0.03283469006419182, 0.05180297791957855, -0.005257680546492338, -0.042213719338178635, -0.0019156745402142406, 0.000006684740128548583, -0.04452645406126976, -0.01904062181711197, 0.008888114243745804, 0.028277164325118065, 0.04365524649620056, -0.041629716753959656, -0.04845111817121506, 0.032339900732040405, -0.0016996456542983651, 0.04400995001196861, 0.005765741225332022, -0.07243400067090988, -0.014501920901238918, -0.0014069804456084967, -0.020645618438720703, -0.019168881699442863, -0.07621390372514725, -0.030602486804127693, -0.025991426780819893, 0.010924705304205418, 0.012768501415848732, -0.03359445556998253, 0.0007579079829156399, 0.07828725874423981, 0.008063693530857563, 0.02813032642006874, 0.02084931917488575, 0.04029730707406998, -0.11697757989168167, 0.007155211176723242, 0.057396139949560165, 0.05097820237278938, -0.00586668448522687, 0.02903115376830101, 0.04485437273979187, 0.004860911518335342, -0.021962741389870644, -0.03471251204609871, -0.05090818181633949, -0.011764490976929665, 0.05786185711622238, 0.037168730050325394, 0.03143111988902092, -0.04763464629650116, -0.03817497938871384, -0.058940958231687546, -0.0006390325143001974, 0.050991374999284744, -0.07384297251701355, 0.029298635199666023, 0.00869627296924591, 0.03016904555261135, 0.002528919605538249, 0.005176246166229248, -0.008565048687160015, 0.03294699639081955, 0.035799454897642136, 0.0009183539659716189, -0.02876608818769455, 0.026996802538633347, 0.0044893138110637665, -0.04530017450451851, -0.025274179875850677, -0.012215872295200825, -0.016481148079037666, 0.05625124275684357, -0.018810205161571503, 0.05325813591480255, -0.03288419544696808, -0.055472951382398605, -0.06427029520273209, 0.0064022960141301155, 0.02617896907031536, -0.06112276390194893, -0.027482682839035988, -0.021214699372649193, -0.047704458236694336, -0.019662633538246155, -0.014654249884188175, -0.003513224655762315, -0.02440609224140644, -0.08800870925188065, 0.0058828555047512054, -0.01930862106382847, -0.03829745948314667, -0.02424377202987671, 0.0062707713805139065, -0.007846858352422714, -0.022391775622963905, 0.015638455748558044, -0.024257173761725426, -0.00705721415579319, 0.035073861479759216, -0.01248299889266491, -0.027930544689297676, 0.061812691390514374, -0.0713815912604332, 0.006141892168670893, -0.010957641527056694, 0.024592241272330284, 0.02922583930194378, 0.03442039340734482, 0.06362272053956985, 0.017531994730234146, -0.03915770724415779, 0.034309424459934235, -0.014185704290866852, -0.016701888293027878, 0.0009786634473130107, 0.007317749317735434, -0.009904568083584309, -0.009669344872236252, 0.017045872285962105, 0.042043790221214294, -0.030938146635890007, -0.008955312892794609, -0.012553420849144459, 0.015738926827907562, -0.009350576438009739, -0.00721540255472064, 0.0023402227088809013, -0.0472855344414711, -0.06385110318660736, -0.02297453209757805, -0.00478987954556942, -0.04192516952753067, 0.008094175718724728, 0.026495004072785378, 0.0017653107643127441, 0.02303299680352211, -0.03801626339554787, -0.00863284058868885, 0.0504310205578804, 0.0404600091278553, -0.01415166538208723, -0.021286683157086372, 0.0045295110903680325, -0.01981569454073906, 0.057495057582855225, 0.03473621606826782, 0.01680745743215084, -0.012264739722013474, 0.006671465002000332, 0.03472490236163139, -0.05333177000284195, -0.018915824592113495, -0.0028271230403333902, 0.0026706543285399675, 0.017801083624362946, -0.01774216815829277, 0.004603447392582893, -0.08475183695554733, -0.002873125486075878, 0.038501519709825516, -0.054942552000284195, -0.04201287776231766, -0.015105179511010647, 0.05068059638142586, -0.056866273283958435, -0.046932414174079895, -0.006961528677493334, 0.03175703063607216, -0.036230575293302536, -0.031815316528081894, 0.006704128812998533, 0.0021979704033583403, 0.03933596983551979, -0.029058657586574554, -0.0028191618621349335, 0.04049859195947647, 0.029401063919067383, 0.008658472448587418, 0.010239208117127419, 0.08205606043338776, 0.017991697415709496, -0.01825074851512909, 0.01991618238389492, -0.027539100497961044, -0.05503596365451813, -0.013569113798439503, -0.012448635883629322, 0.008923301473259926, -0.029298830777406693, 0.03550698235630989, 0.03333255276083946, -0.043405890464782715, 0.0036563437897711992, -0.05815970152616501, -0.0230762530118227, 0.03009071946144104 ]
<p>Let's assume that the aircraft is 1000kg and it is flying in a air density of 1.225kg/m^3 at the speed of sound in air. </p> <p>Just how much energy does it require per second to maintain flying at this speed.(Please make other necessary assumptions.) </p> <p>Thank you.</p>
g5442
[ 0.0007062187069095671, 0.05370193347334862, 0.006475917063653469, 0.04813533276319504, 0.006934856530278921, -0.066043920814991, 0.0018030502833425999, 0.020024854689836502, -0.05265681445598602, 0.010104119777679443, -0.01898551546037197, -0.02560882829129696, -0.08314020931720734, 0.06391406804323196, 0.03927221894264221, 0.02168889157474041, 0.00028779800049960613, -0.025361740961670876, 0.0346570685505867, 0.026728840544819832, -0.030993014574050903, -0.03741888701915741, 0.007161380723118782, -0.01963556557893753, -0.032648827880620956, 0.010214835405349731, -0.029292862862348557, -0.06341124325990677, -0.08107210695743561, -0.018377281725406647, 0.026968060061335564, -0.005720254499465227, 0.0012913058744743466, -0.049627337604761124, -0.05276747792959213, -0.024270012974739075, 0.030591992661356926, 0.03986651450395584, -0.010284116491675377, 0.0008832343737594783, 0.019993988797068596, -0.0375903882086277, -0.01762910932302475, -0.04665515199303627, 0.032078154385089874, 0.062292419373989105, -0.009618932381272316, -0.025772927328944206, -0.041109684854745865, -0.03124653920531273, -0.022404745221138, 0.09008314460515976, 0.007410374004393816, 0.019024262204766273, -0.05349065363407135, -0.0267067588865757, 0.009546874091029167, -0.046005092561244965, -0.022015096619725227, 0.0004070353170391172, -0.0170016847550869, -0.009679139591753483, -0.07412447780370712, 0.024471892043948174, 0.01674616150557995, -0.047537293285131454, -0.032678283751010895, -0.08551792055368423, 0.025306301191449165, 0.028716236352920532, 0.04277986288070679, -0.03846081718802452, -0.02349981665611267, -0.03427405282855034, -0.029083874076604843, -0.053365789353847504, 0.02961019054055214, -0.05236660689115524, 0.03811044991016388, 0.006947290152311325, 0.01501823402941227, -0.037089746445417404, 0.05686430633068085, -0.01701543852686882, 0.018748046830296516, -0.013966059312224388, 0.0031512805726379156, -0.028963223099708557, -0.0017752880230545998, 0.04311046749353409, 0.044662486761808395, 0.014786199666559696, 0.04957103729248047, -0.035176895558834076, 0.031580567359924316, -0.014842560514807701, -0.029810698702931404, 0.06838421523571014, 0.004944093059748411, 0.020635882392525673, -0.020962707698345184, -0.087104432284832, -0.022185156121850014, -0.022811388596892357, -0.002513480605557561, -0.01953154243528843, 0.05065217241644859, 0.02121933363378048, 0.0001258060074178502, -0.016158265992999077, 0.052568282932043076, -0.024256132543087006, 0.004169940948486328, -0.010509699583053589, -0.04469006881117821, -0.04923802241683006, 0.011087188497185707, -0.05846722424030304, -0.016978049650788307, 0.01024921890348196, -0.013504991307854652, 0.01616009697318077, -0.013024412095546722, -0.03425511717796326, 0.010398685932159424, -0.028258882462978363, -0.0016720783896744251, 0.014788391068577766, -0.0022848567459732294, -0.0014756819000467658, -0.011064519174396992, 0.010258539579808712, 0.0010446786182001233, 0.013497802428901196, -0.013534318655729294, 0.0019165128469467163, -0.04243016242980957, 0.027129624038934708, -0.02819804847240448, -0.026499072089791298, 0.028815658763051033, 0.029155312106013298, 0.04305208474397659, 0.011145003139972687, -0.03169768303632736, 0.022455554455518723, 0.01365903951227665, 0.030481766909360886, 0.00783636886626482, 0.0015818780520930886, 0.03103575110435486, 0.010436399839818478, 0.015899188816547394, -0.11950267851352692, 0.004047820810228586, 0.038013800978660583, -0.016678694635629654, 0.04107123613357544, 0.01005048118531704, 0.06432963162660599, 0.05217233672738075, -0.01460854522883892, 0.08388253301382065, 0.0360192134976387, -0.0619160421192646, 0.028576865792274475, 0.06512260437011719, -0.01517869345843792, -0.007552941329777241, 0.02668343111872673, -0.043075159192085266, -0.014965354464948177, 0.020262189209461212, 0.07837259769439697, 0.008901162073016167, -0.021697457879781723, 0.06899156421422958, 0.00350302760489285, -0.024325910955667496, -0.024013426154851913, 0.03522167354822159, 0.031068364158272743, 0.015143672935664654, -0.07092402875423431, -0.013700905255973339, 0.01811821386218071, 0.009480546228587627, -0.00483014015480876, -0.1135188639163971, 0.016623569652438164, -0.008512286469340324, 0.02694539539515972, -0.011158361099660397, 0.011263555847108364, -0.05575587972998619, 0.02216862142086029, 0.05507582798600197, -0.03576645255088806, -0.020254462957382202, 0.010784927755594254, 0.024116497486829758, -0.03006831556558609, 0.025467190891504288, -0.0050280108116567135, 0.03185516968369484, -0.028165295720100403, -0.014815740287303925, -0.015624272637069225, 0.03619609400629997, -0.03376971185207367, 0.013167095370590687, -0.008049664087593555, 0.0038566654548048973, 0.07035121321678162, 0.07942824065685272, 0.034455396234989166, -0.02776918187737465, 0.001364890718832612, -0.004646991845220327, 0.004251181613653898, 0.012917383573949337, 0.03017919696867466, 0.07235415279865265, 0.007775802165269852, -0.060513660311698914, -0.06635377556085587, -0.02474561706185341, -0.05540694296360016, 0.013278059661388397, 0.022902317345142365, -0.0034050375688821077, 0.011939960531890392, -0.030417412519454956, -0.014316491782665253, 0.005963996052742004, 0.06321084499359131, 0.03529103472828865, 0.04080050066113472, -0.010817078873515129, 0.028120288625359535, 0.03692758083343506, 0.07780445367097855, -0.0006368344184011221, 0.036281827837228775, -0.04734502732753754, -0.008441192097961903, -0.026123611256480217, -0.020986590534448624, 0.01337479893118143, 0.04539848491549492, 0.0038443547673523426, -0.011690975166857243, -0.0011932376073673368, 0.021482225507497787, -0.028150444850325584, -0.061010126024484634, -0.0295590627938509, -0.022956181317567825, 0.015592155046761036, 0.015828536823391914, 0.0014179432764649391, -0.04811841994524002, -0.009733566083014011, -0.06714222580194473, -0.05544833093881607, -0.029975004494190216, -0.004648228641599417, -0.06243498623371124, 0.009558569639921188, -0.022327955812215805, 0.00208075949922204, -0.019403126090765, -0.031016752123832703, -0.005568791646510363, 0.036552794277668, -0.07712026685476303, 0.003061909694224596, -0.03107534721493721, 0.028691187500953674, -0.0085154939442873, -0.028657948598265648, -0.018548233434557915, -0.011347160674631596, 0.03566521778702736, 0.02111057937145233, -0.07030189782381058, 0.017476636916399002, 0.025073759257793427, 0.014304731972515583, 0.007736466359347105, -0.027618279680609703, 0.046427782624959946, 0.020710861310362816, 0.035039957612752914, 0.007943683303892612, 0.01886681281030178, 0.07034998387098312, -0.013746118173003197, -0.001942300470545888, -0.030436597764492035, 0.04198151081800461, -0.024463612586259842, 0.004770078230649233, 0.05717701092362404, -0.03967493027448654, 0.07861270755529404, -0.07212455570697784, -0.0037073243875056505, 0.022308725863695145, 0.016141554340720177, 0.021172136068344116, 0.054079003632068634, 0.02338986285030842, -0.014374089427292347, -0.06223548576235771, -0.06060965359210968, -0.0020749990362674, -0.042783401906490326, 0.018332520499825478, -0.0514998584985733, -0.0015238812193274498, -0.04352852329611778, 0.027259033173322678, -0.025353671982884407, 0.01035130862146616, 0.07353730499744415, -0.004016383085399866, 0.0015385531587526202, -0.002296378603205085, -0.019794223830103874, 0.029727011919021606, -0.025357985869050026, -0.06450248509645462, -0.0010157886426895857, -0.04590451344847679, -0.01678387075662613, 0.05944157764315605, 0.008157357573509216, 0.0003348887839820236, 0.11645819991827011, 0.05797102674841881, 0.025892945006489754, -0.015351870097219944, -0.021050309762358665, 0.014342251233756542, 0.010788795538246632, 0.0005472811753861606, -0.018220923840999603, 0.011490382254123688, -0.031123671680688858, 0.04415348917245865, -0.03964507207274437, -0.0019128185231238604, -0.07182914763689041, -0.03744010254740715, -0.02455209381878376, -0.02181972563266754, 0.023465551435947418, -0.014456035569310188, 0.012473192065954208, -0.015073761343955994, -0.025614598765969276, 0.06989441812038422, 0.04023061320185661, -0.048047952353954315, -0.04143020510673523, -0.0782480537891388, 0.006081538274884224, 0.02833086997270584, 0.03480500727891922, -0.007745842915028334, 0.000019912375137209892, -0.026239611208438873, 0.02788327820599079, 0.02097325213253498, 0.01830807514488697, 0.07450700551271439, -0.0015884126769378781, -0.006678757723420858, 0.03421907499432564, 0.03971012681722641, 0.006403426174074411, 0.016571853309869766, -0.04314985126256943, -0.01179046742618084, 0.010003793984651566, -0.008019443601369858, -0.005693421233445406, 0.047913312911987305, -0.008912102319300175, -0.015503356233239174, -0.09730643779039383, -0.04469793662428856, -0.04024132713675499, -0.009407369419932365, -0.007731188554316759, -0.007756854873150587, -0.01691959984600544, -0.027984600514173508, 0.07999259233474731, 0.04846970736980438, 0.01540614664554596, -0.014089982956647873, -0.04888512194156647, 0.017313417047262192, 0.03856487199664116, 0.0178757905960083, -0.026585429906845093, 0.0022157272323966026, 0.02222924493253231, 0.007382963318377733, 0.0046467348001897335, -0.03959396854043007, -0.032848820090293884, -0.04733524098992348, -0.005029291845858097, 0.010231170803308487, -0.007909286767244339, 0.024009834975004196, 0.0599101223051548, -0.026084426790475845, 0.003975614905357361, -0.002073331270366907, -0.014919016510248184, -0.03792710229754448, 0.05536425858736038, 0.018833912909030914, 0.00509305065497756, -0.011944472789764404, 0.0067813945934176445, 0.043035224080085754, -0.05279989913105965, 0.017916597425937653, 0.03854497894644737, -0.07087182998657227, 0.07208982110023499, 0.04234966263175011, -0.010668979957699776, 0.0005270917899906635, -0.05738575756549835, -0.020877396687865257, 0.031115161255002022, 0.025549424812197685, 0.013966744765639305, 0.004962769336998463, 0.0060701509937644005, -0.05432403087615967, -0.02811499498784542, -0.007730668876320124, -0.005701929330825806, -0.015949659049510956, 0.029600810259580612, -0.04667258262634277, 0.018446587026119232, -0.0378340445458889, 0.014094950631260872, -0.027510961517691612, -0.025423377752304077, 0.05283612012863159, 0.04159078001976013, -0.02775675803422928, 0.008042354136705399, 0.007305799517780542, 0.010640551336109638, -0.033846139907836914, 0.02894384041428566, 0.010374416597187519, -0.020460112020373344, -0.01798980124294758, -0.04659215733408928, 0.006091675255447626, -0.06192087009549141, -0.04082134738564491, 0.06563341617584229, 0.014021104201674461, 0.031062250956892967, -0.01855478622019291, -0.019775329157710075, 0.011954612098634243, 0.00161183241289109, 0.06096125394105911, -0.03551404923200607, 0.018978409469127655, 0.053368255496025085, 0.03486337140202522, -0.055334627628326416, -0.03525576740503311, -0.017004763707518578, 0.034443072974681854, -0.018013261258602142, -0.0143558569252491, 0.05865813419222832, -0.02655310370028019, 0.007967302575707436, 0.0053337872959673405, -0.03448747470974922, 0.015492593869566917, -0.06861768662929535, -0.020945237949490547, -0.007677148096263409, -0.025169488042593002, 0.0019436838338151574, 0.012191303074359894, -0.040193479508161545, -0.08301812410354614, 0.05105127766728401, 0.021714000031352043, 0.022616196423768997, -0.02474820986390114, 0.10625291615724564, -0.04390164464712143, 0.02404254674911499, 0.0687209814786911, -0.023388132452964783, -0.01646992564201355, -0.054503943771123886, 0.03408737853169441, 0.029391221702098846, 0.01720963604748249, 0.04247249290347099, 0.0773332417011261, -0.03391245752573013, 0.024553639814257622, 0.018107470124959946, 0.0008663343614898622, 0.02797008492052555, -0.07908564060926437, 0.0008896130602806807, 0.04699108004570007, 0.023636827245354652, 0.04283769428730011, -0.04137757048010826, -0.03665045276284218, -0.09720247238874435, -0.031786900013685226, 0.0009599979966878891, 0.04552339389920235, -0.022779174149036407, -0.011958633549511433, 0.028147054836153984, -0.022046459838747978, 0.059523291885852814, -0.02122780866920948, 0.10297956317663193, 0.06531894207000732, -0.06675064563751221, -0.012201450765132904, -0.04180694743990898, 0.010562884621322155, -0.03363732248544693, 0.012784561142325401, 0.017362352460622787, -0.0028912087436765432, -0.0068558864295482635, 0.07820629328489304, 0.017260542139410973, 0.03850312530994415, -0.0355856828391552, 0.02237945981323719, -0.02174636349081993, -0.015422839671373367, 0.06654022634029388, 0.04994085058569908, -0.014635282568633556, 0.09470227360725403, -0.0322706438601017, 0.008030446246266365, -0.0157419852912426, 0.03748083859682083, 0.010816900990903378, -0.002763308584690094, 0.020143674686551094, -0.05484423786401749, -0.012009060010313988, 0.08150407671928406, 0.031061803922057152, -0.011342138983309269, -0.026606839150190353, -0.03954928368330002, -0.050636548548936844, -0.0029455674812197685, -0.021241256967186928, 0.00685867527499795, -0.02731514908373356, 0.028241880238056183, 0.019999362528324127, 0.013822991400957108, -0.011208660900592804, -0.0021676155738532543, -0.006432211492210627, 0.03926574066281319, 0.012380226515233517, -0.017743948847055435, -0.05068855360150337, -0.005309585481882095, -0.029036587104201317, 0.014777005650103092, 0.032530881464481354, 0.0565173476934433, 0.0011245222995057702, 0.03678467497229576, 0.06709877401590347, 0.018521025776863098, -0.048729270696640015, 0.012958064675331116, 0.038947828114032745, 0.04831480607390404, 0.048758313059806824, -0.02860880270600319, 0.006761843338608742, -0.050381530076265335, -0.005621564108878374, 0.04908696562051773, 0.004751303698867559, -0.02527976594865322, 0.07828852534294128, 0.02700018882751465, 0.0037906973157078028, -0.005189761519432068, -0.01031802874058485, -0.0010988839203491807, -0.03995497152209282, 0.06885349750518799, -0.031055299565196037, 0.020421544089913368, -0.026870103552937508, -0.020989930257201195, 0.035212814807891846, 0.026356590911746025, -0.020727194845676422, -0.00018123426707461476, 0.02160009555518627, -0.024982091039419174, 0.031259581446647644, 0.0014845449477434158, 0.020428212359547615, -0.015850597992539406, -0.01437171921133995, 0.021963004022836685, 0.015243393369019032, -0.008977681398391724, -0.017424259334802628, 0.010002580471336842, 0.005485960282385349, -0.049675244837999344, 0.021632419899106026, 0.06039854511618614, -0.048721831291913986, 0.06485586613416672, -0.04274945333600044, -0.04838252812623978, -0.04085128381848335, -0.006438623648136854, -0.006247352343052626, 0.006619650404900312, 0.01291893795132637, -0.010584859177470207, -0.0017521553672850132, 0.03840501978993416, -0.02419622242450714, 0.04447341337800026, -0.007917715236544609, 0.03349212929606438, 0.02440289780497551, -0.018551478162407875, 0.02415423095226288, 0.03775258734822273, -0.09145299345254898, -0.026034988462924957, 0.0008625492337159812, -0.008628472685813904, -0.006408907473087311, -0.03200865909457207, -0.02935962937772274, -0.032064471393823624, 0.0352398157119751, -0.01243229117244482, 0.0087209427729249, 0.07868000864982605, -0.00296848569996655, 0.035077016800642014, -0.03042089007794857, -0.024339620023965836, 0.01570795848965645, 0.06655610352754593, -0.0022118641063570976, 0.0018388153985142708, -0.02882879041135311, 0.05761405825614929, 0.00788547657430172, -0.07325111329555511, 0.023466773331165314, 0.04060988873243332, -0.008100004866719246, -0.053447969257831573, 0.03902406617999077, 0.051995400339365005, -0.055463436990976334, 0.026793161407113075, 0.001367180491797626, -0.07142804563045502, -0.013820980675518513, 0.03693534433841705, 0.0539395697414875, -0.05462309345602989, -0.009227185510098934, 0.04158291965723038, -0.02988508529961109, -0.04657100886106491, 0.07444892078638077, -0.030451981350779533, -0.04180779680609703, 0.024941369891166687, -0.012199277058243752, 0.04077998548746109, -0.0288571584969759, -0.023013532161712646, -0.02357037365436554, -0.017496895045042038, 0.008381925523281097, 0.03572223335504532, 0.04261317849159241, -0.036052100360393524, -0.027560891583561897, 0.00650173332542181, -0.024879543110728264, 0.0019272284116595984, 0.0011630909284576774, 0.03723260015249252, -0.05872572958469391, -0.003763419110327959, 0.012830796651542187, 0.034481070935726166, -0.03299957513809204, -0.0028938818722963333, -0.017252786085009575, 0.05366967245936394, 0.019168050959706306, 0.021017909049987793, 0.06849975138902664, -0.00904471892863512, -0.0062670232728123665, -0.012798077426850796, -0.009471016004681587, 0.033294495195150375, -0.056891608983278275, -0.0006016222178004682, 0.014224755577743053, 0.032341182231903076, 0.008252264931797981, -0.00765843503177166, -0.054155074059963226, -0.016940416768193245, 0.01672310195863247, 0.00435369648039341, 0.0030094669200479984, 0.06554009020328522, -0.030092820525169373, -0.0523042231798172, -0.029096553102135658, -0.04516635462641716, 0.024954257532954216, 0.05947883427143097, -0.0421641543507576, -0.015603845939040184, -0.05496707931160927, 0.007820834405720234, 0.023062657564878464 ]
<p>Force-Weight <a href="http://en.wikipedia.org/wiki/Pinewood_derby" rel="nofollow">Pinewood Derby</a> Car.</p> <p>I'm trying to make a fast derby car. I was wondering if I could make a car that can drop/eject weight once it comes off of the incline. Would that increase speed or would it make it slower?</p>
g5443
[ 0.012202215380966663, 0.02852385677397251, 0.016196908429265022, -0.017602464184165, 0.06355704367160797, 0.03451541066169739, 0.015710778534412384, 0.017883088439702988, -0.10802523791790009, 0.004074250813573599, 0.011364499107003212, -0.06412620842456818, 0.06394341588020325, 0.004904617089778185, 0.05569518730044365, 0.0330432653427124, 0.04157615825533867, -0.07844285666942596, -0.003815000643953681, -0.00980158057063818, 0.023513467982411385, 0.02969254180788994, -0.03920506313443184, -0.014286535792052746, 0.04795238375663757, -0.009994830936193466, 0.022302264347672462, -0.029464736580848694, -0.031138461083173752, 0.03132105618715286, -0.009971199557185173, -0.00024097479763440788, -0.01130116730928421, -0.028592990711331367, -0.05739246681332588, 0.0037188802380114794, 0.029266275465488434, -0.0013247851748019457, -0.006920011714100838, 0.0026504341512918472, 0.025571992620825768, -0.05521608516573906, 0.024958539754152298, -0.022416099905967712, 0.01950344815850258, -0.011136317625641823, 0.03540119156241417, -0.005402037873864174, -0.026055583730340004, 0.03895070031285286, 0.02323501743376255, -0.022874366492033005, 0.004946625791490078, -0.03469096124172211, -0.04168931394815445, -0.007975813001394272, 0.0424451045691967, 0.014517650008201599, -0.03358720615506172, 0.02664339356124401, -0.07651805877685547, -0.04799952730536461, 0.014962675981223583, 0.01614299602806568, 0.01930326782166958, -0.005557745695114136, 0.02242841012775898, -0.048947785049676895, 0.02021314762532711, 0.022497346624732018, -0.011317462660372257, 0.017807569354772568, 0.028083590790629387, -0.09263984113931656, 0.003936136607080698, 0.007695060223340988, 0.05588311702013016, -0.03490745648741722, -0.006261244881898165, -0.02478576824069023, 0.04234800860285759, 0.0071592777967453, -0.02971252240240574, -0.03563370183110237, 0.015986867249011993, 0.0050427960231900215, 0.0051023331470787525, 0.06993772089481354, 0.01581251434981823, -0.031193846836686134, 0.006900401320308447, -0.05542484298348427, 0.02420678548514843, 0.057251617312431335, 0.023443598300218582, -0.04231185466051102, -0.04842623695731163, 0.03709178790450096, -0.0023742469493299723, -0.023182125762104988, -0.019562838599085808, -0.05983184650540352, 0.09351178258657455, -0.02276584692299366, 0.0028661582618951797, -0.008198837749660015, -0.03310178592801094, -0.00850379467010498, 0.026678012683987617, -0.03793385624885559, 0.007308463100343943, -0.0040596178732812405, -0.058084338903427124, -0.013004150241613388, -0.04487963765859604, -0.057681646198034286, 0.019526662304997444, -0.00974322110414505, -0.04178879037499428, -0.0081178555265069, 0.05604032054543495, -0.044882357120513916, -0.031948938965797424, 0.04084756225347519, -0.03410797938704491, 0.002147986553609371, -0.025105252861976624, 0.0033004034776240587, 0.003674259642139077, -0.0596792995929718, -0.019307823851704597, 0.004897798411548138, 0.038327913731336594, -0.01843656413257122, -0.04851250723004341, 0.015781894326210022, -0.02291274257004261, 0.04002226144075394, 0.00443083792924881, -0.022389618679881096, 0.04072203114628792, 0.042925868183374405, -0.016523245722055435, 0.045123618096113205, -0.030413184314966202, 0.01535192783921957, -0.04039362072944641, 0.05989345908164978, -0.005904465448111296, 0.07305816560983658, 0.00790033396333456, -0.02354959398508072, -0.00778596056625247, -0.010908994823694229, 0.010172784328460693, -0.004189464263617992, 0.04757612198591232, 0.03205921873450279, 0.027770619839429855, -0.01737203076481819, 0.06736819446086884, -0.03710886090993881, -0.00856422632932663, 0.005004617385566235, -0.01621692068874836, 0.058476436883211136, -0.0086234575137496, 0.02283915877342224, 0.024358900263905525, 0.042741868644952774, -0.07227674126625061, -0.006831948645412922, -0.026689933612942696, 0.042050331830978394, 0.010243001393973827, -0.05732189863920212, 0.039588380604982376, -0.04525715112686157, -0.02067991904914379, -0.010536961257457733, -0.016629226505756378, -0.02043795771896839, -0.029970509931445122, 0.019087402150034904, -0.003918057307600975, 0.014707937836647034, -0.012083664536476135, 0.04932952672243118, -0.0941801518201828, 0.015482510440051556, 0.01399881299585104, -0.00976389180868864, 0.005800736602395773, 0.015349187888205051, -0.03635760769248009, -0.015388639643788338, 0.01914740540087223, -0.06112467870116234, 0.016708822920918465, -0.003866354702040553, 0.015801185742020607, 0.02085934765636921, -0.0005387236014939845, -0.006487611215561628, -0.012806801125407219, -0.062362585216760635, 0.016574116423726082, 0.014165311120450497, 0.010684334672987461, -0.04477591812610626, 0.03874243423342705, 0.031640250235795975, 0.0274991262704134, 0.020883215591311455, 0.04768355190753937, -0.005892160348594189, -0.0014999483246356249, 0.019373631104826927, 0.04697331041097641, 0.036483339965343475, 0.033459655940532684, 0.02613252028822899, 0.0016456960001960397, -0.018682194873690605, -0.024797026067972183, -0.03574853762984276, 0.03002106584608555, -0.011493607424199581, -0.01722586341202259, -0.0011888191802427173, 0.0005943611031398177, -0.03980618715286255, 0.019663209095597267, -0.06489114463329315, 0.03224752098321915, -0.013134847395122051, 0.04732577130198479, 0.03405393660068512, -0.013964463956654072, -0.02214827947318554, 0.02501664124429226, -0.04283107444643974, -0.02330266311764717, -0.04617226868867874, -0.03014615923166275, -0.06928740441799164, -0.018756261095404625, -0.012983931228518486, -0.009389417245984077, -0.043911971151828766, 0.020573830232024193, 0.004306817892938852, -0.056980930268764496, -0.002783876610919833, 0.0021117166616022587, -0.005846844520419836, -0.054085586220026016, -0.009611420333385468, -0.02391420491039753, 0.002863667905330658, 0.009747019968926907, 0.025602858513593674, -0.020734356716275215, -0.005368550308048725, -0.06763817369937897, -0.0003746623988263309, -0.002595040248706937, -0.08817188441753387, 0.03518404811620712, 0.0432511530816555, -0.06292188167572021, -0.026423204690217972, 0.007412021979689598, 0.0075797950848937035, -0.027087796479463577, -0.014807636849582195, 0.000324662949424237, -0.038564540445804596, 0.02513137087225914, -0.01878778077661991, 0.01188886072486639, -0.03942876681685448, -0.06352581083774567, 0.03368216007947922, -0.06269511580467224, -0.024680372327566147, 0.04095371440052986, -0.028511209413409233, -0.014597567729651928, 0.024635618552565575, -0.06637921184301376, -0.012149830348789692, 0.016908740624785423, -0.013839435763657093, 0.058345988392829895, 0.071236252784729, -0.018111295998096466, 0.0013368699001148343, -0.008182788267731667, -0.054894834756851196, -0.04734620451927185, -0.05134119838476181, 0.009703670628368855, -0.024502316489815712, -0.0033482953440397978, 0.02458023838698864, -0.011149387806653976, 0.050328053534030914, 0.02498069405555725, -0.05595387518405914, -0.059533316642045975, 0.025888117030262947, -0.0014494089409708977, 0.04573672264814377, -0.08398808538913727, -0.019913073629140854, 0.06216055899858475, -0.023688942193984985, 0.014336058869957924, -0.04221734032034874, 0.0011336365714669228, -0.028765827417373657, -0.006589885801076889, 0.05242369696497917, 0.036630790680646896, 0.05730017274618149, 0.03839674964547157, 0.005145739763975143, 0.04979173094034195, -0.019825207069516182, 0.08253572881221771, 0.04848581179976463, -0.002387751592323184, -0.0005315743619576097, -0.013274949975311756, 0.048885904252529144, 0.02908400259912014, 0.039390090852975845, 0.01085562352091074, 0.02083694376051426, -0.00812629796564579, 0.025805510580539703, -0.016552995890378952, -0.00729707907885313, -0.00007500625360989943, 0.04426699876785278, 0.057201407849788666, -0.0018070057267323136, -0.015783945098519325, 0.0002371452283114195, 0.04900841787457466, -0.06694388389587402, -0.004186948761343956, -0.039214711636304855, 0.018704302608966827, -0.06441590934991837, 0.01280057244002819, -0.007989713922142982, -0.04514944180846214, -0.026542695239186287, -0.007548587862402201, 0.00453444616869092, 0.01323159784078598, 0.02728709951043129, -0.05322348326444626, -0.018439967185258865, -0.05713607743382454, 0.045011866837739944, -0.03486951068043709, 0.020519228652119637, 0.02452787570655346, -0.018071983009576797, -0.0434495285153389, 0.011193817481398582, -0.0769185796380043, 0.024642525240778923, 0.08691436797380447, 0.0006766761653125286, -0.03389427810907364, 0.004278489388525486, 0.0036048556212335825, 0.06166519969701767, 0.03717415779829025, 0.00689678406342864, -0.03516320884227753, -0.0011763678630813956, -0.044785596430301666, 0.013323287479579449, 0.08235770463943481, 0.027839701622724533, -0.018195567652583122, -0.04100681096315384, -0.002262354828417301, 0.012010259553790092, 0.02911217138171196, 0.05905670300126076, -0.033866915851831436, -0.08611536026000977, -0.04090351238846779, 0.056893061846494675, -0.0006652566371485591, 0.08244788646697998, -0.010913782753050327, 0.0777808278799057, -0.007360128685832024, 0.014585777185857296, 0.00794483907520771, 0.0047917901538312435, -0.051405712962150574, -0.020579831674695015, -0.04104826599359512, -0.07608248293399811, -0.01694851741194725, -0.023796258494257927, -0.014602156355977058, 0.015304174274206161, 0.037206538021564484, 0.07550365477800369, -0.03133063390851021, -0.014271428808569908, 0.02863774634897709, -0.006535772699862719, 0.042145051062107086, 0.016137031838297844, -0.017536906525492668, 0.02281900681555271, 0.006732796784490347, -0.023790553212165833, -0.06969811767339706, -0.0087534599006176, 0.0003396226966287941, 0.010879122652113438, 0.023166656494140625, -0.030499540269374847, 0.025535231456160545, 0.1021939367055893, -0.008460108190774918, 0.014696432277560234, 0.04790430888533592, -0.019060885533690453, -0.04278750345110893, 0.059545546770095825, 0.005756314378231764, 0.017030585557222366, -0.009595577605068684, 0.03682747483253479, -0.0664491280913353, -0.030332474038004875, 0.00804345402866602, 0.0006015123799443245, -0.02113884687423706, 0.006352976895868778, -0.027609683573246002, 0.032443176954984665, 0.02328149788081646, 0.006526341196149588, -0.06843263655900955, -0.006221319083124399, 0.031096214428544044, 0.0017705046338960528, 0.027440253645181656, 0.009006334468722343, 0.06438005715608597, 0.0248577781021595, -0.026888908818364143, -0.05723045766353607, 0.024237029254436493, -0.008972223848104477, 0.021077439188957214, -0.03915984928607941, -0.03170385584235191, -0.043189261108636856, -0.002254869556054473, 0.030969852581620216, -0.007502161432057619, 0.01886727102100849, 0.042660199105739594, 0.014093083329498768, 0.03621085733175278, -0.026414649561047554, -0.025907423347234726, -0.006793684791773558, -0.0029862546361982822, -0.10026147961616516, -0.06116067245602608, -0.006641287822276354, -0.04127761721611023, -0.002463783137500286, 0.026021771132946014, 0.007785449270159006, -0.018332725390791893, 0.026504535228013992, -0.04552975669503212, 0.03334817662835121, -0.03425270691514015, 0.03405625745654106, 0.030024945735931396, 0.025789525359869003, -0.02207360416650772, -0.0007059372728690505, -0.05554303899407387, -0.011512571014463902, -0.002203936455771327, -0.0343303307890892, 0.010912788100540638, 0.022227196022868156, 0.06398265063762665, -0.016461748629808426, -0.00743562588468194, 0.03979279100894928, 0.0000457976566394791, 0.06948289275169373, 0.09547918289899826, -0.008572104386985302, 0.005452791694551706, 0.00495946267619729, 0.01934197172522545, 0.03634195774793625, 0.009990513324737549, 0.025019047781825066, 0.04338821768760681, -0.0240227859467268, -0.00043268120498396456, -0.046770643442869186, -0.08544281870126724, 0.03748607635498047, -0.01057144720107317, -0.03651924803853035, -0.0482320636510849, -0.011343143880367279, 0.018930481746792793, -0.022652512416243553, 0.039953216910362244, 0.02376389317214489, -0.054777488112449646, -0.00462682917714119, 0.04325307905673981, 0.02970968931913376, -0.016491934657096863, -0.016770685091614723, -0.03758326545357704, 0.002384762279689312, 0.000495825195685029, 0.09732571244239807, 0.021620072424411774, -0.01132198330014944, -0.014358706772327423, -0.0272614024579525, 0.04083399474620819, -0.030620839446783066, 0.006477460265159607, 0.07566874474287033, -0.012784501537680626, 0.004075168166309595, -0.043510451912879944, 0.037978217005729675, -0.0037373758386820555, 0.042480383068323135, 0.023284582421183586, -0.0663248673081398, -0.00937583390623331, -0.021862441673874855, 0.02795966900885105, 0.010568072088062763, -0.01664862409234047, -0.06494326144456863, -0.011120814830064774, 0.03919786959886551, 0.02174649015069008, 0.029589135199785233, 0.03366436809301376, 0.021126816049218178, -0.005538140423595905, 0.0024304850958287716, 0.057789016515016556, -0.04651699587702751, -0.014143821783363819, -0.005828100256621838, 0.02277640625834465, -0.02794552408158779, 0.017922604456543922, 0.007776913233101368, -0.04942714795470238, -0.00474328501150012, 0.01556535717099905, -0.01568627543747425, -0.05151668190956116, 0.014919890090823174, -0.01471373625099659, 0.002726671751588583, -0.021316921338438988, -0.03527675196528435, -0.034863583743572235, -0.027332700788974762, -0.0704885795712471, 0.014159058220684528, -0.08084230124950409, 0.029468046501278877, 0.012569489888846874, 0.0683971643447876, 0.04199052229523659, 0.017247363924980164, 0.018562152981758118, -0.01067119836807251, -0.08176569640636444, 0.05749230086803436, 0.030957864597439766, 0.017872391268610954, -0.011886081658303738, -0.05136746168136597, 0.0014262259937822819, -0.016395045444369316, 0.03659253939986229, -0.028358766809105873, -0.007903891615569592, 0.04655330255627632, 0.0124584985896945, -0.04131115600466728, 0.044117897748947144, -0.02265988662838936, 0.009305641055107117, -0.012527433224022388, 0.07640552520751953, -0.021430762484669685, 0.005956233479082584, 0.051987212151288986, -0.039840053766965866, 0.013340884819626808, 0.040971480309963226, -0.004954385105520487, 0.045234594494104385, -0.047457415610551834, 0.007767409086227417, -0.0031667540315538645, -0.0363432914018631, 0.05214575305581093, 0.05247322469949722, 0.07051955163478851, 0.018161064013838768, 0.001526911393739283, 0.04980839788913727, 0.06458249688148499, -0.08080344647169113, 0.06360764056444168, 0.00388904707506299, 0.02714180387556553, 0.02963787317276001, -0.022010961547493935, 0.05464424565434456, 0.03791731223464012, -0.042468905448913574, -0.003421952249482274, -0.048858728259801865, -0.007495546247810125, 0.006866089534014463, 0.03864027187228203, -0.003725771326571703, 0.04609169065952301, 0.021346895024180412, 0.011630418710410595, -0.007896041497588158, -0.021056899800896645, 0.023431450128555298, 0.01999114267528057, 0.019351935014128685, 0.02856811322271824, -0.029851926490664482, 0.03331330046057701, -0.014615709893405437, 0.06308126449584961, -0.012159607373178005, -0.0847247764468193, -0.04636351391673088, -0.038050808012485504, 0.03376008942723274, -0.014508092775940895, -0.11774374544620514, 0.03340313211083412, -0.00026180126587860286, -0.005979540757834911, -0.0030610240064561367, 0.017488952726125717, -0.0010342546738684177, 0.01286857295781374, -0.029901325702667236, 0.046595409512519836, -0.037106458097696304, 0.022922992706298828, 0.0629708468914032, -0.042725615203380585, 0.011063164100050926, -0.013666831888258457, 0.04416079819202423, 0.07069386541843414, -0.030895555391907692, -0.09237121045589447, -0.03924647346138954, 0.004353945609182119, -0.030644699931144714, 0.01789700612425804, -0.011932794004678726, 0.07735911756753922, 0.07342293858528137, 0.03171699866652489, -0.05270994082093239, 0.0012373939389362931, -0.09828094393014908, 0.025711113587021828, -0.028825517743825912, 0.008494719862937927, 0.01596839725971222, -0.006159194745123386, -0.029459429904818535, 0.007554622367024422, -0.014210570603609085, 0.02961413376033306, 0.05591229349374771, 0.030344529077410698, -0.03941717371344566, 0.05768305063247681, -0.0315418466925621, 0.02102079428732395, 0.045537807047367096, -0.004836309235543013, -0.029295664280653, -0.01989120803773403, -0.002450323896482587, -0.0236210860311985, 0.006530499551445246, 0.01887567527592182, 0.02400440163910389, 0.026919463649392128, -0.004856662359088659, 0.0021225465461611748, -0.03692431375384331, -0.025011582300066948, 0.02812003158032894, 0.04486330226063728, -0.04136960208415985, 0.022201936691999435, -0.08812540024518967, -0.07308214157819748, 0.033739421516656876, 0.016962358728051186, 0.03967254236340523, 0.02153879962861538, 0.01852334849536419, 0.08059815317392349, 0.029632600024342537, 0.018280360847711563, 0.005452991463243961, 0.02489916980266571, -0.05875995010137558, 0.0021775406785309315, -0.025085395202040672, 0.030121663585305214, -0.04127286374568939, 0.003985912539064884, 0.001725883805193007, -0.03516293317079544, 0.03320916369557381, -0.00508660776540637, -0.0037205982953310013, -0.03786216676235199, -0.027651654556393623, 0.006557547952979803, -0.010962387546896935, 0.012470903806388378 ]
<p>I understand mathematically how one can obtain the conservation equations in both the conservative $${\partial\rho\over\partial t}+\nabla\cdot(\rho \textbf{u})=0$$</p> <p>$${\partial\rho{\textbf{u}}\over\partial t}+\nabla\cdot(\rho \textbf{u})\textbf{u}+\nabla p=0$$</p> <p>$${\partial E\over\partial t}+\nabla\cdot(\textbf{u}(E+p))=0$$</p> <p>and non-conservative forms. However, I am still confused, why do we call them conservative and non-conservative forms? can any one explain from a physical and mathematical point of view?</p> <p>Many off-site threads deal with this question (<a href="http://www.cfd-online.com/Forums/main/75621-conservative-versus-non-conservative-forms.html" rel="nofollow">here</a> and <a href="http://www.cfd-online.com/Forums/main/10994-conservative-non-conservative-form.html" rel="nofollow">here</a>), but none of them provides a good enough answer for me!</p> <p>If any one can provide some hints, I will be very grateful.</p>
g5444
[ 0.0542018823325634, -0.04956585541367531, 0.001549070468172431, 0.06573056429624557, 0.07754155248403549, 0.005709769669920206, 0.05164053291082382, 0.02750301919877529, -0.019361522048711777, -0.022514473646879196, -0.02267404831945896, -0.03294377774000168, 0.019317924976348877, 0.015127215534448624, 0.013024345971643925, 0.022963523864746094, 0.017382968217134476, -0.005876106210052967, 0.008279274217784405, 0.05348384007811546, -0.07732147723436356, 0.021272506564855576, 0.04698579013347626, -0.00577819999307394, -0.01764983870089054, 0.0009320259559899569, 0.004809258971363306, 0.008815432898700237, -0.062237776815891266, -0.02438417077064514, 0.03461777791380882, 0.04013149440288544, 0.09431832283735275, 0.00977037101984024, 0.007031710352748632, -0.02029893919825554, 0.031987790018320084, -0.00846188049763441, 0.04034794867038727, 0.02472837269306183, 0.04912242293357849, 0.009432786144316196, -0.0188079085201025, -0.004863958805799484, 0.01627935655415058, -0.05866599082946777, -0.11214380711317062, -0.0641733780503273, -0.011579688638448715, -0.018223775550723076, 0.051573097705841064, 0.0011455753119662404, 0.014439341612160206, 0.0023596964310854673, -0.030578667297959328, -0.042561378329992294, -0.0038971377070993185, 0.040216464549303055, -0.010933657176792622, -0.02684272825717926, -0.00003187234324286692, -0.045508962124586105, -0.0036472342908382416, 0.06682654470205307, 0.035621874034404755, -0.05885051190853119, 0.03686926141381264, -0.046306319534778595, 0.03910123556852341, -0.006246073171496391, -0.0024523655883967876, 0.014227338135242462, 0.014526872895658016, 0.018721221014857292, -0.0339631550014019, -0.0005253414274193347, -0.012811079621315002, -0.020412225276231766, 0.05705072358250618, -0.05866651237010956, 0.012803328223526478, 0.017274662852287292, 0.01498938538134098, 0.0689002126455307, 0.0024547120556235313, 0.030844993889331818, -0.010544796474277973, 0.004595468286424875, -0.030527355149388313, -0.015973979607224464, -0.036401644349098206, -0.05465419590473175, 0.014904292300343513, -0.001030375948175788, 0.04813505709171295, 0.053292352706193924, -0.004827476572245359, -0.006960655562579632, -0.015628797933459282, -0.0061257933266460896, 0.0011543042492121458, -0.011254222132265568, -0.004976493306457996, -0.003316610585898161, 0.01911945641040802, -0.002591244876384735, 0.030576709657907486, 0.024923525750637054, -0.06695247441530228, -0.016700753942131996, -0.017341839149594307, -0.0008664381457492709, -0.05364018306136131, 0.02791464887559414, -0.03860226273536682, 0.01628398522734642, -0.024102749302983284, -0.019242890179157257, 0.014979997649788857, -0.009113973006606102, 0.061686620116233826, -0.0005126479081809521, 0.08959122747182846, 0.04795725643634796, -0.02120916172862053, -0.0038634140510112047, 0.02074894867837429, 0.04020771011710167, 0.08294914662837982, -0.025080492720007896, -0.011891377158463001, -0.024316331371665, 0.03781989961862564, -0.026178153231739998, -0.0010299148270860314, 0.015963418409228325, -0.10429022461175919, 0.04312632977962494, -0.020226089283823967, -0.015647131949663162, -0.006106788758188486, 0.019049007445573807, 0.011324136517941952, -0.016236543655395508, 0.001765855005942285, -0.018883755430579185, -0.007462733890861273, -0.03828030079603195, 0.028273513540625572, -0.007068445440381765, 0.028652645647525787, 0.021002724766731262, -0.003007299732416868, 0.018802940845489502, 0.02291623130440712, 0.034492816776037216, 0.03358231857419014, -0.04866786673665047, -0.013699911534786224, 0.039107732474803925, 0.03363891690969467, 0.025271175429224968, 0.015378082171082497, -0.00006263796967687085, -0.0710674300789833, 0.03065563179552555, -0.0034743042197078466, -0.10187586396932602, 0.0014193195383995771, -0.024331998080015182, -0.04881211742758751, 0.07699283957481384, 0.04321872442960739, 0.05302729085087776, 0.07500071078538895, 0.008051318116486073, 0.016692671924829483, -0.010637382976710796, -0.012964689172804356, -0.053334373980760574, -0.07226190716028214, 0.003535469062626362, 0.02421773038804531, 0.048475947231054306, 0.055423468351364136, -0.0016282385913655162, -0.045878730714321136, 0.031275954097509384, -0.05470488592982292, -0.008584999479353428, 0.011466377414762974, 0.00578572740778327, 0.026461385190486908, 0.0030319092329591513, -0.03166624531149864, 0.00783395767211914, -0.05926204472780228, -0.00452480698004365, -0.0707508847117424, 0.052654851227998734, -0.048373326659202576, -0.024019606411457062, 0.08457551896572113, 0.008814726956188679, -0.020944735035300255, -0.008389865979552269, -0.03905156999826431, -0.0034715679939836264, 0.014143508858978748, -0.03506668657064438, -0.021195463836193085, -0.0504867359995842, 0.00917096808552742, -0.00539143942296505, -0.0015065174084156752, 0.0029009629506617785, -0.021379254758358, -0.010595613159239292, -0.0957721546292305, 0.0004983763210475445, -0.014230304397642612, -0.019850844517350197, 0.009240700863301754, -0.0066950819455087185, -0.05877244845032692, 0.038009822368621826, 0.03881414979696274, 0.050831783562898636, 0.026671620085835457, -0.0030677763279527426, 0.015056759119033813, 0.038624104112386703, -0.02509406767785549, 0.049518223851919174, 0.007652530912309885, 0.022129736840724945, 0.005770536605268717, 0.0686563029885292, -0.0009001444559544325, 0.023204002529382706, 0.014302082359790802, 0.004472550004720688, 0.04164466634392738, 0.060738999396562576, 0.0062768966890871525, 0.018205400556325912, 0.052182674407958984, 0.02722991071641445, -0.018154768273234367, 0.015908770263195038, 0.0029070039745420218, -0.06356477737426758, 0.04923606291413307, -0.010533676482737064, -0.02783370390534401, 0.011769814416766167, 0.033049192279577255, -0.01828031614422798, -0.06363026052713394, 0.015066883526742458, -0.027705643326044083, 0.05641091614961624, -0.019915897399187088, 0.023166364058852196, -0.037382978945970535, 0.0014760912163183093, 0.008862822316586971, -0.004847276955842972, 0.0404328852891922, 0.002254647668451071, 0.0149656031280756, 0.046493057161569595, 0.01534367073327303, -0.0005699244793504477, -0.020334914326667786, -0.020268989726901054, -0.0196119025349617, -0.047443002462387085, -0.02960328571498394, 0.010164394974708557, 0.03233709931373596, 0.02313656359910965, 0.025821629911661148, 0.009095844812691212, 0.0170412827283144, -0.008142811246216297, -0.011192142963409424, 0.06292156130075455, -0.018902385607361794, 0.008732873946428299, -0.06368281692266464, 0.03954637795686722, 0.01795642077922821, -0.008541036397218704, 0.017514141276478767, -0.03859124705195427, 0.0013727087061852217, -0.08336193859577179, -0.0010211578337475657, -0.00404695188626647, -0.02279803156852722, 0.00250357948243618, -0.007388663943856955, 0.017403751611709595, 0.02526050992310047, 0.05034901201725006, -0.024879492819309235, -0.03466755151748657, 0.03077106736600399, 0.006495211739093065, 0.0014818239724263549, 0.02474888786673546, -0.009010996669530869, 0.026695797219872475, 0.011512174271047115, -0.035774219781160355, 0.024637192487716675, -0.04306897521018982, 0.027762822806835175, -0.0333249531686306, -0.04101743921637535, -0.062070347368717194, -0.012341081164777279, -0.016824990510940552, 0.00932238344103098, 0.024309366941452026, -0.048186831176280975, 0.04062166064977646, 0.0475466325879097, -0.08088771998882294, 0.07439246773719788, 0.008420385420322418, 0.03001023270189762, 0.013303420506417751, -0.04617249593138695, -0.018508726730942726, 0.03419291973114014, 0.021137462928891182, 0.0625850185751915, -0.0577237568795681, -0.006887210067361593, -0.02773732878267765, -0.0010903674410656095, -0.01453192438930273, -0.01702745258808136, -0.02989206276834011, 0.04974212497472763, -0.018954571336507797, -0.008319285698235035, -0.007572486065328121, 0.004446289036422968, 0.016287589445710182, 0.03885846212506294, -0.031010108068585396, -0.001089904922991991, 0.04402398318052292, -0.034123338758945465, 0.009294956922531128, -0.004066877998411655, 0.056395985186100006, -0.030077816918492317, -0.029718197882175446, 0.00820391159504652, 0.06727095693349838, -0.003367791883647442, -0.003117684042081237, 0.07386713474988937, 0.011347262188792229, -0.05655987560749054, -0.04889614135026932, 0.03456062078475952, 0.021268563345074654, 0.017214782536029816, 0.034083858132362366, -0.0005915236542932689, -0.011725792661309242, 0.01333738025277853, -0.0023119626566767693, -0.0706687644124031, -0.03231770917773247, 0.0006920463056303561, -0.004476727917790413, -0.016996843740344048, 0.010587402619421482, 0.0009618980693630874, -0.06264056265354156, -0.010782444849610329, 0.009053962305188179, 0.010377335362136364, -0.03148392587900162, 0.01961292326450348, -0.022919874638319016, -0.04605274274945259, 0.0057168202474713326, 0.004107522312551737, 0.018183499574661255, 0.020330291241407394, -0.033564966171979904, 0.00316844554618001, -0.0029560818802565336, 0.017529385164380074, 0.003092241706326604, -0.01714221015572548, -0.04172723740339279, -0.02265286073088646, 0.04068566486239433, -0.049903322011232376, 0.004397070500999689, -0.03243585675954819, -0.026213252916932106, 0.017332732677459717, -0.08594071865081787, -0.047580692917108536, 0.01821952871978283, 0.046699170023202896, -0.008668184280395508, 0.040087033063173294, -0.018440864980220795, 0.03774762153625488, -0.00358977192081511, 0.033877529203891754, -0.038766395300626755, -0.03455471619963646, 0.0015622416976839304, 0.06797825545072556, 0.10121705383062363, -0.0012667352566495538, -0.029682543128728867, -0.012334746308624744, 0.016393089666962624, 0.038031529635190964, 0.04960350692272186, -0.007877147756516933, 0.06344963610172272, -0.0732228010892868, 0.030435165390372276, -0.10254981368780136, 0.04623233526945114, -0.0628315880894661, -0.045536696910858154, -0.006531199440360069, 0.017992481589317322, 0.029915209859609604, -0.04972127452492714, 0.019298767670989037, 0.0028550520073622465, 0.03523274138569832, -0.05359448492527008, -0.03520292043685913, -0.02798403799533844, -0.022999029606580734, 0.0605921596288681, 0.03557124361395836, -0.018931735306978226, -0.040628742426633835, 0.023364605382084846, 0.009794995188713074, -0.02140597626566887, 0.03852935507893562, 0.06991031765937805, -0.07743887603282928, -0.021416982635855675, 0.03362475708127022, -0.03165362402796745, 0.06106940656900406, 0.005179637111723423, -0.019612334668636322, -0.0020590617787092924, -0.04152375087141991, 0.006186989136040211, 0.006262068636715412, 0.011170129291713238, 0.048529282212257385, -0.04403391852974892, 0.02465476095676422, 0.06777048856019974, 0.004909673240035772, -0.02555895783007145, -0.012793486937880516, -0.014337149448692799, -0.0169006809592247, 0.021657075732946396, 0.00013837777078151703, 0.06554815173149109, -0.001963099231943488, 0.017049342393875122, -0.03215913847088814, -0.011172247119247913, 0.007026062812656164, 0.0385684072971344, -0.01125690620392561, 0.02850414626300335, -0.038258422166109085, 0.00465303473174572, 0.03227309137582779, -0.025483224540948868, 0.036538075655698776, -0.013206674717366695, -0.03400701284408569, -0.062373463064432144, -0.04983110353350639, -0.025434346869587898, -0.033555321395397186, 0.03579118847846985, 0.03274844214320183, 0.07750225067138672, 0.06153269112110138, 0.013517240062355995, 0.03737384453415871, -0.051606640219688416, -0.008770640008151531, -0.03300334885716438, -0.02714783325791359, -0.00921920407563448, -0.04304066672921181, 0.013567915186285973, -0.04494766145944595, -0.040910374373197556, -0.018589138984680176, -0.07737086713314056, 0.07164155691862106, 0.01682799868285656, -0.00995269138365984, 0.05510953813791275, 0.06066909059882164, -0.006012092810124159, -0.05932792276144028, -0.04719371348619461, 0.022641057148575783, 0.07795143127441406, -0.04623610898852348, -0.00012015519314445555, 0.006976473145186901, -0.010517986491322517, -0.029542163014411926, -0.005212082993239164, -0.07017256319522858, -0.03695599362254143, 0.05588299036026001, -0.014878458343446255, -0.028151951730251312, 0.0727357342839241, 0.007320879027247429, 0.09112194925546646, -0.026314053684473038, 0.00897217821329832, 0.024229012429714203, -0.016797153279185295, -0.05294065177440643, -0.01604939065873623, -0.012701496481895447, 0.00933606643229723, 0.0026932319160550833, 0.019788702949881554, 0.06246134266257286, -0.058215945959091187, 0.016491718590259552, -0.019208284094929695, -0.016788095235824585, -0.026200726628303528, -0.044969361275434494, -0.00786424707621336, -0.014537458308041096, 0.022245291620492935, 0.00025027114315889776, 0.01174845639616251, 0.02156362123787403, -0.003475378267467022, 0.013292870484292507, 0.006246189586818218, 0.012773203663527966, -0.04417511820793152, 0.0009130843682214618, 0.014997696503996849, -0.002742833225056529, 0.0186898373067379, -0.06904907524585724, -0.002287959447130561, 0.02062317170202732, -0.01616196148097515, -0.02905922383069992, -0.030772782862186432, 0.026205986738204956, -0.011245856061577797, -0.03703058138489723, 0.000611349125392735, -0.021465955302119255, -0.08470388501882553, -0.015250001102685928, 0.09000155329704285, 0.0722925215959549, -0.011950317770242691, -0.027285652235150337, 0.03418020159006119, 0.037608832120895386, -0.010345139540731907, 0.007473938632756472, 0.05701988562941551, 0.02714027278125286, -0.020393826067447662, -0.03458782285451889, 0.06122579798102379, 0.006930917501449585, 0.027336716651916504, 0.03645322844386101, 0.002645609201863408, 0.043182604014873505, 0.035296350717544556, -0.0028760188724845648, -0.05830015987157822, -0.031220480799674988, 0.06755537539720535, -0.0028270173352211714, -0.07630753517150879, -0.00622426625341177, -0.017041796818375587, -0.06561824679374695, 0.03184770420193672, 0.029801353812217712, -0.014282314106822014, -0.0024178042076528072, -0.04570237547159195, -0.004490116611123085, 0.014509595930576324, 0.03740498423576355, 0.019074583426117897, -0.007005919702351093, 0.02059495821595192, -0.0054613021202385426, -0.025105400010943413, 0.05725730210542679, 0.029849397018551826, -0.05275177210569382, -0.020146653056144714, -0.0003286933933850378, 0.036226749420166016, -0.06699571013450623, 0.048383451998233795, 0.027792882174253464, 0.005716793704777956, 0.03174092248082161, 0.05260258913040161, 0.05897017940878868, 0.010691149160265923, -0.008297562599182129, 0.027111703529953957, 0.015536202117800713, -0.028684275224804878, -0.0898059755563736, -0.01169238518923521, 0.02316475659608841, 0.006869802717119455, -0.09192017465829849, -0.03867844119668007, -0.009828008711338043, -0.014654552564024925, 0.0035388926044106483, 0.041009385138750076, -0.05410272255539894, -0.00036845376598648727, 0.012684786692261696, -0.04520124942064285, 0.04336555674672127, -0.022888053208589554, 0.029940452426671982, 0.00581063237041235, -0.019279202446341515, -0.03658608719706535, -0.01829134300351143, 0.0034762490540742874, 0.0013392622349783778, -0.026198850944638252, -0.020341062918305397, -0.004680028185248375, 0.04178222641348839, -0.007781032472848892, -0.003092755563557148, -0.03993896767497063, 0.019610749557614326, 0.0006325270514935255, -0.000838667678181082, 0.011004221625626087, -0.03466729074716568, -0.07071921974420547, -0.043189823627471924, 0.02113817259669304, 0.02463238500058651, -0.021987902000546455, 0.02768496237695217, 0.034291964024305344, -0.006205035373568535, 0.03692321851849556, 0.000842780340462923, 0.014620033092796803, -0.04230251535773277, 0.002563508227467537, -0.03915402293205261, 0.008125175721943378, -0.01669612154364586, -0.01914338767528534, 0.03162036091089249, -0.028170650824904442, -0.016280509531497955, 0.004664679989218712, 0.015420722775161266, -0.038475245237350464, 0.019578631967306137, -0.049917589873075485, -0.026397285982966423, 0.01763257011771202, 0.037600379437208176, -0.00932867918163538, 0.006885792128741741, 0.029599003493785858, 0.0028218224178999662, -0.025848999619483948, -0.0015292668249458075, -0.02985832281410694, -0.0549507699906826, -0.015384969301521778, 0.016115311533212662, -0.05953855440020561, -0.05638876557350159, -0.08523552864789963, 0.030439408496022224, 0.00521290535107255, -0.04960206151008606, 0.003826947882771492, -0.04253782704472542, 0.07870785146951675, -0.08523237705230713, -0.05025956779718399, -0.007961650379002094, 0.05221224203705788, 0.07043522596359253, 0.023548539727926254, 0.014481575228273869, -0.030776141211390495, 0.017631150782108307, 0.046521108597517014, 0.027762088924646378, -0.08548427373170853, -0.007892535999417305, 0.05191604793071747, -0.025140324607491493, -0.01171261165291071, 0.005096554756164551, 0.007369103375822306, 0.029905634000897408, 0.044741127640008926, 0.08931717276573181, 0.0471348874270916, 0.008144591003656387, 0.04279538244009018, 0.039250608533620834, -0.046676795929670334, 0.002980204299092293, -0.03110680542886257, 0.02156747691333294, 0.06957254558801651, -0.06501661241054535, -0.0014902702532708645, 0.02615131065249443, -0.029802225530147552, -0.010603115893900394, -0.0500725582242012, -0.05385506898164749, 0.03107069991528988 ]
<p>Similar question has been asked but did no get good answers.</p> <p>We know that black hole can confine light, but can we create an ocean black hole - which can confine surface water waves or sound waves in water?</p> <p>Definition:</p> <ul> <li>What is a static water flow which can CONFINE water waves?</li> <li>Is there a configuration confining only surface waves?</li> <li>Is there a configuration confining volume waves?</li> </ul> <p>Description:</p> <p>Inside a confined region any water density perturbations can not propagate outside.</p> <p>PS:</p> <ul> <li>Overall volume of water in the "tank" can not change so the solution when the water is removed faster then the waves travel is ruled out.</li> <li>There possibly can be additional objects presented in the water "tank".</li> <li>It can be some unsual liquid or gas, whith additional "new" properties.</li> </ul> <p>Thanks for your answers.</p>
g5445
[ 0.002600062172859907, 0.025677692145109177, -0.005290870554745197, -0.005947320256382227, 0.035208798944950104, 0.032605066895484924, 0.027835702523589134, -0.040898650884628296, -0.016178105026483536, -0.060221973806619644, 0.025695664808154106, 0.023465922102332115, 0.014808135107159615, 0.02738005295395851, -0.04042183980345726, 0.039711907505989075, 0.04368988424539566, 0.018252668902277946, -0.028452878817915916, -0.049167439341545105, 0.04350043088197708, -0.004009863827377558, 0.03428599610924721, 0.0002563918533269316, -0.037210613489151, 0.03579132258892059, 0.07145345211029053, -0.04966502636671066, 0.0038074490148574114, -0.020958518609404564, 0.02848345972597599, -0.02044924907386303, 0.025789566338062286, 0.019032519310712814, -0.004479116294533014, -0.011639214120805264, -0.025101926177740097, -0.019207166507840157, 0.03664189204573631, 0.05721772462129593, 0.038027673959732056, 0.005230883602052927, -0.051176149398088455, -0.0048322225920856, -0.014216195791959763, -0.04260839521884918, 0.051967158913612366, -0.028721369802951813, 0.026021059602499008, -0.032087188214063644, 0.04087116941809654, -0.0006958697340451181, 0.02177811600267887, 0.0003572613641154021, 0.005050797015428543, 0.04342608153820038, -0.06577157229185104, 0.03848663344979286, 0.03496721759438515, 0.05450854450464249, -0.02113281935453415, -0.023722857236862183, 0.022718673571944237, 0.017209434881806374, 0.04895686358213425, -0.0768684670329094, -0.08258290588855743, 0.0044822851195931435, -0.03907947614789009, 0.045562274754047394, 0.027161022648215294, -0.020949862897396088, -0.02719378098845482, -0.05236020311713219, -0.01035437360405922, 0.07774859666824341, -0.007299169432371855, 0.015139534138143063, -0.039954740554094315, 0.00900288112461567, -0.03400654345750809, -0.010622012428939342, 0.027999212965369225, -0.029327768832445145, 0.0674353688955307, 0.008259251713752747, -0.025222372263669968, 0.0007740929140709341, 0.029641754925251007, -0.024813804775476456, -0.024230867624282837, -0.008195925503969193, 0.045600637793540955, 0.028414955362677574, 0.05264686420559883, 0.023003941401839256, 0.017219973728060722, 0.00409152964130044, 0.03239207714796066, 0.021771114319562912, -0.04578807204961777, 0.029572051018476486, -0.0015177680179476738, 0.011403855867683887, 0.028580961748957634, 0.0010871252743527293, 0.03674917668104172, 0.0019429026870056987, 0.0072177438996732235, -0.0202792901545763, 0.00961238332092762, -0.04455849528312683, 0.017355790361762047, 0.007109195459634066, -0.04920819774270058, -0.012979565188288689, 0.053971339017152786, 0.009128152392804623, 0.04071403667330742, 0.02808440290391445, -0.02299666777253151, 0.05688511207699776, 0.037458959966897964, 0.018084509298205376, 0.05246240645647049, 0.01053067296743393, -0.044266462326049805, 0.04878188297152519, 0.025432651862502098, -0.005519161466509104, 0.0031674702186137438, 0.0244150348007679, -0.051287148147821426, 0.0329492911696434, -0.02712809294462204, -0.008813228458166122, 0.018380871042609215, -0.051990341395139694, -0.0196927972137928, 0.00386426062323153, 0.01888207718729973, -0.018273113295435905, 0.008112575858831406, 0.04059064760804176, 0.007866492494940758, -0.04014197364449501, -0.011693342588841915, 0.029591728001832962, 0.028107084333896637, 0.01456975843757391, 0.004289438482373953, 0.04851518198847771, -0.0003028229111805558, 0.019943218678236008, -0.003386558499187231, -0.00040769149200059474, 0.040259696543216705, 0.06674610078334808, -0.004691750276833773, -0.035862457007169724, 0.015227992087602615, 0.035625383257865906, 0.019174998626112938, 0.027131419628858566, -0.059325337409973145, -0.05758943781256676, 0.029292376711964607, -0.0016775625990703702, 0.0015266351401805878, 0.01104347687214613, -0.0385628342628479, -0.006380819715559483, -0.08399557322263718, 0.12050865590572357, 0.07324805855751038, 0.026836659759283066, 0.04172586277127266, -0.026715561747550964, 0.029110630974173546, 0.0016593371983617544, -0.050248730927705765, -0.016011374071240425, -0.06592864543199539, -0.04011325165629387, 0.0017609952483326197, 0.032221339643001556, -0.02941301465034485, -0.034742679446935654, -0.00223524565808475, 0.03645186126232147, -0.04609404504299164, -0.010032283142209053, 0.012433228082954884, 0.007126735523343086, -0.00251557445153594, -0.015884043648838997, 0.01885310187935829, -0.022128751501441002, -0.015661073848605156, 0.026980729773640633, -0.00726187601685524, -0.0006180762429721653, 0.02078341133892536, -0.016713717952370644, 0.017649779096245766, 0.027169352397322655, -0.028060492128133774, 0.024267546832561493, 0.024930721148848534, 0.02472170628607273, 0.03273468092083931, -0.015011809766292572, 0.04510163515806198, -0.04223832115530968, -0.02645007148385048, 0.021151207387447357, -0.03573696315288544, 0.0206917654722929, -0.022861724719405174, -0.010420825332403183, -0.028655249625444412, 0.0046332888305187225, -0.022650714963674545, 0.04533121734857559, -0.03376602753996849, 0.014573355205357075, -0.04853079468011856, -0.03192866966128349, 0.02807977795600891, 0.0010437954915687442, -0.022154157981276512, -0.033015716820955276, 0.05178326740860939, -0.026644069701433182, -0.006531230639666319, 0.08462026715278625, -0.0342443510890007, 0.032203588634729385, -0.01346283033490181, -0.020002489909529686, 0.06621059030294418, 0.05161259323358536, -0.05446689948439598, -0.014487635344266891, 0.00014749955153092742, -0.014978555962443352, -0.013665834441781044, -0.022613083943724632, 0.04356196150183678, 0.023482486605644226, 0.023403000086545944, -0.03727005422115326, 0.0028818524442613125, -0.00047410951810888946, 0.008747403509914875, -0.006702787708491087, 0.026661686599254608, 0.08066251873970032, -0.054302576929330826, -0.037992168217897415, 0.019202126190066338, 0.048840541392564774, 0.03008398227393627, -0.00019470065308269113, -0.01643257588148117, -0.018468627706170082, -0.027350513264536858, -0.005205742083489895, 0.05253426730632782, 0.04042302444577217, 0.022258486598730087, 0.009695774875581264, 0.007932651787996292, 0.0014305331278592348, -0.015175883658230305, 0.003171049291267991, -0.06091213971376419, -0.005226652137935162, 0.021724309772253036, 0.009036528877913952, 0.050195228308439255, -0.016434434801340103, -0.10357850044965744, 0.03775383159518242, -0.021050957962870598, -0.02036738581955433, 0.011101077310740948, -0.014481285586953163, 0.020966503769159317, -0.06477762758731842, -0.002324701752513647, 0.034617356956005096, 0.004352161660790443, 0.05716688558459282, 0.0057674129493534565, 0.014612659811973572, -0.025194251909852028, 0.017016757279634476, 0.013529866933822632, 0.026125332340598106, 0.03495658189058304, -0.01734556443989277, 0.006066707894206047, 0.027442509308457375, -0.0071661146357655525, 0.03395671769976616, -0.0366336926817894, -0.024297794327139854, 0.03210655227303505, 0.019486229866743088, -0.016519373282790184, 0.02083277702331543, -0.02926790714263916, 0.021938133984804153, 0.019164947792887688, 0.011681981384754181, 0.0296326931566, 0.016504429280757904, -0.017421236261725426, -0.08583732694387436, -0.03073546476662159, -0.03167005255818367, 0.0001274060196010396, 0.0067879753187298775, 0.0637023001909256, 0.057419292628765106, 0.0032544583082199097, -0.015346964821219444, -0.10927659273147583, -0.06615671515464783, -0.01822402887046337, -0.033990759402513504, 0.013645630329847336, -0.001949545694515109, -0.02838413044810295, -0.03367489203810692, 0.03457256406545639, 0.006660135462880135, 0.03775906190276146, 0.003642734605818987, 0.041656844317913055, -0.06953459233045578, -0.012660995125770569, 0.0011739711044356227, -0.056903157383203506, 0.015897639095783234, -0.07075721770524979, -0.06948647648096085, -0.001821175217628479, -0.004162968602031469, 0.05406031012535095, -0.035250820219516754, 0.007949582301080227, -0.03442894294857979, 0.0034996948670595884, 0.05303061008453369, 0.05293721705675125, 0.022140508517622948, -0.021582303568720818, -0.008887724950909615, -0.07342564314603806, -0.037261638790369034, 0.043740250170230865, -0.05217619612812996, 0.0009524273918941617, -0.028165120631456375, 0.07396011054515839, -0.024353820830583572, -0.030194388702511787, -0.0391792356967926, 0.05326320230960846, -0.024480653926730156, -0.0026215296238660812, -0.030450228601694107, 0.004203748889267445, -0.0622713603079319, 0.016311082988977432, 0.04906146228313446, -0.0058226934634149075, 0.0011742139467969537, 0.03745850548148155, -0.019944369792938232, 0.0582737922668457, 0.006177353672683239, -0.08586526662111282, -0.024844950065016747, 0.05475421994924545, 0.01109231449663639, 0.003466786118224263, -0.056096695363521576, -0.04881911352276802, -0.04403454810380936, -0.03243695944547653, -0.09473395347595215, 0.02171570062637329, 0.033239252865314484, -0.0263366661965847, -0.013101058080792427, -0.047581471502780914, 0.0235847570002079, 0.08055925369262695, 0.04048152267932892, -0.018519392237067223, -0.019291216507554054, -0.009940882213413715, -0.025108695030212402, 0.051415108144283295, 0.014337660744786263, -0.08218570053577423, -0.028438864275813103, 0.03314202278852463, 0.0032035282347351313, -0.026562323793768883, -0.0016211901092901826, -0.019930951297283173, -0.011615284718573093, -0.003828809130936861, -0.01914130710065365, 0.0050788880325853825, 0.05771191418170929, 0.013729214668273926, 0.028649955987930298, -0.022825229912996292, 0.0038113310001790524, -0.054864294826984406, 0.019796239212155342, 0.012839308939874172, -0.030984362587332726, 0.009523830376565456, -0.021496988832950592, -0.011480677872896194, -0.012885314412415028, 0.005872449371963739, 0.024223262444138527, -0.0030229452531784773, 0.03144412487745285, -0.060566287487745285, -0.007967423647642136, -0.004850901663303375, -0.015155032277107239, -0.037175606936216354, -0.006298605352640152, 0.049277547746896744, -0.029494432732462883, -0.01373691763728857, 0.06656345725059509, 0.02772802673280239, -0.005582249257713556, -0.024244442582130432, -0.014902140013873577, -0.022064967080950737, 0.00099613843485713, -0.025597920641303062, -0.08498375117778778, -0.08111585676670074, -0.0036902509164065123, -0.04000511392951012, 0.028888361528515816, -0.012673932127654552, 0.022713016718626022, -0.0403996966779232, -0.03927598521113396, 0.035307642072439194, 0.009623310528695583, 0.05648164451122284, -0.05101027339696884, 0.0012128929374739528, -0.07056482136249542, -0.10323839634656906, 0.02721540443599224, 0.046226032078266144, 0.06808516383171082, 0.05656949803233147, 0.05066284164786339, -0.0027147543150931597, 0.0343736857175827, 0.011251125484704971, -0.001653228304348886, -0.03290112689137459, -0.0763421505689621, 0.007264630403369665, 0.0029899142682552338, 0.02585674822330475, 0.04054328799247742, 0.037763357162475586, 0.03246205672621727, -0.022294050082564354, 0.07992994785308838, -0.03622027859091759, 0.006829713936895132, -0.02519199624657631, -0.010859211906790733, 0.002113236812874675, 0.029224157333374023, -0.011305548250675201, -0.019977500662207603, -0.028885437175631523, -0.03243480622768402, -0.023612475022673607, -0.03039122000336647, 0.009055109694600105, -0.025749776512384415, 0.059090666472911835, 0.0007413019193336368, 0.025001361966133118, 0.029522303491830826, 0.004619562067091465, -0.0027763699181377888, 0.048658568412065506, 0.07862550765275955, 0.025265401229262352, -0.022506525740027428, -0.0832846462726593, -0.0035684537142515182, 0.07983016222715378, -0.06559687107801437, -0.00038350923568941653, 0.028954479843378067, 0.019895242527127266, 0.004469686187803745, -0.0008412355091422796, -0.00906048808246851, -0.014006195589900017, 0.05500049889087677, 0.0008131135255098343, -0.008766448125243187, -0.054532118141651154, 0.023979241028428078, 0.04927799105644226, 0.047883011400699615, 0.04615537449717522, 0.011761187575757504, 0.037290409207344055, -0.08420967310667038, 0.04088485985994339, -0.029738541692495346, -0.004051717463880777, 0.048589449375867844, -0.020654497668147087, 0.04613680765032768, 0.036782704293727875, -0.05391444265842438, -0.023747583851218224, 0.0585847906768322, 0.06626567244529724, 0.011970356106758118, -0.04243028908967972, 0.031824707984924316, -0.0529702790081501, -0.06684156507253647, -0.0824461579322815, 0.023409342393279076, -0.042621564120054245, 0.032008327543735504, -0.009329759515821934, -0.002938551362603903, -0.02191849611699581, -0.03815311938524246, -0.030339132994413376, -0.040492817759513855, 0.03438495844602585, 0.09670240432024002, -0.011454562656581402, -0.04829708859324455, 0.019270528107881546, -0.029080508276820183, -0.0061036450788378716, -0.004061514977365732, 0.0041426317766308784, 0.029137136414647102, -0.07041876018047333, -0.00025974935851991177, 0.03978047892451286, -0.027090860530734062, -0.017147228121757507, -0.015690864995121956, 0.0239524208009243, 0.016645807772874832, -0.02503444254398346, 0.0037595804315060377, -0.02036440558731556, 0.027185387909412384, -0.0053658634424209595, -0.06579840928316116, 0.0031819255091249943, -0.0037333955988287926, 0.02825094759464264, 0.003936119843274355, 0.02144276350736618, -0.03380021080374718, -0.003523074323311448, 0.009183826856315136, -0.031045136973261833, 0.0312393456697464, 0.03370819613337517, 0.01694054901599884, -0.013255954720079899, 0.04170995205640793, -0.02680792100727558, 0.009794357232749462, -0.02175716869533062, 0.06200701370835304, 0.025094086304306984, 0.04317454248666763, 0.0007762662135064602, 0.04637119174003601, -0.039244506508111954, 0.010184350423514843, 0.04491443186998367, -0.0006591482670046389, -0.05263013392686844, -0.01780063845217228, 0.024503052234649658, -0.05181264132261276, -0.06530052423477173, -0.01968436688184738, -0.06228606030344963, -0.05223514884710312, 0.061165373772382736, -0.02775678038597107, 0.03006070852279663, -0.05963895842432976, -0.03446818143129349, -0.02932094968855381, 0.028433140367269516, 0.034897349774837494, -0.050715893507003784, -0.038975127041339874, 0.05358157679438591, -0.022023532539606094, 0.06696797907352448, -0.0034942333586513996, 0.01981872320175171, 0.009713984094560146, -0.025947697460651398, 0.002571621909737587, -0.03310265392065048, 0.013605312444269657, 0.05549837648868561, -0.02837829850614071, -0.011093934997916222, 0.009065560065209866, -0.010827161371707916, 0.038208842277526855, -0.04173298552632332, 0.0777219906449318, 0.03925466164946556, -0.056344933807849884, -0.0348019041121006, -0.019632522016763687, 0.04426667094230652, -0.052404168993234634, -0.05652427673339844, 0.01948091946542263, -0.04057500511407852, 0.030351370573043823, -0.014776520431041718, -0.03461074456572533, -0.01913762278854847, 0.0031621160451322794, -0.022801538929343224, 0.050932880491018295, -0.00897723063826561, -0.0010323630413040519, 0.032926931977272034, 0.03972089663147926, 0.003634817199781537, -0.0394088514149189, -0.0018897386034950614, 0.023886296898126602, 0.03514273092150688, -0.0076063829474151134, -0.010998466052114964, 0.01603453792631626, -0.028578292578458786, -0.016240457072854042, 0.009675838053226471, 0.09718964993953705, 0.058856986463069916, 0.004778747446835041, 0.05780641734600067, 0.03355441987514496, -0.04368452727794647, -0.020691076293587685, 0.006421257276087999, -0.07971521466970444, -0.017487969249486923, -0.025456594303250313, 0.0784476101398468, -0.06321632117033005, 0.004058810416609049, 0.06114278361201286, -0.01813061535358429, -0.004468077328056097, 0.0025635932106524706, -0.032838836312294006, 0.04518964886665344, 0.06441967189311981, 0.03488892316818237, -0.01749047450721264, -0.018192576244473457, -0.015182146802544594, -0.02019963599741459, -0.014066290110349655, -0.00001790675196389202, -0.03219166770577431, -0.025253262370824814, -0.020327327772974968, -0.030072491616010666, -0.007626609411090612, -0.011562494561076164, 0.041392263025045395, -0.04576680436730385, -0.06035875156521797, 0.012003597803413868, 0.026626702398061752, -0.01238334085792303, 0.005391784477978945, -0.04951276630163193, -0.02151995711028576, -0.00874831061810255, 0.019870629534125328, 0.03010416403412819, -0.02379179187119007, -0.012991202995181084, -0.0020071330945938826, 0.05300108343362808, -0.004896551836282015, -0.06418761610984802, -0.025505488738417625, -0.07732324302196503, -0.03821064531803131, -0.024441564455628395, -0.0036168296355754137, 0.02153107151389122, -0.006114431656897068, 0.00027204042999073863, -0.013149913400411606, -0.009866486303508282, 0.02785329520702362, 0.019376959651708603, 0.03610328957438469, 0.004057830199599266, -0.05699118226766586, 0.012579016387462616, -0.03111359104514122, 0.0012524628546088934, 0.02999332919716835, 0.002289640950039029, -0.047176435589790344, 0.011171898804605007, 0.030768683180212975, 0.013327843509614468, -0.015476359985768795, 0.08655110746622086, -0.09159261733293533, -0.0016613564221188426, -0.03898134455084801, 0.002189951715990901, -0.005210332106798887, -0.030047301203012466, 0.10249338299036026, 0.044786352664232254, 0.005003930069506168, 0.017391936853528023, -0.011478690430521965, 0.037112824618816376, -0.05159124732017517 ]
<p>Non-linear waves do not superimpose to each other, but why? What characteristics give this property?</p>
g5446
[ 0.031107222661376, 0.019444353878498077, 0.034900568425655365, 0.02115287072956562, 0.016335604712367058, 0.023168379440903664, 0.06793573498725891, -0.0041511449962854385, -0.030034754425287247, -0.03663382679224014, -0.02299584448337555, -0.04795590043067932, -0.0767747238278389, 0.04956570267677307, -0.036340173333883286, -0.041213300079107285, 0.04591698944568634, -0.005346359219402075, 0.05241537094116211, 0.035366497933864594, -0.04204312339425087, -0.014133067801594734, 0.05465599521994591, -0.027495624497532845, -0.01409072894603014, 0.045009832829236984, 0.023778880015015602, -0.05552375689148903, -0.018826281651854515, -0.022376148030161858, 0.028278568759560585, 0.0016930890269577503, 0.00819343701004982, -0.02210552617907524, 0.007628058083355427, 0.03321128711104393, -0.001025459379889071, -0.05538024753332138, 0.03436313197016716, 0.0520838126540184, -0.04556429386138916, 0.02923293597996235, -0.034695882350206375, 0.01044468954205513, -0.030587103217840195, -0.04571285843849182, -0.005162233952432871, 0.018338777124881744, -0.0011098895920440555, -0.08079592138528824, 0.03242411091923714, 0.005923441145569086, 0.07171479612588882, -0.04718007519841194, 0.04056788235902786, 0.02281060628592968, -0.00272866222076118, 0.0357670895755291, 0.032330580055713654, -0.03242391720414162, -0.039267465472221375, -0.011731595732271671, 0.03672723472118378, 0.06581628322601318, 0.03947054594755173, -0.021179508417844772, -0.046628449112176895, -0.059715598821640015, 0.013847960159182549, -0.021446987986564636, -0.030472615733742714, -0.0041185589507222176, -0.03238265961408615, -0.0430418886244297, -0.011523033492267132, 0.01596260629594326, -0.015637336298823357, 0.06896649301052094, -0.06082262843847275, 0.030192507430911064, -0.019037041813135147, -0.02893131785094738, -0.01110293623059988, 0.007607936859130859, 0.06606079638004303, 0.006396160926669836, 0.08973953127861023, -0.037793997675180435, -0.05278852581977844, 0.01631593145430088, 0.05374167487025261, 0.016729678958654404, -0.004211068619042635, 0.04692826047539711, 0.0016860290197655559, -0.007283465005457401, -0.01711982674896717, 0.0026747651863843203, 0.054175615310668945, -0.03994554281234741, -0.00407016696408391, 0.057693496346473694, 0.014308761805295944, -0.02970130182802677, -0.0044879852794110775, -0.022048743441700935, 0.033617518842220306, 0.04057333245873451, -0.030720677226781845, -0.052706148475408554, -0.017249854281544685, 0.010819348506629467, 0.0040165139362216, -0.015869248658418655, -0.035180043429136276, -0.09652863442897797, 0.013128845952451229, 0.0136559484526515, -0.0005518075195141137, 0.026203200221061707, 0.047393426299095154, -0.005299656186252832, -0.00957789458334446, 0.05402238294482231, -0.012208999134600163, 0.006724731530994177, 0.08268893510103226, 0.025264300405979156, 0.06525272876024246, -0.04424172267317772, 0.06956560909748077, 0.05372988060116768, -0.019721196964383125, 0.03312511742115021, 0.029264841228723526, -0.036430131644010544, 0.01395236887037754, -0.03399345651268959, -0.0010173395276069641, 0.024475913494825363, -0.02523261494934559, -0.06368810683488846, 0.06409059464931488, -0.009666429832577705, 0.03579670190811157, -0.1016417145729065, 0.007356566376984119, -0.00962552335113287, 0.005165754351764917, 0.034556128084659576, -0.06131647899746895, 0.0066495053470134735, 0.04377419501543045, -0.014549014158546925, -0.038576629012823105, 0.015065394341945648, 0.007051003631204367, -0.036915965378284454, -0.031037872657179832, -0.027604911476373672, 0.01922597363591194, 0.01288938894867897, -0.04400137811899185, 0.057518236339092255, -0.034527409821748734, -0.05691869184374809, 0.01237638108432293, -0.047542743384838104, -0.012127697467803955, 0.063789963722229, -0.015965251252055168, 0.01327743474394083, 0.010721830651164055, 0.021352192386984825, 0.07368740439414978, 0.07342773675918579, 0.05441077798604965, -0.06289956718683243, 0.04633582755923271, -0.005315868183970451, -0.06622616946697235, -0.0012575293658301234, -0.022049739956855774, -0.008220043033361435, -0.012870963662862778, 0.04748062416911125, -0.004374170675873756, 0.0532563216984272, -0.08247480541467667, 0.014691351912915707, 0.019068587571382523, -0.014451912604272366, -0.007767947390675545, -0.006839624140411615, -0.0002500808041077107, 0.01413603127002716, 0.002933890325948596, 0.014494728296995163, -0.010918720625340939, -0.023127591237425804, -0.008617582730948925, 0.04731256142258644, 0.07401980459690094, -0.05685918405652046, 0.00020199790014885366, 0.03140731528401375, -0.001993879908695817, 0.03930094465613365, 0.05978458374738693, 0.012475620955228806, -0.006126989144831896, -0.037409260869026184, -0.051460251212120056, -0.07072711735963821, -0.01595379039645195, -0.027256352826952934, -0.001161488238722086, -0.01802036724984646, -0.05230375751852989, 0.013228506781160831, -0.01591549813747406, 0.04086374491453171, 0.004975928459316492, 0.015141687355935574, -0.033408015966415405, -0.00960194319486618, 0.019613001495599747, 0.03171248361468315, 0.060642775148153305, -0.015084678307175636, -0.007782552391290665, -0.032239917665719986, 0.02652200497686863, -0.02397247776389122, 0.04457554966211319, -0.015700293704867363, 0.027092013508081436, 0.003710189601406455, 0.005612949840724468, 0.02813013456761837, 0.0082979341968894, -0.008635478094220161, -0.020076902583241463, -0.029951080679893494, 0.01867283508181572, -0.05123640596866608, -0.011807722970843315, -0.0041579799726605415, -0.032630063593387604, 0.022480113431811333, -0.014843345619738102, -0.02205854468047619, -0.06807354092597961, 0.051411379128694534, 0.023173002526164055, -0.028749512508511543, 0.01648428477346897, 0.045566920191049576, -0.06526094675064087, -0.014343628659844398, -0.0069051142781972885, 0.05145344138145447, 0.02141202799975872, -0.03419482335448265, -0.06421549618244171, -0.06281587481498718, -0.006025748327374458, 0.04549297317862511, -0.025347905233502388, -0.011767750605940819, 0.009469178505241871, 0.056410618126392365, 0.013394756242632866, 0.04880835488438606, -0.05617636442184448, 0.0038999735843390226, 0.013287336565554142, 0.04253063723444939, -0.001136526931077242, 0.04152432084083557, 0.003989037126302719, 0.002602537162601948, -0.02240598015487194, -0.0036505560856312513, 0.0016059934860095382, -0.06205148249864578, 0.06741618365049362, 0.034312427043914795, -0.026400553062558174, 0.07024247199296951, -0.03825347125530243, -0.0020231842063367367, -0.01906454563140869, 0.03192213550209999, -0.04975608363747597, 0.018684053793549538, 0.006182362325489521, -0.026682361960411072, 0.017780553549528122, -0.010883648879826069, 0.020745106041431427, 0.00799715705215931, 0.026742903515696526, -0.02835208550095558, 0.018437594175338745, 0.002665633335709572, -0.011083295568823814, -0.03340725228190422, -0.0429866760969162, 0.032222893089056015, 0.011894557625055313, 0.0542328841984272, 0.02229251340031624, 0.00628319289535284, -0.033922962844371796, 0.04043314978480339, 0.02161317504942417, -0.0038262391462922096, 0.01466805674135685, 0.006504214368760586, -0.07864701747894287, -0.07273366302251816, -0.007882646284997463, 0.0052641029469668865, 0.014750921167433262, 0.013464163057506084, 0.008045406080782413, -0.013325316831469536, -0.0022896775044500828, -0.02267037332057953, -0.024733858183026314, 0.013756435364484787, 0.01684066653251648, 0.028836337849497795, 0.011864575557410717, -0.0433296374976635, -0.008132919669151306, 0.018033677712082863, -0.0014102512504905462, 0.07848729938268661, 0.05977172777056694, -0.0005595709080807865, -0.07829438149929047, -0.006176298018544912, -0.048361409455537796, -0.0070907967165112495, 0.015300783328711987, -0.0011323802173137665, -0.0025907685048878193, 0.028481027111411095, -0.00947167444974184, 0.03346845880150795, 0.034839119762182236, -0.030226806178689003, -0.01241537556052208, 0.042617011815309525, 0.027149228379130363, -0.0074362680315971375, 0.02527281828224659, 0.008396821096539497, 0.060298558324575424, -0.028501015156507492, 0.004052906297147274, -0.03536657989025116, 0.03769933804869652, 0.07392045855522156, -0.005990206263959408, 0.037057146430015564, -0.013786384835839272, -0.0020190554205328226, 0.03172141686081886, -0.016714654862880707, 0.016127442941069603, -0.03704719617962837, 0.03048344887793064, -0.019157735630869865, 0.021814698353409767, 0.02209053561091423, -0.013359464704990387, 0.011797909624874592, 0.074461929500103, -0.023056726902723312, -0.008639597333967686, -0.03890012949705124, -0.03844033554196358, -0.004244867712259293, -0.014941769652068615, 0.00041678588604554534, 0.008556605316698551, -0.0007324849138967693, -0.042988456785678864, -0.004207303281873465, -0.002222358947619796, -0.04259912669658661, 0.00396790262311697, -0.023479115217924118, 0.02223537489771843, -0.0314846895635128, -0.01651707850396633, 0.03555254638195038, -0.02161383256316185, 0.0065603358671069145, 0.011672762222588062, -0.06516251713037491, 0.0330544114112854, -0.03026282787322998, 0.04993173107504845, 0.01094614714384079, -0.06223248690366745, -0.03249421715736389, -0.03794369474053383, 0.03331446275115013, 0.005326175130903721, -0.06679891794919968, 0.03405322507023811, 0.048263635486364365, 0.04722525551915169, -0.05856766179203987, -0.009817530401051044, 0.027435442432761192, -0.0196976400911808, 0.034852977842092514, -0.06052529811859131, 0.006374587770551443, 0.014427495189011097, 0.005643005482852459, 0.051337216049432755, -0.026046356186270714, -0.027309952303767204, 0.021970918402075768, -0.057574160397052765, 0.010472962632775307, 0.03116139955818653, -0.010266007855534554, 0.015786057338118553, -0.05666586756706238, -0.03115379996597767, 0.07225073128938675, 0.028150169178843498, 0.05089373514056206, -0.014086535200476646, -0.0345739871263504, 0.026886742562055588, -0.03465011343359947, 0.059588707983493805, 0.09044428914785385, -0.03545333072543144, -0.017472682520747185, -0.09610424190759659, 0.04157219082117081, -0.003587361890822649, 0.030237704515457153, 0.013327393680810928, -0.0343116857111454, -0.024211011826992035, -0.03494787588715553, -0.07199717313051224, 0.023738939315080643, 0.01157640852034092, -0.029949413612484932, -0.0015191447455435991, 0.011607148684561253, -0.05358012020587921, 0.005086776800453663, 0.007945527322590351, 0.00021691713482141495, 0.005217156372964382, -0.015917422249913216, 0.02771446295082569, -0.0101931719109416, 0.05567404255270958, -0.0033944786991924047, 0.01197435986250639, 0.06443501263856888, -0.04296290874481201, -0.017771469429135323, 0.011675073765218258, -0.010006488300859928, -0.043002910912036896, -0.04023608937859535, 0.00912684015929699, -0.011191239580512047, 0.046257294714450836, 0.05257440358400345, -0.013323575258255005, 0.01995524950325489, -0.04859321936964989, 0.04843372479081154, 0.023848460987210274, -0.005248811095952988, 0.011392517946660519, 0.026666348800063133, -0.010845977813005447, 0.012581822462379932, 0.00078423204831779, -0.08149278163909912, 0.02368946745991707, 0.04080098867416382, -0.027926022186875343, 0.0034313255455344915, -0.07515659928321838, 0.04392203688621521, -0.009573666378855705, -0.0053858403116464615, 0.00015295147022698075, 0.07153800874948502, 0.11487177014350891, 0.01886310800909996, -0.03698071092367172, 0.01800304837524891, -0.008749865926802158, -0.04968775436282158, -0.04779043048620224, -0.026816293597221375, 0.006028383504599333, -0.025990428403019905, 0.027551153674721718, -0.03784584626555443, -0.06492260843515396, 0.015225633978843689, 0.005063564050942659, 0.006238406058400869, 0.014924501068890095, -0.012897709384560585, 0.06893394887447357, 0.031472139060497284, -0.06268887966871262, -0.0437774620950222, 0.08045579493045807, 0.04298650845885277, 0.0210254043340683, 0.0024785336572676897, 0.052047692239284515, -0.022509874776005745, 0.11090315878391266, -0.033176347613334656, 0.02141142264008522, 0.010483186691999435, -0.03778429329395294, -0.023244936019182205, 0.04858062416315079, -0.049742408096790314, 0.047535642981529236, 0.04652639105916023, -0.012931635603308678, 0.03277183696627617, -0.015732664614915848, 0.028395557776093483, -0.004696652293205261, 0.009804187342524529, -0.005333899520337582, 0.027716446667909622, 0.011213370598852634, -0.014044885523617268, 0.022054899483919144, -0.01366330310702324, -0.04990266636013985, 0.008463901467621326, -0.031431835144758224, -0.061784494668245316, 0.03544038534164429, 0.048653848469257355, 0.030904842540621758, -0.004035085905343294, 0.022677654400467873, -0.039723873138427734, -0.015995189547538757, 0.03666449338197708, 0.003183480352163315, 0.01887064054608345, -0.024511687457561493, 0.027658425271511078, 0.041260477155447006, -0.013313709758222103, -0.019067997112870216, 0.00840666051954031, -0.00743964733555913, -0.009198466315865517, -0.011826442554593086, -0.003953929990530014, 0.015642818063497543, -0.015386810526251793, 0.022084984928369522, 0.030356137081980705, -0.03048660047352314, -0.004601371940225363, 0.005302819423377514, -0.011390355415642262, -0.010765169747173786, -0.00951103214174509, -0.017881400883197784, -0.021140478551387787, -0.004816795699298382, -0.040398597717285156, 0.04769719019532204, -0.02659171260893345, -0.01947253756225109, 0.024554762989282608, 0.031088953837752342, -0.05742640048265457, 0.04509244114160538, -0.04509640112519264, 0.07316634804010391, 0.029415877535939217, -0.016474632546305656, 0.03680957481265068, 0.009822238236665726, -0.026940641924738884, -0.06432534754276276, 0.041155267506837845, -0.052266743034124374, 0.03681127354502678, 0.016938794404268265, -0.015225752256810665, 0.01636441983282566, -0.0498603992164135, -0.0185344647616148, -0.02484903857111931, -0.020425468683242798, -0.02850441075861454, 0.05735264718532562, -0.05835476517677307, -0.006434739101678133, 0.06347014755010605, -0.04668721929192543, -0.017292562872171402, -0.08287745714187622, 0.015277468599379063, 0.03724236413836479, 0.045113518834114075, 0.035379111766815186, -0.018302084878087044, 0.01699073053896427, 0.012313861399888992, -0.050437092781066895, 0.07432041317224503, -0.10189937800168991, 0.05810186266899109, 0.014402512460947037, -0.049798447638750076, 0.006408129818737507, 0.1063479334115982, 0.02084539085626602, -0.039832666516304016, -0.01917901262640953, 0.051331810653209686, -0.0017726258374750614, -0.03208306059241295, -0.039451271295547485, -0.011869525536894798, 0.02333749644458294, 0.0009951598476618528, 0.010754487477242947, 0.04754367098212242, -0.049398135393857956, -0.027309289202094078, -0.013782014138996601, 0.02352500520646572, -0.005074819549918175, 0.02079722471535206, -0.028323838487267494, -0.0521811842918396, -0.011115293949842453, 0.02305757813155651, 0.02789130248129368, 0.04739745706319809, 0.0238938070833683, -0.03410685434937477, -0.020661482587456703, -0.00399478804320097, -0.01071098167449236, -0.01199903804808855, 0.026293575763702393, -0.0006447501364164054, -0.021797051653265953, -0.03725938871502876, -0.016881084069609642, -0.029514586552977562, 0.021390559151768684, -0.0341576524078846, 0.040883149951696396, 0.02333005517721176, 0.014177841134369373, -0.030915968120098114, 0.02086160145699978, 0.015245881862938404, 0.018289076164364815, -0.007378285750746727, 0.026016535237431526, -0.022054297849535942, -0.01428778562694788, 0.025928163900971413, 0.0422377735376358, -0.03362993896007538, -0.010017390362918377, 0.004604130517691374, 0.028873251751065254, 0.024702657014131546, -0.02253553830087185, -0.005001372657716274, -0.019755514338612556, -0.018916551023721695, -0.08387263864278793, 0.004448979161679745, 0.030125560238957405, -0.02961902506649494, 0.011730257421731949, -0.10040841996669769, -0.027658702805638313, -0.0227496474981308, -0.026473961770534515, 0.01607820950448513, 0.0355069562792778, 0.012184163555502892, 0.05150986090302467, 0.008188961073756218, -0.05379046872258186, 0.012145863845944405, -0.05485863983631134, 0.0032903493847697973, -0.01170811615884304, 0.02435045689344406, 0.028091061860322952, -0.033827491104602814, -0.012426733039319515, -0.06352216005325317, 0.01956573687493801, -0.005104920361191034, 0.015777286142110825, 0.0064671882428228855, -0.0846998542547226, -0.019864629954099655, -0.05441248044371605, 0.002718090545386076, -0.11108044534921646, -0.01585567183792591, 0.02077382057905197, 0.06620853394269943, 0.038436491042375565, 0.01066319365054369, 0.03087010607123375, -0.033347759395837784, -0.03357179835438728, -0.04479963704943657, -0.007157009560614824, -0.019947772845625877, 0.015274938195943832, 0.009272463619709015, 0.02857864834368229, -0.05692971870303154, -0.037905968725681305, 0.046539537608623505, -0.027010932564735413, 0.03842729330062866, 0.08642532676458359, -0.014323160983622074, -0.029503677040338516, -0.0026564865838736296, 0.06225109472870827, -0.03615691885352135, 0.015562079846858978, -0.05352979525923729, -0.01544850692152977, -0.03716269135475159, -0.033031389117240906, 0.009697895497083664, -0.036841414868831635, -0.029498271644115448 ]
<p>I am looking at a 2 Nucleon potential of the form $$V(r)=V_0(r)[a+bI_1\cdot I_2]$$ Where a and b are constants. $I_1,I_2$ are isospins. $V_0(r)$ is of the square well form. My goal is to find an equality for a and b, given that deuteron exists, and that diproton and dineutrons do not. </p> <p>My approach has been the following:</p> <p>2 nucleons can either be in an isosinglet or an isotriplet. The Isosinglet has I=0 and is the following: $$|00\rangle=\frac{1}{\sqrt2}(pn-np),I_1\cdot I_2=-\frac34$$ The isotriplet has I=1 and $$|11\rangle=pp,I_1\cdot I_2=\frac12$$ $$|10\rangle=\frac{1}{\sqrt2}(pn+np),I_1\cdot I_2=\frac12$$ $$|1-1\rangle=nn,I_1\cdot I_2=\frac12$$ So I get the following equations based on V</p> <p>$$\text{Isosinglet: }\frac{V(r)}{V_0(r)}=a-\frac34 b$$ $$\text{Isotriplet: }\frac{V(r)}{V_0(r)}=a+\frac12 b$$</p> <p>Now I am supposed to use the fact that $V_0(r)$ is of the square well form to create inequalities, but I am unsure of where the inequalities come from.</p>
g5447
[ -0.04902666434645653, 0.01756785437464714, 0.0202019065618515, 0.01572839915752411, 0.06681433320045471, -0.012615309096872807, 0.0008414640324190259, 0.020384088158607483, -0.010162794962525368, -0.0509304404258728, -0.11323833465576172, 0.015238402411341667, -0.028082706034183502, 0.007773005403578281, 0.013566166162490845, 0.010308119468390942, 0.013186235912144184, -0.024158429354429245, 0.011994466185569763, -0.03213120251893997, -0.03260127827525139, 0.007539951242506504, 0.017323629930615425, -0.06437349319458008, 0.0455942377448082, -0.012306558899581432, 0.020347967743873596, 0.01882198639214039, -0.10135719925165176, 0.020992876961827278, 0.001836237614043057, -0.005692659877240658, 0.06433901935815811, 0.018740633502602577, 0.017291447147727013, -0.029823841527104378, 0.0388542078435421, -0.010629751719534397, 0.015477530658245087, -0.03426114097237587, -0.018273238092660904, -0.035512525588274, -0.018027348443865776, 0.06682334840297699, -0.03255561739206314, -0.021275971084833145, 0.020995818078517914, 0.011272788047790527, -0.001133657991886139, -0.001397957792505622, 0.042790547013282776, 0.033044978976249695, 0.04583306238055229, -0.05901176109910011, -0.04612215608358383, 0.04602990299463272, 0.025283392518758774, -0.032805830240249634, 0.011732932180166245, 0.06631731986999512, -0.034291822463274, 0.013323127292096615, 0.02267221361398697, 0.01775803230702877, 0.07646972686052322, -0.035084281116724014, -0.008541123010218143, -0.04032692313194275, -0.004045372363179922, -0.011412378400564194, -0.013808785937726498, -0.05071524158120155, 0.01797880232334137, -0.0023942517582327127, -0.004961835220456123, 0.006820457987487316, 0.025292472913861275, 0.02933449111878872, -0.048996325582265854, 0.02769359201192856, -0.020983723923563957, -0.001211559516377747, -0.011711283586919308, 0.060955192893743515, 0.048944536596536636, 0.025844993069767952, 0.04627969488501549, -0.023591423407197, 0.017901290208101273, 0.0545746386051178, -0.012449093163013458, 0.00017622625455260277, -0.013885918073356152, -0.033864859491586685, 0.010630848817527294, -0.02401086688041687, -0.01306099072098732, 0.037134263664484024, 0.004625414498150349, 0.00663915928453207, -0.005784874316304922, 0.0044464529491961, 0.03885090723633766, -0.0427204966545105, -0.03962337225675583, -0.0013048177352175117, -0.009190212935209274, 0.012189689092338085, 0.0031968411058187485, -0.02148006297647953, -0.03137049078941345, -0.030920827761292458, 0.014655382372438908, 0.027538415044546127, -0.012620300985872746, 0.01142172608524561, 0.010010686703026295, -0.04687298834323883, -0.001240302692167461, 0.07313147932291031, 0.016194956377148628, 0.03244493901729584, -0.0028500345069915056, 0.058420468121767044, 0.026549216359853745, -0.02162308804690838, -0.013862431980669498, 0.026004238054156303, 0.0592435821890831, 0.007585329934954643, 0.014661186374723911, -0.05457114800810814, -0.030884306877851486, 0.022121889516711235, -0.013892227783799171, -0.015964724123477936, 0.039214763790369034, 0.006471177563071251, -0.020938660949468613, -0.03746036812663078, 0.05667233094573021, 0.01925368793308735, -0.016763687133789062, 0.0010381692554801702, -0.018136974424123764, -0.0002072621282422915, -0.018468543887138367, -0.023464344441890717, -0.0345177985727787, -0.018478786572813988, -0.03583959490060806, -0.0044646370224654675, 0.021106695756316185, -0.006181201431900263, 0.015720032155513763, 0.009510917589068413, -0.018030885607004166, -0.0605146624147892, 0.014752663671970367, 0.007316285278648138, 0.026157237589359283, -0.014479784294962883, -0.048742204904556274, -0.0019116951152682304, -0.002150533488020301, -0.0002891789481509477, 0.055279962718486786, -0.04841955751180649, 0.022432424128055573, -0.08548274636268616, -0.04969874396920204, 0.022169355303049088, 0.03974219784140587, -0.009726199321448803, -0.0036685923114418983, 0.007617840077728033, -0.08457999676465988, 0.013830584473907948, 0.04077072814106941, -0.014996367506682873, -0.007178049068897963, 0.032447464764118195, -0.013728860765695572, 0.057973284274339676, -0.0766051858663559, -0.046512704342603683, 0.024440135806798935, -0.0047730146907269955, -0.07300660014152527, -0.0026454017497599125, -0.01976761966943741, 0.022946897894144058, 0.050411902368068695, 0.05575158819556236, 0.01619766093790531, -0.03792715072631836, 0.05719660595059395, -0.06315932422876358, 0.08200357109308243, 0.015392126515507698, -0.08237817138433456, -0.004671964328736067, 0.019432075321674347, -0.016961678862571716, 0.016474606469273567, 0.011128220707178116, 0.05226293206214905, 0.012056229636073112, 0.04406741261482239, 0.00430449889972806, -0.04642101377248764, -0.04689259082078934, -0.012895380146801472, 0.020038504153490067, -0.02637431211769581, -0.017945196479558945, 0.011536178179085255, 0.030791599303483963, -0.06091746315360069, 0.0011468438897281885, 0.015708936378359795, -0.03160079941153526, 0.03614337742328644, 0.06072912737727165, 0.004030828829854727, 0.00840967707335949, -0.07373136281967163, 0.05773521587252617, 0.06619098037481308, 0.008433205075562, -0.02345607988536358, -0.06122501194477081, -0.024108219891786575, -0.028449667617678642, 0.004757773131132126, 0.013499507680535316, -0.05875176563858986, 0.009980134665966034, -0.021993082016706467, -0.029054079204797745, -0.05408401042222977, 0.005970580969005823, -0.06489633023738861, 0.07307162135839462, 0.06530234962701797, 0.03956983610987663, 0.025004377588629723, -0.0023976874072104692, -0.003475235076621175, 0.07934287190437317, -0.01946370303630829, -0.035336367785930634, -0.0966474860906601, 0.007102408912032843, -0.05905766412615776, 0.023754993453621864, 0.06584224104881287, 0.01280729379504919, -0.04643883928656578, -0.06729544699192047, 0.004225612618029118, -0.022691024467349052, 0.013472783379256725, 0.010447797365486622, -0.0505581758916378, 0.023290352895855904, -0.03962945565581322, -0.0218457393348217, 0.03344214707612991, 0.040007349103689194, 0.004567483440041542, 0.0537073016166687, -0.0062949275597929955, 0.005292626563459635, 0.024189749732613564, -0.030668223276734352, 0.047314781695604324, -0.03773775324225426, -0.009313907474279404, 0.0063808271661400795, 0.014333394356071949, 0.012040523812174797, -0.020652368664741516, 0.016290511935949326, 0.03939281031489372, -0.06149037554860115, -0.01807723008096218, -0.033461593091487885, 0.04106677323579788, 0.0003324169374536723, -0.011603443883359432, 0.051380693912506104, 0.034713245928287506, -0.006859363988041878, -0.016722362488508224, 0.026250088587403297, -0.03676864877343178, -0.022890157997608185, -0.0000729066232452169, 0.005248195957392454, 0.003365991171449423, 0.021180562674999237, -0.028722407296299934, -0.024136492982506752, -0.004212459549307823, -0.08463679254055023, 0.004390109796077013, -0.022257724776864052, 0.0429406575858593, 0.021201374009251595, -0.05874887481331825, 0.025576690211892128, -0.02033158764243126, -0.020924510434269905, 0.03333911672234535, 0.025391288101673126, 0.05480710044503212, -0.013372279703617096, 0.03564988076686859, -0.009165959432721138, -0.012862799689173698, -0.012212147936224937, 0.028353046625852585, 0.09220573306083679, -0.012458058074116707, -0.02180696278810501, -0.027768194675445557, 0.03101879358291626, -0.08874097466468811, -0.015205100178718567, 0.03980901837348938, -0.009045210666954517, 0.030792316421866417, -0.013658883981406689, -0.03136717900633812, -0.04400626942515373, -0.014187514781951904, 0.06523191928863525, 0.08744839578866959, 0.010634804144501686, 0.004415387287735939, 0.0011263905325904489, -0.08643615990877151, 0.018647450953722, 0.0030602042097598314, 0.01596640609204769, 0.024575531482696533, -0.006254411302506924, 0.024227965623140335, -0.007725934963673353, -0.037829454988241196, 0.004921073094010353, 0.0926591157913208, 0.03805764392018318, -0.008813324384391308, 0.006594511680305004, 0.010243220254778862, 0.004348572343587875, -0.03649777173995972, -0.012203526683151722, 0.013130012899637222, -0.005069815553724766, 0.014599606394767761, -0.025652628391981125, -0.0033992512617260218, -0.007109438069164753, -0.0003733913763426244, 0.011546717956662178, 0.041424743831157684, 0.024389125406742096, 0.02375379391014576, 0.04527093097567558, 0.04574112594127655, 0.032265614718198776, -0.012274547480046749, -0.03173051401972771, 0.01830902509391308, 0.0265580452978611, -0.0003834008821286261, 0.015596658922731876, 0.05859117582440376, -0.016090376302599907, 0.038333140313625336, 0.046528346836566925, -0.013684945181012154, -0.07286729663610458, 0.0066159749403595924, -0.06648968905210495, 0.032640401273965836, -0.008640133775770664, -0.008148803375661373, -0.020458880811929703, -0.07057379931211472, 0.024701107293367386, -0.003484009765088558, 0.0019390764646232128, 0.038225118070840836, -0.06387146562337875, -0.05644974857568741, -0.008898225612938404, -0.013305846601724625, -0.05366840586066246, 0.005872737616300583, -0.056146007031202316, 0.03594835847616196, -0.05034434795379639, -0.041755251586437225, 0.024932177737355232, -0.013893049210309982, 0.006147532258182764, 0.010368971154093742, 0.03037395142018795, 0.0613112673163414, 0.03067781589925289, -0.010929672047495842, -0.012282011099159718, 0.005761625245213509, -0.010822996497154236, -0.013435191474854946, -0.053767334669828415, -0.007127823773771524, 0.042766351252794266, -0.0004698942939285189, -0.04626964405179024, 0.08366746455430984, 0.02371222898364067, 0.07341041415929794, 0.048737429082393646, 0.055832330137491226, 0.02967381291091442, -0.01533033512532711, 0.021423952654004097, -0.0014755422016605735, 0.03687206283211708, -0.07276669889688492, 0.0006143994978629053, -0.054226599633693695, -0.03535567596554756, -0.04210205376148224, 0.034934088587760925, 0.03111235983669758, -0.0005883061094209552, -0.013334731571376324, -0.009951931424438953, 0.017079593613743782, 0.07113128155469894, -0.07213371247053146, -0.05246352776885033, -0.017604172229766846, 0.0014034474734216928, -0.020436665043234825, 0.004827328957617283, -0.005226385314017534, -0.07273491472005844, -0.031245000660419464, -0.01274297758936882, 0.008691349066793919, 0.007258591707795858, 0.010412808507680893, 0.05935224890708923, -0.013558789156377316, 0.000619591970462352, 0.0521487221121788, -0.0258665569126606, 0.03688358515501022, -0.010242423042654991, -0.10890721529722214, 0.05868856608867645, -0.08002051711082458, -0.06668614596128464, -0.016410568729043007, 0.02244945801794529, 0.005678634159266949, -0.026127878576517105, -0.016344159841537476, 0.009934680536389351, 0.0193221103399992, -0.006318866740912199, -0.02938084863126278, -0.02522580325603485, -0.025361448526382446, 0.010294975712895393, -0.04722701013088226, 0.09062738716602325, 0.04154525697231293, -0.011670452542603016, -0.013137293048202991, -0.006369989365339279, -0.00244337716139853, 0.0028275202494114637, -0.018611764535307884, 0.022529078647494316, 0.033355049788951874, 0.02006480284035206, 0.04827779904007912, -0.009509393014013767, 0.04774627089500427, -0.004960133694112301, 0.04827423393726349, 0.053769391030073166, -0.04345491901040077, 0.02915741316974163, -0.004969539120793343, 0.013719085603952408, -0.0016186634311452508, 0.07172702252864838, 0.019459756091237068, 0.009295374155044556, 0.015438186936080456, -0.012283312156796455, 0.006328344810754061, -0.007633406203240156, 0.05610546097159386, 0.05062999576330185, 0.004989111330360174, 0.004263832233846188, -0.004991278052330017, 0.011314209550619125, -0.026269348338246346, -0.045185260474681854, 0.09379132091999054, 0.005509250797331333, 0.014056052081286907, -0.018691491335630417, 0.03186210244894028, -0.02671435847878456, -0.06801073253154755, -0.07156319171190262, 0.009759691543877125, 0.053193602710962296, 0.004415060859173536, -0.02795741707086563, -0.050368987023830414, -0.019859230145812035, 0.016344275325536728, 0.013921206817030907, -0.054990869015455246, -0.023609770461916924, -0.02371346205472946, -0.0006811016355641186, 0.03550935909152031, -0.005212679039686918, 0.003999507520347834, 0.021431591361761093, -0.08033829927444458, -0.039526697248220444, -0.03659417852759361, -0.061316896229982376, 0.016150858253240585, 0.02022181823849678, -0.013278394937515259, 0.047166790813207626, -0.048589784651994705, 0.025594189763069153, 0.013943400233983994, -0.08713290840387344, 0.0010415647411718965, 0.04542257636785507, -0.02398807927966118, -0.004899788647890091, 0.052379075437784195, 0.016651680693030357, -0.021074410527944565, 0.06500249356031418, -0.032317113131284714, 0.009026623331010342, -0.020703691989183426, -0.00785038247704506, 0.026132451370358467, -0.04176676645874977, 0.04844966158270836, -0.0019336611730977893, 0.013311431743204594, -0.016623398289084435, 0.022138062864542007, 0.023479117080569267, -0.028336595743894577, -0.007013462018221617, 0.018111679702997208, 0.008721337653696537, -0.0592341274023056, 0.01176801323890686, 0.035779401659965515, -0.015126417391002178, -0.010790543630719185, 0.07312522828578949, 0.0011739832116290927, -0.03674442321062088, -0.03148328512907028, -0.00619901530444622, -0.01681862212717533, 0.0004064241948071867, -0.04372599720954895, -0.0680169016122818, 0.0009604209335520864, 0.010535862296819687, 0.010675996541976929, -0.043142225593328476, -0.03708813712000847, 0.01234001386910677, 0.016177456825971603, -0.029658431187272072, 0.03525235131382942, 0.02624758891761303, -0.018464580178260803, 0.03219154477119446, -0.0336286835372448, 0.02613312005996704, -0.06293418258428574, -0.006688757333904505, 0.02373824082314968, 0.03397148475050926, -0.04585298150777817, 0.009150296449661255, 0.023819727823138237, -0.04349339380860329, 0.0030518134590238333, 0.04062648117542267, -0.0024329328443855047, -0.04789634793996811, 0.026537680998444557, -0.013820193707942963, -0.015249887481331825, -0.06224062666296959, 0.044912513345479965, 0.0618479922413826, 0.008349829353392124, 0.02074725739657879, 0.017530672252178192, 0.03907090425491333, 0.030549421906471252, 0.02697102539241314, -0.038817379623651505, 0.004750282038003206, -0.05335607752203941, -0.020332999527454376, -0.02177237533032894, 0.04295967519283295, 0.02635449729859829, 0.020990479737520218, 0.0025554855819791555, 0.046674925833940506, 0.05825522541999817, -0.004521104507148266, 0.0611342154443264, 0.026296958327293396, 0.04959811270236969, -0.021845510229468346, -0.00703200651332736, 0.01833914965391159, 0.07196182757616043, -0.009825903922319412, 0.015578838996589184, 0.0014842319069430232, -0.0232721995562315, -0.03174496069550514, 0.026637880131602287, 0.0008612971287220716, -0.04140995815396309, -0.06871700286865234, -0.022159023210406303, 0.07391048967838287, -0.06591980904340744, -0.004061182960867882, 0.021539224311709404, 0.012532742694020271, 0.004518573172390461, -0.014025678858160973, -0.011013871990144253, -0.06363854557275772, -0.006394381634891033, -0.022064238786697388, -0.04948180913925171, 0.009626256301999092, 0.012937001883983612, 0.04568634182214737, -0.00752644008025527, 0.030278773978352547, 0.01037403754889965, -0.005194924771785736, 0.01677175611257553, -0.028570177033543587, 0.014395742677152157, -0.05960278958082199, -0.0013772877864539623, 0.02696812152862549, -0.03867044299840927, -0.06328559666872025, 0.014558911323547363, 0.07845085859298706, 0.026583746075630188, 0.008051315322518349, 0.03202733397483826, 0.0018334779888391495, -0.003769718576222658, -0.025539236143231392, -0.04794794321060181, -0.01440650038421154, 0.03526896983385086, -0.009938990697264671, 0.014116231352090836, 0.01133311539888382, 0.022630318999290466, -0.046463966369628906, 0.022321632131934166, -0.043357592076063156, -0.01699475757777691, 0.025154776871204376, -0.025074534118175507, -0.0625372901558876, 0.03141635283827782, -0.028695477172732353, -0.035937756299972534, -0.02084050513803959, 0.1105940043926239, -0.020214997231960297, -0.06426001340150833, 0.011898092925548553, 0.07025334239006042, 0.03171767666935921, -0.02439989522099495, -0.026396363973617554, 0.033581968396902084, -0.07466886937618256, -0.018108148127794266, -0.06341296434402466, -0.013880999758839607, 0.0019943753723055124, -0.0017233602702617645, 0.08009682595729828, -0.02774168737232685, 0.010344386100769043, -0.08295499533414841, -0.012174919247627258, -0.007024950347840786, 0.01347817201167345, 0.06594514101743698, -0.04405226558446884, -0.01630157046020031, 0.013942262157797813, 0.011805188842117786, -0.05108616128563881, 0.022469820454716682, 0.03294571116566658, -0.02817775309085846, 0.025451114401221275, -0.022906428202986717, 0.015458823181688786, 0.013872801326215267, -0.01198457833379507, 0.0066679599694907665, -0.04157106578350067, 0.01032417081296444, -0.00018438269034959376, 0.05919378995895386, -0.055957965552806854, 0.023770401254296303, 0.08607921004295349, -0.05773305147886276, 0.026036584749817848, -0.02298184297978878, 0.00650868471711874, -0.016560617834329605, 0.09231206029653549, 0.00586254708468914, 0.02771901711821556, 0.0010428664973005652, -0.03159810230135918 ]
<p>This question is not about phase velocity changed which causes refraction, but about the real time itself being slower by the gravity of any object (from general relativity).</p> <p>If so, would this mean any light traveling inside a glass would be slower than in the air because it is directly affected by gravity of glass? Does this effect also contribute to refraction? How much this effect cause the light to slow down?</p>
g5448
[ 0.037131037563085556, 0.08358018845319748, 0.030467797070741653, 0.03424958139657974, -0.005573117174208164, -0.014016840606927872, 0.04492291063070297, 0.033432163298130035, -0.013830139301717281, -0.008427826687693596, 0.0537751242518425, -0.023327486589550972, -0.016934821382164955, 0.013248494826257229, -0.013478584587574005, 0.013754742220044136, 0.060592878609895706, -0.028770919889211655, -0.019929029047489166, 0.008367195725440979, 0.02724212408065796, -0.044986430555582047, -0.006814564578235149, -0.05267338827252388, -0.04200979322195053, 0.01686875708401203, 0.02446553111076355, -0.04244029521942139, -0.07548880577087402, 0.020377730950713158, 0.05317318066954613, -0.013553142547607422, -0.019614895805716515, -0.05469415336847305, 0.027588529512286186, -0.03827366232872009, 0.05448145791888237, 0.014435453340411186, -0.000493856961838901, -0.005653244908899069, 0.004359400365501642, 0.03258480876684189, -0.019328143447637558, -0.013692134991288185, 0.03463795408606529, 0.018648184835910797, 0.022153183817863464, 0.022619852796196938, -0.04031538590788841, -0.06090308725833893, -0.0585147924721241, 0.055655594915151596, -0.00026446321862749755, 0.03695138916373253, 0.0259811133146286, -0.013135651126503944, 0.004066660534590483, 0.04151860997080803, 0.05238392576575279, 0.011348025873303413, -0.020813509821891785, -0.01868823915719986, 0.0012272100429981947, 0.005926058162003756, 0.009844498708844185, 0.025339139625430107, -0.05252200737595558, -0.06135660782456398, 0.07571322470903397, -0.046652086079120636, -0.0180245079100132, 0.03325042501091957, -0.011831198818981647, -0.043610911816358566, -0.0002071933849947527, -0.0003195877361577004, 0.007688438985496759, 0.008421262726187706, -0.013378208503127098, 0.007776556070894003, -0.0005962076247669756, -0.03415727987885475, -0.013936172239482403, 0.033148352056741714, 0.02747480198740959, -0.03138188645243645, -0.0014692842960357666, 0.024223828688263893, 0.031106289476156235, -0.005646555684506893, 0.0938832014799118, -0.08709615468978882, 0.03020138293504715, 0.0652315616607666, 0.02092987671494484, 0.0205675195902586, -0.021703308448195457, 0.023967701941728592, -0.02316395938396454, 0.008686376735568047, -0.034168973565101624, -0.018115291371941566, -0.0001369711826555431, 0.04030151292681694, -0.004414716269820929, -0.026872698217630386, 0.04524020105600357, -0.027520572766661644, -0.025263410061597824, 0.02359192818403244, 0.005986788775771856, -0.07739037275314331, -0.029514184221625328, -0.03804168105125427, -0.03191642090678215, -0.016233228147029877, 0.09357520192861557, -0.037408772855997086, 0.009254173375666142, 0.06254251301288605, 0.014295653440058231, 0.04996052011847496, -0.018013162538409233, 0.06651294231414795, 0.006647489033639431, 0.007881700992584229, 0.00901100505143404, 0.020930569618940353, 0.03384377434849739, 0.018853848800063133, -0.05298998951911926, 0.03393620625138283, -0.007905199192464352, 0.012240099720656872, -0.053627315908670425, 0.01302607823163271, 0.06038385257124901, -0.012447708286345005, 0.005584519822150469, -0.01883186399936676, 0.02801930531859398, -0.02909332700073719, -0.010376576334238052, -0.018226416781544685, -0.029112858697772026, -0.005772764328867197, 0.01802748255431652, 0.037119295448064804, -0.009457929991185665, 0.0010710667120292783, 0.00932509545236826, 0.013702194206416607, 0.01407537516206503, -0.011265709064900875, 0.015452812425792217, -0.007233616895973682, 0.007447212468832731, -0.005301299039274454, 0.03281109407544136, 0.03672012686729431, 0.039750657975673676, -0.026364464312791824, 0.027228042483329773, 0.020912406966090202, -0.06137513369321823, -0.0018861397402361035, -0.019589770585298538, -0.018890973180532455, 0.022153783589601517, -0.11339372396469116, -0.05661793798208237, -0.012427029199898243, -0.007015683688223362, 0.09253818541765213, 0.04218752309679985, 0.04695258289575577, 0.05110351741313934, 0.026271861046552658, -0.0677289366722107, 0.014893820509314537, -0.021975534036755562, -0.05338436737656593, -0.0839720368385315, -0.09152451902627945, 0.019793063402175903, -0.002357001882046461, 0.028607605025172234, 0.004294560756534338, -0.05080242082476616, -0.015398348681628704, -0.039325278252363205, -0.03642578423023224, -0.00013402989134192467, -0.007790516596287489, 0.011574266478419304, -0.0020470404997467995, 0.0265334639698267, 0.01357244048267603, -0.07178515940904617, 0.07622476667165756, -0.02559824101626873, 0.02954772859811783, 0.06673642992973328, -0.05597073957324028, 0.03304921090602875, 0.0054899342358112335, -0.06422789394855499, -0.03496203571557999, -0.0009528587106615305, -0.014907978475093842, 0.0625452920794487, 0.032731398940086365, 0.07081320881843567, -0.03521091490983963, 0.0336124449968338, 0.04053134471178055, -0.0063902451656758785, 0.011070390231907368, 0.031606558710336685, 0.08296114951372147, -0.020485274493694305, 0.08476216346025467, -0.010820374824106693, 0.0002107721084030345, 0.010956297628581524, -0.06390676647424698, 0.008554522879421711, -0.01429105456918478, 0.029974909499287605, -0.014296324923634529, 0.024682579562067986, 0.03511796146631241, -0.030947839841246605, 0.0007996389758773148, 0.029153544455766678, 0.040513936430215836, -0.06374888867139816, 0.019115960225462914, 0.019345059990882874, -0.011882573366165161, 0.01041052583605051, -0.018324006348848343, -0.014397037215530872, 0.010028512217104435, -0.00929946918040514, -0.02615073323249817, 0.002722817938774824, -0.02677900902926922, 0.023480212315917015, 0.02769480086863041, 0.05253898352384567, 0.04128488525748253, -0.033369824290275574, -0.014552216976881027, -0.04059957340359688, 0.03524152189493179, -0.013374188914895058, 0.023825647309422493, -0.004607649520039558, -0.008200505748391151, -0.026011552661657333, -0.0015944552142173052, -0.0024418248794972897, -0.02125977724790573, -0.013890111818909645, 0.01088343933224678, -0.009281261824071407, 0.09833117574453354, 0.023438801988959312, 0.05653867870569229, 0.011171737685799599, 0.015720339491963387, 0.04303646460175514, -0.028431132435798645, -0.010917632840573788, 0.008651738986372948, -0.01386088877916336, -0.008128910325467587, 0.021125489845871925, -0.0165737085044384, -0.042675308883190155, -0.045077383518218994, -0.10925136506557465, -0.010135462507605553, -0.029298631474375725, -0.06831265985965729, -0.005057279020547867, 0.03415738418698311, -0.00422045448794961, 0.01988363079726696, -0.0105904471129179, 0.06428579241037369, 0.028354115784168243, 0.027824554592370987, -0.00030789896845817566, 0.06209124997258186, 0.04060901328921318, -0.03898221626877785, -0.03037351369857788, 0.0190884992480278, 0.01189486775547266, -0.02961394190788269, 0.025667423382401466, 0.05360537767410278, 0.03349988907575607, 0.0011097588576376438, -0.05009526014328003, -0.021864313632249832, 0.020259153097867966, -0.04533613473176956, 0.04805011302232742, 0.1100098267197609, -0.024955112487077713, 0.09035581350326538, -0.026747843250632286, 0.007880492135882378, -0.015038028359413147, 0.03781668096780777, -0.005714788567274809, -0.006679539103060961, 0.03136275336146355, 0.003146727103739977, -0.07502086460590363, 0.012087507173418999, 0.01735517382621765, -0.011182746849954128, 0.0585598424077034, 0.014809072017669678, -0.0005237304721958935, 0.02157518081367016, 0.005433836951851845, -0.02701369673013687, -0.04803399369120598, -0.0022517347242683172, -0.06291629374027252, 0.04972906410694122, -0.03734979033470154, 0.02825300022959709, 0.05329132825136185, 0.03267192095518112, 0.018281761556863785, -0.003710712306201458, -0.021328607574105263, 0.019314933568239212, 0.043259430676698685, 0.019476663321256638, 0.01146874949336052, -0.017619330435991287, -0.0064980206079781055, 0.007964393123984337, 0.07336009293794632, -0.026989473029971123, 0.005189479794353247, -0.04129907488822937, -0.04504919797182083, 0.00867487397044897, -0.000767041405197233, 0.07879653573036194, 0.03928809612989426, -0.06218494102358818, -0.023325886577367783, -0.05890911817550659, 0.04650652036070824, 0.016746772453188896, -0.03146124258637428, -0.01691425032913685, 0.020719990134239197, 0.001482754829339683, -0.013373554684221745, 0.05225030705332756, -0.018266092985868454, 0.047944679856300354, -0.021584386005997658, 0.05976558104157448, 0.039322178810834885, 0.008927703835070133, 0.024222509935498238, -0.020876025781035423, -0.0042830039747059345, 0.013083532452583313, 0.05820378288626671, 0.003687329590320587, 0.05676542967557907, 0.01024600025266409, -0.0030100916046649218, -0.009064432233572006, -0.010055753402411938, -0.04912295192480087, 0.013304615393280983, -0.038310907781124115, -0.046920500695705414, -0.020931750535964966, 0.012895387597382069, 0.03368597850203514, -0.00849437527358532, 0.02794228121638298, -0.019771551713347435, 0.0030045441817492247, -0.0025187013670802116, 0.021522320806980133, -0.004809551406651735, 0.026342682540416718, 0.02660459093749523, 0.04461868852376938, -0.012853448279201984, 0.006919856648892164, 0.05351011082530022, -0.005076353903859854, -0.06600740551948547, 0.004249909892678261, -0.025296106934547424, -0.010046004317700863, -0.07020781934261322, -0.0798817127943039, 0.04634058102965355, 0.05726097896695137, 0.0043767825700342655, -0.001811389927752316, 0.06682835519313812, 0.04091262444853783, 0.037943802773952484, 0.018576567992568016, -0.035981472581624985, 0.002324064262211323, 0.005258283577859402, 0.04078324884176254, 0.0568142794072628, -0.006875291001051664, -0.06089763343334198, -0.04265664890408516, 0.028781462460756302, -0.013165449723601341, -0.020684698596596718, 0.01841086521744728, -0.012680561281740665, 0.031680379062891006, 0.02404903620481491, -0.02517123706638813, 0.023813527077436447, 0.017701875418424606, 0.002528942422941327, 0.023357221856713295, 0.06599783152341843, -0.020762795582413673, 0.003119813045486808, 0.05421941354870796, -0.018489716574549675, 0.012634974904358387, 0.014211946167051792, -0.019130101427435875, -0.04758283868432045, 0.02144380286335945, 0.015794498845934868, -0.025505267083644867, -0.05013111233711243, -0.001814037561416626, -0.05540168285369873, 0.00013638153905048966, -0.02674044668674469, 0.00975029356777668, -0.02787284553050995, 0.05739014968276024, 0.016750862821936607, 0.03762269765138626, -0.021533319726586342, -0.016377108171582222, -0.01517507340759039, -0.04952848702669144, -0.031252678483724594, -0.027211137115955353, -0.016848832368850708, -0.015278437174856663, -0.020970094949007034, 0.06031098589301109, 0.053343724459409714, 0.01175336167216301, -0.05097491294145584, 0.02153223194181919, 0.004677589517086744, -0.006174738053232431, -0.055760107934474945, -0.00009917828720062971, 0.06659390777349472, -0.04767575114965439, -0.0031911067198961973, -0.027963340282440186, -0.08854348212480545, 0.08970274031162262, -0.030800141394138336, -0.06466428935527802, 0.03935370221734047, -0.06800676137208939, -0.04777286574244499, -0.03894710913300514, -0.04044804349541664, 0.024305282160639763, 0.011506706476211548, 0.00235049263574183, -0.010922442190349102, -0.019956910982728004, -0.03852856904268265, -0.017116444185376167, 0.020155703648924828, -0.0701511800289154, -0.000008820356924843509, 0.016047311946749687, -0.01922464929521084, -0.014987772330641747, -0.02655142731964588, 0.07217806577682495, -0.012384402565658092, -0.01646771840751171, -0.00010386553185526282, 0.008356817066669464, 0.03669776767492294, -0.059752438217401505, -0.026150427758693695, -0.016377301886677742, 0.03878045827150345, -0.04445645585656166, -0.00018135903519578278, 0.012186193838715553, -0.025073319673538208, 0.01841316558420658, 0.0328044518828392, 0.051809050142765045, 0.001241822843439877, -0.0016482622595503926, 0.015363485552370548, -0.020970923826098442, -0.006833399645984173, -0.0035010334104299545, 0.037511538714170456, -0.02474917098879814, -0.017145462334156036, -0.004971060436218977, 0.03591269254684448, 0.02897072397172451, 0.025931542739272118, 0.014647599309682846, -0.10317070782184601, 0.008931218646466732, -0.013003336265683174, 0.04195977747440338, 0.0035809159744530916, -0.01668693497776985, -0.01713941991329193, -0.014843912795186043, 0.05965610221028328, -0.0074655585922300816, -0.002073070965707302, 0.021494541317224503, 0.00803771335631609, 0.07233907282352448, -0.006552049424499273, 0.0375165194272995, -0.03010011836886406, -0.028498556464910507, 0.05566182732582092, -0.049786731600761414, 0.036932118237018585, 0.049675095826387405, -0.010066390968859196, -0.03440767526626587, -0.00857558473944664, -0.06822139024734497, 0.042345184832811356, -0.02484896406531334, 0.010445991531014442, -0.020106660202145576, -0.03302796185016632, -0.0299143735319376, -0.05959421768784523, -0.008308780379593372, -0.028050661087036133, 0.03896414861083031, -0.003553954418748617, -0.013754363171756268, -0.024004871025681496, 0.005822601728141308, 0.0018511738162487745, -0.014925780706107616, 0.003776234108954668, 0.0011829212307929993, -0.0011343511287122965, -0.03154493495821953, -0.02047235704958439, 0.06279389560222626, 0.0059473710134625435, -0.05474943295121193, 0.01568416692316532, -0.042704492807388306, -0.08174443244934082, -0.05538608506321907, -0.06682570278644562, -0.012192454189062119, -0.017409637570381165, 0.037110090255737305, -0.031031064689159393, 0.06713695824146271, 0.011003470048308372, 0.003822904545813799, 0.041094254702329636, -0.08422525972127914, -0.01166844554245472, -0.03098955750465393, -0.022572163492441177, -0.010626777075231075, 0.0877697765827179, 0.011551945470273495, 0.02963295392692089, 0.01721130684018135, 0.05224700644612312, 0.005644641816616058, -0.045675698667764664, -0.03337753936648369, -0.012349422089755535, -0.02620629221200943, -0.025796325877308846, -0.07578454911708832, 0.019518908113241196, -0.023608235642313957, 0.030163168907165527, -0.024191848933696747, 0.013344615697860718, 0.026752153411507607, -0.05871617794036865, -0.01857655681669712, -0.0217007864266634, 0.013356724753975868, 0.013015631586313248, -0.03591016307473183, -0.032160528004169464, -0.019701018929481506, 0.05572015419602394, 0.009449009783565998, -0.019638093188405037, 0.006437316071242094, -0.03340510278940201, -0.0036893924698233604, 0.02373456582427025, -0.023949839174747467, -0.058877523988485336, 0.04096480458974838, -0.07653304189443588, 0.04371367767453194, 0.07385869324207306, -0.03655628487467766, 0.006395178381353617, -0.047067172825336456, -0.016777891665697098, -0.046116072684526443, -0.027378294616937637, 0.022144740447402, -0.05133038014173508, -0.010955487377941608, -0.07444994151592255, 0.08591459691524506, 0.0037205691915005445, -0.07328250259160995, -0.05502922832965851, 0.0007661026902496815, -0.01485531311482191, 0.049211230129003525, -0.01608981005847454, 0.03506327420473099, 0.014922724105417728, -0.049114394932985306, 0.0336093008518219, 0.019590547308325768, 0.03928057849407196, -0.032694004476070404, 0.005023662466555834, 0.025493977591395378, 0.037960235029459, 0.0181041918694973, -0.04660964384675026, -0.03165149688720703, 0.023668577894568443, 0.0420449823141098, 0.02827008254826069, 0.04992096871137619, 0.03816364333033562, 0.01072275172919035, -0.01286510843783617, 0.0565565787255764, -0.031006574630737305, 0.017892546951770782, 0.017232056707143784, -0.07603105902671814, -0.009516242891550064, 0.006083362270146608, -0.018821801990270615, 0.030271878466010094, -0.03883117437362671, -0.039537619799375534, 0.04595238342881203, 0.025952817872166634, -0.04101116210222244, -0.050348225980997086, -0.07170557975769043, -0.011034663766622543, -0.019902130588889122, -0.01277079340070486, -0.016704382374882698, -0.0054203225299716, -0.031137941405177116, -0.04703202471137047, -0.023043600842356682, 0.019983353093266487, 0.05426701158285141, 0.021032217890024185, 0.011952687986195087, -0.016540488228201866, 0.022576825693249702, -0.029191814363002777, -0.009494565427303314, -0.026502249762415886, -0.02591845765709877, 0.019917408004403114, -0.026201607659459114, -0.07848695665597916, -0.004249230958521366, -0.051912933588027954, -0.004176712594926357, 0.014136656187474728, 0.031114669516682625, -0.06676642596721649, -0.05333003029227257, -0.025931915268301964, 0.04455581307411194, -0.016244452446699142, -0.011417397297918797, 0.016067378222942352, -0.013200338929891586, 0.03256556764245033, -0.0009978385642170906, -0.03436894342303276, 0.018019355833530426, 0.023408303037285805, 0.02685614489018917, 0.01505742035806179, -0.018909865990281105, 0.021012824028730392, 0.06185629591345787, 0.0016373650869354606, 0.032851189374923706, -0.0035306529607623816, 0.035071562975645065, -0.004877392668277025, -0.030498074367642403, 0.05708249285817146, -0.04033322632312775, -0.008680256083607674, 0.0030972198583185673, -0.021280091255903244, 0.009887711144983768, -0.004129291512072086, -0.03928569704294205, -0.023529358208179474, 0.027600368484854698, -0.0006783782737329602, 0.001279633492231369, -0.0037272050976753235, -0.05765073746442795, -0.04231421649456024, 0.07585782557725906, 0.03625112026929855 ]
<p>This problem is similar, but also different question from my previous question. They are both unfortunately long.</p> <p><strong>Problem/Solution #1</strong></p> <p><img src="http://img215.imageshack.us/img215/6696/problem2f.jpg" alt="">! <img src="http://img59.imageshack.us/img59/4281/sol2pp.jpg" alt="">!</p> <p><strong>Quick Concept Check</strong></p> <p>a) Could someone briefly explain to me why the block on top can accelerate, but the one hanging on the pulley does not?</p> <p><strong>Problem/Solution #2</strong></p> <p>Consider the set up below. What is the minimum force required so that the 3kg block remains on the 8kg block? Given that the coefficient of static friction between the blocks is 0.8 and the coefficient of kinetic friction between the 8kg block and the surface is 0.4.</p> <p><img src="http://img714.imageshack.us/img714/1299/contr.jpg" alt="">!</p> <p><img src="http://img163.imageshack.us/img163/5941/contrd.jpg" alt="">!</p> <p>$\sum F_x' = F - (N' + \mu_k n) = 8a$</p> <p>$\sum F_y' = n = (8g + \mu_ s N)$</p> <p>$\sum F_x = N' = 3a$</p> <p>$\sum F_y = \mu_s N = 3g$</p> <p>Solving the systems of equations above, you should get that $F_{min} = 11g(\mu_k + \frac{1}{\mu_s}) = 177.87N$</p> <p><strong>Point of the question and why the heck is this so long</strong></p> <p>Notice how the 3kg block is actually "attached" tot he 8kg block, yet the solution here didn't include it in its free-body diagram and they even included the reaction force from the 3kg on the 8kg.</p> <p>Compared with the cart problem where the hanging mass is also touching the cart, no reaction force was drawn and they even treated the three mass as a single mass. David explained this to me last night and I thought I got it, but I went to bed and started thinking about it and it became even more confusing!</p> <p>Could you have solved the first problem with the cart WITHOUT taking all three mass into the cart's free body diagram? Is there another way of applying Newton's Second Law to the cart problem?</p>
g5449
[ 0.0361185222864151, 0.02681509591639042, 0.023744840174913406, -0.013079731725156307, 0.021032515913248062, 0.02255597896873951, 0.02547507733106613, -0.008860952220857143, -0.03397507965564728, -0.014211629517376423, -0.013141877949237823, 0.011165344156324863, 0.005014297552406788, -0.01448794174939394, -0.010714653879404068, 0.06196867674589157, 0.10390793532133102, -0.03157437965273857, 0.04307237267494202, -0.0024646189995110035, -0.020089466124773026, 0.032927848398685455, -0.09302403777837753, -0.07043734192848206, -0.026892228052020073, -0.03167113661766052, 0.00480669317767024, -0.027759360149502754, -0.06490819156169891, 0.052588339895009995, -0.050454966723918915, -0.030323360115289688, 0.003033893881365657, -0.06737268716096878, -0.06964324414730072, -0.021862231194972992, 0.08084665983915329, 0.03368204087018967, -0.03312147781252861, 0.01436493918299675, 0.005007407162338495, -0.0473308339715004, 0.019166624173521996, -0.009281131438910961, -0.06371590495109558, -0.01661570928990841, -0.036695677787065506, -0.011639014817774296, 0.022731609642505646, -0.009727977216243744, -0.014904890209436417, 0.03528866544365883, 0.035020459443330765, -0.03001532144844532, -0.04271797835826874, 0.0741988942027092, 0.05117938667535782, 0.008802011609077454, -0.04569243639707565, 0.03386233001947403, -0.08783859759569168, -0.010215980000793934, 0.06457841396331787, -0.04264000058174133, 0.003516456577926874, -0.06736015528440475, 0.008636990562081337, 0.03929324075579643, 0.013465006835758686, -0.018310772255063057, -0.008250056765973568, -0.007813542149960995, 0.04242316260933876, -0.06994596123695374, 0.0007509266724810004, 0.01678363047540188, 0.004550037439912558, -0.0023836251348257065, 0.041886188089847565, 0.0067741116508841515, -0.00003153303623548709, 0.04595031216740608, -0.017316201701760292, 0.018185516819357872, -0.0136339720338583, 0.004869752563536167, -0.013199717737734318, -0.017311731353402138, -0.051021941006183624, 0.04873129725456238, 0.0005600036820396781, 0.03226790204644203, 0.04026129096746445, 0.03310879319906235, -0.020845234394073486, 0.031805507838726044, 0.0156860314309597, 0.06919025629758835, 0.03143053501844406, 0.01180772390216589, -0.030138853937387466, -0.03870977833867073, -0.014096231199800968, -0.0037582318764179945, 0.03361158072948456, -0.023750072345137596, 0.026806067675352097, 0.062433741986751556, 0.00554471742361784, -0.042606171220541, -0.029924381524324417, -0.02863846719264984, -0.03599781543016434, -0.0677536353468895, 0.0246853269636631, -0.06414583325386047, 0.022777287289500237, 0.026507500559091568, 0.006074058823287487, -0.003442497691139579, -0.02492799051105976, -0.009037292562425137, -0.01336929202079773, 0.041530270129442215, 0.01894989237189293, -0.10278524458408356, 0.021234922111034393, 0.004538349341601133, 0.00939206127077341, -0.034177515655756, -0.02005590684711933, -0.0014248564839363098, 0.015042305923998356, -0.006344576366245747, -0.01847759261727333, 0.015167463570833206, -0.004608287010341883, 0.025772642344236374, 0.030510947108268738, -0.021493395790457726, -0.053370486944913864, -0.047692637890577316, -0.03911419212818146, 0.03230632469058037, -0.028345568105578423, 0.04122147336602211, 0.004824124742299318, 0.027705008164048195, 0.08231639117002487, -0.04841360077261925, 0.005464320071041584, 0.041667819023132324, -0.010150312446057796, -0.012963769026100636, 0.05976872146129608, 0.025289181619882584, 0.07410372793674469, 0.01865648850798607, 0.048848241567611694, 0.0013248110190033913, 0.035323452204465866, -0.05801727622747421, 0.030723659321665764, -0.014692709781229496, -0.07253007590770721, 0.013695969246327877, 0.026444563642144203, -0.06838922947645187, 0.05737465247511864, -0.031362708657979965, -0.06396923214197159, -0.03752746805548668, 0.01988290436565876, 0.06192021071910858, -0.01847747154533863, -0.006333633325994015, 0.06872519850730896, -0.02868700958788395, 0.018219538033008575, 0.010354387573897839, 0.032902415841817856, -0.0225499477237463, 0.02310137264430523, 0.05024510994553566, -0.008994504809379578, 0.016117088496685028, 0.02903127670288086, 0.02754269167780876, -0.0069283004850149155, -0.011573493480682373, -0.07179725915193558, 0.023104028776288033, 0.00786135159432888, 0.07135077565908432, -0.09876561164855957, 0.03264504298567772, -0.004434571601450443, -0.05403289571404457, 0.00602298229932785, -0.04359864071011543, 0.03615200147032738, 0.02505115233361721, 0.001918109366670251, -0.027472732588648796, -0.03232646733522415, -0.020890500396490097, 0.016094857826828957, -0.005274264141917229, 0.021066712215542793, -0.010265794582664967, -0.005699388217180967, 0.04819897934794426, -0.06754259020090103, 0.04934973269701004, -0.04785702005028725, -0.06740399450063705, 0.009060250595211983, 0.025728369131684303, -0.02197098918259144, 0.012606148608028889, 0.0033162604086101055, -0.019767768681049347, -0.0215629730373621, 0.024597501382231712, -0.03712762892246246, -0.015451510436832905, -0.018267089501023293, -0.03996841982007027, -0.047624945640563965, 0.025511588901281357, -0.052808042615652084, -0.005464262794703245, -0.02671506628394127, -0.04871365800499916, 0.023345403373241425, 0.027724649757146835, -0.014096169732511044, 0.011810320429503918, -0.00010158526129089296, 0.05338594689965248, 0.03651372343301773, -0.037667952477931976, -0.017511358484625816, -0.06566343456506729, 0.03546768054366112, -0.0075659253634512424, 0.06140373647212982, 0.03748583421111107, 0.03192480280995369, 0.024087803438305855, -0.0011478244559839368, 0.010623165406286716, -0.030569398775696754, -0.013835208490490913, 0.03989754617214203, 0.03584981709718704, -0.020682627335190773, 0.027839142829179764, -0.030480651184916496, -0.056479983031749725, 0.00568737369030714, -0.036700259894132614, 0.009897606447339058, 0.11975320428609848, -0.11993059515953064, 0.023756222799420357, -0.030743880197405815, -0.06837624311447144, 0.015311931259930134, -0.008497712202370167, -0.057256195694208145, -0.026497500017285347, -0.007891593500971794, 0.0013047981774434447, -0.018380120396614075, -0.02049139514565468, -0.017172904685139656, 0.002226916141808033, -0.03815275803208351, 0.02932598441839218, 0.029457999393343925, 0.00229287869296968, -0.005557219963520765, -0.04117587208747864, 0.02092145010828972, 0.03764066845178604, -0.0038447310216724873, 0.00300103728659451, -0.03981903940439224, 0.02548520267009735, -0.035429395735263824, 0.05183044448494911, 0.07608774304389954, 0.0746692419052124, -0.008096574805676937, 0.0457080639898777, -0.042808786034584045, -0.08540131151676178, -0.032627418637275696, -0.04841157793998718, 0.10467437654733658, -0.011125091463327408, 0.0037524926010519266, 0.03767569363117218, 0.04629068821668625, 0.026087289676070213, -0.017388002946972847, -0.03901617228984833, 0.03443222492933273, 0.05480137839913368, 0.019663896411657333, 0.08330310136079788, -0.0086222467944026, -0.02950085513293743, -0.03762747719883919, -0.00782888662070036, 0.03857240080833435, 0.000996018759906292, -0.024665582925081253, -0.026859836652874947, -0.015670549124479294, -0.03653642162680626, -0.008849618956446648, -0.004224700387567282, 0.031508222222328186, 0.03296765312552452, -0.05971520394086838, 0.03063049167394638, 0.01088019646704197, -0.04837670177221298, -0.01070670410990715, 0.05671688914299011, 0.010304620489478111, -0.028112104162573814, -0.030453398823738098, -0.055192649364471436, 0.03056017868220806, 0.024354998022317886, 0.03356083855032921, -0.03557867556810379, -0.01678279973566532, -0.00012995683937333524, -0.020990891382098198, -0.036745697259902954, -0.05039726570248604, 0.006635194644331932, -0.013937286101281643, 0.0311397947371006, -0.030828189104795456, -0.03807326778769493, 0.07184155285358429, -0.016074925661087036, -0.004864867310971022, 0.05042988434433937, 0.003990962170064449, 0.03033331222832203, 0.002117134863510728, 0.006551607511937618, -0.016490332782268524, -0.004377131350338459, 0.01860407553613186, 0.07125939428806305, 0.006445955950766802, 0.028776271268725395, 0.028344903141260147, -0.0038155289366841316, -0.008213777095079422, 0.037535421550273895, 0.0005451589822769165, -0.03157968819141388, 0.03639702871441841, -0.041535384953022, -0.04266974702477455, -0.033618200570344925, 0.05921078845858574, -0.052585482597351074, 0.053449951112270355, 0.003630136139690876, -0.012907974421977997, 0.03516935184597969, 0.04902487248182297, -0.01900961622595787, -0.04831909388303757, 0.040555037558078766, -0.0017465670825913548, 0.057701777666807175, -0.012980571016669273, -0.008036527782678604, 0.017354879528284073, -0.036774780601263046, -0.006390496622771025, 0.029663486406207085, 0.0069737727753818035, 0.03378612920641899, 0.02406718023121357, 0.017199695110321045, 0.06716448813676834, -0.0020357216708362103, -0.0051262760534882545, -0.01976456493139267, -0.004112808499485254, 0.023282544687390327, -0.05363788455724716, 0.0051089390181005, -0.03404669091105461, -0.02479105070233345, -0.010039977729320526, -0.027271980419754982, 0.028528202325105667, 0.02253098227083683, -0.009359404444694519, -0.08280426263809204, -0.028757454827427864, -0.00954375509172678, -0.0034629779402166605, -0.07014627009630203, 0.003993942867964506, 0.04396285489201546, -0.012260571122169495, 0.009223945438861847, 0.013389922678470612, 0.03999514877796173, 0.005742124281823635, -0.05003455653786659, -0.03359270468354225, -0.008232546038925648, 0.015408067964017391, 0.012549487873911858, 0.03771709278225899, 0.006985203828662634, -0.041838254779577255, 0.031699489802122116, -0.026040099561214447, 0.00319083034992218, -0.001465069130063057, 0.05462970212101936, 0.04074679687619209, 0.06480617076158524, 0.009407381527125835, 0.06118255481123924, 0.005582690238952637, 0.06606265157461166, -0.018067017197608948, 0.036307863891124725, 0.00826340913772583, 0.05155292525887489, -0.012334772385656834, 0.008388441987335682, 0.025075118988752365, -0.048160675913095474, -0.004905231762677431, -0.00021518675202969462, -0.023094773292541504, 0.028287280350923538, -0.002724580466747284, 0.045539747923612595, 0.06561169773340225, 0.042292799800634384, 0.014027991332113743, 0.034438371658325195, 0.0008206646889448166, 0.020709626376628876, 0.018660012632608414, -0.02494647167623043, -0.015299714170396328, 0.004532313905656338, -0.015593252144753933, -0.002790350466966629, -0.03550473228096962, -0.01437925174832344, 0.012887801043689251, -0.011874833144247532, -0.019544776529073715, 0.08504454046487808, -0.049003083258867264, 0.03710564225912094, 0.031195228919386864, 0.05857108533382416, 0.06283752620220184, -0.04320213571190834, 0.010791746899485588, 0.020501313731074333, -0.029102375730872154, -0.006021131295710802, 0.04926073178648949, -0.03063051961362362, -0.05388840287923813, 0.04257725179195404, -0.008266420103609562, -0.0024803527630865574, 0.04291995242238045, -0.03049076348543167, -0.04440944641828537, -0.017922578379511833, -0.06559070944786072, 0.03988983854651451, 0.02020495943725109, -0.04946950823068619, 0.005234485492110252, 0.003901965683326125, -0.024261021986603737, -0.002194820437580347, 0.03560851886868477, 0.0014561520656570792, 0.020835472270846367, 0.0006163364741951227, 0.028408674523234367, -0.030159881338477135, 0.011142637580633163, 0.08467089384794235, -0.032084181904792786, 0.061101485043764114, 0.03562841936945915, 0.018039651215076447, -0.005183340050280094, 0.024758590385317802, 0.05115285888314247, -0.01071880292147398, -0.010974700562655926, -0.014231345616281033, 0.046514805406332016, 0.009955234825611115, 0.07002339512109756, -0.03490365296602249, -0.011910410597920418, -0.006384755950421095, -0.03622714802622795, -0.03829267621040344, -0.0258095134049654, 0.059624262154102325, -0.04557251185178757, 0.008497636765241623, 0.02782271057367325, -0.008709986694157124, -0.024800261482596397, -0.003801040118560195, 0.03768715634942055, -0.014105312526226044, 0.03378860279917717, -0.032982662320137024, 0.012589044868946075, -0.06014507636427879, -0.006712247617542744, 0.0351179838180542, -0.025142032653093338, -0.03004554659128189, -0.027227135375142097, -0.06494804471731186, 0.05039220675826073, -0.016501715406775475, -0.03126847743988037, 0.03347289562225342, -0.0173881184309721, 0.004649098496884108, -0.03335142508149147, 0.01694672182202339, -0.015672435984015465, -0.016430577263236046, -0.007282804232090712, -0.04013559967279434, 0.04289042577147484, 0.03889717161655426, 0.04631523787975311, 0.04049127548933029, 0.024027323350310326, 0.023057596758008003, 0.004295655060559511, 0.04713919013738632, 0.017668776214122772, 0.023604633286595345, -0.001075252192094922, 0.019872909411787987, 0.02633422054350376, 0.030035462230443954, 0.05208813399076462, 0.07501193881034851, -0.07296212762594223, -0.0019268147880211473, 0.0036524771712720394, 0.04243357852101326, -0.04907361790537834, -0.00844313483685255, 0.027275389060378075, -0.04969914257526398, -0.04193185269832611, -0.011249211616814137, -0.05611668899655342, -0.044691361486911774, 0.053363822400569916, -0.0302440132945776, -0.027941325679421425, 0.045697856694459915, -0.048336420208215714, 0.007487697061151266, -0.00041182368295267224, -0.0648522675037384, -0.020529920235276222, -0.007906957529485226, -0.01637025736272335, 0.007370558101683855, 0.004912067204713821, 0.05588683858513832, 0.058496762067079544, -0.014228882268071175, -0.017121557146310806, 0.048467572778463364, 0.04278947040438652, -0.04482913389801979, 0.03295342996716499, 0.00823589600622654, -0.04028979316353798, 0.05494018644094467, 0.020782675594091415, 0.0025556813925504684, 0.0005859134253114462, 0.005543355830013752, 0.0039525567553937435, 0.030155638232827187, 0.031193599104881287, -0.062290258705616, 0.030677510425448418, -0.019932353869080544, 0.01649792678654194, -0.05454597249627113, -0.03676708787679672, 0.014478202909231186, -0.01941671594977379, 0.02072228118777275, 0.060013994574546814, -0.012874209322035313, 0.040662072598934174, 0.0015373507048934698, -0.04005333408713341, -0.0019325708271935582, 0.0009646026883274317, 0.058501631021499634, -0.05610327795147896, 0.028517186641693115, -0.029020123183727264, 0.008234469220042229, -0.05283838137984276, -0.0013532062293961644, -0.033885613083839417, 0.053565412759780884, -0.03398049250245094, -0.077515609562397, 0.053211864084005356, -0.0018868623301386833, -0.04864522069692612, -0.006102557759732008, -0.04726549983024597, -0.03345026075839996, -0.030289776623249054, 0.020975325256586075, -0.022840024903416634, -0.0478673130273819, -0.023255232721567154, -0.010866987518966198, 0.053842902183532715, 0.03593233600258827, -0.02030208893120289, -0.007686825469136238, -0.012896209955215454, -0.042917344719171524, -0.029546169564127922, 0.0335242934525013, -0.05809248238801956, 0.028715752065181732, -0.0420977883040905, 0.010911224409937859, 0.004255212377756834, -0.017363011837005615, -0.012106630019843578, 0.03564221039414406, 0.003347045974805951, 0.043227676302194595, -0.02455168403685093, -0.01346409972757101, 0.008996518328785896, -0.02603139728307724, 0.002290027216076851, 0.009290732443332672, -0.051432907581329346, 0.03505309298634529, -0.03229614719748497, 0.010888648219406605, -0.00914352759718895, 0.00421922467648983, 0.024240626022219658, 0.0032708593644201756, 0.06259755790233612, 0.042769309133291245, -0.017599325627088547, 0.01635703258216381, -0.00959775596857071, -0.002422494813799858, -0.04689662903547287, 0.025193924084305763, 0.026507116854190826, -0.013229112140834332, 0.019845174625515938, 0.011786307208240032, -0.05418157950043678, 0.0096424650400877, -0.006374777760356665, 0.06799381226301193, 0.0003839730634354055, 0.013260383158922195, -0.061621587723493576, -0.034212589263916016, 0.007984080351889133, 0.0037378042470663786, -0.05392100289463997, -0.014698125422000885, 0.02326049655675888, 0.028229638934135437, -0.013982271775603294, -0.00839649885892868, -0.03892943635582924, -0.0316593162715435, -0.08449513465166092, 0.0017586168833076954, -0.05181633308529854, -0.07852070033550262, -0.025066496804356575, -0.03825032711029053, -0.02728658728301525, -0.02192659303545952, -0.008843304589390755, 0.03284648805856705, -0.02886801026761532, -0.05091219022870064, 0.005584222264587879, 0.03576328232884407, 0.013239803723990917, 0.004348378628492355, -0.017904385924339294, -0.009891816414892673, 0.05382565036416054, 0.02202560007572174, 0.0013750109355896711, -0.08482597023248672, -0.014959496445953846, 0.009419601410627365, 0.0010449732653796673, -0.01802099123597145, -0.011218901723623276, 0.0606539212167263, 0.013349013403058052, -0.023563096299767494, 0.03225007653236389, 0.037918053567409515, -0.07516201585531235, -0.011660131625831127, 0.032115086913108826, -0.0275031179189682, -0.03757541999220848, 0.006625778041779995, 0.03850432112812996, 0.014244779013097286, -0.0013931822031736374, 0.019263632595539093, -0.01639437861740589, -0.051243189722299576, 0.08814045786857605, -0.06224404647946358, -0.00004426221494213678, -0.014287110418081284 ]
<p>So - a little bit of background. Obviously from Einstein's equations it's shown that energy can be converted to matter and vice versa; in essence, energy and matter are different manifestations of the same "stuff". </p> <p>Now, I've done a bit of reading about the interplay between space and time. Some of what I've read would seem to indicate that just like energy and matter, space and time are different manifestations of the same "stuff", though the majority of what I've read seems to indicate that this isn't the case.</p> <p>So I got to thinking...what if space and time aren't the same thing, but there's interplay between them? What if one is a function of the other? And so I come to my question:</p> <p>Could space be a function of time? Or vice versa?</p> <p>From what I've gathered, our universe is expanding at a faster and faster rate. If space is a (seemingly exponential) function of time, then it makes complete sense that as more and more time passes, the amount of space in existence would increase.</p> <p>In addition (also from what I gather), nothing can go faster than the speed of light. We know that the closer to the speed of light that something is going, the more time slows down for that something, until the speed of light is reached and time stops for whatever it is. </p> <p>Since we're outside observers, a light year is the distance <em>we perceive</em> light to travel in one year. But since (for the light) time stops completely, "how far it travels in a year" becomes meaningless to the light itself. Because no time is passing for it, wherever light goes, it effectively goes that distance in a relative time frame of zero seconds.</p> <p>This phenomenon would also make sense if space is a function of time; if there is no time affecting that light, there would be no space affecting it either. If from the light's perspective time has stopped completely, then from its perspective there would be no distance between it and any destination in the universe; any journey the light made would be instantaneous. Again, that's from the perspective of the light itself, not the perspective of someone who's observing the light.</p> <p>So does that make any sense? Could space be a function of time?</p> <p>Note: I am not a physicist. I am a lay-scientist, in the very loosest definition of that term. I ask this question assuming there are glaring errors and inaccuracies, which is why I'm asking it here - so you can all point me in the right direction.</p>
g11
[ 0.02718912437558174, -0.038036104291677475, 0.03538615629076958, -0.025719335302710533, 0.017051871865987778, -0.0026972487103194, 0.046149853616952896, 0.011690454557538033, -0.02440585382282734, -0.048444245010614395, 0.03524342179298401, -0.010524408891797066, 0.06547016650438309, 0.017445072531700134, -0.026452168822288513, -0.03278191760182381, 0.06803799420595169, -0.040445540100336075, 0.0012988426024094224, -0.023092685267329216, 0.010502141900360584, -0.005572378635406494, -0.00405948655679822, -0.014839605428278446, -0.046996694058179855, -0.03374848514795303, 0.024072181433439255, -0.03821400925517082, -0.016506385058164597, 0.05546167492866516, 0.022225582972168922, 0.013870377093553543, -0.01665271632373333, -0.03434641286730766, 0.0012947545619681478, 0.003749796887859702, -0.012885834090411663, 0.0009003200684674084, 0.050284359604120255, 0.01682114601135254, -0.02976066991686821, 0.014543603174388409, 0.011822541244328022, 0.018160177394747734, 0.07771995663642883, 0.043346941471099854, -0.03668994829058647, 0.03959459066390991, 0.032721180468797684, -0.05581542104482651, -0.02438853122293949, 0.02878497913479805, -0.011625156737864017, 0.03888716548681259, 0.028408443555235863, -0.04800628125667572, 0.0681309774518013, -0.010574325919151306, 0.05579890310764313, 0.05295952782034874, -0.01181734912097454, 0.021270576864480972, 0.02911563031375408, 0.04634198546409607, 0.05217030644416809, -0.022887812927365303, -0.006372408475726843, -0.03784168139100075, 0.04919659346342087, -0.03321043401956558, 0.03745827451348305, -0.058085307478904724, -0.047972436994314194, -0.015464208088815212, 0.050825078040361404, 0.02818472869694233, 0.025313032791018486, -0.0015731343301013112, 0.02032661996781826, 0.024657199159264565, -0.03254921734333038, -0.026572206988930702, 0.0022536320611834526, 0.02752380445599556, 0.024528365582227707, -0.054294273257255554, 0.0038562628906220198, -0.012680348940193653, -0.03561609238386154, 0.04812595620751381, 0.038117825984954834, -0.0001689260097919032, 0.08776339888572693, 0.0303192175924778, -0.0669512078166008, 0.029162786900997162, 0.00749246496707201, 0.022641194984316826, -0.02612527459859848, 0.030497830361127853, -0.07522672414779663, -0.0276925228536129, 0.04825243726372719, 0.03047720342874527, 0.0417361706495285, -0.0706401988863945, 0.004136941395699978, -0.02425270713865757, -0.059988100081682205, -0.027545856311917305, -0.004512156825512648, -0.005146631505340338, -0.030489230528473854, -0.032390255481004715, -0.045588698238134384, -0.04562852904200554, 0.02644653059542179, -0.02646651118993759, -0.02596801146864891, 0.035732269287109375, 0.020806921645998955, 0.0317218042910099, 0.002651994349434972, -0.04217645898461342, -0.05347850173711777, 0.000590224692132324, -0.03516338765621185, 0.022233756259083748, -0.026042258366942406, -0.0027690830174833536, -0.023407522588968277, 0.03363604098558426, -0.003256651107221842, 0.06107060983777046, -0.020044054836034775, -0.021390870213508606, -0.0029000930953770876, 0.0036541682202368975, -0.042037371546030045, 0.061772361397743225, 0.03595370799303055, -0.07046323269605637, -0.02377423271536827, 0.019744114950299263, -0.0684850662946701, 0.01335396058857441, -0.029302701354026794, 0.006013012491166592, -0.01966935023665428, 0.014926427975296974, 0.0199802964925766, 0.10711777210235596, -0.02432948723435402, -0.012043961323797703, 0.0291121993213892, -0.03941914066672325, -0.014172918163239956, -0.0005804532556794584, -0.03335098177194595, -0.02753288485109806, 0.029385050758719444, 0.001998117659240961, 0.009080345742404461, -0.038776978850364685, -0.04364641383290291, 0.02566944994032383, 0.01806432008743286, -0.04410417750477791, -0.023761894553899765, -0.04826163128018379, -0.0562162771821022, 0.0274820476770401, 0.006868112366646528, 0.028750436380505562, -0.0013393990229815245, -0.01159423217177391, 0.03819522261619568, 0.030267182737588882, -0.0994047299027443, 0.008236781693994999, -0.06328020244836807, -0.03508074954152107, -0.012713838368654251, -0.028130263090133667, 0.004568380303680897, -0.0026837470941245556, 0.012718244455754757, 0.0030541308224201202, -0.06513405591249466, -0.009036573581397533, -0.02947787009179592, -0.04094425216317177, 0.0036318672355264425, 0.020916592329740524, -0.015985168516635895, 0.031795527786016464, -0.018043527379631996, -0.017926255241036415, -0.05986001342535019, 0.008199682459235191, -0.04860660061240196, -0.005919673014432192, 0.05060006305575371, -0.0016495821764692664, 0.03848277032375336, 0.008049419149756432, -0.059389423578977585, -0.04797060415148735, -0.015046256594359875, -0.0030130776576697826, 0.08098261058330536, -0.007349050138145685, 0.012620605528354645, 0.020238345488905907, -0.022968405857682228, -0.006818750407546759, -0.007890768349170685, 0.013819131068885326, -0.03573574125766754, 0.006725320126861334, -0.028918549418449402, -0.0024716120678931475, 0.058922383934259415, -0.045575015246868134, 0.009996318258345127, -0.05600231885910034, -0.009651439264416695, -0.04350362345576286, -0.026254795491695404, 0.06502671539783478, -0.06232524290680885, 0.04213042929768562, 0.010197496972978115, 0.004228199832141399, -0.004486147779971361, 0.003693808102980256, 0.0014306931989267468, -0.02566778101027012, 0.0392395555973053, -0.00948408991098404, -0.017052026465535164, -0.01080695353448391, -0.0604461207985878, 0.05054240673780441, 0.06476610153913498, -0.12107719480991364, -0.019292272627353668, -0.046125683933496475, 0.020621366798877716, -0.03153311833739281, 0.053589385002851486, 0.006241805385798216, -0.06314520537853241, 0.01835564523935318, -0.004937186371535063, -0.05426453799009323, -0.0019424424972385168, 0.04642948508262634, -0.07631199806928635, -0.05157739296555519, 0.01293012872338295, 0.011838655918836594, 0.000756752910092473, 0.025051299482584, -0.0025226862635463476, -0.016213558614253998, -0.06328615546226501, 0.058575376868247986, -0.019097112119197845, 0.014441845007240772, 0.00025674476637504995, 0.003080611117184162, 0.02647571824491024, 0.0012113521806895733, 0.004807424731552601, 0.026680100709199905, 0.0055170911364257336, -0.06568360328674316, 0.05031021684408188, -0.031168682500720024, 0.018138350918889046, 0.014510499313473701, -0.07875725626945496, 0.029936783015727997, 0.034638967365026474, -0.039219412952661514, 0.029542988166213036, 0.04857821762561798, -0.008391485549509525, 0.03675343468785286, -0.014987732283771038, 0.018398553133010864, 0.004152224864810705, 0.024093182757496834, -0.024744020774960518, 0.040035102516412735, 0.038221217691898346, -0.03152826428413391, -0.04673906788229942, -0.043765682727098465, 0.003641237271949649, -0.07651454955339432, 0.016171026974916458, 0.05419540032744408, 0.01847180165350437, 0.003621163312345743, -0.04936693608760834, -0.01971760019659996, -0.028249206021428108, -0.0331026166677475, 0.05845455452799797, 0.07753618061542511, -0.03255412355065346, 0.03794807568192482, 0.028369152918457985, 0.029237911105155945, -0.031518228352069855, 0.018407780677080154, 0.03412088379263878, 0.011849325150251389, 0.01455792784690857, -0.03424917533993721, -0.034832753241062164, 0.010765573009848595, 0.05112852528691292, -0.0330825112760067, -0.02098516933619976, -0.054357368499040604, -0.027260582894086838, 0.012261023744940758, -0.031658634543418884, -0.02280415967106819, -0.03134005144238472, -0.014877598732709885, -0.06364987790584564, 0.01991324871778488, 0.0021533139515668154, 0.03351801261305809, 0.02875375561416149, 0.05557870492339134, 0.018027542158961296, 0.03988945484161377, -0.03773615136742592, 0.09818458557128906, 0.014093826524913311, 0.029681190848350525, -0.004253316670656204, 0.025881150737404823, -0.007768434938043356, 0.0247269868850708, 0.04678291454911232, -0.02787182480096817, 0.061422694474458694, 0.011524123139679432, 0.02645055390894413, 0.024850081652402878, 0.028891531750559807, 0.06929752975702286, -0.013712194748222828, -0.06278712302446365, 0.00924171693623066, -0.06461359560489655, 0.05970146879553795, 0.012511315755546093, -0.0127126295119524, 0.004333346616476774, 0.010837862268090248, -0.003372031729668379, -0.02618025802075863, -0.008618978783488274, 0.036290884017944336, -0.010575992986559868, -0.030505763366818428, -0.030967241153120995, 0.06420030444860458, -0.041733939200639725, 0.0010901889763772488, -0.05439893901348114, -0.024137919768691063, 0.030467672273516655, 0.028816809877753258, 0.034983087331056595, 0.05613170191645622, 0.06638205051422119, 0.034716345369815826, -0.027981095016002655, -0.044681668281555176, -0.021249592304229736, -0.014441289938986301, -0.03616690635681152, 0.06916549056768417, -0.00498755369335413, -0.007821899838745594, -0.019559945911169052, 0.03192729130387306, 0.039345547556877136, -0.02435344085097313, -0.012823077850043774, -0.03944999724626541, -0.018668603152036667, -0.011704591102898121, -0.012839351780712605, 0.026524579152464867, -0.011332627385854721, -0.008891263045370579, 0.027709098532795906, 0.08046580851078033, -0.05727185681462288, -0.023353030905127525, -0.04368835315108299, 0.0034963488578796387, 0.005059465300291777, -0.016087714582681656, -0.01658199355006218, -0.0003569767577573657, 0.02239236980676651, 0.026966573670506477, -0.053197167813777924, 0.031266238540410995, 0.04014520347118378, 0.021348709240555763, 0.011936312541365623, 0.03755864500999451, 0.054783377796411514, 0.0011222315952181816, 0.029549315571784973, 0.05061810463666916, -0.01729976013302803, -0.060296837240457535, -0.007577760145068169, 0.008260918781161308, 0.08799007534980774, 0.02631433494389057, 0.03931669890880585, 0.008915593847632408, 0.04711061343550682, 0.026985064148902893, 0.0718713030219078, 0.03355209156870842, 0.015611736103892326, 0.043795146048069, -0.015617555007338524, 0.05014098435640335, 0.01606619730591774, -0.016389280557632446, 0.01795627921819687, -0.03263239562511444, -0.06828313320875168, 0.007021560799330473, -0.03237554803490639, -0.034548595547676086, 0.0864776074886322, -0.017804807052016258, -0.027423039078712463, -0.019102012738585472, -0.03308086097240448, -0.023520635440945625, 0.0028094137087464333, 0.025272024795413017, 0.025212841108441353, -0.05897345021367073, 0.02175944112241268, 0.04548419266939163, -0.02233247272670269, 0.0324852280318737, 0.028761006891727448, -0.010153820738196373, -0.02610483393073082, -0.01375818345695734, 0.059839554131031036, 0.022590845823287964, -0.03649597987532616, -0.038738496601581573, -0.0022692729253321886, -0.009389323182404041, -0.008273839019238949, -0.0603514201939106, 0.0026290223468095064, -0.02126489207148552, -0.008110434748232365, -0.009157134220004082, -0.062095221132040024, 0.03777449578046799, -0.0574483796954155, 0.00407324219122529, -0.002305772854015231, -0.03796202316880226, 0.025097908452153206, 0.02965037152171135, -0.06313222646713257, 0.02276400662958622, -0.0838296040892601, 0.01313759759068489, -0.006458437070250511, 0.008650240488350391, -0.010428273119032383, 0.03693128749728203, 0.03329822048544884, -0.025142353028059006, -0.009596122428774834, 0.009373530745506287, 0.011364302597939968, -0.019685229286551476, -0.02739821933209896, -0.002929984126240015, -0.017793964594602585, -0.018014872446656227, 0.01495517510920763, -0.06209149211645126, 0.070015087723732, 0.001637600944377482, 0.02413605898618698, -0.03884526714682579, 0.057677578181028366, 0.05845428630709648, -0.0526515357196331, -0.05012083798646927, -0.002706199185922742, 0.048368584364652634, -0.02708493173122406, -0.05238554626703262, 0.01837540790438652, 0.04552812874317169, -0.015841636806726456, 0.05723509192466736, -0.006976458244025707, -0.0047950721345841885, 0.010274356231093407, 0.01838255487382412, 0.012306478805840015, 0.03879011049866676, 0.006052837707102299, 0.04177432879805565, -0.03858913481235504, -0.039126165211200714, -0.013578370213508606, -0.021458826959133148, 0.017195433378219604, 0.03025202639400959, 0.026991071179509163, -0.02348540537059307, -0.04507861286401749, 0.01185224112123251, 0.052513618022203445, -0.021209223195910454, -0.009421437978744507, -0.04808765649795532, -0.002146841026842594, 0.01276647299528122, -0.05514741688966751, -0.006819613743573427, -0.02004069648683071, -0.00938860047608614, -0.009605501778423786, 0.0024326446000486612, 0.051047299057245255, 0.012661850079894066, -0.03550997003912926, -0.006036703009158373, -0.036604683846235275, 0.042198941111564636, 0.02256076969206333, -0.030477061867713928, 0.011428596451878548, -0.002258138731122017, -0.03248055651783943, 0.063941590487957, -0.05339522659778595, -0.014743220992386341, 0.026686372235417366, 0.022429950535297394, 0.0035940883681178093, 0.015681413933634758, -0.02408425137400627, 0.004938986152410507, 0.017691558226943016, 0.0276055708527565, -0.05952049046754837, -0.0393068753182888, -0.02244541607797146, 0.03346744179725647, -0.02417481690645218, 0.030768554657697678, -0.02616722695529461, -0.021640485152602196, 0.062214445322752, 0.020757200196385384, -0.05662653595209122, 0.04879340901970863, -0.03853679820895195, -0.04250388592481613, -0.06936932355165482, 0.0379277728497982, -0.04518510773777962, -0.01615414395928383, -0.03727742284536362, -0.015522587113082409, -0.012956150807440281, -0.02840685471892357, 0.07840532809495926, 0.01902107708156109, 0.0005093453219160438, 0.08415471762418747, -0.034235741943120956, 0.020209819078445435, 0.025929192081093788, -0.04554194211959839, 0.007043223828077316, 0.08078503608703613, -0.05192429572343826, 0.03343648090958595, 0.0438961423933506, 0.00213423278182745, 0.01584859937429428, -0.05435747280716896, 0.002958332421258092, -0.01924251951277256, -0.023088762536644936, 0.015895308926701546, 0.026763224974274635, 0.048763006925582886, 0.016382912173867226, 0.023232407867908478, -0.0143465306609869, -0.02509606070816517, 0.025608321651816368, -0.05788537859916687, 0.05718578025698662, 0.01907852292060852, 0.00701270904392004, 0.034168265759944916, -0.006288562435656786, -0.0010802453616634011, 0.022533467039465904, -0.023487411439418793, -0.007429576478898525, -0.0011545750312507153, -0.009647929109632969, 0.003648515557870269, -0.013390235602855682, -0.036777857691049576, -0.03615522012114525, 0.023234901949763298, 0.04507050663232803, -0.0021436219103634357, -0.028820978477597237, 0.037130847573280334, -0.021369028836488724, -0.03981160372495651, 0.00789410900324583, -0.0034603646490722895, -0.014488783665001392, -0.04946160688996315, 0.0024471792858093977, 0.021378502249717712, 0.041867081075906754, -0.015676621347665787, 0.009907389990985394, 0.0021234152372926474, -0.07303111255168915, -0.017809143289923668, -0.011013844050467014, -0.05732117220759392, 0.03448587656021118, 0.02532998099923134, 0.09806054830551147, -0.010674379765987396, 0.000601133971940726, -0.008636864833533764, -0.04722997173666954, -0.011259214952588081, 0.01075716782361269, -0.018911821767687798, 0.018179163336753845, -0.008773177862167358, 0.03530100733041763, -0.07124939560890198, -0.00208973023109138, 0.015494180843234062, 0.03430576249957085, 0.009285267442464828, 0.05252983421087265, -0.011618015356361866, 0.07208319008350372, -0.029767438769340515, 0.02184547297656536, 0.007368570659309626, -0.06746625900268555, -0.06527767330408096, -0.06843770295381546, -0.011127167381346226, -0.008000207133591175, -0.03948366269469261, -0.046703822910785675, 0.0176257211714983, 0.02623719535768032, 0.10062867403030396, -0.018953708931803703, -0.04693612456321716, -0.015301331877708435, -0.037311214953660965, 0.02908932976424694, 0.01766962558031082, -0.02247871458530426, 0.030635206028819084, -0.010731253772974014, -0.002238387707620859, -0.0008218910079449415, -0.05675562843680382, 0.0064024669118225574, 0.09601626545190811, 0.1144104078412056, -0.058707382529973984, 0.013205139897763729, -0.02434518188238144, 0.02801525965332985, 0.01985006593167782, -0.04046718776226044, 0.015238902531564236, -0.03547895327210426, -0.058355122804641724, -0.013281701132655144, 0.001610788400284946, -0.06940493732690811, -0.010042385198175907, 0.03768138587474823, 0.01780002936720848, -0.038311779499053955, -0.0004899289924651384, 0.002613567980006337, 0.05892951413989067, 0.013802994973957539, 0.01753988116979599, -0.004406369756907225, -0.02067095786333084, 0.031430307775735855, 0.03032517433166504, 0.024967363104224205, -0.02526627667248249, -0.019963759928941727, -0.06458493322134018, -0.013591784052550793, -0.005381369963288307, 0.043404046446084976, 0.020415397360920906, -0.04881858080625534, 0.0036787274293601513, -0.013343360275030136, 0.06651812791824341, 0.011854979209601879, -0.0390472412109375, 0.08064373582601547, -0.0034225755371153355, 0.03764307498931885, 0.06983976066112518, -0.021422356367111206, -0.021217171102762222, 0.004823034163564444, -0.046367671340703964, 0.03153467923402786, -0.008239290677011013, 0.009683419950306416, -0.009885632432997227, 0.012017586268484592, -0.013745822943747044, -0.022997461259365082, -0.000495129672344774, 0.0722651556134224 ]
<p>How is the speed of an object in space measured? Also more importantly how do you measure your own speed in space? On the road we use a speedometer which tells us the speed easily. How is it done in space?</p>
g5450
[ 0.020518571138381958, -0.006492295302450657, 0.010951705276966095, -0.030941449105739594, 0.010075220838189125, -0.02604185789823532, 0.017402540892362595, 0.06434682756662369, -0.006082545500248671, -0.009016568772494793, 0.012929300777614117, 0.033701688051223755, 0.016106558963656425, 0.05084501951932907, 0.05105939134955406, -0.05371127277612686, 0.04355786740779877, -0.04837418720126152, 0.04031796753406525, 0.0476577952504158, 0.09104008227586746, 0.021121177822351456, 0.023954078555107117, -0.046947937458753586, -0.05780671164393425, -0.02535809949040413, -0.0058393217623233795, -0.07922239601612091, 0.023976558819413185, -0.010015453211963177, 0.05438016727566719, 0.008672565221786499, -0.02002359926700592, -0.06228259950876236, 0.012743419967591763, 0.00862807035446167, -0.021575644612312317, 0.007191662210971117, 0.0349077470600605, 0.004345187917351723, -0.07245144248008728, -0.08583356440067291, -0.045665379613637924, 0.0008477484225295484, 0.05774569883942604, 0.03162618726491928, -0.04221196100115776, -0.012324808165431023, 0.06436704844236374, 0.07811906933784485, -0.04946977272629738, 0.03039965033531189, 0.04591061547398567, 0.01770397275686264, -0.013658239506185055, -0.025126075372099876, -0.01873065158724785, 0.0034339409321546555, 0.05584631487727165, -0.03078765980899334, -0.009573406539857388, -0.013444388285279274, 0.004224758595228195, 0.02643328346312046, 0.020203782245516777, 0.028396861627697945, 0.004768773447722197, -0.011178099550306797, 0.019378263503313065, -0.026027139276266098, 0.02525167539715767, -0.0016310918144881725, 0.002711113542318344, -0.06468003988265991, -0.09536483883857727, 0.026909714564681053, 0.06074512377381325, 0.00012542451440822333, 0.04789877310395241, 0.07017676532268524, 0.03373417258262634, 0.0036441986449062824, -0.017574533820152283, -0.01588503271341324, 0.0024626238737255335, -0.009885658510029316, -0.045003458857536316, -0.00022933371656108648, -0.034585632383823395, -0.036607347428798676, 0.005442214198410511, 0.0026339725591242313, 0.037572022527456284, 0.0013515191385522485, -0.021221168339252472, -0.004903931636363268, -0.034010376781225204, 0.04252836853265762, -0.03262236714363098, 0.04820264130830765, -0.05229635164141655, -0.017058661207556725, -0.0023432972375303507, 0.012264467775821686, 0.026264028623700142, 0.005071259569376707, -0.019652295857667923, -0.014615126885473728, -0.03839420527219772, -0.03552279993891716, -0.027523303404450417, -0.0725318044424057, 0.003598205978050828, -0.023627907037734985, -0.01693817973136902, -0.03102715127170086, 0.04967906326055527, 0.03047356568276882, -0.02095651812851429, -0.013305824249982834, -0.021118322387337685, 0.029032543301582336, 0.012179539538919926, 0.005419516004621983, -0.012017149478197098, 0.04053013026714325, 0.023384515196084976, -0.07277481257915497, -0.001646500895731151, 0.04694385081529617, -0.034547414630651474, 0.024673955515027046, 0.014274565503001213, -0.030533866956830025, -0.07265922427177429, 0.03822213411331177, 0.007588974200189114, -0.004738460294902325, 0.01337498426437378, 0.004008871968835592, 0.029521413147449493, -0.04049522429704666, 0.013973919674754143, -0.020992711186408997, -0.006034009624272585, -0.016904743388295174, -0.02192346751689911, 0.02295401692390442, -0.0007879623444750905, 0.017123637720942497, 0.0396663062274456, 0.07791056483983994, 0.029633037745952606, -0.005807397421449423, 0.006987292319536209, -0.03002774529159069, 0.03334074094891548, 0.06975708156824112, 0.04012937471270561, 0.04068230837583542, 0.0747031569480896, -0.007785140071064234, -0.02113378793001175, 0.04792947694659233, -0.05009220167994499, -0.011644764803349972, -0.011634423397481441, -0.008711582981050014, 0.016477113589644432, -0.02275346964597702, -0.0007455547456629574, -0.016447532922029495, -0.017267350107431412, -0.00688130734488368, -0.02293091081082821, -0.02197590284049511, 0.015878310427069664, 0.046588923782110214, -0.056379757821559906, -0.009357554838061333, 0.05110159143805504, -0.0493425615131855, 0.02908765710890293, -0.05611434951424599, -0.039344366639852524, 0.012829015031456947, 0.013603408820927143, -0.01961616240441799, -0.01701170951128006, 0.03816676512360573, 0.026299024000763893, -0.026178130879998207, -0.019384149461984634, -0.014773370698094368, 0.00887125451117754, 0.009417662397027016, 0.05259334668517113, 0.017281753942370415, 0.03318636119365692, -0.01324389036744833, -0.006284243892878294, 0.00784119963645935, 0.012205708771944046, 0.012757651507854462, 0.04335428774356842, -0.04618113115429878, -0.013008719310164452, -0.008139442652463913, 0.04485202953219414, 0.025485603138804436, 0.09740442782640457, 0.03271159529685974, -0.007103797979652882, 0.00010542948439251631, -0.019502222537994385, 0.029877055436372757, -0.04805009439587593, -0.051264140754938126, -0.01990377902984619, -0.006423605140298605, 0.014340842142701149, -0.04587956517934799, 0.05416466295719147, -0.024743463844060898, -0.003747594775632024, 0.013251962140202522, -0.051773395389318466, 0.051885493099689484, 0.07020071893930435, 0.01736207865178585, -0.007936648093163967, -0.01982888951897621, -0.05919111520051956, -0.009069329127669334, 0.0373205728828907, 0.020038994029164314, 0.010797609575092793, 0.02280818484723568, 0.00769790867343545, 0.002135629067197442, 0.009548383764922619, -0.040267474949359894, 0.015301566570997238, -0.041732799261808395, -0.007817360572516918, -0.05266081541776657, 0.011015999130904675, -0.014910710044205189, 0.005078896880149841, -0.015509868040680885, -0.01121403556317091, 0.0017882285173982382, -0.04509145766496658, -0.07474979758262634, -0.0257636159658432, 0.035124242305755615, -0.02556396834552288, 0.052022360265254974, -0.08106881380081177, -0.018322380259633064, -0.02738814242184162, 0.06743737310171127, -0.008053343743085861, -0.006122070364654064, 0.019597280770540237, -0.046576663851737976, -0.009328057989478111, 0.04298867657780647, 0.013943759724497795, 0.02314227633178234, -0.029015256091952324, 0.03727919980883598, 0.018421193584799767, -0.07014887034893036, -0.02586648054420948, -0.03773688152432442, 0.04080940783023834, -0.059739869087934494, 0.05709674581885338, -0.014683675020933151, 0.016938578337430954, 0.04811244457960129, -0.04111955314874649, -0.008416798897087574, -0.05628106743097305, -0.03111678548157215, 0.017803963273763657, -0.000033893153158714995, 0.02370312623679638, -0.008315022103488445, 0.02822849154472351, -0.0015008976915851235, -0.03960495814681053, -0.03818118944764137, 0.050669584423303604, 0.08192417025566101, 0.03563036024570465, 0.0035086844582110643, 0.0504746288061142, -0.06099831312894821, 0.06465526670217514, -0.002650669775903225, 0.03580411896109581, -0.018256574869155884, 0.008834458887577057, -0.04463135451078415, 0.00046137033496052027, -0.027061879634857178, -0.032479654997587204, -0.037571970373392105, 0.07273708283901215, 0.04189777746796608, -0.04019507020711899, 0.005456031300127506, -0.016989104449748993, 0.001019762479700148, -0.06023833155632019, -0.015153991058468819, -0.010825342498719692, -0.028992585837841034, 0.011557082645595074, -0.04124930128455162, 0.007998500019311905, -0.027817614376544952, -0.020897507667541504, -0.01570722460746765, 0.06254295259714127, -0.00036445114528760314, -0.033503659069538116, -0.05305647850036621, -0.018570002168416977, 0.02362380549311638, -0.017156455665826797, 0.0075635528191924095, -0.027456896379590034, -0.003046786179766059, -0.019306888803839684, 0.02038385719060898, 0.027892064303159714, 0.0386093407869339, 0.02601459063589573, 0.003577334340661764, -0.04783889278769493, -0.023424144834280014, -0.010582019574940205, 0.03482312336564064, 0.012127946130931377, 0.017378315329551697, -0.04925932362675667, -0.04946856200695038, 0.06352338194847107, -0.009353221394121647, -0.03167510777711868, -0.07449878007173538, -0.03727063909173012, 0.03836503252387047, -0.0034397102426737547, 0.029722578823566437, 0.017412973567843437, -0.04071522504091263, 0.019544677808880806, 0.05928950384259224, 0.04221178591251373, 0.05403245612978935, -0.020926423370838165, -0.05784248560667038, 0.07562592625617981, -0.025062689557671547, 0.04544506222009659, -0.0022327753249555826, -0.008011134341359138, 0.03215872123837471, 0.004117660224437714, -0.014275123365223408, 0.04392640292644501, -0.049315307289361954, -0.0048808082938194275, -0.0071669695898890495, -0.0021612185519188643, -0.04771794006228447, 0.03510428965091705, 0.019153207540512085, 0.011960899457335472, -0.08126220852136612, 0.004710861016064882, 0.00032958658994175494, -0.037786658853292465, 0.002744470490142703, 0.014743557199835777, -0.051314353942871094, -0.011939731426537037, -0.057314854115247726, -0.02048708125948906, -0.028215117752552032, 0.0237735603004694, -0.025482136756181717, 0.007136424072086811, 0.014315194450318813, 0.007805615663528442, 0.03220202401280403, -0.03930983692407608, 0.0920257717370987, -0.011742799542844296, -0.04484681785106659, -0.015244978480041027, -0.05129850283265114, -0.003405830357223749, -0.049463894218206406, 0.0011914547067135572, -0.008232771418988705, -0.07219793647527695, 0.055279385298490524, -0.004079750739037991, -0.06497964262962341, -0.007078342139720917, 0.03100336343050003, 0.01519455574452877, -0.00877040158957243, 0.033098004758358, -0.00972071010619402, 0.022424904629588127, 0.003365675685927272, 0.009043554775416851, -0.02185032144188881, -0.050492703914642334, 0.06216318905353546, 0.029668116942048073, 0.05434570834040642, 0.0177582036703825, 0.05253905430436134, 0.06488841772079468, -0.028128115460276604, 0.05497848987579346, 0.08985268324613571, -0.03589176386594772, -0.014304912649095058, 0.07353027909994125, 0.02842296101152897, 0.008937494829297066, -0.0488368384540081, -0.005189279559999704, 0.05781629681587219, 0.037929411977529526, -0.004670700058341026, -0.07507660239934921, 0.0005774887395091355, -0.039002493023872375, -0.007546935696154833, -0.04454551637172699, -0.016036219894886017, -0.01657206006348133, 0.04362868890166283, -0.05236908420920372, -0.009582973085343838, -0.034365326166152954, -0.004419087432324886, -0.05711540952324867, -0.0074823349714279175, 0.022127564996480942, -0.026949811726808548, -0.04511508718132973, -0.004099265672266483, 0.027105193585157394, 0.010726758278906345, -0.016758065670728683, 0.024011600762605667, -0.0032243430614471436, -0.012050017714500427, -0.033665891736745834, 0.001554943504743278, 0.0039773257449269295, -0.04609213024377823, -0.027136385440826416, 0.01645762473344803, 0.02444676123559475, 0.04684263467788696, -0.010542402043938637, 0.02234727330505848, -0.045049265027046204, -0.05871496722102165, 0.0093618743121624, -0.00007169299351517111, 0.019469918683171272, -0.044105444103479385, -0.013847125694155693, -0.0174309890717268, -0.05704763904213905, 0.005003194324672222, -0.014065609313547611, -0.0009922661120072007, 0.013075821101665497, 0.041295479983091354, -0.01650487445294857, -0.02870848774909973, -0.08247297257184982, -0.0015926276100799441, -0.006562331225723028, -0.03236691281199455, -0.025762297213077545, -0.037200842052698135, -0.03279203549027443, 0.019389132037758827, -0.026204656809568405, -0.016615351662039757, 0.015575340948998928, 0.016100019216537476, 0.01672927476465702, -0.04921703040599823, -0.06081555038690567, 0.03596169874072075, 0.048552826046943665, 0.08944431692361832, -0.016579069197177887, 0.019105706363916397, 0.006396775133907795, -0.028236079961061478, 0.05974002927541733, -0.03362475335597992, 0.07310263067483902, -0.0086447112262249, -0.04989311844110489, -0.007117823231965303, 0.044372282922267914, -0.022444307804107666, 0.029136596247553825, 0.007956458255648613, -0.05760396271944046, -0.009511170908808708, 0.05022415891289711, -0.004430282395333052, 0.032182108610868454, -0.019700825214385986, -0.042833007872104645, -0.005605400539934635, -0.05741794407367706, -0.04408830776810646, 0.00142365088686347, -0.025890963152050972, 0.056226324290037155, 0.036842189729213715, -0.029656877741217613, 0.029965991154313087, -0.02430618368089199, 0.026036493480205536, 0.03716318681836128, -0.0015402360586449504, 0.023962467908859253, -0.04829130694270134, 0.01941889151930809, -0.004491274245083332, -0.06713498383760452, -0.017793023958802223, -0.038899365812540054, -0.05489975959062576, -0.03070876933634281, 0.013983439654111862, 0.012740439735352993, 0.008858704939484596, -0.0439935103058815, -0.014761311002075672, 0.03956538438796997, 0.020963022485375404, 0.037609074264764786, -0.01165766827762127, -0.031275674700737, -0.07045365869998932, 0.0558379702270031, 0.024240899831056595, 0.030925203114748, 0.011761905625462532, -0.037742696702480316, 0.013577671721577644, -0.009758003056049347, -0.012549723498523235, -0.006646181456744671, 0.006093134637922049, 0.04000036045908928, -0.003312653163447976, -0.012287448160350323, 0.008012757636606693, 0.0407007597386837, 0.05756212770938873, 0.01800573617219925, -0.020973151549696922, -0.025083960965275764, 0.022258881479501724, 0.02374844066798687, 0.019910678267478943, -0.010861066170036793, -0.04700840264558792, 0.020293407142162323, 0.005752989556640387, -0.03395198658108711, -0.018712572753429413, -0.07775463908910751, -0.007092096842825413, -0.011724280193448067, 0.04259788617491722, 0.01975797675549984, 0.09256309270858765, -0.07051592320203781, 0.0002566252660471946, 0.05100126564502716, 0.004451263230293989, 0.006743593607097864, 0.017501670867204666, 0.015284918248653412, -0.027409406378865242, 0.06411870568990707, -0.052217934280633926, 0.01732064038515091, 0.01191801205277443, 0.005297655705362558, 0.07046738266944885, -0.025863567367196083, 0.041577816009521484, 0.04436900094151497, -0.06424084305763245, 0.006043465342372656, 0.0016780655132606626, 0.01736046001315117, -0.022138074040412903, 0.03624613583087921, 0.001326854806393385, 0.034513991326093674, 0.04029737412929535, 0.022630374878644943, 0.0013464989606291056, -0.00840445514768362, -0.031041542068123817, -0.01494898647069931, 0.0266534723341465, 0.01757057011127472, 0.026730099692940712, 0.02924274653196335, 0.011200353503227234, 0.030529474839568138, 0.08479190617799759, 0.010816166177392006, 0.012022915296256542, 0.05838754028081894, -0.0052000912837684155, -0.02250058203935623, 0.03007606603205204, -0.06474548578262329, -0.028409942984580994, -0.025491604581475258, 0.013096089474856853, 0.004788069054484367, -0.0432821661233902, -0.0490277037024498, -0.04895929992198944, -0.023259446024894714, 0.036046527326107025, 0.022878404706716537, 0.07270592451095581, 0.03341333195567131, 0.044184360653162, -0.019538892433047295, -0.02853967249393463, 0.009107828140258789, -0.02620737999677658, -0.021833883598446846, 0.03802228346467018, 0.0006858053966425359, 0.023330513387918472, -0.043452195823192596, 0.003496825462207198, -0.0036574704572558403, -0.04970842972397804, -0.06812194734811783, 0.004960129503160715, -0.0030407027807086706, 0.015153632499277592, -0.00024747190764173865, 0.03734210878610611, -0.044714171439409256, 0.060317687690258026, -0.00714609632268548, -0.01811307668685913, 0.027509596198797226, 0.06513221561908722, -0.005728619638830423, 0.061303336173295975, -0.00267300964333117, 0.008688733913004398, -0.01336806919425726, -0.023371756076812744, 0.06298606842756271, -0.11610090732574463, -0.01646375097334385, -0.021164393052458763, -0.008821370080113411, -0.06636353582143784, 0.011144924908876419, -0.0574764683842659, 0.034433312714099884, 0.06776167452335358, -0.034624673426151276, -0.02033507078886032, -0.04587216302752495, 0.05202285572886467, 0.07968314737081528, 0.04817429557442665, 0.008168439380824566, -0.07265232503414154, -0.02477208897471428, 0.023539887741208076, -0.013150352984666824, 0.024764198809862137, 0.0032644905149936676, 0.04902765527367592, 0.020141957327723503, -0.024043641984462738, -0.028354685753583908, -0.036885764449834824, -0.004927577450871468, -0.020122788846492767, -0.04529410973191261, -0.012689963914453983, 0.029342055320739746, 0.009969950653612614, 0.1026415154337883, -0.008114705793559551, 0.00014734458818566054, 0.002193588763475418, 0.04706577956676483, -0.03304784744977951, 0.05901127681136131, -0.04763760417699814, 0.03313339501619339, 0.050588421523571014, 0.027858588844537735, 0.03735821694135666, -0.04606948792934418, 0.03838099166750908, 0.07504162192344666, -0.05121015012264252, -0.05122051015496254, 0.04926973208785057, 0.025424225255846977, 0.039627429097890854, 0.016488244757056236, 0.0375625416636467, -0.005727188196033239, -0.06008811667561531, -0.013825594447553158, 0.05405614525079727, -0.03711213171482086, -0.02001548558473587, 0.0444268062710762, 0.05151926726102829, 0.01964440755546093, -0.004558902699500322, -0.051309190690517426, -0.03309347853064537, 0.019010933116078377, -0.03205374628305435, -0.02326536551117897, 0.005310749635100365, 0.008554133586585522, 0.02682371996343136, -0.006495144218206406, 0.039540767669677734, -0.055941142141819, -0.05645712837576866, 0.005057482980191708, 0.0067905825562775135 ]
<p>When did astronomers realise that the stars were similar to the Sun? I'm not asking for when this was established, but when also the hypothesis was first proposed. </p>
g5451
[ 0.03787549212574959, -0.002188519574701786, 0.03284374251961708, -0.02961115352809429, -0.03536493331193924, 0.011573579162359238, 0.019748924300074577, -0.022903507575392723, 0.011539471335709095, -0.017940087243914604, 0.023724548518657684, 0.056623123586177826, 0.04446830600500107, 0.022175336256623268, 0.04830273985862732, 0.03319892659783363, 0.013289017602801323, -0.00822974368929863, 0.04202858358621597, 0.019256649538874626, 0.0028344839811325073, 0.017324553802609444, 0.018916131928563118, -0.021787090227007866, -0.0892840176820755, -0.008398332633078098, -0.049128443002700806, -0.04440133273601532, 0.04763699695467949, -0.04211489483714104, 0.11454688012599945, 0.026196856051683426, 0.0663173645734787, -0.007216187193989754, 0.049790654331445694, -0.08498302847146988, -0.05095045641064644, 0.020745079964399338, -0.004382223356515169, -0.006107307504862547, 0.03468303009867668, 0.05298830196261406, 0.030206065624952316, 0.07123565673828125, 0.010593087412416935, -0.05784827098250389, -0.009952587075531483, 0.001588504179380834, 0.04755886271595955, -0.03182978928089142, 0.011937074363231659, 0.06154118478298187, 0.05406351760029793, -0.010477119125425816, -0.012039721012115479, 0.009989679791033268, 0.031977422535419464, -0.009341421537101269, 0.09598083794116974, -0.01396180596202612, -0.027575161308050156, 0.014540523290634155, -0.024065883830189705, 0.03068120777606964, 0.015106555074453354, 0.011527896858751774, 0.06115336716175079, 0.03224455937743187, 0.05620487779378891, -0.014421410858631134, 0.027073191478848457, -0.02154839038848877, -0.0035006050020456314, 0.049410346895456314, -0.0022980610374361277, -0.011456500738859177, -0.01786968670785427, -0.01494844350963831, -0.019413603469729424, 0.0002589857904240489, 0.06164204701781273, -0.06664203852415085, -0.015212763100862503, 0.031303174793720245, 0.04197884723544121, -0.05106006935238838, -0.01687622256577015, 0.037928394973278046, 0.01995893195271492, -0.004081083461642265, -0.03079346753656864, -0.059789951890707016, 0.022117627784609795, -0.045257072895765305, 0.019775191321969032, -0.0037880470044910908, 0.02246330864727497, -0.012985972687602043, -0.04308507964015007, 0.02550276182591915, -0.07427172362804413, -0.015430302359163761, -0.0003281014214735478, 0.05030246451497078, 0.008912306278944016, 0.07315525412559509, 0.03325917199254036, -0.03714985400438309, -0.0124792056158185, -0.010085978545248508, 0.010255594737827778, -0.041046664118766785, 0.03243233263492584, -0.048859842121601105, -0.04296071454882622, -0.017607556656003, 0.06889039278030396, -0.06254679709672928, 0.038728658109903336, 0.03359858691692352, -0.03131765499711037, -0.022130493074655533, 0.006712844595313072, 0.059679124504327774, -0.03401555120944977, -0.05029000714421272, 0.013028823770582676, -0.026217101141810417, 0.000530327029991895, -0.07810113579034805, 0.0006177806062623858, 0.0007388152298517525, -0.04258241876959801, -0.02888128161430359, 0.0009554025600664318, 0.004705567378550768, 0.0287221260368824, -0.06329604238271713, 0.013503048568964005, 0.03478308022022247, -0.002475085901096463, 0.044468823820352554, 0.03721274808049202, -0.033804841339588165, 0.005508300848305225, 0.03398684784770012, 0.0010093867313116789, -0.0410027951002121, -0.047626812011003494, 0.006550705060362816, -0.016112003475427628, 0.07459546625614166, 0.015132497996091843, -0.053053319454193115, -0.030965175479650497, -0.014973564073443413, -0.0073670679703354836, 0.01145945768803358, -0.001090140314772725, 0.027303779497742653, 0.019181231036782265, -0.03879046067595482, -0.019993290305137634, -0.01598578505218029, -0.019845133647322655, 0.03236168995499611, 0.009043853729963303, -0.07249538600444794, -0.00524098752066493, 0.020938782021403313, -0.03815317526459694, 0.01351203117519617, -0.0038654059171676636, -0.013145501725375652, 0.008088775910437107, 0.005032592453062534, -0.00960339792072773, -0.048675112426280975, -0.02356198988854885, 0.03096676990389824, -0.026752866804599762, -0.03644690662622452, -0.05002286285161972, 0.04025794193148613, -0.0016375924460589886, 0.0027243769727647305, -0.008193685673177242, -0.06434530019760132, -0.014604344964027405, 0.012432323768734932, -0.010550345294177532, -0.009005875326693058, -0.03147338703274727, 0.01477023120969534, 0.030516941100358963, 0.01745176687836647, 0.011148510500788689, -0.02166612260043621, -0.012784630991518497, 0.07818389683961868, -0.06763462722301483, 0.06312591582536697, -0.025592021644115448, -0.008987054228782654, -0.05730902776122093, 0.03018549270927906, 0.026544632390141487, -0.020067812874913216, 0.0920381024479866, 0.022757742553949356, -0.032688070088624954, 0.004936639219522476, 0.012487792409956455, 0.002743338467553258, -0.029164928942918777, 0.03955058380961418, -0.03334468975663185, 0.05271210893988609, 0.025610247626900673, 0.022783592343330383, -0.029411565512418747, 0.0018115504644811153, 0.07508707046508789, -0.04775834456086159, -0.03189663961529732, 0.03797294199466705, -0.0044281394220888615, 0.06357111781835556, 0.040543146431446075, -0.023833105340600014, -0.036420296877622604, -0.012153482995927334, 0.0014255366986617446, 0.025877684354782104, -0.019670836627483368, -0.027601422742009163, -0.006722650490701199, -0.06093619391322136, 0.02221992425620556, 0.03040398471057415, -0.02316330559551716, -0.023606887087225914, -0.015945911407470703, 0.006856959778815508, 0.0032679298892617226, -0.03586607798933983, 0.024682145565748215, -0.04605028033256531, -0.04013270139694214, 0.031665440648794174, 0.01999860256910324, 0.033298466354608536, -0.05847884342074394, 0.004825560841709375, -0.004109404049813747, 0.017266342416405678, 0.004390356596559286, 0.04777194932103157, -0.03430342301726341, -0.021868932992219925, -0.012093842029571533, -0.02811456099152565, 0.004743850324302912, -0.048197828233242035, 0.02952052280306816, 0.01376180537045002, -0.05882934853434563, 0.02130320854485035, 0.07126548141241074, -0.09215307235717773, 0.09195907413959503, 0.014619458466768265, 0.036718618124723434, -0.00019334086391609162, -0.0768309012055397, 0.026935817673802376, -0.009550363756716251, -0.040370747447013855, -0.009522263891994953, -0.02666269987821579, 0.052524808794260025, -0.013429863378405571, -0.05951884388923645, -0.021172555163502693, 0.0018849183106794953, -0.012901190668344498, 0.008788246661424637, 0.01517124380916357, -0.007831263355910778, -0.003271925263106823, 0.02231510728597641, 0.016903843730688095, 0.0023515198845416307, 0.03468860685825348, 0.0069491504691541195, 0.03712652996182442, 0.0545312836766243, 0.0816364735364914, -0.10361082851886749, 0.030695263296365738, 0.04487621411681175, 0.006253066472709179, -0.0308070108294487, 0.006529681850224733, 0.11056403070688248, -0.006532432045787573, -0.05887030437588692, -0.009256327524781227, -0.012289871461689472, -0.03539370000362396, 0.0015885505126789212, 0.008970770053565502, -0.028098629787564278, 0.03392510488629341, -0.04435434564948082, -0.007810101844370365, -0.009067010134458542, 0.01862558163702488, 0.04776248708367348, -0.016117850318551064, 0.023891394957900047, -0.019288664683699608, -0.02712424471974373, -0.03299439325928688, 0.03909430280327797, 0.03601550683379173, -0.008669151924550533, 0.005906456615775824, -0.04639758542180061, -0.02557176910340786, -0.03185106813907623, -0.010873557068407536, -0.052325159311294556, -0.01867644675076008, -0.09185928851366043, 0.035175908356904984, -0.022498203441500664, -0.03524240851402283, 0.020474405959248543, -0.03411811217665672, 0.027726339176297188, 0.0897599458694458, -0.0053884293884038925, -0.02201366052031517, 0.040331870317459106, 0.05891617015004158, 0.014431842602789402, 0.01147505734115839, -0.014427353627979755, 0.009130876511335373, 0.028270825743675232, -0.0009686219273135066, 0.008019833825528622, -0.0018666326068341732, -0.041935697197914124, 0.022820942103862762, 0.0030269939452409744, 0.05006524547934532, 0.02306823804974556, -0.03780866414308548, 0.015262598171830177, -0.002127382205799222, 0.005289885215461254, 0.029077883809804916, 0.0019517047330737114, -0.016431046649813652, 0.02729788050055504, -0.0482964888215065, 0.019184505566954613, 0.03597166761755943, -0.018087198957800865, 0.046320002526044846, -0.012974374927580357, 0.011455065570771694, 0.011640101671218872, -0.07397877424955368, 0.06232917308807373, 0.023353878408670425, -0.014405767433345318, 0.027099041268229485, 0.000585142697673291, 0.02553418092429638, 0.031975120306015015, 0.028458496555685997, 0.049424976110458374, -0.007751442492008209, 0.017641501501202583, -0.04811646789312363, 0.057392898947000504, -0.04594883695244789, 0.024466101080179214, -0.0024371235631406307, 0.01834976114332676, -0.03775576502084732, 0.038883574306964874, 0.009073099121451378, -0.012518695555627346, -0.02238396555185318, -0.01982227712869644, -0.02508273348212242, 0.0014053056947886944, -0.04387236014008522, 0.05236947908997536, 0.03329458832740784, -0.014194332994520664, -0.013012345880270004, -0.006034560035914183, -0.0022525887470692396, -0.01511519867926836, 0.003593763103708625, -0.011421171948313713, -0.009640911594033241, -0.01282631978392601, 0.009555460885167122, 0.05790381133556366, 0.039792902767658234, 0.006099871825426817, 0.0011315440060570836, 0.07433285564184189, 0.03284277021884918, -0.03621063753962517, 0.05443523824214935, -0.03329189494252205, -0.024111688137054443, 0.05825039744377136, 0.030338913202285767, -0.010527007281780243, -0.04369045048952103, -0.00025135179748758674, -0.009507134556770325, 0.0707281306385994, -0.008778641000390053, 0.03571750223636627, 0.030327850952744484, -0.02028893306851387, -0.010342060588300228, 0.015433632768690586, -0.007090715691447258, -0.01668412610888481, -0.008382591418921947, -0.001398933702148497, 0.015340692363679409, -0.002107814187183976, -0.014404553920030594, 0.035255398601293564, 0.05639905855059624, -0.026985563337802887, 0.048296671360731125, -0.04125877842307091, 0.009931658394634724, 0.022352617233991623, -0.04221730679273605, -0.013607228174805641, 0.06554413586854935, -0.047442786395549774, 0.015835152938961983, -0.03408866375684738, -0.01510701421648264, -0.0035697584971785545, 0.06091004237532616, 0.035867176949977875, -0.01462261937558651, 0.002341132378205657, 0.03175947070121765, 0.09545613080263138, 0.011026415973901749, -0.05529677867889404, 0.014429846778512001, -0.0004850063123740256, -0.03911064565181732, -0.032143548130989075, 0.0176572035998106, 0.026488952338695526, -0.015726609155535698, 0.010316025465726852, -0.05806560441851616, -0.02108352817595005, -0.05016722157597542, 0.053902190178632736, 0.0021919412538409233, -0.02215132862329483, 0.012023481540381908, 0.011430449783802032, -0.003423529677093029, -0.022335581481456757, 0.020647728815674782, -0.004723528400063515, 0.009578200988471508, -0.03551339730620384, -0.03316529840230942, -0.06304645538330078, -0.09283590316772461, 0.052062056958675385, 0.011388515122234821, -0.026104958727955818, -0.058516208082437515, -0.046351052820682526, -0.03117811679840088, 0.020640432834625244, 0.0528295673429966, -0.06341703981161118, 0.07486005872488022, 0.0025936309248209, 0.0016205448191612959, 0.03023577108979225, 0.020934300497174263, -0.024557219818234444, -0.07547050714492798, 0.031032945960760117, 0.030455313622951508, 0.0365743525326252, 0.03496205434203148, 0.004600598011165857, 0.0781899094581604, -0.02138858661055565, 0.014269026927649975, -0.040335800498723984, -0.017460862174630165, 0.05928836017847061, -0.09081094712018967, -0.033624086529016495, -0.07471228390932083, -0.0413142666220665, 0.04522890970110893, -0.0025721355341374874, 0.03166894614696503, -0.029548095539212227, -0.006298221182078123, 0.014417709782719612, -0.05507650971412659, -0.008458578959107399, 0.043164417147636414, 0.025639252737164497, -0.05524085462093353, 0.010387125425040722, -0.007435557432472706, -0.016447214409708977, 0.054747965186834335, 0.055521007627248764, -0.06405787914991379, -0.08715452998876572, -0.023163538426160812, 0.0412474200129509, -0.01355377770960331, 0.007507042959332466, 0.009765156544744968, -0.0511990524828434, 0.015743907541036606, 0.019155267626047134, -0.08131290227174759, 0.007724617142230272, 0.03424382954835892, 0.004393038805574179, 0.037578582763671875, -0.034745220094919205, 0.0015747443540021777, -0.012215951457619667, -0.02016647905111313, 0.016002638265490532, -0.04846755415201187, 0.020965544506907463, 0.0014538747491315007, -0.03351904824376106, -0.045022398233413696, -0.0414685420691967, -0.013525108806788921, 0.05494294315576553, -0.024408502504229546, 0.027605151757597923, -0.01826528087258339, 0.00767830153927207, -0.03846416994929314, 0.06051182746887207, -0.05022715404629707, 0.04438379406929016, -0.0035821255296468735, -0.004474945366382599, 0.031893279403448105, -0.04315480589866638, -0.05036446824669838, 0.08026670664548874, -0.05265676975250244, -0.015607405453920364, -0.026433857157826424, -0.026166126132011414, 0.025304488837718964, 0.012600915506482124, 0.0031606450211256742, 0.013613330200314522, -0.033021148294210434, 0.02842302992939949, -0.014292138628661633, -0.035812392830848694, -0.02048005722463131, -0.013847677037119865, -0.039952509105205536, -0.006810535676777363, 0.06940042227506638, -0.01659344881772995, -0.0015111013781279325, -0.014173838309943676, -0.06955971568822861, 0.07663004100322723, 0.038478534668684006, -0.022045260295271873, -0.0018034507520496845, 0.039615925401449203, -0.01998039148747921, 0.06850683689117432, -0.01333093736320734, 0.016890758648514748, 0.0037097560707479715, -0.012626374140381813, 0.026018643751740456, -0.019844170659780502, -0.06387359648942947, -0.014862463809549809, 0.015284876339137554, -0.03764563798904419, 0.03338012099266052, 0.002337347250431776, 0.06284009665250778, -0.04141731560230255, -0.03295714780688286, 0.02305535599589348, 0.032698266208171844, -0.029844747856259346, 0.0005996109684929252, -0.008872032165527344, -0.001107637188397348, -0.015003264881670475, -0.046828076243400574, 0.007848696783185005, -0.013841521926224232, 0.027690201997756958, -0.06600426882505417, -0.013349744491279125, 0.0212381761521101, -0.02503279782831669, -0.004728460684418678, -0.04411211609840393, -0.02094908058643341, -0.03954320028424263, 0.044235050678253174, -0.01837773621082306, -0.021034900099039078, -0.006414269562810659, -0.0026625085156410933, -0.04728720709681511, -0.012704083696007729, -0.019365450367331505, -0.03544247895479202, -0.03074396215379238, -0.015765966847538948, 0.03425642102956772, 0.018727608025074005, 0.01671283319592476, 0.034347355365753174, 0.012064198032021523, -0.06875832378864288, -0.05589032545685768, -0.00009956118447007611, -0.0012561064213514328, -0.02174745500087738, 0.014886713586747646, -0.008698105812072754, 0.05634921044111252, -0.09512409567832947, -0.03534253314137459, 0.007674580439925194, 0.014031244441866875, 0.032115574926137924, 0.015096701681613922, -0.008178581483662128, -0.0614631362259388, 0.01401194091886282, 0.018879394978284836, -0.01146322675049305, 0.023952839896082878, 0.02824416570365429, -0.010975680314004421, -0.0007688374607823789, 0.039132025092840195, 0.020817873999476433, 0.005630142521113157, 0.012736380100250244, -0.02162167802453041, -0.025282692164182663, 0.046635232865810394, -0.032008446753025055, -0.06194064021110535, 0.012281701900064945, -0.01896127499639988, -0.020920347422361374, 0.05819197744131088, -0.026728805154561996, 0.024659065529704094, -0.019145306199789047, -0.003214505035430193, -0.02512054704129696, -0.036015331745147705, -0.00799085944890976, 0.030396144837141037, -0.005409016273915768, 0.01058986410498619, 0.043372124433517456, -0.05556212365627289, 0.049803756177425385, -0.06972669810056686, -0.006785515695810318, 0.041367411613464355, 0.033978838473558426, 0.016090188175439835, 0.04012060910463333, 0.03779945522546768, -0.03244758024811745, -0.05685843527317047, -0.047316376119852066, -0.020231785252690315, 0.018599260598421097, -0.018748778849840164, -0.057957492768764496, 0.03989121690392494, -0.0031474283896386623, 0.039147645235061646, 0.054423149675130844, 0.03149104863405228, -0.019719798117876053, 0.023956649005413055, -0.0611855648458004, 0.04218589887022972, 0.03524414449930191, -0.024472840130329132, 0.012543813325464725, -0.04652756080031395, 0.0023267485667020082, -0.023626651614904404, -0.009099957533180714, -0.005585580598562956, 0.015550725162029266, -0.03965064510703087, 0.0005937466630712152, 0.07668806612491608, 0.004678425379097462, -0.00231398968026042, -0.07790899276733398, -0.04267067089676857, 0.03882381692528725, -0.004194225184619427, -0.06741484254598618, 0.01543869636952877, 0.078757144510746, -0.052680302411317825, 0.02357163280248642, 0.07499901205301285, 0.03178695961833, -0.015839677304029465, 0.02253018692135811, 0.004688324872404337, -0.018882613629102707, -0.044897325336933136, 0.049676813185214996, 0.043727897107601166, 0.021015804260969162, 0.028306353837251663, 0.003105789888650179, 0.022723130881786346, 0.0010838010348379612 ]
<ol> <li><p>We all know that wavefunction collapse when it is observed. Uncertainty principle states that $\sigma_x \sigma_p \geq \frac {\hbar}{2}$. When wavefunction collapse, doesn't $\sigma_x$ become $0$?, as we will know the location of the particle. Or does standard deviation just become smaller?</p></li> <li><p>After collapse occurs, what happens to the particle? Does the particle resurrect into a wavefunction form?</p></li> <li><p>What can be an observer that triggers wavefunction collapse? (electron wavefunction does not collapse when meeting with electrons; but some macroscopic objects seem to become observers....)</p></li> <li><p>What happens to the energy of a particle/wave packet after the collapse?</p></li> </ol>
g5452
[ 0.021409479901194572, -0.007024439517408609, 0.012874344363808632, -0.0169195756316185, 0.03002018667757511, 0.01954483613371849, 0.005720165558159351, 0.06019946560263634, -0.035881951451301575, -0.04142557084560394, -0.056855544447898865, -0.020136773586273193, 0.009879273362457752, -0.035440895706415176, 0.015129001811146736, -0.003498910926282406, 0.12134700268507004, 0.0010007504606619477, 0.03688898682594299, 0.02814055234193802, -0.026546470820903778, -0.00009285494888899848, -0.00029038070351816714, -0.0027235045563429594, 0.006737878546118736, 0.02509201318025589, -0.002049158327281475, 0.005330565385520458, -0.005523798521608114, 0.0019786746706813574, 0.018384963274002075, 0.029045339673757553, 0.051148608326911926, -0.0595347136259079, 0.057089708745479584, 0.015743475407361984, 0.06148454546928406, -0.019437791779637337, -0.002263447968289256, 0.020980214700102806, -0.040982089936733246, -0.002268643118441105, -0.0020731992553919554, -0.06264262646436691, 0.032703764736652374, 0.039864055812358856, -0.02908017672598362, -0.027537859976291656, 0.0314832478761673, -0.04946852847933769, 0.0005584206664934754, 0.031408827751874924, 0.03300245478749275, 0.04832760617136955, 0.06704104691743851, 0.05544527620077133, 0.002421935787424445, -0.020980384200811386, 0.0798175260424614, -0.02145145647227764, 0.016957325860857964, 0.011052936315536499, -0.0066133649088442326, -0.04223544895648956, 0.028566693887114525, -0.02882937714457512, -0.0986177995800972, 0.015106662176549435, 0.009593536145985126, -0.055411700159311295, 0.014504593797028065, -0.029863689094781876, -0.05593172088265419, -0.03726224973797798, -0.0034907034132629633, -0.0005585631006397307, -0.005698677618056536, -0.006956061348319054, -0.04025271162390709, 0.03351890668272972, -0.04979981482028961, -0.017203545197844505, 0.033693477511405945, 0.020263176411390305, -0.002187528647482395, -0.022468935698270798, -0.008482628501951694, 0.06523166596889496, -0.007702414877712727, 0.021694425493478775, 0.02688267081975937, -0.0677919015288353, 0.02256685681641102, -0.032191935926675797, -0.02128474973142147, -0.004815424792468548, -0.0223374180495739, 0.015994153916835785, 0.007113257423043251, 0.02463650144636631, 0.01867680437862873, -0.0555877722799778, -0.004761751741170883, -0.021784845739603043, -0.03285777196288109, -0.007909473031759262, -0.056920625269412994, 0.03207016363739967, 0.053387533873319626, -0.0436098538339138, 0.04577608034014702, -0.02481008507311344, 0.008341189473867416, -0.06218403950333595, -0.01533026248216629, -0.02219877392053604, 0.05406173691153526, -0.010440414771437645, -0.012834995985031128, 0.05413227155804634, 0.04579843953251839, -0.00797391775995493, 0.037735678255558014, -0.01017569750547409, -0.022331111133098602, 0.00818975456058979, -0.014302304945886135, 0.020381856709718704, 0.009502841159701347, 0.017734181135892868, 0.048654381185770035, 0.0443463996052742, -0.07118210196495056, 0.05082106217741966, 0.007364863529801369, 0.04333348944783211, -0.020089317113161087, 0.01726430095732212, 0.04578040540218353, -0.010310180485248566, 0.0145419305190444, -0.014867808669805527, 0.0439847968518734, -0.015097097493708134, 0.0013595884665846825, -0.03569827973842621, 0.04543587565422058, -0.013711139559745789, -0.029648328199982643, 0.03943768888711929, -0.07980690896511078, 0.010118032805621624, -0.022297777235507965, -0.048173025250434875, 0.05549263954162598, -0.03083682432770729, 0.07173258066177368, -0.008298572152853012, -0.01576158218085766, -0.024523723870515823, 0.09098309278488159, -0.006271434016525745, 0.001997211016714573, 0.0030048296321183443, -0.0773305594921112, -0.007721246685832739, 0.03144865855574608, -0.101689413189888, 0.050674717873334885, -0.038313958793878555, -0.01628950983285904, -0.008311714045703411, -0.000654769130051136, 0.051197752356529236, -0.0015076702693477273, 0.05063975602388382, -0.056402090936899185, -0.02561620995402336, 0.042494140565395355, 0.022881826385855675, 0.008029443211853504, 0.03521042317152023, 0.03508089482784271, -0.08564451336860657, 0.05118867754936218, 0.04464701935648918, 0.03938960283994675, 0.00678329449146986, -0.03891817480325699, -0.005920864176005125, -0.03818970173597336, -0.055391475558280945, -0.012357409112155437, 0.018222708255052567, 0.016646774485707283, 0.00450626527890563, 0.02242867834866047, -0.08072151243686676, -0.03343898802995682, 0.011722427792847157, 0.0016642927657812834, 0.027926404029130936, 0.02062416262924671, 0.006264674477279186, -0.013112830929458141, 0.020743144676089287, -0.0582764632999897, 0.004027245566248894, -0.05819117650389671, -0.040026746690273285, 0.04761384055018425, -0.0339045450091362, 0.016888387501239777, -0.030290042981505394, -0.017985409125685692, -0.0071373204700648785, 0.027979776263237, 0.031513381749391556, 0.0064662969671189785, -0.014681285247206688, 0.009583053179085255, 0.02632015012204647, 0.049084991216659546, -0.024681711569428444, 0.020135419443249702, 0.06059977784752846, -0.07300975173711777, -0.053361643105745316, 0.001878618262708187, 0.024779723957180977, -0.07117696106433868, 0.02911921590566635, -0.014330916106700897, 0.054704342037439346, 0.04904533922672272, 0.09450720995664597, -0.029230857267975807, -0.03628135845065117, 0.07265669107437134, -0.025529155507683754, -0.011043528094887733, 0.032829392701387405, -0.039155397564172745, -0.011220286600291729, 0.04436064884066582, -0.05687421187758446, -0.0028172777965664864, 0.03273409977555275, 0.026573026552796364, -0.054851070046424866, 0.0044894288294017315, 0.02292606420814991, -0.025603068992495537, -0.00040244130650535226, -0.007660565432161093, -0.025497129186987877, -0.034121546894311905, 0.045570097863674164, -0.04626503586769104, -0.042271483689546585, 0.00800970196723938, 0.05202364921569824, -0.0012260080548003316, -0.020919397473335266, 0.01650387793779373, -0.030977612361311913, 0.020199578255414963, 0.028320500627160072, -0.019093332812190056, -0.02966359257698059, 0.032940786331892014, 0.05560145527124405, -0.006745552644133568, 0.08444128185510635, 0.005683526396751404, -0.0006758904200978577, -0.033858466893434525, -0.017499644309282303, 0.02208656445145607, -0.09010426700115204, -0.032831721007823944, 0.013706410303711891, -0.08787564188241959, -0.04207324609160423, 0.00453451182693243, -0.07777827978134155, 0.03063526377081871, -0.0044599734246730804, 0.021585922688245773, -0.03579898551106453, 0.0026544900611042976, -0.026876850053668022, -0.010960279032588005, 0.02654844895005226, -0.024997780099511147, -0.02001006342470646, 0.023844601586461067, -0.007919357158243656, -0.037653692066669464, 0.025227583944797516, -0.017428165301680565, -0.04328105226159096, -0.04950861632823944, 0.00048545838217251003, 0.030067456886172295, 0.07124055922031403, -0.040809266269207, -0.009972432628273964, -0.05951482057571411, 0.0158402007073164, -0.007087420206516981, 0.00787457823753357, -0.031125668436288834, -0.0407775342464447, -0.021479174494743347, 0.019862916320562363, -0.04124811664223671, 0.05429086834192276, -0.03115328960120678, -0.02422391064465046, -0.02390662208199501, -0.015124715864658356, -0.03995067998766899, -0.05580843612551689, 0.04766157642006874, -0.007565389387309551, 0.012010553851723671, 0.050530992448329926, -0.012974398210644722, -0.027403751388192177, -0.0012442830484360456, -0.01991940476000309, 0.02868744172155857, -0.012873968109488487, 0.04977741464972496, -0.0023325071670114994, -0.02330567128956318, 0.0017998479306697845, 0.00804812926799059, 0.06813982129096985, 0.04074110835790634, 0.022994209080934525, 0.00822401326149702, -0.023474693298339844, 0.025029513984918594, 0.03423105180263519, -0.015433469787240028, -0.0483928918838501, 0.04092048853635788, -0.04193385690450668, 0.012792881578207016, 0.018582316115498543, 0.01718476042151451, -0.02119525708258152, -0.004373934119939804, 0.006437425501644611, 0.00517747038975358, -0.05510517209768295, 0.01639752835035324, -0.007002676371484995, -0.012377399019896984, -0.10085844248533249, 0.04815630987286568, 0.012753087095916271, -0.022942010313272476, -0.019217899069190025, 0.0084482841193676, 0.03049561195075512, 0.029373973608016968, -0.02274993807077408, -0.017131002619862556, -0.01981406658887863, -0.01659112423658371, 0.034921687096357346, 0.003992091398686171, -0.046857915818691254, 0.035134151577949524, 0.011963753961026669, -0.04049539566040039, 0.01254837866872549, 0.009737418964505196, 0.018004396930336952, 0.026799354702234268, -0.046144645661115646, 0.052157510071992874, -0.004428124986588955, -0.011651335284113884, -0.022141551598906517, 0.015528049319982529, -0.014360216446220875, 0.021995784714818, -0.03169509395956993, 0.013097795657813549, -0.02507685497403145, 0.08177776634693146, -0.005549214314669371, 0.018889186903834343, -0.019249489530920982, 0.024781135842204094, 0.017194461077451706, -0.004324045497924089, 0.06305716931819916, -0.0008064718567766249, -0.008937858045101166, 0.057291943579912186, 0.007316187955439091, 0.005744970869272947, -0.04157038405537605, -0.022083431482315063, -0.06062453240156174, 0.009682842530310154, 0.004942395258694887, 0.023501839488744736, -0.04936865717172623, 0.003515429561957717, -0.005534308962523937, 0.0211823470890522, -0.012043206952512264, -0.003178336890414357, 0.01297302357852459, 0.013467704877257347, -0.020620331168174744, 0.024677857756614685, 0.01602979190647602, -0.07540880888700485, 0.032737307250499725, 0.04070568457245827, -0.045821867883205414, -0.041952718049287796, -0.031835947185754776, 0.030753573402762413, 0.027943018823862076, 0.034446295350790024, 0.008556561544537544, -0.05424818396568298, 0.018511561676859856, 0.022404324263334274, -0.03534350171685219, -0.03461867570877075, 0.07287667691707611, 0.04595504701137543, -0.012222981080412865, 0.010628756135702133, 0.0063312361016869545, -0.01878977008163929, 0.06147341802716255, -0.06101621687412262, -0.013376474380493164, 0.06437931954860687, 0.01165725477039814, -0.02810082770884037, 0.023000966757535934, 0.0032974928617477417, -0.042241182178258896, 0.044303156435489655, -0.06612221896648407, -0.012821399606764317, 0.05285344645380974, -0.007366695906966925, 0.008885875344276428, -0.05851390212774277, -0.020502375438809395, -0.005475407000631094, 0.031336668878793716, 0.001213595038279891, -0.019799353554844856, -0.07753240317106247, -0.05329640582203865, -0.011002583429217339, 0.019488416612148285, -0.028123639523983, -0.007821605540812016, 0.04991652071475983, -0.04387964308261871, 0.038835909217596054, -0.02647513896226883, -0.03361542895436287, -0.00021017320977989584, 0.06510016322135925, -0.08567473292350769, 0.002704694401472807, -0.024431606754660606, 0.009354137815535069, -0.012110334821045399, -0.03092619962990284, -0.0048979721032083035, -0.007242819759994745, -0.0027723447419703007, 0.018858039751648903, -0.05046863481402397, -0.0088771628215909, 0.021190160885453224, 0.01472725160419941, -0.001949148834683001, 0.00494541646912694, -0.0067595564760267735, 0.005310253705829382, -0.007727285381406546, 0.04693859815597534, 0.03521979600191116, -0.06206896901130676, -0.07613755017518997, -0.043372660875320435, 0.017684558406472206, -0.017686229199171066, 0.04152915999293327, 0.06898187100887299, -0.005030666943639517, 0.02366975136101246, -0.024340001866221428, 0.002948410576209426, 0.0011649883817881346, -0.016132095828652382, 0.003651372855529189, -0.0077275726944208145, -0.022806702181696892, -0.06535741686820984, 0.031117914244532585, -0.059390805661678314, -0.014057626947760582, -0.039883073419332504, 0.004855980630964041, 0.03682800009846687, -0.01866273581981659, 0.011095226742327213, 0.016629934310913086, -0.042974043637514114, -0.011742428876459599, 0.004413182381540537, 0.032367557287216187, 0.03611589968204498, -0.010487444698810577, 0.05165649205446243, 0.009043131954967976, 0.014207911677658558, 0.034838344901800156, -0.04259353131055832, 0.005526465829461813, 0.014839982613921165, 0.05331914871931076, -0.0027531629893928766, 0.07005074620246887, 0.004869760014116764, 0.11373858153820038, -0.0007224876317195594, -0.008413857780396938, -0.03613131120800972, 0.08316605538129807, 0.04150591418147087, -0.022415490821003914, -0.022089865058660507, 0.011662429198622704, -0.02938290499150753, -0.0000206709883059375, -0.00927906297147274, 0.01160411722958088, 0.05773068591952324, -0.020230181515216827, -0.07825882732868195, -0.03874243050813675, 0.001952502061612904, -0.042929600924253464, 0.03839075565338135, 0.02063346467912197, 0.06042216718196869, -0.009901029989123344, -0.004637738689780235, 0.005619334056973457, -0.004062933847308159, 0.033216286450624466, 0.01539956871420145, 0.03001895174384117, 0.024515895172953606, 0.0053873611614108086, -0.004406009800732136, 0.04300513118505478, 0.006422943435609341, -0.062038350850343704, -0.006803215481340885, -0.09588087350130081, 0.026394005864858627, -0.0013288470217958093, 0.029242420569062233, -0.027336768805980682, -0.09388137608766556, 0.023094192147254944, 0.012940865010023117, -0.04303661361336708, 0.05644771456718445, 0.049555715173482895, 0.02831043116748333, -0.023297512903809547, 0.03723934292793274, 0.027727477252483368, 0.006712509319186211, -0.0022203584667295218, -0.03201565518975258, -0.02064177766442299, -0.0017439668299630284, 0.03569668158888817, -0.003124520881101489, 0.011504603549838066, 0.0710797980427742, -0.05475898087024689, 0.03214814141392708, -0.005713410675525665, -0.04395497962832451, 0.0322871059179306, -0.002602506661787629, -0.03456272929906845, -0.028083529323339462, -0.01037970744073391, 0.0319623164832592, 0.007692417129874229, 0.05914737656712532, -0.05537028983235359, 0.015466442331671715, 0.04616286978125572, -0.08194471150636673, 0.043267980217933655, 0.04959983378648758, -0.04888426139950752, 0.020605897530913353, -0.017099307850003242, 0.006721405312418938, 0.028174858540296555, 0.05952005460858345, -0.03671138361096382, 0.041014425456523895, -0.0030302826780825853, -0.023211833089590073, 0.02376997284591198, 0.05014708638191223, 0.03228702396154404, -0.07090817391872406, 0.04114503785967827, -0.01417565904557705, 0.0006682922248728573, 0.015525704249739647, -0.0075091286562383175, 0.05393555760383606, 0.012358519248664379, 0.10411079227924347, -0.04140324890613556, -0.09705903381109238, 0.034733355045318604, 0.045776307582855225, -0.01541175413876772, -0.0749804750084877, -0.012491045519709587, 0.017276057973504066, 0.005599691532552242, -0.014590446837246418, -0.031153472140431404, 0.008649623021483421, 0.03783896565437317, 0.02510000951588154, -0.010882609523832798, 0.012199556455016136, -0.02062789350748062, -0.025261342525482178, -0.04195303097367287, 0.0045111654326319695, -0.03175380825996399, 0.018748875707387924, 0.016374308615922928, -0.03448466584086418, -0.07997957617044449, -0.022443845868110657, -0.05098715052008629, -0.050150275230407715, -0.05914255604147911, -0.061875633895397186, -0.0383913516998291, 0.007353353779762983, -0.01869436725974083, 0.00804599653929472, 0.03580206260085106, -0.012861576862633228, 0.028549205511808395, -0.018685894086956978, 0.04536830261349678, 0.021174520254135132, -0.03348354995250702, 0.010407567955553532, 0.01416189968585968, -0.033200331032276154, 0.01383906602859497, -0.03696297109127045, -0.007891729474067688, -0.0202955175191164, 0.006021174136549234, 0.013826578855514526, -0.09785643965005875, -0.0003296273644082248, -0.042881738394498825, 0.06594213098287582, -0.011045712977647781, -0.010349469259381294, 0.0031199550721794367, 0.01476921234279871, 0.00009339863026980311, -0.006866660434752703, -0.013041811995208263, 0.03720293194055557, 0.01571073569357395, -0.034634605050086975, -0.04051250219345093, -0.05135906860232353, 0.019738925620913506, 0.0442156121134758, 0.040969595313072205, 0.016288338229060173, -0.026052547618746758, -0.0037346803583204746, -0.00007959624053910375, -0.0035613703075796366, 0.04853909835219383, 0.07297804951667786, 0.007583341095596552, 0.016657551750540733, -0.020073555409908295, -0.012722262181341648, 0.04121691361069679, 0.06662018597126007, -0.0002779753995127976, -0.014058862812817097, 0.017038920894265175, 0.03980771452188492, -0.020129268988966942, -0.07087553292512894, 0.07253550738096237, -0.02072877064347267, -0.04967799782752991, -0.03874744847416878, 0.03422679752111435, 0.0499488040804863, 0.024509303271770477, -0.05520329624414444, 0.005365647841244936, 0.03039349615573883, -0.013103838078677654, 0.023819254711270332, -0.006116486620157957, 0.006415948271751404, -0.01376000139862299, 0.0036388267762959003, -0.008504916913807392, 0.033318616449832916, -0.026760267093777657, -0.004875850863754749, 0.039988886564970016, 0.01058398187160492, 0.06872374564409256, 0.05563460662961006, -0.013233943842351437, -0.053986337035894394, 0.0286807119846344, 0.029182499274611473, -0.0037731349002569914, 0.0568905770778656, -0.04736476019024849, -0.006816560868173838, -0.028560172766447067, -0.029089929535984993, -0.02536705881357193, 0.025321032851934433, 0.005742868408560753 ]
<p>If a body is under non-uniform circular motion, will it experience or will there be any impact of centrifugal force on the body upon eliminating the centripetal force? update-sorry.the title of question was incorrect.</p>
g5453
[ 0.037904445081949234, 0.0175554770976305, 0.026642266660928726, 0.058873455971479416, 0.02135615050792694, 0.011049616150557995, 0.05288822203874588, 0.042334314435720444, -0.0022797572892159224, 0.0076838769018650055, -0.022853359580039978, -0.062018316239118576, -0.04686161130666733, -0.023687569424510002, 0.0025247845333069563, -0.025421177968382835, 0.03503674641251564, -0.06564543396234512, -0.01489302609115839, 0.09499732404947281, -0.04236387461423874, 0.028221288695931435, -0.018408454954624176, -0.003910733386874199, -0.025307318195700645, 0.02524239756166935, -0.04915237799286842, -0.028736479580402374, -0.01874958723783493, 0.009538416750729084, -0.02989760972559452, -0.004297191277146339, -0.024846093729138374, -0.07856827974319458, -0.03838380426168442, 0.013148874044418335, 0.06419285386800766, -0.0002496723900549114, -0.017682313919067383, -0.03161724656820297, 0.01796680875122547, 0.060162752866744995, 0.0043273987248539925, -0.011640852317214012, 0.03236010670661926, 0.028786277398467064, 0.024518124759197235, -0.004946611355990171, 0.0017815908649936318, 0.04770318418741226, -0.06118414178490639, -0.0699683129787445, 0.005681360140442848, -0.006590079981833696, -0.016051463782787323, -0.013438733294606209, 0.11258161067962646, -0.04473072290420532, -0.040562327951192856, -0.022205185145139694, -0.06735185533761978, 0.004375868942588568, 0.014502523466944695, -0.03125656396150589, -0.00428466172888875, -0.023778505623340607, -0.037285216152668, 0.01256638951599598, -0.01552559807896614, 0.00006244807445909828, 0.0036018171813338995, 0.03102724440395832, -0.04848030209541321, -0.044386256486177444, -0.02234542742371559, 0.09031839668750763, 0.018986547365784645, -0.04929063469171524, 0.009087602607905865, -0.022473350167274475, -0.0318918339908123, 0.05689222738146782, 0.03219299018383026, 0.02474856749176979, 0.06387604027986526, -0.027871333062648773, -0.04950585961341858, -0.04285850375890732, -0.010709768161177635, -0.00869038701057434, 0.07144387066364288, -0.05181572958827019, 0.03550304099917412, 0.016513841226696968, 0.00195425096899271, -0.03320711478590965, 0.01312767993658781, 0.07066572457551956, 0.03700930252671242, -0.022260742262005806, -0.018129808828234673, 0.0003094781131949276, 0.015973547473549843, -0.049944788217544556, 0.03195677697658539, -0.0358959436416626, 0.06353326886892319, -0.01483777817338705, -0.06500021368265152, -0.0232168547809124, -0.03485860303044319, -0.06348541378974915, 0.014168793335556984, -0.013107242062687874, 0.019910790026187897, -0.06431281566619873, 0.05378175154328346, -0.011819603852927685, -0.020818138495087624, -0.0009302771650254726, 0.01733914390206337, 0.05968659743666649, 0.014467606320977211, 0.03951052576303482, -0.03637376055121422, -0.008412498980760574, -0.014003016985952854, 0.02788645587861538, 0.05641523003578186, -0.034283850342035294, 0.04003886505961418, 0.021126825362443924, -0.009229352697730064, 0.007320401258766651, 0.004127258900552988, 0.03369223326444626, -0.03038521483540535, -0.003646887606009841, 0.03973851352930069, -0.05138414725661278, 0.013115661218762398, -0.010873991996049881, 0.04719945043325424, 0.02342316508293152, -0.002569714793935418, -0.04301610216498375, 0.016603799536824226, 0.02734113298356533, 0.036979712545871735, 0.01702835038304329, 0.022260405123233795, 0.005051350221037865, 0.024564681574702263, -0.08839273452758789, 0.004903388675302267, -0.0042956238612532616, -0.009455906227231026, 0.04100426286458969, 0.012610947713255882, 0.00861735362559557, 0.0227223951369524, 0.02071218192577362, 0.04882431775331497, 0.006931976415216923, -0.0219741091132164, 0.00007484683737857267, -0.0715259313583374, -0.022922338917851448, 0.04075348749756813, -0.01838042214512825, -0.06189550459384918, -0.0032079494558274746, 0.017101580277085304, 0.09876058995723724, -0.01692301034927368, 0.020447706803679466, -0.03130069375038147, -0.006576553452759981, -0.021510720252990723, -0.015011132694780827, 0.04175698384642601, 0.043327007442712784, -0.010130302980542183, -0.04783356934785843, 0.002464398741722107, 0.05486074090003967, 0.037483204156160355, 0.101331926882267, -0.0580441951751709, 0.018235912546515465, -0.002357506426051259, -0.037281494587659836, -0.018495839089155197, 0.02883269637823105, -0.05851273611187935, 0.004445544444024563, 0.033468205481767654, 0.02581869624555111, -0.04505129158496857, -0.0289806816726923, 0.010984999127686024, 0.0031085943337529898, 0.009018829092383385, -0.032551102340221405, -0.021828368306159973, -0.023132655769586563, 0.002009311690926552, -0.01609799452126026, 0.06048525497317314, -0.05719630420207977, 0.04203496873378754, 0.007089376449584961, -0.01248279120773077, 0.051991336047649384, -0.08169145882129669, 0.0370197556912899, 0.02518056519329548, 0.04171089455485344, -0.03159502521157265, 0.008448376320302486, 0.02376377210021019, -0.009275185875594616, -0.051357291638851166, -0.015433340333402157, -0.024805990979075432, -0.02953208237886429, -0.06226694956421852, -0.04179668426513672, 0.015367410145699978, -0.009237054735422134, 0.00873871985822916, 0.01458471268415451, 0.021164987236261368, -0.05193422734737396, -0.011621780693531036, 0.07395441830158234, 0.02564508467912674, -0.043618518859148026, -0.0008809745777398348, -0.023935478180646896, 0.029946181923151016, -0.04451173543930054, -0.008531331084668636, -0.0403132326900959, 0.028102289885282516, -0.0185963436961174, 0.020772401243448257, -0.010404763743281364, 0.04779990017414093, -0.01787932775914669, -0.0006691163871437311, -0.0398184172809124, -0.01960005983710289, 0.027397911995649338, 0.027470814064145088, 0.034569382667541504, -0.04487789794802666, -0.015505700372159481, -0.06432685256004333, 0.02031577192246914, -0.05941686034202576, -0.019555969163775444, -0.018124112859368324, 0.06200879067182541, -0.07526273280382156, -0.05274534225463867, 0.006305679678916931, -0.013417312875390053, 0.0004121226374991238, 0.05582362413406372, -0.030767755582928658, 0.057090092450380325, -0.05496884509921074, 0.08655289560556412, 0.009097985923290253, 0.01624315045773983, 0.019574487581849098, -0.0152963288128376, -0.07043897360563278, 0.02152993157505989, -0.037986837327480316, -0.006732453592121601, 0.012148777954280376, 0.043255094438791275, 0.00004823208655579947, -0.009878898970782757, 0.0021686546970158815, -0.010266163386404514, -0.039709873497486115, -0.015374711714684963, -0.015100054442882538, 0.001802573329769075, 0.023608524352312088, 0.012629270553588867, 0.026562899351119995, 0.010372639633715153, 0.04698988422751427, -0.04251828044652939, 0.0044139982201159, -0.04037576913833618, -0.022036084905266762, -0.026813702657818794, 0.002365976106375456, -0.008099876344203949, -0.07722213864326477, 0.04264547675848007, -0.03352702781558037, -0.05718931183218956, 0.014115160331130028, 0.037511758506298065, -0.007544458378106356, 0.07803773134946823, 0.03319768235087395, 0.02330685406923294, -0.06867019832134247, -0.019435778260231018, -0.010479483753442764, -0.020269926637411118, 0.00751367025077343, 0.053991712629795074, 0.01768907904624939, -0.03520605340600014, -0.03130220249295235, -0.03405804932117462, 0.054740194231271744, 0.047070056200027466, -0.0012170851696282625, 0.006829373072832823, 0.015082758851349354, -0.039466410875320435, 0.033015038818120956, 0.04018920660018921, -0.033282238990068436, 0.010733147151768208, -0.07558423280715942, 0.017966609448194504, -0.012522668577730656, 0.036804016679525375, 0.03415985032916069, 0.028810327872633934, 0.06038900837302208, -0.060224924236536026, 0.049890756607055664, -0.07010338455438614, -0.021236412227153778, 0.04981687292456627, 0.022734759375452995, 0.027297670021653175, 0.02140875533223152, 0.021616686135530472, 0.09093867987394333, -0.023249326273798943, 0.04657288268208504, -0.05240069329738617, 0.01664014346897602, -0.008817574009299278, 0.026139184832572937, 0.02767055481672287, -0.09474359452724457, 0.010415008291602135, 0.01250908337533474, -0.03468617424368858, 0.0361797958612442, 0.07402180880308151, 0.018363909795880318, 0.011557476595044136, 0.023365555331110954, 0.011417857371270657, -0.055662382394075394, -0.016779066994786263, -0.03187118470668793, -0.01688115857541561, -0.008686626330018044, -0.0162875484675169, 0.02484096959233284, 0.023304758593440056, 0.042865682393312454, 0.01897287555038929, 0.009890487417578697, -0.0160995963960886, 0.03248262032866478, -0.005523817613720894, -0.028588850051164627, -0.00977301225066185, -0.03604065254330635, 0.02370956726372242, -0.035894881933927536, 0.018707184121012688, -0.00023837725166231394, 0.004477035719901323, 0.05244491249322891, -0.0005233444389887154, 0.00786913838237524, 0.023427827283740044, 0.07082954794168472, 0.017122536897659302, -0.008543571457266808, -0.09441672265529633, 0.032979175448417664, -0.01754133403301239, 0.028452953323721886, 0.023935066536068916, -0.02281300723552704, 0.06498861312866211, 0.05988496541976929, 0.03895494341850281, -0.00827862974256277, 0.00036352346069179475, -0.05423355475068092, -0.020749714225530624, -0.018686652183532715, 0.005551020614802837, -0.04573123902082443, -0.024687958881258965, 0.05858386680483818, -0.01021480094641447, -0.03648883476853371, 0.03136304020881653, 0.009321833960711956, 0.019664321094751358, 0.010583288036286831, 0.007184707559645176, 0.00606389669701457, 0.044794660061597824, -0.024711091071367264, 0.02629813179373741, 0.04005151987075806, -0.026815887540578842, -0.03651503473520279, 0.000524968549143523, -0.016565566882491112, 0.009081512689590454, 0.013334332033991814, 0.011191878467798233, -0.02031180076301098, 0.0179757010191679, -0.046874988824129105, -0.01369843352586031, 0.033508289605379105, 0.015157700516283512, -0.028776168823242188, 0.033164069056510925, 0.04450211301445961, -0.029771246016025543, -0.04359328746795654, 0.07763570547103882, -0.02057223580777645, -0.02566465362906456, -0.02115868590772152, -0.014775308780372143, -0.035826195031404495, -0.029079150408506393, -0.03967425227165222, -0.011605213396251202, -0.038922738283872604, -0.004438258241862059, -0.0603443868458271, -0.025150300934910774, -0.020457496866583824, 0.041494160890579224, -0.023818306624889374, -0.03776169568300247, -0.009190008044242859, 0.025737378746271133, -0.03268107771873474, 0.019497238099575043, -0.000386489846277982, 0.010413513518869877, -0.019585318863391876, 0.06751599907875061, -0.03678540140390396, 0.014085906557738781, 0.04340951144695282, 0.024095017462968826, -0.04612162709236145, 0.0005087528843432665, 0.059672750532627106, 0.0005011743633076549, 0.050417426973581314, 0.012064718641340733, 0.009342909790575504, -0.03469783440232277, 0.017876267433166504, -0.053866852074861526, 0.04856596142053604, 0.022562677040696144, 0.03519292548298836, -0.002910051727667451, 0.006563760340213776, 0.024853013455867767, -0.014850851148366928, 0.010872144252061844, -0.017600832507014275, -0.03292178362607956, 0.0351179800927639, 0.03586560860276222, 0.028172150254249573, -0.03935719653964043, -0.05777105316519737, 0.04717768356204033, -0.03071555681526661, -0.019562168046832085, 0.02782326005399227, -0.011361224576830864, -0.04001406207680702, 0.06309148669242859, 0.019696401432156563, 0.006900022272020578, 0.014520191587507725, 0.023434238508343697, -0.012931599281728268, 0.0017314704600721598, -0.01779000088572502, 0.010349767282605171, -0.05173209309577942, -0.008015728555619717, -0.04198136925697327, -0.008465836755931377, 0.01973084919154644, -0.04548582434654236, 0.04532444477081299, 0.045444685965776443, 0.0010859457543119788, -0.013057802803814411, 0.008647172711789608, -0.024970663711428642, 0.03432188928127289, 0.02374204806983471, 0.029808878898620605, 0.08593481034040451, 0.026339713484048843, 0.04369967430830002, 0.036615241318941116, 0.023804813623428345, -0.03254776448011398, -0.04342572018504143, 0.033302344381809235, -0.0026962566189467907, 0.08769571781158447, -0.0154355987906456, -0.030164409428834915, -0.05623231828212738, 0.007183652836829424, 0.06251811236143112, -0.04990070313215256, 0.023854736238718033, -0.016608228906989098, 0.025748245418071747, -0.0097311120480299, -0.01101983617991209, -0.01939503476023674, 0.021802440285682678, -0.003725114045664668, 0.01662834733724594, -0.052328962832689285, 0.05067211389541626, 0.0254935622215271, 0.018501989543437958, 0.03329163417220116, -0.0681469663977623, 0.0013726154575124383, -0.01104910857975483, 0.07292795181274414, -0.0055448757484555244, 0.001235967269167304, -0.00010559077054494992, -0.03366616368293762, -0.06825985014438629, 0.06594785302877426, 0.006096630822867155, 0.04507279396057129, -0.048795465379953384, -0.022780759260058403, -0.002980454359203577, 0.0005811134469695389, 0.030568670481443405, -0.06408821046352386, 0.04454285278916359, -0.04320552572607994, 0.08225280791521072, 0.007765729445964098, -0.03553428873419762, 0.013911621645092964, -0.017325453460216522, -0.002973813097923994, 0.06458363682031631, -0.03463422879576683, 0.039724644273519516, -0.003119242610409856, -0.04022201895713806, 0.03553703799843788, -0.023627370595932007, -0.0005703326314687729, 0.02685648575425148, -0.010119561105966568, 0.023480908945202827, -0.02740880474448204, 0.03996042162179947, 0.022364044561982155, 0.031968023627996445, 0.01696191541850567, -0.03982529789209366, 0.03177061304450035, -0.010801042430102825, 0.017495902255177498, 0.03749265894293785, 0.007134512532502413, -0.05042387917637825, 0.024454260244965553, -0.028635352849960327, 0.009695314802229404, 0.02291007898747921, 0.0037091069389134645, -0.004807375371456146, 0.038643717765808105, -0.08279285579919815, -0.0109410360455513, -0.031711433082818985, -0.011565351858735085, -0.010185242630541325, -0.04011118412017822, -0.04712803289294243, 0.08739727735519409, 0.03901341184973717, -0.02675403282046318, 0.040575042366981506, -0.04880745708942413, 0.0005539323901757598, 0.06579208374023438, 0.0015474536921828985, -0.006160933990031481, -0.037873901426792145, 0.019300181418657303, 0.01268819160759449, -0.002654118463397026, 0.04593908041715622, -0.05774936452507973, 0.007982052862644196, 0.09653685986995697, 0.0028104810044169426, 0.038625918328762054, 0.037349969148635864, 0.05694500729441643, -0.05831977725028992, -0.1514325737953186, 0.01556126307696104, 0.009103978052735329, 0.012776989489793777, 0.015669891610741615, -0.011254196986556053, -0.027592046186327934, 0.007448198739439249, -0.02914532460272312, -0.01286156103014946, -0.02571556344628334, 0.004184491466730833, -0.04505284130573273, -0.004636297468096018, -0.01447780430316925, -0.026497701182961464, -0.03338557109236717, -0.03161848708987236, -0.01348855346441269, 0.008074329234659672, -0.021750466898083687, -0.015592087060213089, 0.02427087351679802, -0.05847236514091492, 0.012814885936677456, 0.0000781448106863536, -0.01377816405147314, -0.009367055259644985, -0.02151975966989994, 0.0354745052754879, 0.01671488583087921, 0.002478621434420347, -0.0527363084256649, -0.11248614639043808, 0.05986444279551506, 0.04161151498556137, 0.0069778538309037685, -0.010383211076259613, 0.030046096071600914, 0.06747253984212875, -0.040256138890981674, 0.026651613414287567, 0.04129593446850777, -0.014612036757171154, -0.003517818171530962, -0.04452643170952797, -0.013321716338396072, 0.04337747395038605, 0.0006360023398883641, 0.011889622546732426, -0.03444761782884598, -0.016110869124531746, 0.08227365463972092, 0.029527459293603897, 0.02390226535499096, -0.009541085921227932, -0.019590264186263084, 0.02577449008822441, -0.0693431943655014, -0.02488281950354576, 0.015642601996660233, 0.043472785502672195, -0.03574863821268082, 0.023299822583794594, -0.03028293512761593, 0.02276979200541973, 0.013972900807857513, 0.02129294164478779, -0.012262269854545593, -0.02407853491604328, -0.016913050785660744, 0.008725609630346298, -0.04372111335396767, 0.005688849370926619, 0.05350084230303764, 0.013912136666476727, -0.028076115995645523, 0.05550635606050491, -0.035990163683891296, -0.01747393049299717, -0.03862008824944496, -0.007112413179129362, -0.020622801035642624, -0.02403697371482849, -0.021543415263295174, -0.027368655428290367, -0.013760140165686607, -0.03353816643357277, -0.053771618753671646, -0.009560302831232548, 0.01728583313524723, 0.005392606370151043, -0.05623069405555725, -0.03363414481282234, -0.024601874873042107, -0.048634763807058334, -0.017778566107153893, -0.001314271125011146, 0.0025699094403535128, 0.0255216546356678, -0.031379032880067825, 0.02157488837838173, 0.01374952495098114, -0.02762174978852272, 0.05060737207531929, 0.07688532024621964, -0.002581738168373704, 0.02154034748673439, -0.05296536907553673, 0.021518882364034653, 0.026462873443961143, -0.04354332014918327, -0.02770049311220646, -0.06322586536407471, -0.0372328944504261, -0.02027108147740364, -0.012910407036542892, -0.029972465708851814, 0.046826813369989395, -0.039520714432001114, 0.012590832076966763, -0.016937075182795525, 0.014989277347922325, 0.026599545031785965 ]
<p>How can I determine the direction of the force acting due to gyroscopic couple on a car's wheels when it is taking a turn to it's left side?</p>
g5454
[ 0.027528323233127594, 0.025346549227833748, -0.013973533175885677, 0.0026861855294555426, 0.07892576605081558, -0.006599167827516794, 0.051240090280771255, -0.01605828106403351, -0.02897951751947403, -0.030326981097459793, 0.013795092701911926, -0.02248866856098175, 0.021605046465992928, 0.0020524875726550817, 0.0762735903263092, -0.004758812952786684, 0.0462191067636013, -0.005083721596747637, -0.02770213596522808, 0.020863112062215805, 0.04877474531531334, 0.00010639402171364054, -0.04817973077297211, 0.02506105601787567, -0.0216507688164711, -0.04196535795927048, 0.02192596346139908, 0.0010113583412021399, 0.033227819949388504, -0.011836997233331203, 0.02009444124996662, -0.011623178608715534, 0.040591076016426086, -0.043433912098407745, -0.047713544219732285, -0.012218162417411804, 0.04831334203481674, -0.011501602828502655, 0.012063794769346714, -0.027020109817385674, 0.031877271831035614, -0.02814691886305809, 0.024322180077433586, 0.02543517015874386, 0.03454289585351944, -0.03293845057487488, -0.010548929683864117, -0.017596688121557236, 0.005516292992979288, 0.017117075622081757, -0.058684494346380234, 0.04973363131284714, 0.028233932331204414, -0.027903486043214798, 0.03056228905916214, 0.000015839183106436394, 0.03885585814714432, 0.013621936552226543, 0.03219812363386154, -0.0017757125897333026, -0.0623653307557106, 0.0538235604763031, 0.04070785641670227, 0.019393861293792725, -0.00038867915282025933, -0.02401150017976761, 0.021375132724642754, 0.009908226318657398, 0.05777880921959877, 0.00903142336755991, -0.011298410594463348, 0.037012044340372086, 0.05265863239765167, -0.017095711082220078, -0.07271269708871841, 0.019548235461115837, 0.02908962033689022, 0.02344648726284504, 0.03195235878229141, 0.005572711583226919, -0.01929815486073494, 0.023749185726046562, -0.03229844942688942, -0.05768842622637749, 0.05334531143307686, 0.006844447460025549, -0.0015695231268182397, 0.0054487986490130424, -0.008324731141328812, -0.020905179902911186, 0.030130023136734962, -0.017634253948926926, 0.060637377202510834, 0.03876684233546257, -0.007185881957411766, -0.06827311217784882, -0.0439063161611557, 0.03119061142206192, 0.024610912427306175, 0.024086173623800278, -0.051185090094804764, 0.0077590132132172585, -0.031862519681453705, -0.017654288560152054, 0.036283813416957855, -0.0003573503054212779, 0.022857876494526863, 0.0494726300239563, 0.00038876841426827013, -0.10264717042446136, -0.02231888473033905, -0.038638778030872345, 0.008904054760932922, 0.0034086399246007204, 0.0110379159450531, -0.0136738745495677, 0.027824612334370613, -0.03230041265487671, 0.041030820459127426, 0.04285922273993492, -0.009043153375387192, -0.024765603244304657, -0.053502216935157776, 0.04670369252562523, 0.027544062584638596, -0.018048232421278954, -0.05747372657060623, 0.02422036975622177, 0.01896761544048786, 0.043824631720781326, 0.05434517562389374, 0.009003700688481331, 0.09289859980344772, -0.02986893616616726, -0.02190767601132393, 0.047336552292108536, -0.012602679431438446, 0.04773595184087753, 0.021060794591903687, 0.027033653110265732, 0.027848118916153908, -0.01255748700350523, 0.022199634462594986, 0.01936046965420246, 0.04065359756350517, 0.06566541641950607, -0.022288110107183456, 0.0364995151758194, 0.05874602869153023, -0.010140351951122284, -0.02003190666437149, 0.021252280101180077, 0.03307867795228958, -0.03515087440609932, 0.023257233202457428, -0.04033529385924339, 0.031068230047822, -0.013635892421007156, -0.017766105011105537, 0.02377835102379322, 0.026091232895851135, -0.02667411044239998, 0.006953090894967318, 0.005512472707778215, -0.06006099656224251, -0.01987961120903492, -0.05467803031206131, -0.04662542790174484, 0.01217798050493002, 0.004891735035926104, -0.0815935954451561, -0.03363543003797531, 0.010374261997640133, 0.06259287893772125, 0.0299567598849535, 0.07667572796344757, -0.016897553578019142, -0.05068260431289673, 0.10804706811904907, 0.09235838055610657, 0.06284741312265396, -0.035671643912792206, 0.06449642777442932, 0.04683371260762215, -0.025028198957443237, -0.07203890383243561, -0.0024323398247361183, 0.023075859993696213, -0.1174144521355629, -0.01201815064996481, -0.045352429151535034, 0.03878311812877655, -0.030020371079444885, 0.03904453665018082, -0.029969695955514908, -0.017549041658639908, -0.03821057826280594, -0.08016107231378555, -0.005102113820612431, 0.019224287942051888, -0.062312282621860504, 0.0014653470134362578, 0.049195729196071625, 0.05105550214648247, -0.07087525725364685, -0.052695535123348236, 0.025246117264032364, 0.02235410548746586, 0.05663122981786728, -0.04403546079993248, -0.02271631918847561, 0.061907291412353516, -0.05905862897634506, -0.011617320589721203, -0.049270931631326675, 0.001775058452039957, -0.01915043592453003, -0.013490636833012104, 0.002713605063036084, 0.03438452258706093, 0.04342113062739372, 0.046819526702165604, -0.02246205508708954, -0.0005749254487454891, -0.033660486340522766, -0.0006869473145343363, -0.02769898809492588, 0.0031969130504876375, -0.003905852558091283, -0.034724172204732895, 0.0032209286000579596, -0.008269261568784714, 0.028744667768478394, -0.037208132445812225, 0.05224227532744408, 0.012721339240670204, 0.008725102990865707, 0.036577221006155014, 0.015064486302435398, -0.0053505017422139645, 0.011308343149721622, -0.020592303946614265, -0.03372698649764061, -0.0044283256866037846, 0.0035340820904821157, 0.006238751113414764, 0.037797052413225174, 0.010647179558873177, 0.01500968262553215, 0.029200712218880653, 0.016160717234015465, -0.010219008661806583, -0.022611325606703758, 0.02980690635740757, -0.0000748064776416868, -0.005980177316814661, -0.03972020745277405, -0.006139114033430815, -0.047923434525728226, 0.027160635218024254, -0.03616875782608986, -0.029781432822346687, 0.06736715883016586, 0.06167282909154892, -0.01426530908793211, 0.013495165854692459, 0.026131395250558853, -0.02623901702463627, 0.025831252336502075, 0.012673505581915379, -0.01512840110808611, 0.047000702470541, -0.00580452848225832, 0.027182500809431076, -0.023724153637886047, -0.04946185275912285, 0.024377640336751938, 0.00019635999342426658, -0.05394672229886055, 0.03149344027042389, 0.013096376322209835, 0.029727987945079803, 0.042141128331422806, 0.02692781761288643, 0.025680944323539734, 0.02028157375752926, -0.006115360651165247, 0.02533593401312828, -0.04145142063498497, -0.01745271123945713, -0.040250614285469055, 0.0009735613130033016, 0.0426064133644104, 0.006551347207278013, 0.037436723709106445, -0.00978157576173544, 0.02752920612692833, 0.009984741918742657, 0.016207799315452576, 0.022272169589996338, 0.029265843331813812, -0.017377087846398354, 0.008990089409053326, -0.026403728872537613, 0.02654545195400715, -0.004827456083148718, 0.02119666337966919, -0.05654135346412659, 0.02712359093129635, 0.0747319832444191, -0.04117894545197487, 0.015419195406138897, 0.017521599307656288, -0.03754241764545441, -0.04354346543550491, 0.004836393520236015, -0.0033824648708105087, -0.02291811816394329, -0.07573287934064865, 0.007524022366851568, -0.03811780363321304, -0.08109566569328308, -0.005870717111974955, 0.007498156279325485, 0.025494135916233063, 0.0484413281083107, -0.003703137394040823, -0.0091595109552145, 0.03862915560603142, -0.036145638674497604, 0.044304851442575455, 0.05693230405449867, 0.0017936890944838524, -0.017121244221925735, 0.000993735040538013, 0.05926099047064781, -0.023748580366373062, -0.006686241831630468, 0.02580505795776844, 0.04367290437221527, -0.0058985683135688305, -0.012755155563354492, 0.009600836783647537, -0.01773937977850437, -0.04016316682100296, 0.056607507169246674, -0.0036781516391783953, 0.015173094347119331, 0.05599841848015785, -0.027442151680588722, -0.00871497392654419, -0.005054048728197813, -0.013251633383333683, -0.010959099978208542, -0.0009983765194192529, -0.04281967505812645, 0.006197902839630842, -0.015100900083780289, -0.010398169979453087, 0.0659855306148529, -0.027684392407536507, -0.03252001106739044, -0.0995345413684845, 0.002441725693643093, 0.051671188324689865, -0.05202697217464447, -0.056358493864536285, 0.03546628728508949, -0.028873248025774956, -0.013941299170255661, -0.01590026542544365, -0.03553863242268562, 0.031295742839574814, 0.013101154007017612, 0.016939254477620125, -0.04549515247344971, 0.03462166339159012, -0.04416518285870552, -0.018431775271892548, 0.02522779256105423, 0.013392830267548561, 0.0500086285173893, 0.013346293941140175, 0.045148953795433044, 0.05707855895161629, -0.03287492319941521, 0.0065365624614059925, 0.011997132562100887, 0.02811513841152191, 0.019903985783457756, 0.03313932567834854, -0.07120571285486221, -0.0156541895121336, -0.014053692109882832, -0.0013954732567071915, -0.005855928640812635, 0.016841892153024673, 0.028923407196998596, -0.04006534814834595, -0.023329317569732666, -0.0290212482213974, 0.04212397336959839, -0.00944745633751154, 0.03044678270816803, -0.009776960127055645, 0.03033129684627056, -0.017446910962462425, 0.0007548494613729417, 0.042429544031620026, 0.010097241029143333, 0.04632554203271866, -0.002547462470829487, -0.007177175022661686, 0.020581116899847984, 0.07498259842395782, 0.014518167823553085, -0.06696899235248566, 0.05521952733397484, 0.06374231725931168, 0.02837689220905304, -0.021911466494202614, 0.06644144654273987, 0.03129684925079346, -0.02213577926158905, -0.05774301290512085, 0.038358863443136215, 0.009114413522183895, -0.025248633697628975, 0.02773894928395748, -0.036467764526605606, 0.030640924349427223, 0.018104050308465958, -0.012309565208852291, -0.00892169401049614, -0.04843180626630783, 0.03203285112977028, -0.0010236421367153525, -0.02148398570716381, 0.021557651460170746, -0.03345569968223572, 0.0037351236678659916, 0.038143694400787354, -0.03234759345650673, -0.03481139615178108, 0.0009324603597633541, -0.0019496837630867958, -0.03560859337449074, -0.030078671872615814, 0.04119090735912323, -0.03415282443165779, -0.051552921533584595, -0.009182323701679707, -0.050246529281139374, 0.031032968312501907, -0.02609933726489544, 0.030658315867185593, -0.006478565279394388, -0.0019618389196693897, -0.04736272245645523, 0.019722046330571175, -0.04807618632912636, -0.0024279465433210135, -0.05026900768280029, -0.0015362633857876062, -0.029097139835357666, 0.027024216949939728, 0.009860503487288952, -0.024800198152661324, -0.009240019135177135, 0.015316625125706196, -0.041650719940662384, -0.029098814353346825, 0.02800305001437664, 0.006690858863294125, -0.05357668921351433, 0.012516971677541733, 0.03185306116938591, 0.032082270830869675, 0.02624492719769478, -0.033813394606113434, -0.034291673451662064, 0.03622269257903099, 0.07302048057317734, -0.06845243275165558, -0.01174959447234869, -0.022574832662940025, 0.052171383053064346, -0.0009317375370301306, 0.042883504182100296, -0.023942183703184128, 0.012865380384027958, -0.008617156185209751, -0.01876613311469555, -0.07512770593166351, -0.0408119261264801, 0.012200144119560719, -0.028374608606100082, -0.008158059790730476, -0.018705260008573532, -0.006137628108263016, -0.06720445305109024, -0.0020880228839814663, 0.027466410771012306, 0.048661358654499054, 0.006055766716599464, 0.04250440001487732, 0.07956699281930923, -0.04335347190499306, -0.004713074304163456, 0.028143854811787605, 0.006018575746566057, 0.040149446576833725, 0.06501884758472443, 0.025681033730506897, 0.005821605212986469, 0.04142075031995773, 0.0011618416756391525, 0.01342776045203209, 0.03591354191303253, 0.01632201112806797, -0.027083855122327805, 0.013476415537297726, -0.03542748838663101, -0.017166346311569214, -0.00860687531530857, 0.007959900423884392, -0.014542984776198864, 0.034440137445926666, -0.0077927871607244015, -0.0286384429782629, -0.032259441912174225, -0.0236622616648674, 0.0186605304479599, 0.020465604960918427, 0.007382990792393684, -0.09942170977592468, 0.09538284689188004, -0.030252644792199135, 0.015818065032362938, -0.025017494335770607, -0.041386332362890244, 0.022919628769159317, -0.021746613085269928, 0.008943638764321804, -0.042043719440698624, 0.04072294384241104, -0.03054402396082878, -0.012181194499135017, 0.04461107403039932, -0.012178435921669006, -0.06586825102567673, 0.06485279649496078, -0.009565000422298908, -0.01869192160665989, 0.009535087272524834, -0.014004797674715519, -0.0558873787522316, -0.03650565817952156, -0.002430314663797617, -0.007501572370529175, 0.056129489094018936, -0.04284466803073883, 0.04177821800112724, 0.018490692600607872, -0.0034832728561013937, -0.02366580069065094, -0.05987585708498955, 0.020226705819368362, 0.02733818255364895, 0.017158977687358856, -0.03740301355719566, -0.07767538726329803, -0.0402558408677578, 0.03903258964419365, 0.06739284098148346, -0.011826429516077042, -0.03667858988046646, 0.019637737423181534, 0.002258386928588152, 0.045650530606508255, -0.031213896349072456, -0.0001960916124517098, 0.041868168860673904, 0.057406824082136154, -0.03329010680317879, 0.05358321964740753, -0.044602490961551666, -0.02491605468094349, 0.018566731363534927, -0.03444758430123329, -0.04892566800117493, 0.024768853560090065, 0.018089015036821365, 0.03005918301641941, -0.045116398483514786, 0.004353225696831942, -0.018557609990239143, 0.09948834031820297, 0.041742920875549316, 0.01188842486590147, -0.0015149501850828528, 0.026467841118574142, 0.0159798301756382, -0.026173116639256477, 0.01302835252135992, -0.052147433161735535, 0.008723839186131954, -0.011018294841051102, -0.0037233736366033554, -0.04228322207927704, -0.03780584782361984, -0.009947662241756916, -0.04602055996656418, 0.049294594675302505, -0.007657004985958338, 0.03834987431764603, 0.025380443781614304, 0.0008058082312345505, -0.016329851001501083, -0.055168427526950836, -0.01083526760339737, 0.015077531337738037, -0.0054591866210103035, -0.04546539857983589, -0.05235791578888893, 0.040159087628126144, -0.09311197698116302, -0.027881238609552383, 0.010339295491576195, 0.020518571138381958, 0.050709739327430725, -0.03943377360701561, -0.021969808265566826, -0.02422185428440571, 0.015140014700591564, 0.049367159605026245, -0.05839560925960541, 0.046141766011714935, 0.06301970034837723, 0.07571286708116531, 0.0126639474183321, 0.033576302230358124, -0.06710274517536163, -0.023633450269699097, -0.054201629012823105, -0.03146258369088173, -0.012466751039028168, 0.010555583983659744, 0.025039955973625183, 0.03757594898343086, -0.006082781590521336, -0.03211763873696327, 0.011271406896412373, -0.00602142745628953, -0.039703283458948135, 0.026133928447961807, 0.04231484979391098, 0.010100354440510273, 0.004819911904633045, 0.002852036152034998, 0.011392788030207157, -0.019028855487704277, -0.030444208532571793, -0.010833395645022392, -0.06891779601573944, 0.027554243803024292, -0.03530121222138405, -0.008398587815463543, -0.0043918476440012455, -0.02781011164188385, -0.05876174941658974, -0.09543322771787643, -0.027973780408501625, 0.024088559672236443, -0.012180499732494354, -0.013941398821771145, -0.013412971049547195, -0.04765286296606064, 0.002829000586643815, 0.012645612470805645, 0.0018730920273810625, 0.016222992911934853, -0.04862763360142708, 0.012232680805027485, -0.053707320243120193, -0.06683693826198578, 0.06242187321186066, -0.05035240948200226, -0.036628641188144684, -0.0173968318849802, -0.01800995133817196, 0.040250036865472794, -0.007430458907037973, -0.036574408411979675, -0.02299053780734539, 0.02650073729455471, -0.01634589023888111, 0.09997852146625519, -0.06407056748867035, 0.04009702801704407, 0.05412080138921738, -0.03603668510913849, 0.028788482770323753, 0.049483247101306915, 0.02699202485382557, -0.06786001473665237, -0.06170544773340225, -0.008877582848072052, -0.03331548348069191, 0.010506375692784786, -0.027578117325901985, 0.021468710154294968, -0.034590139985084534, 0.007084991317242384, 0.054795946925878525, 0.05691114440560341, 0.05657195299863815, 0.044127557426691055, 0.02985955961048603, 0.03406921774148941, 0.00832153670489788, -0.03697805479168892, -0.00025837196153588593, -0.03450058400630951, -0.09814166277647018, -0.0397830568253994, -0.023315178230404854, -0.0033749439753592014, 0.03994780033826828, -0.0090246070176363, -0.0036590546369552612, 0.06533967703580856, 0.025858726352453232, 0.03223986178636551, -0.0552448146045208, -0.00593888945877552, -0.037682581692934036, -0.0354265421628952, -0.018044883385300636, 0.024449199438095093, 0.014290128834545612, -0.11347202211618423, 0.018703538924455643, -0.04475979134440422, -0.017556793987751007, -0.0044815135188400745, -0.0009074868867173791, 0.03926554322242737, -0.00835318025201559, 0.0060636913403868675, -0.004031365737318993, 0.025394175201654434, -0.05572739243507385, -0.022026946768164635, -0.024312082678079605, -0.00817781686782837, -0.04950011894106865, 0.021968424320220947, 0.004667819943279028, 0.019682858139276505, -0.025517858564853668, -0.009401816874742508, 0.014780458062887192, -0.036012835800647736, -0.0010237219976261258, -0.015301519073545933, -0.06810472905635834, -0.02451103925704956 ]
<p>In "String Theory and M-Theory: a modern introduction" by K.Becker, M. Becker and J.H.Schwarz, they say that BPS D-brane is stable as it preserves half of the Supersymmetry. I really want to understand more about this statement and see detail calculations. What is the mechanism of D-brane stability? Is there any derivation for the instability of space-filling D-brane (so that open string tachyon will be eliminated from the theory)? </p> <p>Thank you.</p>
g5455
[ 0.03460869565606117, 0.05594421923160553, -0.0006963142077438533, 0.0013658769894391298, 0.0038173666689544916, 0.05396007373929024, 0.022861506789922714, 0.014833574183285236, -0.014308669604361057, -0.06879321485757828, -0.037202540785074234, 0.026862341910600662, 0.03561295196413994, 0.037053484469652176, 0.05591568350791931, 0.0037254542112350464, -0.01996905542910099, 0.022165572270751, 0.046544399112463, -0.05018945038318634, -0.0023839857894927263, -0.002413682173937559, 0.01057102344930172, -0.046399958431720734, -0.031728655099868774, 0.017774779349565506, 0.04106050357222557, -0.01944546028971672, 0.006270203273743391, 0.024691976606845856, 0.04360285401344299, 0.033150479197502136, 0.05932166427373886, -0.004365064669400454, -0.021158812567591667, -0.05250385403633118, 0.027422994375228882, -0.004542605020105839, -0.01345671247690916, -0.04030724614858627, 0.006428322289139032, -0.03956198692321777, 0.013163377530872822, -0.03873273730278015, -0.003983506001532078, -0.06599012762308121, -0.07132060080766678, 0.005497197154909372, -0.03173862770199776, -0.03526071831583977, 0.006154724396765232, 0.025825347751379013, 0.08070965111255646, -0.03798588737845421, -0.017892034724354744, -0.02560664899647236, 0.01601698249578476, 0.013400830328464508, 0.01678280159831047, 0.009004737250506878, -0.003978753928095102, 0.01999298669397831, 0.011307512409985065, 0.08581731468439102, 0.009533981792628765, -0.03955129534006119, -0.04398998245596886, -0.07772909849882126, 0.09116246551275253, 0.019730033352971077, 0.012443340383470058, -0.04416107013821602, 0.024230586364865303, -0.023153170943260193, -0.015571135096251965, 0.022884977981448174, -0.01961185224354267, -0.013944168575108051, -0.02388322353363037, -0.01982538029551506, 0.004455540794879198, 0.019051970914006233, 0.0031229460146278143, -0.04517296701669693, 0.010006794705986977, -0.05014752224087715, -0.007049626670777798, 0.002651158021762967, -0.03255689516663551, 0.020489223301410675, -0.03446032479405403, -0.04024187847971916, -0.04022125154733658, -0.015241657383739948, 0.040173839777708054, 0.04158986359834671, 0.005118157248944044, 0.07023637741804123, -0.04412243515253067, -0.06976917386054993, 0.02690540999174118, -0.04067974537611008, 0.02149304933845997, 0.04703981429338455, -0.012132091447710991, 0.03374071419239044, 0.021996738389134407, 0.022814616560935974, 0.018399566411972046, 0.028194798156619072, -0.03273012861609459, 0.030080309137701988, -0.01710527390241623, -0.03099866397678852, -0.04547044634819031, 0.0034863250330090523, 0.0003326935402583331, -0.0014847860438749194, 0.03622428700327873, -0.03151531517505646, 0.10082419216632843, -0.0331081785261631, -0.031186543405056, 0.003911900334060192, -0.03557202219963074, -0.038020819425582886, -0.03453545272350311, -0.036726102232933044, 0.09755901247262955, -0.013261553831398487, -0.01204539556056261, 0.020415134727954865, -0.009157859720289707, -0.017698027193546295, 0.043932147324085236, 0.02634112536907196, 0.017208324745297432, 0.044911857694387436, -0.0074196746572852135, -0.07638950645923615, -0.02630619704723358, 0.010791116394102573, 0.018549352884292603, 0.04124526306986809, -0.018525589257478714, 0.0443025566637516, 0.026269536465406418, 0.006193047389388084, -0.015538938343524933, 0.03285945951938629, 0.030262762680649757, 0.10175997018814087, -0.016288619488477707, -0.06041170656681061, -0.015408405102789402, 0.0359216183423996, 0.04078099504113197, -0.003662426257506013, -0.027878601104021072, 0.03493016958236694, 0.017736036330461502, 0.004174402914941311, -0.05200077220797539, 0.01322530210018158, -0.0602768212556839, 0.01108460035175085, 0.004596579819917679, -0.06050380691885948, -0.02025071531534195, -0.044110048562288284, -0.027686914429068565, 0.035804711282253265, 0.03162606433033943, 0.07774785161018372, -0.025859734043478966, -0.0013775437837466598, -0.0035499739460647106, 0.011300604790449142, 0.07036956399679184, 0.008062954992055893, 0.01799892447888851, -0.020172161981463432, -0.0220261812210083, -0.03370121121406555, 0.04399673268198967, 0.05666228383779526, 0.0593906044960022, -0.03887972980737686, -0.022772643715143204, 0.02824857458472252, -0.027313001453876495, -0.005179565865546465, -0.0290388111025095, 0.06467439234256744, 0.013157443143427372, -0.03863071650266647, 0.03359033912420273, -0.0495760552585125, 0.030361957848072052, 0.06586266309022903, -0.027842042967677116, 0.020069343969225883, 0.010892405174672604, -0.01958099752664566, -0.003948419354856014, -0.027524279430508614, -0.017627717927098274, 0.003732465673238039, 0.0331672802567482, -0.024740811437368393, 0.0033427528105676174, 0.0002531882200855762, 0.03624734655022621, 0.023427370935678482, 0.014415896497666836, -0.030901456251740456, -0.0029039913788437843, 0.04163981229066849, 0.02034643292427063, -0.028468631207942963, 0.009247868321835995, -0.0010656348895281553, 0.04017384722828865, 0.11024931073188782, -0.021522877737879753, 0.03607722744345665, -0.019026324152946472, -0.013174513354897499, 0.015879102051258087, -0.022252017632126808, -0.05834421515464783, -0.047243814915418625, -0.014029812067747116, 0.049358468502759933, 0.04264926165342331, 0.022388659417629242, 0.028683925047516823, -0.009132775478065014, 0.06535346806049347, 0.037829719483852386, 0.016499660909175873, 0.04848242178559303, -0.030477356165647507, 0.04192240908741951, 0.031222673133015633, 0.007269307971000671, 0.009516139514744282, -0.0072483341209590435, -0.03826645389199257, -0.028752172365784645, -0.0022856437135487795, -0.047234997153282166, 0.04259733110666275, -0.023261796683073044, -0.033368393778800964, -0.0363888293504715, -0.02912316471338272, 0.02908877283334732, -0.03122546710073948, -0.05529828369617462, 0.008814124390482903, 0.01787063479423523, -0.002418285934254527, -0.0344172827899456, -0.10125839710235596, 0.003528259228914976, 0.022325916215777397, -0.04784245789051056, -0.01951654627919197, 0.016886238008737564, -0.021522121503949165, -0.009060068055987358, -0.012572354637086391, 0.03928447514772415, -0.008162664249539375, -0.0022593019530177116, -0.004455103073269129, 0.004303227178752422, -0.02021583542227745, -0.019426431506872177, -0.04047687351703644, 0.02117352932691574, 0.004250993020832539, -0.010586625896394253, -0.041983332484960556, -0.01887570321559906, 0.025935707613825798, -0.010198574513196945, 0.03277435898780823, -0.019700709730386734, -0.022195816040039062, 0.019141174852848053, -0.05628211796283722, 0.004288314841687679, -0.033257316797971725, 0.05745710805058479, 0.01161083485931158, -0.02476709894835949, -0.012129963375627995, -0.029693517833948135, -0.006679287180304527, 0.010517522692680359, -0.0009743939735926688, 0.0036861577536910772, 0.018810883164405823, 0.04408527538180351, -0.0881178081035614, -0.03450095281004906, 0.0031731082126498222, -0.002291642362251878, -0.03417602926492691, -0.03918598219752312, -0.0039217048324644566, 0.02317763864994049, -0.06154310330748558, 0.04248302802443504, -0.010800308547914028, 0.015824604779481888, 0.049978651106357574, 0.0012323795817792416, -0.0037484290078282356, -0.001054460764862597, 0.022904006764292717, -0.048786867409944534, 0.04300951212644577, -0.009067930281162262, -0.0319310687482357, -0.0033952260855585337, -0.05583219975233078, 0.051314111799001694, -0.0060832323506474495, -0.004818676970899105, 0.027107510715723038, 0.03132385015487671, -0.030525028705596924, 0.02302396669983864, 0.015814758837223053, 0.01125525776296854, 0.0381162166595459, 0.04856571555137634, 0.029370345175266266, 0.01108766719698906, -0.015013533644378185, -0.02607114240527153, 0.05185209959745407, 0.09405776113271713, 0.04006087779998779, -0.029199941083788872, 0.032850876450538635, -0.04842999204993248, 0.005131211131811142, 0.05065734684467316, -0.016386346891522408, 0.02394746243953705, -0.024718934670090675, 0.0783749371767044, 0.03584342822432518, 0.008021309971809387, 0.02026909403502941, -0.008542943745851517, -0.022703438997268677, -0.047556180506944656, -0.03638307377696037, -0.009442179463803768, -0.038817837834358215, -0.013769557699561119, 0.02238408476114273, -0.0224763136357069, -0.04083004966378212, -0.038257479667663574, -0.004944787826389074, -0.0488603338599205, 0.02178252674639225, 0.026735788211226463, 0.025221798568964005, -0.03281363472342491, -0.025742538273334503, 0.036968205124139786, -0.021722767502069473, 0.042725421488285065, 0.011955886147916317, 0.020069746300578117, 0.010586664080619812, 0.03079921007156372, 0.03006075881421566, -0.0023375703021883965, -0.033622369170188904, -0.035011641681194305, -0.08396027237176895, 0.02456844411790371, -0.0003829210181720555, -0.00512817595154047, 0.02342659793794155, -0.05084696412086487, 0.026215029880404472, 0.011430516839027405, -0.031088661402463913, 0.048702824860811234, 0.008212038315832615, -0.044419486075639725, 0.01410461775958538, 0.0018410594202578068, -0.06657147407531738, -0.07859987020492554, -0.03771871700882912, 0.05345110222697258, -0.03291935473680496, 0.013189333491027355, 0.0181892029941082, 0.05598906800150871, 0.059084244072437286, 0.013652537949383259, -0.053263407200574875, -0.06027369201183319, 0.007886753417551517, -0.004360363353043795, 0.04533541947603226, -0.04606086388230324, 0.08439913392066956, -0.024923553690314293, 0.025220973417162895, -0.025772839784622192, -0.025738293305039406, 0.015786059200763702, -0.03429984673857689, 0.03479991853237152, 0.010678405873477459, -0.012661335058510303, -0.0019468979444354773, 0.037342023104429245, 0.045080963522195816, 0.004667612258344889, 0.011491748504340649, -0.014207418076694012, -0.0812041237950325, 0.022451326251029968, -0.027180984616279602, -0.04253210872411728, -0.02781250700354576, 0.04018072783946991, 0.06797294318675995, -0.02967682108283043, 0.047995567321777344, -0.019429832696914673, -0.03367455676198006, -0.01245452743023634, -0.041519761085510254, -0.03612321615219116, 0.016868039965629578, -0.015704112127423286, -0.012624355964362621, 0.04524918273091316, 0.03310885652899742, 0.0071684932336211205, -0.009066224098205566, 0.014619813300669193, -0.0075108748860657215, -0.030662260949611664, 0.04544203355908394, -0.005713865626603365, -0.05540882423520088, -0.03830602020025253, -0.010524297133088112, 0.054557058960199356, 0.037000078707933426, -0.006687270011752844, 0.006146163679659367, -0.05429648235440254, -0.01412398461252451, 0.012308849021792412, 0.03823992237448692, -0.021041641011834145, 0.005327184218913317, -0.0647738054394722, 0.040792934596538544, 0.010827799327671528, -0.06360099464654922, -0.05131620168685913, 0.018774379044771194, -0.0380554236471653, 0.02887256257236004, -0.028433699160814285, 0.05822987109422684, 0.057717207819223404, -0.04602504149079323, -0.03521613031625748, 0.028224274516105652, -0.014375523664057255, -0.05813627317547798, 0.040830329060554504, -0.02711528167128563, 0.04454642906785011, 0.030388033017516136, -0.050441328436136246, 0.0038040769286453724, 0.024402691051363945, 0.025316668674349785, -0.04727255553007126, -0.040265824645757675, -0.05850088223814964, -0.025536131113767624, -0.05794750899076462, 0.07834583520889282, -0.008413569070398808, -0.03058243915438652, 0.051938459277153015, -0.016791831701993942, 0.0036527798511087894, -0.02154391258955002, -0.022041412070393562, -0.007284840103238821, 0.025467898696660995, -0.03849736228585243, 0.1047312393784523, 0.019990457221865654, -0.06776925176382065, 0.0176482405513525, 0.03242202475667, -0.03286142274737358, -0.03859864920377731, -0.0442332923412323, -0.01747305877506733, 0.029252024367451668, 0.03360557183623314, 0.0128730908036232, 0.06963344663381577, -0.05429581180214882, 0.01585964486002922, 0.029897740110754967, -0.002418860560283065, -0.02305075339972973, -0.053533896803855896, 0.04288240522146225, -0.010003584437072277, -0.028535904362797737, -0.05622342973947525, 0.019433114677667618, 0.002520694863051176, -0.0035723443143069744, 0.035725969821214676, 0.024701325222849846, 0.012517589144408703, -0.02571217156946659, 0.030461061745882034, -0.011164184659719467, -0.030310291796922684, 0.022598030045628548, -0.0032497537322342396, -0.015907300636172295, -0.07281102240085602, -0.05151611939072609, 0.044571761041879654, 0.009288831613957882, -0.008689818903803825, 0.019005103036761284, 0.05220087990164757, -0.013400173746049404, -0.03351255878806114, 0.018496502190828323, 0.007059866562485695, -0.011979215778410435, 0.01834409311413765, -0.012611842714250088, 0.005441563203930855, 0.006146574858576059, 0.02007182687520981, -0.010389397852122784, -0.04079854488372803, 0.053535860031843185, -0.011980954557657242, -0.06729592382907867, 0.005452503450214863, -0.015204600989818573, 0.06404081732034683, 0.011369287967681885, -0.027247166261076927, -0.007809214759618044, -0.07112512737512589, 0.001727899070829153, -0.04744534566998482, 0.020811062306165695, 0.0006697127246297896, 0.04975892975926399, -0.01119130477309227, -0.08712804317474365, -0.003360650036484003, -0.02333642728626728, 0.033942509442567825, 0.05517973378300667, 0.013888138346374035, -0.024906303733587265, 0.10849562287330627, 0.004907526541501284, 0.02097013033926487, 0.02959216758608818, 0.06619986146688461, 0.006992348004132509, 0.013186338357627392, -0.014877700246870518, -0.06810006499290466, 0.05891117826104164, 0.012416396290063858, 0.07467783987522125, 0.01317119412124157, 0.00550480792298913, 0.06434816867113113, -0.0024736402556300163, 0.0012844341108575463, -0.04601288586854935, 0.06738365441560745, 0.017782241106033325, -0.00012959132436662912, 0.016422925516963005, -0.02297871932387352, 0.0760103166103363, -0.0689917802810669, 0.07374299317598343, 0.017181402072310448, 0.0411471426486969, 0.052883852273225784, 0.014540341682732105, -0.03415327146649361, -0.02194138616323471, 0.0058065857738256454, 0.008649254217743874, 0.02796245366334915, 0.02511226013302803, -0.05375085771083832, -0.028837421908974648, 0.021531768143177032, -0.011221135966479778, -0.02796855755150318, -0.001535896328277886, 0.004349862691015005, -0.01490448135882616, 0.060011062771081924, -0.09071870893239975, 0.025704722851514816, -0.017589565366506577, 0.030270865187048912, -0.022254306823015213, -0.0291067473590374, 0.050669796764850616, -0.03154284134507179, -0.02633379027247429, -0.025242798030376434, 0.03675994649529457, -0.007086046971380711, -0.06528738886117935, 0.014134529046714306, 0.023725207895040512, 0.03322926536202431, -0.05269088223576546, -0.011959167197346687, 0.013028171844780445, -0.05475294962525368, -0.07019709795713425, -0.057150401175022125, -0.017690356820821762, -0.1024598777294159, 0.013513936661183834, -0.03146042674779892, 0.017556602135300636, -0.025144334882497787, 0.03340286388993263, 0.07515821605920792, 0.009524532593786716, -0.011444313451647758, 0.07571175694465637, 0.024337375536561012, 0.006022003013640642, 0.022404130548238754, -0.03971026465296745, 0.02281777188181877, -0.04749187082052231, 0.043933503329753876, 0.0062639424577355385, 0.0023654717952013016, -0.011615780182182789, 0.0000682066529407166, 0.03156062215566635, -0.006431914400309324, 0.031449589878320694, 0.035579778254032135, -0.023467935621738434, 0.007066285237669945, 0.06340504437685013, 0.08798590302467346, -0.007717728149145842, 0.046363554894924164, 0.013702738098800182, -0.005314625333994627, 0.01624351553618908, 0.005014733411371708, -0.010215799324214458, -0.0106875104829669, 0.012000495567917824, -0.0070802257396280766, 0.07386726140975952, -0.013803972862660885, -0.0006896993145346642, -0.02984253130853176, -0.006360967177897692, 0.09513607621192932, 0.019628774374723434, 0.0008350966963917017, -0.07106154412031174, -0.030489755794405937, -0.07786820828914642, 0.0014705103822052479, 0.002836651401594281, -0.07379298657178879, 0.06017181649804115, -0.008483982644975185, 0.06491901725530624, -0.053255774080753326, 0.03746293485164642, -0.043398741632699966, -0.032635997980833054, -0.03202850744128227, -0.02189800515770912, -0.019894937053322792, 0.002676034811884165, -0.01349787600338459, -0.04655949026346207, -0.03531155362725258, -0.005156750325113535, -0.014206386171281338, 0.013113788329064846, 0.05131318047642708, -0.04185808449983597, -0.008854328654706478, -0.005705625284463167, -0.00040315682417713106, -0.005317327566444874, 0.0226996298879385, 0.029621249064803123, -0.012629511766135693, 0.0007211678894236684, 0.06765734404325485, -0.0029815109446644783, -0.004727749153971672, -0.02196039818227291, -0.06018328294157982, -0.026475373655557632, 0.02005554363131523, -0.05151800811290741, -0.0016106704715639353, 0.02978193759918213, -0.019446581602096558, 0.015410443767905235, -0.009939229115843773, -0.017243297770619392, -0.021754860877990723, 0.016164183616638184, -0.002979154698550701, -0.028506595641374588, -0.03664897009730339, 0.01218968816101551, 0.045272111892700195, 0.03475644439458847, 0.005235551856458187, 0.014443918131291866, -0.009418550878763199, 0.006611678283661604, 0.016500696539878845, -0.03811481222510338, -0.011984819546341896 ]
<p>How does the temperature vary along the length of the rod if its both ends are at different temperature. As an example, consider the problem:</p> <blockquote> <p>20 cm long rod has rod at one end 100 ºC and another end at 0 ºC. Find the temperature at the center of the rod when it's in thermal steady state.</p> </blockquote>
g5456
[ 0.0872112438082695, 0.012480920180678368, 0.02208986133337021, -0.03639982268214226, 0.04335624352097511, -0.07548080384731293, 0.02915375865995884, 0.024715717881917953, -0.060322895646095276, 0.01798262819647789, -0.03552635386586189, 0.09363967925310135, -0.02462567202746868, -0.013150544837117195, 0.06137046217918396, -0.00606456259265542, 0.07425608485937119, -0.013422602787613869, 0.04733681678771973, 0.06350914388895035, -0.03339577838778496, 0.020802080631256104, -0.0063696070574223995, 0.006152320187538862, -0.03523414209485054, -0.06401323527097702, 0.01118138711899519, 0.003110643709078431, -0.03408624976873398, -0.030151749029755592, -0.049169495701789856, -0.004212190397083759, 0.009054580703377724, -0.019262146204710007, 0.013775551691651344, -0.019003350287675858, 0.044632457196712494, -0.013369307853281498, -0.00543894013389945, -0.037905700504779816, 0.01073832344263792, 0.0039761681109666824, 0.03859950229525566, 0.016148315742611885, 0.045895032584667206, -0.0135880745947361, -0.06299082934856415, -0.002043523360043764, -0.06647633016109467, 0.008138051256537437, 0.05890600010752678, 0.043317634612321854, 0.045809339731931686, -0.03472929447889328, 0.010021059773862362, 0.0027866996824741364, -0.0518745556473732, 0.040380194783210754, 0.0456862710416317, 0.032916564494371414, 0.04259319603443146, -0.013274945318698883, -0.020182549953460693, -0.045037925243377686, 0.015512076206505299, -0.04547707363963127, 0.01269847434014082, -0.004131365567445755, -0.027483968064188957, 0.04295850172638893, -0.018668686971068382, -0.05662548542022705, -0.00797184370458126, 0.01905500516295433, -0.09373728930950165, -0.030159730464220047, -0.0019470081897452474, -0.006182252429425716, -0.016610313206911087, 0.0009950509993359447, -0.07158130407333374, 0.01589309796690941, 0.0006457613199017942, 0.025125090032815933, -0.0012017268454656005, 0.03471676632761955, -0.013827280141413212, 0.061346814036369324, -0.06994031369686127, -0.0010319121647626162, -0.047252871096134186, 0.01872768998146057, 0.1178513616323471, 0.06691698729991913, 0.03375377506017685, -0.04544784501194954, -0.010398614220321178, 0.015596151351928711, 0.00917846616357565, 0.04837808385491371, -0.027775881811976433, 0.003993482794612646, 0.00005688717283192091, 0.038674600422382355, -0.06497250497341156, -0.028239015489816666, 0.021634360775351524, -0.014428431168198586, -0.07012652605772018, 0.019453542307019234, -0.0026698706205934286, -0.06412327289581299, -0.08685916662216187, 0.01173876691609621, -0.014768009074032307, 0.03491338714957237, 0.048676747828722, 0.04401976242661476, -0.014093034900724888, 0.006917829625308514, 0.005140128079801798, -0.00787835568189621, 0.00887747947126627, 0.041444070637226105, 0.033059440553188324, -0.0010517183691263199, 0.03395872935652733, -0.021060166880488396, 0.0033935722894966602, 0.024068301543593407, 0.038626596331596375, 0.05229659378528595, -0.01973787322640419, -0.022567883133888245, -0.0023727831430733204, 0.0012633120641112328, 0.013525239191949368, 0.06718192994594574, -0.012001690454781055, 0.057867348194122314, -0.004497692920267582, -0.03971586003899574, -0.008760455995798111, -0.04689478874206543, -0.03135766461491585, 0.021544303745031357, -0.030036577954888344, -0.04862687364220619, 0.006747818551957607, -0.04476810246706009, 0.007121679838746786, 0.03928527608513832, 0.008337768726050854, -0.008277250453829765, -0.006647726520895958, 0.035962946712970734, 0.013790552504360676, -0.0367400161921978, 0.04851197823882103, -0.0024893314111977816, -0.010063187219202518, -0.007783984299749136, 0.01712685637176037, -0.009130213409662247, -0.10171449184417725, 0.020757043734192848, -0.015144804492592812, -0.014774293638765812, -0.014975881204009056, -0.030888624489307404, -0.09046413749456406, 0.0029974288772791624, -0.01737556979060173, 0.02131775952875614, 0.012597349472343922, 0.010312840342521667, 0.06671225279569626, 0.018228745087981224, 0.029838450253009796, -0.0028243933338671923, -0.021082907915115356, -0.0035545961000025272, 0.07584317773580551, -0.021399330347776413, -0.022801799699664116, 0.07420423626899719, 0.01641721837222576, -0.0466211698949337, -0.08898232132196426, -0.06690152734518051, -0.008084380999207497, -0.03424284979701042, -0.04383913800120354, 0.036607760936021805, -0.03289352357387543, -0.060165081173181534, -0.0002037834346992895, -0.0600682757794857, -0.07261189073324203, 0.007749598938971758, 0.030362531542778015, 0.005870519205927849, 0.025339873507618904, 0.04950243607163429, -0.06087806448340416, -0.01171626802533865, -0.02900370955467224, -0.012040026485919952, 0.0030680669005960226, -0.01912788860499859, 0.02606876567006111, 0.03743883594870567, -0.03062528558075428, 0.10373271256685257, -0.012736312113702297, 0.006827167700976133, 0.048632435500621796, 0.025271300226449966, 0.022874008864164352, -0.013499289751052856, 0.06120510399341583, 0.022037377581000328, -0.037659596651792526, -0.022926965728402138, -0.013091275468468666, -0.0237350445240736, -0.011668780818581581, -0.015267478302121162, 0.002441221382468939, 0.04475404694676399, -0.0395381785929203, 0.016851209104061127, 0.021413791924715042, 0.03445149585604668, 0.052767314016819, -0.017674989998340607, 0.03464459627866745, 0.03308887034654617, -0.034790847450494766, -0.017131026834249496, -0.016922608017921448, -0.02384435012936592, -0.003874354064464569, 0.0768517553806305, -0.019509777426719666, -0.021671107038855553, 0.044217392802238464, -0.027183912694454193, 0.015835117548704147, 0.04412871226668358, 0.044852450489997864, 0.026683945208787918, 0.00032002993975766003, 0.057043299078941345, -0.036201417446136475, -0.052822545170784, -0.07986718416213989, 0.022081373259425163, 0.006963610649108887, -0.08395899832248688, -0.02882351353764534, 0.000206198645173572, 0.031350381672382355, 0.03768528625369072, -0.0207862239331007, -0.019988689571619034, -0.05645476281642914, 0.020208898931741714, 0.016866901889443398, 0.03854057937860489, -0.03337656706571579, -0.0225025936961174, 0.046813953667879105, 0.0031256587244570255, -0.03342971205711365, -0.017369840294122696, 0.036579351872205734, -0.0523841492831707, -0.021870750933885574, 0.025661494582891464, 0.06715861707925797, 0.04500199854373932, 0.0012356723891571164, 0.04329872131347656, 0.04826481267809868, -0.031232528388500214, -0.024479441344738007, 0.0496525876224041, -0.011758451350033283, -0.02436506375670433, -0.015461320988833904, -0.004949810914695263, 0.03096502088010311, -0.021430671215057373, 0.0359814390540123, 0.020335547626018524, -0.011766450479626656, -0.04326651617884636, -0.014477340504527092, -0.0008967218454927206, -0.027422688901424408, -0.016354309394955635, -0.013954074122011662, -0.0006663648528046906, 0.04340760037302971, 0.014976742677390575, -0.03917834162712097, -0.05449613928794861, 0.07465026527643204, -0.023245828226208687, 0.01155894249677658, -0.04701127111911774, 0.05534649267792702, 0.030299659818410873, -0.01600152812898159, 0.03149387985467911, -0.03141523525118828, 0.018781837075948715, 0.07473143935203552, 0.026671886444091797, -0.006773419212549925, -0.000155190602527, 0.0030954652465879917, 0.03254864737391472, -0.02084980718791485, -0.018926946446299553, 0.017361551523208618, -0.01074889861047268, -0.077680803835392, 0.019826781004667282, -0.06953965872526169, -0.0034608759451657534, -0.03142496943473816, -0.05142189934849739, 0.032497912645339966, -0.009804035536944866, 0.03329138830304146, 0.031144797801971436, 0.07109212130308151, 0.05875373259186745, -0.053265344351530075, -0.028391126543283463, -0.010406259447336197, 0.023879410699009895, 0.01768997125327587, -0.011877613142132759, 0.009896106086671352, 0.0016199636738747358, 0.04016048088669777, 0.02917281538248062, -0.005082966294139624, -0.02424613945186138, -0.00993321556597948, -0.00026757741579785943, -0.047737378627061844, 0.03980633616447449, 0.003287554020062089, 0.004977871663868427, -0.02282799780368805, 0.01708928868174553, 0.031252939254045486, -0.01161389984190464, 0.03758225962519646, 0.006059638690203428, 0.025409147143363953, 0.04197598621249199, 0.04989269748330116, -0.01798258349299431, 0.03226577490568161, -0.03917326033115387, 0.02933810092508793, -0.010081884451210499, -0.0702139362692833, -0.012680867686867714, 0.010520922020077705, 0.006031491328030825, -0.017006563022732735, 0.055120911449193954, -0.038294143974781036, 0.03575849533081055, 0.008892127312719822, 0.0067971739917993546, -0.0314418189227581, -0.06003640592098236, -0.019721511751413345, 0.024466663599014282, 0.002190838335081935, 0.004992205649614334, -0.005087682511657476, -0.08740058541297913, 0.04399922490119934, -0.027333900332450867, -0.017635527998209, 0.034724727272987366, 0.0026929923333227634, -0.005118312314152718, 0.08802249282598495, 0.022262990474700928, 0.03885834664106369, -0.017993729561567307, -0.016725478693842888, -0.030804390087723732, 0.046827346086502075, -0.038326848298311234, -0.05267113447189331, -0.0057859574444592, 0.0428503081202507, -0.05574944615364075, 0.0014720415929332376, -0.01691438816487789, -0.05271121487021446, 0.02322259731590748, 0.0052987392991781235, -0.03919085115194321, 0.06088682636618614, -0.05816897004842758, 0.06758745014667511, 0.03423737734556198, 0.005456350278109312, -0.030100584030151367, -0.031522009521722794, -0.03485827147960663, -0.061298005282878876, -0.05808921903371811, 0.021931713446974754, 0.019201284274458885, 0.030528878793120384, -0.00866095069795847, 0.04360242933034897, -0.006659528240561485, -0.03699532523751259, -0.004146577790379524, -0.05531587824225426, 0.005783202592283487, -0.02654196508228779, 0.018062744289636612, -0.04219045490026474, -0.015406127087771893, -0.020931968465447426, 0.055890005081892014, 0.00470324419438839, 0.0174091886729002, -0.008942877873778343, -0.011107368394732475, -0.041909292340278625, -0.014732285402715206, 0.04072898253798485, -0.03286309912800789, 0.011708779260516167, -0.01161766704171896, -0.007742789573967457, 0.027353690937161446, -0.043431833386421204, -0.006331267766654491, -0.024536455050110817, -0.014842933975160122, 0.027409300208091736, 0.0415184386074543, 0.005180207081139088, -0.03903093934059143, -0.014675522223114967, -0.04259037598967552, 0.0019835964776575565, -0.020420510321855545, -0.05726323649287224, -0.05045466497540474, 0.030103027820587158, -0.0020883954130113125, 0.004635172430425882, 0.044679973274469376, 0.01976596936583519, 0.07170533388853073, 0.006025398150086403, 0.03846251592040062, 0.014687325805425644, -0.04506026953458786, -0.009273374453186989, -0.03895651549100876, 0.05546395853161812, -0.02529302053153515, -0.05065568909049034, 0.002680098172277212, 0.007354325149208307, -0.0036275924649089575, 0.05817362666130066, -0.06528576463460922, -0.030369073152542114, -0.01180790364742279, 0.03290018066763878, -0.015113814733922482, 0.009125683456659317, 0.05130606144666672, 0.0005859552184119821, 0.06087066978216171, -0.01672270894050598, -0.04478805884718895, -0.015636172145605087, -0.004948061890900135, 0.03448610007762909, -0.004186328966170549, -0.006964081898331642, 0.040004387497901917, 0.01914692483842373, 0.05073142051696777, -0.044265273958444595, 0.0814364030957222, 0.001311760046519339, 0.015221365727484226, -0.035062141716480255, 0.013592207804322243, 0.02341645210981369, 0.02350565232336521, 0.008148759603500366, -0.0250097643584013, -0.001419633161276579, -0.008373221382498741, 0.009143791161477566, -0.07265885174274445, 0.004025084897875786, 0.037929631769657135, -0.0031513699796050787, -0.028254372999072075, -0.0024747103452682495, -0.021163154393434525, 0.017918413504958153, 0.0038497447967529297, -0.05467110872268677, -0.0062093837186694145, -0.060762129724025726, 0.006025887560099363, 0.0008026361465454102, 0.019110457971692085, 0.004049344453960657, 0.013684429228305817, -0.015648838132619858, -0.025959184393286705, -0.00976748950779438, -0.03862767666578293, -0.0000569107141927816, -0.025095082819461823, 0.0479535311460495, 0.011804372072219849, 0.04421529918909073, 0.026107709854841232, -0.008678346872329712, -0.044216081500053406, -0.020141638815402985, -0.02691197209060192, 0.04889160394668579, 0.021774228662252426, 0.017450684681534767, 0.08032016456127167, -0.0004537015047390014, 0.020681193098425865, 0.014710784889757633, -0.005327374674379826, 0.02146514505147934, -0.0072370367124676704, 0.009293929673731327, 0.017024917528033257, 0.009925981983542442, -0.030583642423152924, 0.05044019967317581, -0.021404286846518517, 0.00010782106255646795, -0.06628274917602539, -0.11279812455177307, -0.0016278870170935988, 0.08731169253587723, 0.05465823784470558, 0.0923251360654831, -0.031923457980155945, -0.03888311609625816, -0.04412773251533508, 0.056796204298734665, -0.01253940723836422, -0.09237078577280045, -0.006575955543667078, 0.010349639691412449, 0.03851139545440674, -0.07384629547595978, 0.030540335923433304, -0.04204085096716881, 0.02378661371767521, 0.025091351941227913, 0.03844797611236572, 0.0005859549273736775, -0.0055452389642596245, -0.007495804689824581, 0.04840477183461189, -0.03527653589844704, -0.039779726415872574, -0.028821449726819992, 0.058152228593826294, -0.02249184623360634, -0.01682598516345024, -0.04322635382413864, 0.019955584779381752, -0.004809441976249218, 0.020378420129418373, 0.0012036656262353063, 0.020351938903331757, 0.02814541757106781, 0.0022448415402323008, 0.029822736978530884, 0.047731198370456696, 0.0016240525292232633, 0.002868162002414465, 0.027557210996747017, 0.018534360453486443, 0.032982613891363144, 0.00789633858948946, 0.001689127879217267, -0.013731544837355614, -0.03441423922777176, -0.05399412661790848, -0.03295370191335678, 0.02183970808982849, -0.033769119530916214, 0.015038453042507172, 0.020551370456814766, -0.012468996457755566, -0.037328798323869705, -0.022050978615880013, 0.0671607106924057, 0.052766624838113785, -0.07358277589082718, -0.020268792286515236, 0.0272145327180624, -0.019797785207629204, 0.007112883031368256, -0.028918547555804253, -0.06714683771133423, 0.015597064048051834, -0.009543739259243011, 0.03199872374534607, -0.023496102541685104, 0.07164561003446579, 0.05557098239660263, 0.09308429062366486, 0.015067013911902905, -0.03372045233845711, 0.027725841850042343, 0.022664228454232216, -0.025649257004261017, -0.013874765485525131, -0.015276730991899967, 0.004033970180898905, -0.07263945043087006, 0.016009636223316193, 0.01525524165481329, 0.00944147165864706, -0.05072064325213432, 0.04123854637145996, 0.060236141085624695, 0.014260939322412014, 0.03261754289269447, -0.02184124104678631, -0.01563389226794243, 0.008742298930883408, -0.05113615095615387, -0.006201616022735834, 0.02404414676129818, 0.06287923455238342, 0.008826213888823986, 0.06547828018665314, 0.014247343875467777, -0.038513828068971634, 0.02448548749089241, -0.04866437241435051, -0.03830024600028992, -0.047642458230257034, -0.003385139163583517, 0.04471460357308388, 0.05326354131102562, 0.05147234722971916, 0.0015701878583058715, -0.010085007175803185, -0.06211724132299423, -0.02631518803536892, 0.03617588430643082, -0.029584258794784546, 0.006586470641195774, -0.0678485780954361, -0.006263735704123974, 0.035268545150756836, 0.03408447280526161, -0.00984953437000513, 0.08937976509332657, -0.014818553812801838, -0.01240214891731739, 0.08267831802368164, -0.022903667762875557, -0.02095121704041958, 0.005841387435793877, 0.0023942869156599045, -0.01891854964196682, -0.021161487326025963, 0.027590984478592873, 0.010931812226772308, 0.02372373826801777, -0.015789343044161797, -0.007903250865638256, 0.04077676683664322, 0.025588763877749443, 0.0048035974614322186, -0.03735443577170372, 0.009179405868053436, -0.02614440955221653, -0.021548138931393623, -0.003007841994985938, 0.05015421286225319, 0.034959081560373306, -0.008903579786419868, -0.029515575617551804, 0.009388793259859085, -0.04441296309232712, 0.009511907584965229, 0.03582363948225975, 0.00043494257261045277, -0.06370633095502853, -0.03290601074695587, -0.016194192692637444, -0.04668755829334259, -0.018592268228530884, -0.03503992035984993, -0.0057775345630943775, 0.028564827516674995, -0.021766938269138336, -0.011256816796958447, 0.053635306656360626, 0.028433173894882202, -0.01694018766283989, -0.02417229488492012, 0.014372778125107288, 0.036219272762537, -0.011563662439584732, -0.01051345095038414, 0.02837914600968361, -0.0130723612383008, 0.02722017839550972, -0.029105741530656815, -0.03293554112315178, -0.03735971450805664, 0.006743615493178368, 0.012297146953642368, -0.05858159437775612, 0.07065881788730621, 0.01985587738454342, -0.02850998193025589, -0.00976839940994978, -0.02553541399538517, -0.025746051222085953, 0.002161809243261814, -0.01399692427366972, 0.01481512002646923, -0.01011463813483715, 0.03214143216609955, -0.03915434330701828, 0.02615046687424183, -0.044567883014678955, -0.0032786978408694267, -0.02877662517130375, -0.05619946867227554, 0.05119660869240761, 0.0333794541656971, -0.05569018796086311, -0.03138049691915512 ]
<p>I was looking at rockets and stuff and thought about how they move through a vacuum using newtons 3rd law, and then I started thinking of any other ways you could move through a vacuum without using this and then I thought about the photon. I then thought how does the photon move through a vacuum? So I searched it online and couldn't find an answer. So my question is simply how does a photon move through a vacuum? Is it because its massless? Is it because it is thrown from an electron or whatever like a rock from a slingshot? Or is it something completely different? I'm very curious!</p>
g5457
[ 0.020138584077358246, -0.015151457861065865, -0.01296206284314394, 0.04831641539931297, 0.025503451004624367, 0.055387016385793686, -0.035740356892347336, 0.03917625918984413, -0.004057253245264292, -0.018244992941617966, 0.005521726794540882, -0.0015820125117897987, 0.03823448717594147, -0.0066394200548529625, -0.062552809715271, -0.015126693993806839, 0.10437560081481934, -0.013117723166942596, 0.05439796298742294, 0.017186058685183525, -0.005673640873283148, 0.033522117882966995, -0.018603233620524406, -0.04070407524704933, -0.03504545986652374, -0.007980216294527054, 0.012296066619455814, 0.021168561652302742, 0.03308091312646866, -0.019221659749746323, 0.02225414291024208, -0.036636412143707275, 0.011027379892766476, -0.0373503714799881, 0.02672695741057396, 0.004787514451891184, 0.0096407076343894, 0.019718756899237633, 0.021568574011325836, 0.020710397511720657, -0.04362310841679573, -0.0048604365438222885, -0.019562402740120888, 0.014708268456161022, 0.031002262607216835, 0.0074829403311014175, -0.015861069783568382, -0.026809610426425934, -0.024226728826761246, 0.005313789006322622, -0.02080552466213703, -0.021513422951102257, -0.050779327750205994, 0.030164387077093124, 0.007733576465398073, -0.07124219089746475, 0.057652413845062256, -0.00609968975186348, 0.12216396629810333, -0.0037805933970957994, -0.020537586882710457, -0.047716230154037476, 0.10504717379808426, 0.025908827781677246, 0.05479586124420166, -0.008307325653731823, -0.037845414131879807, 0.020552553236484528, -0.0033146776258945465, 0.012201751582324505, 0.057588011026382446, -0.03517688438296318, -0.006059706676751375, -0.07496075332164764, -0.007849031127989292, -0.023906609043478966, -0.002531470265239477, -0.02912474051117897, 0.023115070536732674, -0.02803405188024044, 0.007492853328585625, -0.031024189665913582, 0.019705187529325485, -0.04007299989461899, 0.09510036557912827, -0.035319771617650986, -0.02546439692378044, -0.020035868510603905, -0.013432476669549942, -0.02595849521458149, 0.007711127400398254, 0.02245461754500866, 0.0633678138256073, 0.03524044156074524, -0.04339675232768059, -0.031755231320858, -0.03144971653819084, 0.08822142332792282, -0.011722877621650696, -0.02298296056687832, -0.010932372882962227, 0.00968613475561142, 0.06020279601216316, 0.03055330365896225, 0.052507560700178146, 0.019286777824163437, -0.011567221954464912, -0.03364745154976845, 0.028910351917147636, -0.03425005078315735, -0.008534758351743221, -0.03249092027544975, 0.03865530341863632, -0.032108258455991745, -0.0014001165982335806, -0.021761765703558922, 0.012739041820168495, 0.007693924475461245, 0.07589831203222275, 0.049827996641397476, 0.08250465989112854, 0.06730405986309052, -0.03724800422787666, -0.03277410939335823, -0.019147496670484543, -0.026372279971837997, 0.011514775454998016, -0.033343199640512466, -0.009994705207645893, 0.012637726962566376, -0.010615034028887749, 0.022243119776248932, -0.02491682954132557, -0.010132960043847561, -0.013509074226021767, 0.024241648614406586, 0.027910299599170685, -0.0005959022091701627, -0.011505909264087677, -0.01488578226417303, 0.05916179344058037, -0.020018845796585083, 0.0014578496338799596, -0.007562426384538412, -0.013623303733766079, -0.0006454263348132372, -0.009711131453514099, 0.007923666387796402, -0.0005810933071188629, -0.006784817203879356, 0.08265531808137894, 0.11526495963335037, -0.013469649478793144, -0.037227049469947815, 0.07069433480501175, -0.030930137261748314, 0.035913534462451935, 0.027452504262328148, -0.04428403452038765, -0.023940106853842735, 0.03967953473329544, -0.015616280026733875, 0.004876537248492241, -0.04289022460579872, -0.028747690841555595, -0.015210345387458801, -0.016920926049351692, -0.07271715998649597, -0.020340925082564354, -0.0459996797144413, 0.013600763864815235, -0.027085453271865845, -0.008243597112596035, 0.05978639796376228, -0.04942568764090538, 0.018778132274746895, 0.06601124256849289, -0.0012058423599228263, 0.003166685113683343, -0.047658808529376984, -0.024547986686229706, -0.032479941844940186, 0.028360461816191673, -0.027081280946731567, -0.021274561062455177, 0.025335373356938362, 0.01567767560482025, -0.002950056688860059, -0.02050868794322014, -0.012750581838190556, -0.02828097715973854, -0.04267507791519165, 0.035202477127313614, 0.01888665370643139, -0.036269158124923706, -0.026616673916578293, -0.010618522763252258, -0.029838556423783302, 0.001965222880244255, 0.03247304633259773, -0.023802384734153748, 0.019635410979390144, -0.00937712099403143, 0.008466613478958607, -0.00286508584395051, -0.04010043293237686, 0.01281045749783516, -0.004389224573969841, 0.02132612094283104, 0.013948475010693073, 0.06537158787250519, 0.022918222472071648, 0.046233486384153366, -0.003692828817293048, -0.03155522421002388, 0.02536485530436039, -0.04796665906906128, -0.041649580001831055, -0.0018160237232223153, -0.007753588724881411, -0.033041391521692276, -0.03885344788432121, 0.026584317907691002, -0.034098830074071884, 0.009858912788331509, 0.01241657231003046, -0.0860222727060318, -0.035035640001297, 0.01870272308588028, 0.041323188692331314, -0.005413385573774576, -0.03308602422475815, -0.016463156789541245, -0.002386915497481823, 0.06853307038545609, 0.04185938090085983, -0.05579192191362381, 0.027157055214047432, 0.021588154137134552, 0.029805026948451996, 0.019341597333550453, -0.009991935454308987, 0.005818765144795179, -0.02721264958381653, 0.0459638312458992, -0.10840580612421036, 0.03155495598912239, 0.004729889333248138, -0.0014668498188257217, -0.006944060791283846, 0.03609057515859604, -0.058929312974214554, -0.015913479030132294, 0.0023473971523344517, -0.016166891902685165, 0.015242667868733406, 0.01891675405204296, 0.011242922395467758, -0.025755835697054863, -0.04787406325340271, 0.00748973386362195, -0.030657242983579636, -0.008885977789759636, -0.001261974684894085, -0.04084872454404831, -0.0312683992087841, -0.04394374042749405, 0.036147575825452805, 0.015808861702680588, -0.027687959372997284, -0.07005634903907776, 0.04727974906563759, 0.039087820798158646, -0.0761914998292923, 0.035492461174726486, -0.02562744729220867, 0.05392638221383095, -0.039151161909103394, 0.018731066957116127, -0.057809267193078995, 0.012701437808573246, 0.022144632413983345, -0.03518156707286835, -0.023895686492323875, 0.03258853778243065, -0.06293944269418716, -0.004143949598073959, -0.02504986897110939, -0.026834726333618164, -0.048435863107442856, -0.03123299591243267, -0.015425184741616249, 0.0163566991686821, 0.0160507969558239, -0.019700927659869194, 0.056565288454294205, 0.034808963537216187, -0.009395009838044643, -0.06818998605012894, 0.007179414387792349, 0.025240272283554077, -0.01558255311101675, -0.031367041170597076, -0.02488679625093937, -0.0395008847117424, 0.030183980241417885, -0.055728524923324585, -0.05038267746567726, -0.04450006037950516, 0.02979126013815403, 0.018334250897169113, 0.05589420720934868, -0.024218712002038956, 0.05466078594326973, 0.001352565479464829, -0.008219701237976551, -0.018741032108664513, 0.05567402392625809, -0.016858942806720734, 0.06694034487009048, -0.062170226126909256, -0.013517883606255054, 0.019176237285137177, -0.005872008856385946, 0.06267834454774857, 0.06023876368999481, -0.011794699355959892, 0.011251557618379593, -0.014021921902894974, -0.0379183366894722, -0.006193647626787424, 0.001356119872070849, -0.07835394889116287, -0.018114419654011726, -0.04411908984184265, 0.02325824648141861, -0.01159842312335968, 0.0335003063082695, 0.05205840989947319, -0.03796752169728279, 0.05478869751095772, -0.04399111866950989, -0.054132744669914246, 0.06997261941432953, 0.01375666819512844, 0.048069510608911514, 0.00832319911569357, -0.005939525552093983, -0.0053090001456439495, -0.005144563969224691, 0.06659889966249466, 0.01590259000658989, -0.016952795907855034, 0.011437988840043545, -0.051099978387355804, 0.018791785463690758, -0.016671234741806984, 0.038347307592630386, 0.070652537047863, -0.0368824303150177, -0.0017625640612095594, -0.010500272735953331, 0.06191403418779373, -0.0265361275523901, 0.002921078819781542, 0.013091675005853176, 0.03883153945207596, -0.027409212663769722, 0.029730437323451042, 0.04313736408948898, -0.023209616541862488, -0.04449964314699173, -0.030285770073533058, 0.06791625916957855, -0.031271349638700485, -0.039940644055604935, 0.06055767089128494, -0.004204047843813896, -0.049188535660505295, 0.0050549875013530254, -0.019585629925131798, -0.0047655836679041386, 0.052918557077646255, -0.008520024828612804, 0.02912377566099167, 0.03707881644368172, -0.06583566218614578, 0.014884760603308678, 0.007840036414563656, -0.026835309341549873, 0.06976384669542313, -0.0020934627391397953, -0.016791583970189095, 0.002718987176194787, 0.02344140037894249, -0.020180942490696907, 0.018352651968598366, -0.03197113424539566, -0.007134796120226383, -0.027464240789413452, 0.05540713295340538, 0.1058650091290474, -0.005613154266029596, -0.023477699607610703, -0.009112930856645107, 0.05174831673502922, 0.013916043564677238, -0.05976241081953049, 0.008422666229307652, -0.05118965357542038, -0.043975282460451126, 0.003142541740089655, -0.038241371512413025, -0.013565990142524242, 0.00006181735807331279, 0.03516993299126625, -0.033494580537080765, 0.08045503497123718, -0.06515361368656158, 0.022219209000468254, -0.021752774715423584, -0.011529877781867981, 0.056352995336055756, 0.015645846724510193, -0.019471289590001106, 0.07045548409223557, 0.055361293256282806, 0.006010046694427729, 0.041225023567676544, 0.002258556429296732, 0.0002100626443279907, 0.02704230137169361, 0.026030879467725754, 0.08184249699115753, -0.012605657801032066, 0.03715893253684044, -0.04188692569732666, 0.002770273946225643, 0.047649603337049484, -0.010983271524310112, 0.09747219830751419, -0.00626132870092988, 0.005346284247934818, 0.04086214303970337, -0.04967271536588669, 0.02835822105407715, 0.0037483549676835537, 0.02037830464541912, -0.01514552440494299, 0.010938615538179874, 0.009275144897401333, 0.03157196193933487, -0.08929166942834854, -0.0036388260778039694, -0.034541282802820206, 0.03430142253637314, -0.023228425532579422, -0.0005612426903098822, 0.043506596237421036, 0.012001791968941689, -0.07744491100311279, 0.012120489962399006, 0.0761452466249466, 0.03414350375533104, 0.03087603487074375, -0.014095303602516651, -0.02407817170023918, 0.005317061673849821, -0.021146345883607864, 0.018868044018745422, 0.03699902072548866, 0.024979837238788605, -0.06853240728378296, 0.034830715507268906, 0.007436931133270264, -0.04485161229968071, -0.007063457742333412, 0.009480147622525692, -0.019871016964316368, -0.059523362666368484, 0.03742729499936104, 0.005322641227394342, 0.011403990909457207, -0.030647791922092438, -0.03751862421631813, 0.0065882098861038685, -0.03963186964392662, 0.03579813987016678, -0.03099394589662552, -0.024647198617458344, 0.007482356391847134, 0.02949211560189724, -0.029495690017938614, 0.006089558359235525, -0.02996595948934555, -0.01883341185748577, 0.00804139208048582, 0.03110402263700962, 0.05630955845117569, -0.0284102912992239, -0.025351133197546005, -0.030617788434028625, -0.04404369369149208, -0.003588941413909197, 0.004019278101623058, -0.07952969521284103, 0.0037573319859802723, -0.021389678120613098, -0.021152691915631294, 0.010454394854605198, 0.0037283769343048334, -0.015958048403263092, -0.10246075689792633, -0.01991678588092327, 0.03717929869890213, -0.0017517785308882594, -0.025810038670897484, -0.02485468052327633, 0.043869879096746445, 0.010035060346126556, -0.03988360986113548, 0.07389295846223831, 0.040952783077955246, 0.03741518035531044, 0.018216773867607117, 0.018381230533123016, -0.0711471289396286, 0.019719470292329788, -0.023771850392222404, 0.003637987654656172, -0.02860780619084835, -0.05190194398164749, 0.0941803976893425, 0.0043604401871562, -0.06515305489301682, -0.021459119394421577, 0.05920800194144249, 0.009135091677308083, 0.029284460470080376, -0.014011719264090061, -0.036894455552101135, -0.0412687286734581, -0.0030048848129808903, 0.06249595433473587, 0.008029084652662277, 0.019302943721413612, 0.027881011366844177, -0.0025572828017175198, 0.06999760121107101, -0.00510211568325758, -0.057300206273794174, 0.022198667749762535, -0.04034115746617317, -0.02267586812376976, -0.062109000980854034, 0.027288813143968582, -0.04055112972855568, -0.001962241716682911, -0.007292560767382383, -0.03166776895523071, 0.004715896677225828, 0.016231080517172813, 0.0038871150463819504, -0.00490660360082984, -0.02511095441877842, -0.02997332438826561, 0.019041093066334724, -0.03532497212290764, -0.004906032234430313, 0.037669092416763306, -0.04090665280818939, 0.033093199133872986, -0.0642666220664978, 0.030711134895682335, 0.005093553103506565, -0.012244008481502533, 0.012142186053097248, -0.02457962930202484, -0.07660157233476639, 0.018420815467834473, 0.06834451854228973, 0.052524663507938385, 0.05088547244668007, -0.061427515000104904, -0.043567609041929245, 0.06314780563116074, -0.005651444662362337, 0.008519022725522518, 0.04781031981110573, -0.020332295447587967, -0.031812962144613266, 0.02330775186419487, -0.010942903347313404, -0.030615409836173058, -0.007671717554330826, -0.006455914117395878, 0.025729022920131683, -0.037623994052410126, -0.0028048830572515726, 0.033419203013181686, 0.033136703073978424, 0.013090821914374828, -0.007752639707177877, 0.02651415951550007, 0.004150773398578167, 0.02670525573194027, -0.02623407170176506, 0.008165715262293816, 0.043710868805646896, 0.024731438606977463, -0.03848116844892502, 0.01851717382669449, -0.02138683758676052, -0.028181936591863632, 0.01668231189250946, -0.008006440475583076, -0.04745306074619293, -0.023587802425026894, 0.044955942779779434, -0.018915483728051186, -0.03859635815024376, -0.037747155874967575, 0.01466334704309702, 0.03412657976150513, 0.04299153387546539, -0.01741080731153488, 0.00485054450109601, 0.03832283243536949, 0.05838530510663986, -0.021295158192515373, -0.013238231651484966, -0.05596352741122246, 0.012778131291270256, 0.01831708289682865, 0.022869642823934555, -0.005593738052994013, -0.0649372860789299, -0.0066464790143072605, 0.013195201754570007, 0.012355431914329529, 0.013512547127902508, 0.013869200833141804, 0.006343455519527197, 0.039473757147789, -0.0021626523230224848, 0.08567628264427185, -0.010042672976851463, -0.015990331768989563, -0.007571933791041374, -0.027185186743736267, -0.038831789046525955, -0.0006750126485712826, -0.034229494631290436, 0.04989861696958542, 0.009341838769614697, 0.044470854103565216, -0.03506090119481087, 0.00984267145395279, -0.000008329537195095327, -0.09513504803180695, -0.023015517741441727, -0.004569947253912687, 0.007864689454436302, 0.013756572268903255, 0.07460413873195648, 0.027369143441319466, 0.007735223043709993, -0.030315611511468887, 0.004706650506705046, 0.008385025896131992, 0.08040754497051239, -0.024128364399075508, -0.025446072220802307, 0.07191847264766693, 0.01065806020051241, -0.05735854059457779, -0.014696856029331684, 0.06352303922176361, -0.02656438760459423, 0.00225731055252254, -0.03250524029135704, 0.019339049234986305, 0.03191426396369934, -0.03393617644906044, -0.005659338086843491, 0.06753918528556824, -0.020301640033721924, 0.04722295701503754, -0.012005736120045185, -0.05397423356771469, 0.03496163710951805, -0.07272479683160782, 0.03168070688843727, -0.017544671893119812, -0.015648968517780304, -0.010966895148158073, 0.020177185535430908, -0.06000467389822006, 0.008912445046007633, 0.013719097711145878, -0.067066989839077, 0.03323500603437424, -0.018119657412171364, 0.015015238896012306, 0.012316391803324223, 0.012005854398012161, -0.016054298728704453, 0.004703349433839321, -0.050887979567050934, 0.03439730405807495, 0.03682147338986397, -0.01567428559064865, -0.04078948497772217, 0.015478468500077724, 0.018632331863045692, -0.02969134971499443, -0.020336201414465904, 0.057123009115457535, -0.026091856881976128, -0.06336237490177155, -0.037575751543045044, 0.04726981744170189, -0.012560058385133743, -0.02731320820748806, -0.04139043763279915, 0.0416066013276577, 0.021119287237524986, -0.01896299421787262, -0.035240162163972855, -0.011773282662034035, 0.022184280678629875, -0.02279326505959034, 0.006576312240213156, -0.053964998573064804, 0.007576144766062498, 0.030628420412540436, -0.0021674083545804024, -0.04391619935631752, 0.05609587952494621, -0.019917814061045647, 0.03371834382414818, -0.0404728502035141, -0.051503878086805344, -0.018183687701821327, 0.05577827990055084, -0.03136904537677765, -0.041006531566381454, -0.023825079202651978, -0.001711769262328744, -0.014183728024363518, 0.040206171572208405, 0.08007754385471344, 0.02116735465824604, 0.0662928968667984, 0.0046803271397948265, -0.03296651691198349, 0.02170597016811371, -0.002528829500079155, -0.022321119904518127, 0.019368546083569527, 0.011698379181325436, 0.012828652746975422, -0.023014169186353683, -0.004138599615544081, -0.02607199363410473, -0.04090726748108864, 0.008801388554275036, -0.025034872815012932 ]
<p>Galileo discovered that the distance fallen is proportional to the square of the time it has been falling.Why is it proportional to the square of the time and not just time? i.e $d \propto t^2$ why not just $d \propto t$</p> <p>I know this question involves some common sense which i'am not able to use for some reason!</p>
g5458
[ 0.09320230782032013, 0.007941802963614464, -0.010186928324401379, -0.04585309699177742, 0.019267890602350235, 0.07211928814649582, 0.053696081042289734, -0.03769482299685478, 0.011574178002774715, -0.033600397408008575, -0.02182033658027649, -0.03321721404790878, 0.09048926830291748, 0.0034220728557556868, -0.023378537967801094, 0.043983228504657745, 0.10650242865085602, -0.06530840694904327, 0.015557615086436272, 0.02495848760008812, -0.001195778837427497, -0.04649215191602707, -0.006298110820353031, -0.03398566320538521, -0.036529507488012314, -0.023675398901104927, 0.06919331848621368, -0.005636331159621477, -0.015112737193703651, 0.03974517434835434, 0.011326196603477001, 0.025017039850354195, 0.01353665255010128, -0.004774631466716528, 0.007314851973205805, -0.01756771095097065, 0.031147116795182228, 0.022998128086328506, 0.07072725892066956, 0.02535942941904068, 0.009546459652483463, -0.06570657342672348, -0.06323923915624619, 0.023996438831090927, 0.01319044642150402, 0.008695521391928196, -0.03266497328877449, 0.020398857071995735, -0.031093785539269447, -0.03488282859325409, -0.030953112989664078, 0.04038384184241295, 0.03147120773792267, -0.053459543734788895, -0.030736491084098816, -0.005097282584756613, 0.03509948402643204, -0.05436326935887337, 0.0031407757196575403, 0.040337443351745605, 0.0000561549277335871, 0.003314410103484988, -0.0033004542347043753, 0.012157787568867207, 0.07430287450551987, -0.04611878842115402, -0.034932591021060944, 0.023231899365782738, -0.0008257918525487185, 0.014807615429162979, -0.009265461936593056, -0.06598075479269028, -0.004537984263151884, 0.038211166858673096, -0.05518961697816849, -0.031791042536497116, 0.03873394802212715, -0.014091228134930134, -0.025527924299240112, -0.01371222734451294, 0.0019205963471904397, 0.025311267003417015, 0.02802995592355728, 0.026839498430490494, 0.054329123347997665, -0.04482195898890495, 0.06372596323490143, 0.004346149507910013, -0.025786984711885452, 0.03560285270214081, -0.05181920528411865, -0.07299208641052246, 0.07847300171852112, 0.059934359043836594, -0.04849279671907425, -0.02639750950038433, -0.05852368101477623, 0.011395917274057865, 0.01801287569105625, 0.041267555207014084, -0.01991037093102932, -0.0438053123652935, 0.04874546453356743, -0.028305329382419586, 0.023801613599061966, 0.013344991020858288, 0.0601351298391819, 0.019901780411601067, 0.004443017300218344, -0.03775059059262276, 0.0031943751964718103, -0.014458485879004002, -0.021275337785482407, -0.03284573182463646, -0.0065587786957621574, -0.02727009914815426, 0.025807030498981476, -0.045982085168361664, -0.042523860931396484, 0.0471225269138813, -0.03790340945124626, 0.031098827719688416, -0.012363324873149395, 0.03223827853798866, -0.00709172710776329, 0.05176020413637161, 0.015162218362092972, 0.014559620060026646, 0.017104655504226685, 0.00563513720408082, -0.005869660526514053, 0.0283100213855505, -0.014004780910909176, 0.06421733647584915, -0.006141824182122946, 0.05118357762694359, 0.005978426896035671, 0.022514788433909416, -0.033895064145326614, 0.045834220945835114, -0.025362957268953323, -0.005983367562294006, 0.018162742257118225, -0.03751916065812111, -0.013498653657734394, 0.04480096325278282, -0.007642616052180529, -0.016113895922899246, 0.02559151127934456, -0.009843487292528152, 0.012579762376844883, 0.030499553307890892, 0.020543323829770088, -0.05294172465801239, 0.01283850148320198, -0.046585723757743835, -0.06105270981788635, -0.0008753983420319855, -0.02542375959455967, -0.0273982472717762, 0.05673141032457352, -0.0035505290143191814, -0.04028380289673805, 0.008928647264838219, -0.06456508487462997, 0.07725358009338379, -0.012320462614297867, 0.009440342895686626, -0.014157472178339958, -0.08145220577716827, -0.019470928236842155, -0.0014868404250591993, 0.07474326342344284, 0.01415878813713789, -0.028623471036553383, 0.030327269807457924, -0.017210867255926132, -0.006028007250279188, 0.0019154406618326902, 0.003540940582752228, 0.0444972887635231, -0.005689237266778946, -0.00383925624191761, 0.023654844611883163, -0.021323008462786674, 0.007355794310569763, 0.06863610446453094, -0.0033920309506356716, -0.053759701550006866, 0.03165823593735695, 0.01048158761113882, -0.029017072170972824, -0.027268344536423683, 0.0188620425760746, -0.019689420238137245, -0.02770080417394638, -0.005191632080823183, -0.025681061670184135, -0.03866719454526901, 0.09909714758396149, 0.06072661653161049, -0.007257393095642328, 0.06213407963514328, 0.027445489540696144, 0.02264951542019844, -0.02540752850472927, -0.01726437173783779, 0.007264501415193081, 0.025420112535357475, 0.022243447601795197, -0.04421158879995346, -0.0015674310270696878, 0.03633168339729309, 0.017719963565468788, -0.0771486759185791, -0.012178878299891949, 0.0067006442695856094, 0.05627721548080444, -0.00620616041123867, 0.01278792042285204, -0.07278783619403839, -0.03975685313344002, 0.012211079709231853, -0.03025859408080578, 0.01485596876591444, 0.017468100413680077, -0.054964710026979446, 0.004932955838739872, -0.033713728189468384, 0.0306704044342041, -0.028868695721030235, -0.007847031578421593, -0.040384382009506226, 0.0488131120800972, 0.03261277452111244, 0.036112044006586075, 0.03599020466208458, -0.09346247464418411, 0.03258805721998215, 0.02779744379222393, 0.04846188798546791, -0.037719469517469406, -0.0008574899984523654, 0.0153341731056571, 0.02299526520073414, -0.020452765747904778, -0.02113267406821251, -0.015479960478842258, 0.007148366887122393, -0.0016994033940136433, -0.02881499193608761, -0.03345286846160889, -0.03643585741519928, -0.051229823380708694, 0.0006982087506912649, 0.020695148035883904, -0.024990832433104515, -0.0077767400071024895, -0.05606095492839813, 0.035941872745752335, -0.02852453850209713, -0.02156304009258747, 0.00413318257778883, 0.0036074332892894745, 0.0037540460471063852, 0.047079138457775116, -0.07598292827606201, 0.0005276513402350247, -0.002167906379327178, -0.03172565624117851, 0.01908612623810768, 0.028111422434449196, 0.00680038845166564, 0.01880265772342682, -0.07481593638658524, -0.0053313374519348145, -0.009086969308555126, -0.06992996484041214, -0.015867169946432114, 0.002443081932142377, 0.03909020125865936, 0.00177489104680717, -0.12162408977746964, 0.021027946844697, -0.004340737126767635, -0.05593910440802574, 0.05076979845762253, 0.055588994175195694, -0.03457559645175934, -0.006983929313719273, -0.029740454629063606, -0.0010016763117164373, 0.033446040004491806, -0.003054521046578884, 0.008990004658699036, 0.06009126827120781, 0.027171410620212555, 0.006255568005144596, -0.01254968997091055, -0.011969202198088169, -0.0005359193892218173, 0.0420704148709774, 0.038920704275369644, 0.008558020927011967, 0.05349770188331604, 0.029377451166510582, 0.029617691412568092, -0.0524691604077816, -0.0565926693379879, -0.030548982322216034, 0.03432055190205574, 0.04011526331305504, 0.014550254680216312, -0.022617368027567863, -0.046975165605545044, 0.009007122367620468, -0.018393803387880325, 0.03276132792234421, -0.009664660319685936, 0.06396376341581345, -0.006742279510945082, -0.07515290379524231, -0.09564857184886932, -0.04942482337355614, 0.019408417865633965, -0.0019972180016338825, -0.05583173409104347, 0.06276863813400269, 0.0038186272140592337, -0.021565349772572517, 0.007903430610895157, -0.015731699764728546, -0.002071729162707925, -0.05390229821205139, -0.028584931045770645, 0.007553251460194588, 0.023115532472729683, 0.035992130637168884, 0.04209911823272705, 0.03875644877552986, -0.024218106642365456, -0.015111749060451984, -0.057678136974573135, -0.010759775526821613, 0.03984717279672623, -0.012569617480039597, 0.027118701487779617, 0.0032732528634369373, 0.022822460159659386, -0.008923489600419998, 0.026291577145457268, -0.051352374255657196, -0.012010075151920319, 0.004237413872033358, 0.04329632595181465, 0.08096925169229507, -0.03241709619760513, 0.04697319120168686, 0.00015626344247721136, -0.036268576979637146, 0.030879221856594086, 0.019323276355862617, -0.011944148689508438, 0.048001233488321304, 0.01103484071791172, 0.01287742517888546, 0.03735777363181114, 0.02298157848417759, -0.018637830391526222, 0.014093967154622078, 0.014161518774926662, 0.005068363156169653, -0.022761628031730652, 0.07811088114976883, 0.09245660156011581, -0.04613532871007919, 0.004748421721160412, -0.011646927334368229, -0.035190727561712265, -0.024088332429528236, 0.0034280940890312195, 0.00490120192989707, 0.02654590643942356, -0.013904493302106857, 0.08477920293807983, -0.06811100244522095, 0.01668732427060604, -0.006419326178729534, -0.03245145082473755, -0.0532856322824955, 0.008462808094918728, -0.035213254392147064, -0.027796398848295212, -0.021780317649245262, -0.02338649332523346, 0.04668916389346123, -0.00121440296061337, 0.05039657652378082, -0.006605222821235657, -0.028334233909845352, -0.005969235207885504, 0.0060907993465662, 0.04069145768880844, -0.002047439571470022, 0.05475439876317978, -0.02462555654346943, 0.06006135791540146, -0.004082653671503067, 0.015034395270049572, 0.02463768981397152, -0.043974846601486206, -0.06479475647211075, -0.03333132341504097, -0.043447140604257584, 0.045859407633543015, 0.033421531319618225, 0.06734001636505127, 0.008809272199869156, 0.03210878744721413, -0.022706210613250732, 0.07627115398645401, 0.026103604584932327, 0.011355462484061718, -0.035905901342630386, -0.020781120285391808, 0.05417439714074135, -0.00342772388830781, -0.022352896630764008, -0.024669107049703598, 0.008588077500462532, -0.040900714695453644, 0.02851467952132225, 0.02135811746120453, 0.022982805967330933, -0.04729751870036125, 0.033140894025564194, 0.029610952362418175, 0.049113817512989044, 0.019966525956988335, 0.018468329682946205, 0.036728426814079285, 0.002547950716689229, -0.012851258739829063, -0.040268674492836, -0.0034086331725120544, 0.016361350193619728, 0.031040331348776817, -0.07746117562055588, 0.022089052945375443, -0.01786322519183159, -0.03428814187645912, 0.010903150774538517, 0.056716110557317734, -0.03157384693622589, -0.012197030708193779, 0.0037440559826791286, -0.059170838445425034, 0.023919403553009033, 0.0005928620812483132, 0.04951450973749161, -0.020275358110666275, -0.02360565960407257, -0.0411040298640728, 0.008098467253148556, 0.03188974782824516, -0.02304077334702015, -0.0363050177693367, -0.010340443812310696, -0.02427498623728752, -0.03291431814432144, -0.006649256218224764, -0.04233821481466293, -0.019875243306159973, 0.00833575427532196, 0.03451099619269371, -0.0137863177806139, -0.028163088485598564, 0.0043997811153531075, 0.08253912627696991, -0.07190927118062973, -0.024388834834098816, -0.06593801081180573, -0.019405897706747055, 0.014901239424943924, 0.005966580007225275, 0.039717573672533035, -0.04026057943701744, -0.09247513115406036, 0.02600945346057415, -0.04953215271234512, 0.054301660507917404, -0.033421099185943604, -0.01417792122811079, -0.047706980258226395, -0.009086965583264828, -0.014209596440196037, 0.02564297243952751, 0.005300066899508238, -0.017294922843575478, 0.013177864253520966, -0.040705811232328415, 0.06667644530534744, 0.0030957933049649, 0.040791552513837814, -0.016261454671621323, 0.004325294867157936, 0.07729053497314453, -0.011458822526037693, -0.00823230855166912, 0.029600467532873154, 0.018030760809779167, -0.029668031260371208, 0.018705345690250397, 0.05651411414146423, -0.014098677784204483, -0.03741304203867912, 0.04336954653263092, 0.008698781952261925, 0.035377539694309235, 0.04662119597196579, 0.014066844247281551, 0.004116920754313469, 0.026182247325778008, -0.02710706926882267, 0.052215490490198135, -0.027368303388357162, -0.09346971660852432, -0.026848984882235527, 0.06283771246671677, -0.008196436800062656, 0.006277706474065781, -0.027260208502411842, -0.00016879044414963573, -0.025330597534775734, -0.045142412185668945, 0.0162280835211277, -0.03177298977971077, 0.01901957392692566, 0.04872990772128105, -0.05885211005806923, -0.07926784455776215, -0.027407867833971977, 0.05964275822043419, 0.03874936327338219, 0.053764160722494125, -0.02384411171078682, -0.01731942594051361, -0.010890604928135872, 0.018741538748145103, -0.008320600725710392, 0.007571632973849773, 0.04423729330301285, -0.013164781033992767, 0.006812636274844408, -0.022392896935343742, -0.0001615555229363963, -0.002722539473325014, -0.027646848931908607, -0.0595756359398365, -0.04482616111636162, 0.03806213662028313, -0.03875477984547615, -0.06235041469335556, 0.044782619923353195, -0.013603533618152142, -0.04243563860654831, 0.02835248038172722, 0.05415866896510124, 0.012379414401948452, 0.0003225272230338305, -0.00993095152080059, -0.04916806146502495, 0.008591138757765293, 0.03528929501771927, 0.028135819360613823, 0.04297829791903496, -0.0331435427069664, -0.07655411958694458, -0.07772909849882126, -0.0536569245159626, 0.018340330570936203, -0.055887989699840546, 0.00901122111827135, -0.029062950983643532, -0.040686920285224915, -0.037854742258787155, -0.02404448576271534, -0.025463981553912163, 0.04327308386564255, 0.038788776844739914, -0.008572273887693882, -0.025967225432395935, -0.02585308626294136, -0.013300471007823944, -0.08246591687202454, -0.015893228352069855, -0.008981989696621895, 0.00397561676800251, -0.016633756458759308, 0.04844900965690613, -0.018747026100754738, -0.04730837047100067, 0.10966435074806213, -0.006824858952313662, -0.0005260827601887286, 0.013069255277514458, -0.01680395007133484, -0.019507095217704773, 0.03779052570462227, 0.002770226215943694, 0.03236277401447296, 0.036287106573581696, -0.030527831986546516, 0.0268715713173151, -0.025483349338173866, -0.03727378696203232, 0.01113553810864687, -0.0331023707985878, -0.04281838983297348, -0.01718488335609436, 0.009457782842218876, 0.0020356636960059404, 0.007396311033517122, -0.04264162853360176, 0.03890514373779297, 0.016744863241910934, -0.010229652747511864, 0.0022476227022707462, 0.03451171889901161, 0.02294875495135784, -0.012198958545923233, -0.0003764328430406749, 0.012742536142468452, -0.002096503274515271, -0.02469461038708687, 0.06687689572572708, 0.00949629582464695, -0.005367503501474857, 0.03911048546433449, -0.004462956450879574, 0.00488011259585619, 0.008899923413991928, -0.027394888922572136, -0.04360973834991455, -0.003117054933682084, 0.046730175614356995, 0.003406955860555172, 0.007159006781876087, -0.030716300010681152, 0.005512806586921215, 0.043462201952934265, 0.027665337547659874, -0.01482872199267149, 0.03430608659982681, -0.010377769358456135, -0.04767570272088051, 0.024715907871723175, 0.013701408170163631, -0.013513435609638691, -0.02842540293931961, -0.04554220661520958, -0.02207355573773384, 0.015017008408904076, -0.02629011683166027, -0.006939857266843319, 0.04955413192510605, -0.021980920806527138, -0.08409535139799118, 0.01728927530348301, 0.006837546359747648, 0.013269521296024323, 0.004651692695915699, -0.03627209737896919, -0.020525924861431122, -0.0014559206319972873, 0.04200451821088791, 0.06427653133869171, -0.054827917367219925, -0.015050324611365795, 0.011181985959410667, 0.040188807994127274, 0.024597587063908577, -0.009211714379489422, -0.04078539088368416, -0.06668791174888611, 0.040956009179353714, -0.015804246068000793, -0.006664457730948925, 0.036797139793634415, -0.002161505399271846, 0.0193339791148901, 0.05666802078485489, 0.036603622138500214, 0.028815655037760735, 0.01277952827513218, -0.008388547226786613, 0.06380501389503479, 0.0037662475369870663, -0.013169150799512863, -0.018753323704004288, 0.028804538771510124, -0.030224911868572235, 0.024419762194156647, -0.003209098009392619, 0.03177890181541443, 0.027714453637599945, -0.005495472811162472, 0.01554173231124878, -0.05155898258090019, -0.011524885892868042, 0.03813273459672928, 0.040351755917072296, 0.034477349370718, -0.04702514782547951, 0.024323688820004463, 0.035264234989881516, 0.0034725680015981197, 0.009190451353788376, -0.02430914156138897, -0.03493411839008331, -0.015382823534309864, -0.06990829110145569, 0.022958602756261826, -0.12952016294002533, 0.022341616451740265, -0.022576570510864258, 0.03381513059139252, -0.086960069835186, 0.05266469717025757, 0.00853035133332014, 0.03884505853056908, 0.06171755492687225, 0.02596662938594818, -0.006998984143137932, -0.030420418828725815, 0.019901741296052933, 0.02066071145236492, -0.0002601438027340919, -0.023868929594755173, 0.0716961920261383, -0.01674054190516472, -0.015181198716163635, 0.0182033758610487, -0.0006025028415024281, -0.017206883057951927, -0.04482452943921089, 0.008366421796381474, 0.04252977669239044, 0.04232865944504738, -0.06010618805885315, 0.014832409098744392, -0.02610866352915764, -0.01907278783619404, 0.04714471474289894, 0.03739981725811958, -0.04057292640209198, 0.017091765999794006, -0.05099623277783394, -0.000574331555981189, -0.011198087595403194, -0.007350440137088299, -0.0036196173168718815, 0.03508854657411575, 0.021096814423799515, 0.004647963214665651, -0.025463037192821503, 0.005447137635201216, 0.03585625812411308 ]
<p>I have used a new term <a href="https://drive.google.com/file/d/0B5sD2PI0YoRvMmwyeE04emptTzQ/edit?usp=sharing" rel="nofollow">spinning apparatus</a> as I was unable to name it. I have tied a thread to a stone and was spinning it and I heard a sound something like that of a rotating propellor of a helicopter and then this idea stuck my mind </p> <p>can i calculate it? if yes then how can any one suggest me something and also if any extra information any one needs regarding that apparatus feel free to comment</p>
g5459
[ 0.014880084432661533, 0.018994653597474098, 0.0011155325919389725, -0.04383142292499542, 0.03452552482485771, 0.006120140664279461, 0.059548284858465195, 0.008214019238948822, -0.035656917840242386, -0.0019331226358190179, -0.04703642055392265, -0.008360769599676132, 0.039709195494651794, 0.017833009362220764, 0.008041744120419025, -0.006758568808436394, 0.05324092134833336, -0.0037116475868970156, 0.030617568641901016, -0.002808134537190199, 0.021936340257525444, -0.023799296468496323, -0.018258564174175262, -0.03786064311861992, -0.041984930634498596, -0.012194331735372543, -0.0058252871967852116, 0.008617772720754147, -0.05380302667617798, 0.002480756025761366, -0.056588064879179, -0.041321225464344025, 0.020100247114896774, 0.02628212794661522, -0.02992427907884121, -0.030017774552106857, 0.014968272298574448, 0.017265407368540764, 0.022358635440468788, 0.030155910179018974, -0.007969473488628864, 0.024812206625938416, 0.016553238034248352, -0.005233848933130503, 0.037472497671842575, 0.07972504943609238, 0.07488622516393661, 0.021067984402179718, -0.022693801671266556, 0.01292618177831173, -0.039753541350364685, -0.01117322314530611, 0.00837079156190157, 0.049120303243398666, -0.019596682861447334, 0.01818852126598358, -0.01146548893302679, -0.030628927052021027, 0.06602484732866287, -0.0012721715029329062, -0.07182953506708145, 0.04154074937105179, -0.011924752034246922, 0.03222569823265076, 0.023788804188370705, -0.023095810785889626, 0.006784343160688877, -0.006879898719489574, 0.04687567055225372, 0.08092662692070007, 0.05753073841333389, -0.046546585857868195, 0.05177588015794754, 0.02221454307436943, -0.07988369464874268, 0.05366556718945503, -0.030496323481202126, 0.013569836504757404, 0.00031275939545594156, 0.026767006143927574, -0.009037314914166927, -0.007246031425893307, -0.04247335344552994, -0.020844262093305588, 0.020426543429493904, -0.035785481333732605, 0.001038524555042386, 0.015364130958914757, 0.012468609027564526, 0.005624003242701292, 0.050236526876688004, -0.0493607223033905, 0.08297231048345566, 0.04058625549077988, 0.0014137066900730133, -0.008609396405518055, -0.0553928017616272, 0.030293723568320274, -0.04441511631011963, -0.002416162518784404, 0.004242393653839827, -0.014789600856602192, 0.0023548053577542305, -0.014196837320923805, 0.01659557595849037, 0.03222467005252838, 0.02691294066607952, -0.05195413902401924, 0.010828089900314808, 0.0037674917839467525, 0.03501134738326073, -0.05479789897799492, 0.013059575110673904, -0.030885891988873482, -0.04541923478245735, -0.06783793121576309, 0.06525945663452148, 0.014154037460684776, 0.029911603778600693, 0.01890343613922596, 0.06538871675729752, -0.049208126962184906, -0.00766865024343133, 0.12028289586305618, -0.011786426417529583, 0.028182392939925194, 0.01089758425951004, -0.023259149864315987, 0.015056668780744076, -0.009487406350672245, 0.02136342227458954, -0.008167746476829052, 0.059590715914964676, -0.0221150703728199, 0.04292219132184982, 0.06324633955955505, 0.00012820072879549116, -0.011166083626449108, 0.0035890666767954826, 0.03439168259501457, 0.04326452687382698, -0.05918717384338379, -0.017295019701123238, -0.023109201341867447, 0.024159621447324753, 0.008286461234092712, 0.024961402639746666, -0.020373409613966942, 0.038872431963682175, 0.02353818528354168, -0.00438418984413147, 0.05818606913089752, -0.006443934515118599, -0.024775929749011993, 0.04652543365955353, -0.006659770384430885, 0.025909878313541412, 0.04643242433667183, 0.02082550898194313, -0.0199001245200634, 0.032180752605199814, -0.03593225032091141, 0.03280559554696083, 0.001955165294930339, -0.09112343192100525, -0.01806383766233921, -0.03659394383430481, 0.0029326777439564466, -0.034749340265989304, -0.04638752341270447, 0.0064752534963190556, 0.025386998429894447, 0.049688201397657394, -0.010905787348747253, 0.02766096033155918, 0.03005564585328102, 0.04124073311686516, -0.0030187787488102913, -0.014256179332733154, -0.01785665936768055, 0.017308875918388367, -0.004299553576856852, 0.007674118969589472, -0.020786374807357788, -0.043287795037031174, 0.03629327565431595, 0.029432591050863266, -0.04322038218379021, -0.03163899481296539, 0.0021796859800815582, -0.010597866959869862, 0.029410721734166145, 0.004652724135667086, -0.0031105619855225086, -0.02190076932311058, -0.031103409826755524, 0.011325033381581306, -0.00936094205826521, -0.02049555629491806, 0.048371702432632446, 0.0460529625415802, 0.04492338374257088, 0.0681893453001976, -0.03791709616780281, 0.028096426278352737, -0.06862269341945648, 0.015817267820239067, 0.0037183803506195545, 0.019706202670931816, 0.04447341337800026, 0.08366195857524872, 0.03569527342915535, -0.03915933147072792, 0.02823522314429283, -0.05219491198658943, 0.013362042605876923, 0.0365893617272377, 0.03592640161514282, 0.0011740329209715128, 0.0002407670981483534, 0.02867645025253296, -0.012284192256629467, 0.03786274045705795, 0.02761063538491726, -0.0058913202956318855, -0.037931159138679504, 0.03938676789402962, -0.017192449420690536, -0.004053123295307159, 0.056831832975149155, 0.006006892304867506, -0.10632478445768356, 0.056655384600162506, -0.0327734500169754, 0.039137642830610275, 0.024729304015636444, 0.018797773867845535, -0.03218993544578552, -0.02905118651688099, 0.028819143772125244, 0.06909297406673431, -0.014943217858672142, 0.0038650052156299353, -0.054594140499830246, -0.05023696646094322, -0.014413537457585335, 0.008652564138174057, 0.01906055025756359, 0.050702400505542755, 0.018165742978453636, 0.016490718349814415, -0.06330260634422302, -0.04403761029243469, 0.023641427978873253, -0.054302606731653214, -0.01747981086373329, -0.025652751326560974, 0.024503272026777267, -0.0430406853556633, 0.0036798217333853245, 0.001698774634860456, -0.01676715910434723, 0.04385679215192795, -0.0010229902109131217, -0.08297234028577805, -0.019522951915860176, -0.017528964206576347, -0.024011310189962387, -0.025345055386424065, 0.01948978751897812, -0.06118273735046387, -0.04734921455383301, 0.059038806706666946, 0.03283289447426796, -0.04676666483283043, -0.012493396177887917, 0.017005858942866325, 0.036608386784791946, -0.01809793896973133, 0.03719066455960274, 0.015799134969711304, -0.00920848548412323, -0.019915182143449783, 0.056400179862976074, -0.044251907616853714, -0.03495369106531143, 0.016165973618626595, 0.009037720039486885, -0.05172579362988472, 0.007769339252263308, -0.03407512605190277, 0.013865952380001545, 0.015363716520369053, -0.024657828733325005, 0.02408854477107525, 0.06986350566148758, 0.0737391784787178, 0.0337127149105072, 0.03326436132192612, 0.05337347462773323, 0.04057871177792549, -0.044390719383955, -0.020150385797023773, -0.020208977162837982, -0.016605043783783913, 0.01993844099342823, 0.01277659647166729, -0.04689596965909004, 0.01447706762701273, 0.03883446380496025, -0.05706954002380371, 0.016947265714406967, 0.04725797846913338, -0.057489536702632904, -0.015286470763385296, 0.0486857146024704, 0.054849110543727875, -0.0002293591678608209, -0.006339618004858494, 0.044966984540224075, -0.016698449850082397, -0.08078044652938843, 0.03406687453389168, -0.009023349732160568, 0.01570201851427555, 0.04461149498820305, -0.04864324629306793, 0.03696395829319954, -0.024409299716353416, -0.10184185951948166, -0.00038601396954618394, -0.009492536075413227, -0.06350051611661911, -0.04148488864302635, -0.024399755522608757, -0.051397137343883514, -0.014577219262719154, 0.05605398118495941, -0.0066907997243106365, -0.014233793132007122, -0.023788059130311012, -0.054871223866939545, 0.013424822129309177, -0.042146340012550354, -0.051297444850206375, 0.08536019176244736, -0.011403060518205166, -0.002997263800352812, 0.047019943594932556, -0.01945200189948082, 0.021449878811836243, 0.023783937096595764, -0.01072468888014555, -0.009602926671504974, 0.06209211051464081, 0.017023270949721336, 0.03281093388795853, 0.055578477680683136, 0.003316023387014866, -0.007455423939973116, -0.005651166662573814, -0.009804719127714634, 0.009253120049834251, -0.0372103713452816, 0.028964387252926826, -0.02143917605280876, 0.006718780379742384, 0.04244217649102211, -0.05744211748242378, 0.025486474856734276, -0.03429264575242996, -0.018860820680856705, -0.030602749437093735, -0.04050822928547859, -0.03775481879711151, -0.019979236647486687, 0.005127268377691507, -0.06761517375707626, -0.08718804270029068, -0.004626085050404072, -0.040147438645362854, 0.05959627777338028, 0.01785576529800892, 0.0033268576953560114, -0.04997050017118454, 0.03610748052597046, 0.02063409797847271, -0.004061092156916857, -0.0031735277734696865, -0.06329207867383957, 0.0158411655575037, -0.060758017003536224, -0.017655786126852036, -0.0645061582326889, 0.03240661323070526, 0.023795878514647484, -0.04690517857670784, -0.08721073716878891, -0.06789948046207428, -0.010670874267816544, 0.05370460823178291, -0.013417388312518597, 0.027250973507761955, 0.019878176972270012, 0.04011468589305878, 0.03651793673634529, 0.032501962035894394, 0.005242545157670975, -0.012038431130349636, -0.03122241422533989, -0.032332561910152435, 0.08848946541547775, -0.02389073744416237, -0.06415633112192154, 0.014800160191953182, 0.009404401294887066, 0.023897476494312286, 0.0061501008458435535, 0.0004510188300628215, 0.06044105440378189, -0.03474728763103485, 0.028401166200637817, 0.0278561320155859, -0.013861019164323807, -0.10487557202577591, -0.01683276705443859, 0.013202923350036144, -0.043053772300481796, -0.010959837585687637, -0.08850350230932236, 0.03431883826851845, -0.009243719279766083, -0.004137183073908091, 0.036483827978372574, -0.03413499891757965, 0.05612107366323471, -0.03803287073969841, 0.002224302850663662, 0.04076392203569412, -0.016003059223294258, -0.006321905180811882, -0.02243410237133503, -0.002388129010796547, 0.02790663205087185, 0.008819358423352242, 0.03807925805449486, -0.03245002031326294, -0.017596812918782234, -0.030500469729304314, -0.03829484432935715, -0.058242928236722946, -0.00003169411138514988, -0.042878132313489914, -0.01587904430925846, -0.010249843820929527, 0.04399793595075607, 0.01892056316137314, -0.025550981983542442, -0.0175616554915905, 0.03191770240664482, -0.045122887939214706, -0.02078920789062977, 0.0027641511987894773, 0.00413676630705595, 0.029345398768782616, -0.009917020797729492, -0.04973451420664787, -0.08246096968650818, -0.01255527138710022, -0.047614045441150665, -0.007305593229830265, -0.04332207515835762, -0.00000288749583887693, 0.09550096839666367, -0.03328656032681465, 0.002047631423920393, -0.0364798866212368, -0.009633395820856094, -0.03906673938035965, -0.007572022266685963, -0.04651165381073952, 0.025150014087557793, -0.02825956605374813, -0.05434030294418335, 0.04350527375936508, -0.014105292037129402, -0.04414637014269829, 0.050809845328330994, 0.0015679480275139213, -0.010290996171534061, -0.011704505421221256, 0.054396145045757294, -0.008073662407696247, -0.07573558390140533, 0.024831781163811684, -0.03683621063828468, -0.01419655792415142, -0.051244281232357025, -0.020632708445191383, 0.06043344736099243, 0.034343115985393524, -0.0012462881859391928, 0.00697079673409462, 0.04177703708410263, -0.0018237660406157374, -0.004821498412638903, -0.025653887540102005, 0.03611847385764122, 0.020575840026140213, 0.09336913377046585, -0.009905394166707993, -0.007420537061989307, -0.023810312151908875, 0.01868198998272419, 0.0018944519106298685, -0.028800541535019875, 0.02985524944961071, 0.02618802711367607, -0.005323929712176323, 0.02941296622157097, -0.0014364555245265365, -0.017246440052986145, -0.019012700766324997, -0.009824247099459171, -0.10737419873476028, -0.03201761096715927, -0.021363165229558945, 0.029343508183956146, 0.03569537773728371, 0.06226463243365288, 0.0320659875869751, -0.0488724447786808, -0.005385534837841988, -0.04428359493613243, 0.03545748442411423, -0.037511616945266724, 0.029019951820373535, -0.01579848863184452, -0.03270972892642021, -0.01723841391503811, -0.04198339581489563, 0.006890506483614445, 0.023107558488845825, 0.030728425830602646, 0.03917783126235008, -0.029052434489130974, 0.014394118450582027, 0.014170661568641663, 0.058181069791316986, 0.0013547709677368402, -0.022327249869704247, 0.07075047492980957, 0.05533744394779205, -0.0474436916410923, -0.03713354468345642, 0.012325596995651722, -0.015481042675673962, -0.033368196338415146, -0.018465274944901466, 0.006571268662810326, 0.03107190690934658, 0.024694006890058517, 0.0064191026613116264, 0.016871774569153786, -0.015781549736857414, 0.018212560564279556, -0.030647961422801018, -0.040724724531173706, 0.036848634481430054, 0.021819474175572395, -0.08418091386556625, -0.017145484685897827, -0.0664532482624054, 0.013659844174981117, 0.019881997257471085, -0.0185783002525568, 0.010079428553581238, -0.03261600807309151, -0.009830311872065067, 0.03629845753312111, -0.008483811281621456, 0.0672706663608551, 0.057442557066679, 0.025723686441779137, 0.030458852648735046, 0.013649382628500462, -0.026692548766732216, 0.0031529574189335108, -0.047698646783828735, 0.0021317903883755207, 0.013737538829445839, 0.05528136342763901, -0.05502183362841606, -0.03844008594751358, 0.002272531623020768, -0.030876832082867622, -0.012382055632770061, 0.039716508239507675, 0.035351261496543884, -0.020840579643845558, 0.07194775342941284, -0.02832651138305664, 0.031283188611269, -0.015390685759484768, -0.026885366067290306, 0.05689207464456558, -0.021989984437823296, -0.0089791938662529, 0.036383964121341705, -0.015525094233453274, -0.00284184655174613, 0.030168306082487106, 0.06693870574235916, 0.010101142339408398, -0.002104054670780897, 0.03843372315168381, 0.04692856967449188, -0.029424935579299927, 0.07429313659667969, -0.013029888272285461, 0.08931088447570801, -0.02105805277824402, -0.020738163962960243, -0.06645572185516357, 0.010356451384723186, -0.00836209673434496, -0.03996006399393082, -0.025546982884407043, 0.007333878893405199, -0.0075586894527077675, -0.03998762369155884, -0.01643037609755993, 0.03241235762834549, 0.024029146879911423, -0.017353978008031845, 0.0658392533659935, -0.012555857188999653, 0.009134725667536259, 0.05502001941204071, 0.08311925083398819, 0.00038523130933754146, 0.0770152360200882, 0.00003214795287931338, 0.04866519570350647, 0.0038269676733762026, -0.04746048152446747, 0.04821324348449707, -0.041140131652355194, -0.001593816909007728, -0.053938690572977066, -0.01915627531707287, -0.04579765722155571, -0.03238038346171379, 0.034669242799282074, 0.006613193079829216, -0.036902088671922684, 0.07366988062858582, -0.028524797409772873, 0.008795485831797123, -0.016347715631127357, 0.0013633201597258449, -0.022736340761184692, -0.021906256675720215, -0.06788564473390579, -0.05214336887001991, 0.039288539439439774, -0.04674306884407997, -0.015005606226623058, 0.005942018702626228, -0.002843491267412901, 0.000009210678399540484, -0.00958089530467987, -0.07432527095079422, -0.02219328284263611, 0.0036182913463562727, -0.016648072749376297, 0.02279207482933998, -0.05620110034942627, 0.027493098750710487, -0.011957673355937004, -0.06913864612579346, -0.012874394655227661, -0.01831558160483837, 0.012077391147613525, -0.01745779812335968, 0.0024834147188812494, -0.010784078389406204, 0.02022659219801426, 0.017370689660310745, -0.06484297662973404, 0.03754295036196709, 0.04675903543829918, 0.04132847860455513, -0.042334284633398056, -0.015642181038856506, -0.01799595169723034, 0.03329504281282425, 0.012807788327336311, -0.039752811193466187, -0.03402823954820633, 0.0045767067931592464, 0.04163796454668045, 0.03413322940468788, 0.013991393148899078, -0.0006754614878445864, -0.018590977415442467, 0.025190655142068863, -0.013633542694151402, -0.03162943199276924, 0.025258174166083336, 0.02829056605696678, 0.030585961416363716, -0.06238562986254692, -0.004715265240520239, -0.0341421514749527, 0.048502177000045776, 0.014397951774299145, 0.04634561017155647, -0.07304848730564117, -0.009889299981296062, -0.03352472931146622, 0.009614448063075542, -0.01075840461999178, 0.0044853221625089645, -0.0197584368288517, -0.016314946115016937, 0.015590113587677479, 0.03551401570439339, 0.03302957862615585, 0.0018971847603097558, 0.019399579614400864, -0.003309009363874793, -0.008831022307276726, 0.013110140338540077, -0.03634762391448021, -0.02893218770623207, -0.013251501135528088, 0.02939816750586033, -0.017896883189678192, 0.024047547951340675, 0.011240711435675621, -0.024697549641132355, -0.009622869081795216, -0.030242998152971268, 0.024492647498846054, -0.0042146495543420315, -0.011327963322401047, 0.03549047186970711, 0.05475275218486786, -0.03733525425195694, 0.04792395979166031, 0.026422517374157906, 0.030520571395754814, -0.025152647867798805, 0.07441453635692596, -0.042076509445905685, -0.03690455108880997, 0.046534206718206406, 0.0017634202959015965, -0.03820613771677017, 0.007199733518064022, 0.02457641437649727, 0.008598722517490387, 0.004823946859687567, -0.03595144301652908, -0.02927418239414692, 0.006505225785076618, 0.009272560477256775 ]
<p>We know that a simple application of Gauss's law tells us that the field inside of a uniformly charged spherical shell is zero. Does this hold for all uniformly charged closed surfaces? If so, how could we prove this? Or does it hold only for certain shapes? </p>
g5460
[ 0.041501399129629135, -0.025984138250350952, 0.0073129949159920216, -0.020131835713982582, 0.08268687129020691, 0.07026257365942001, 0.009738784283399582, -0.0029302816838026047, 0.005143324378877878, -0.024264749139547348, -0.08161011338233948, -0.0018383704591542482, 0.028881490230560303, -0.025752225890755653, -0.06280647218227386, -0.02134172059595585, 0.01028243824839592, -0.032719120383262634, -0.004620592575520277, 0.07098700106143951, 0.0078125, -0.037826742976903915, 0.054598815739154816, 0.005621880292892456, -0.00593140535056591, 0.020694030448794365, -0.007215068209916353, -0.013501782901585102, -0.010765442624688148, -0.08685952425003052, 0.03968863934278488, -0.02927151694893837, 0.020922845229506493, -0.05105576291680336, -0.009645805694162846, -0.029482463374733925, 0.008748852647840977, 0.01824902556836605, -0.03870328888297081, 0.016132663935422897, 0.060879144817590714, -0.008013458922505379, 0.060952767729759216, 0.015870090574026108, -0.012125031091272831, 0.007003340870141983, -0.002778897061944008, 0.07247443497180939, 0.020199211314320564, -0.005327163264155388, -0.0354606993496418, -0.01139925792813301, 0.035448312759399414, -0.09610924124717712, -0.012266584672033787, -0.0506768636405468, -0.01805565506219864, 0.0027353332843631506, -0.0010199528187513351, 0.012105820700526237, -0.027446428313851357, -0.006250114180147648, -0.04296903312206268, 0.02254394441843033, 0.011276058852672577, 0.049978673458099365, -0.04404785856604576, -0.030705641955137253, 0.014384258538484573, -0.013874677009880543, 0.029768776148557663, -0.06104438379406929, -0.027021773159503937, -0.0840265154838562, 0.021422551944851875, 0.02518463134765625, 0.020561452955007553, 0.0004852286074310541, -0.006821960210800171, -0.05689718946814537, -0.046702608466148376, -0.00043555008596740663, 0.03809170052409172, -0.00719804922118783, 0.0691985934972763, -0.036717500537633896, 0.008380841463804245, -0.036909814924001694, 0.03393270820379257, 0.019252952188253403, -0.002196274232119322, 0.03002488799393177, 0.03265977278351784, 0.03154129162430763, -0.010148839093744755, -0.023008905351161957, 0.019531963393092155, 0.004785770550370216, -0.03948783129453659, -0.019778432324528694, -0.008980588056147099, 0.0003786919987760484, -0.010752074420452118, 0.021148614585399628, 0.054111480712890625, 0.03393059968948364, 0.006713933777064085, -0.0012946914648637176, 0.03422161936759949, 0.005930276587605476, 0.002143295481801033, -0.011993013322353363, -0.013683718629181385, -0.040830716490745544, -0.001983858412131667, 0.007562143262475729, 0.09552589803934097, -0.08796951919794083, -0.007458379026502371, 0.05083361640572548, -0.017874768003821373, 0.08196477591991425, -0.03644877299666405, 0.02439190447330475, -0.004993204027414322, 0.045365966856479645, -0.003012207569554448, 0.0033432357013225555, -0.0057999189011752605, 0.020745737478137016, -0.014959032647311687, 0.01993107795715332, -0.005000803153961897, 0.014456095173954964, -0.005141230765730143, 0.06644424051046371, -0.01224120520055294, -0.04264079034328461, 0.022606516256928444, -0.04346729442477226, -0.01514207199215889, -0.014903634786605835, -0.0038127971347421408, 0.005029326770454645, 0.05232556164264679, -0.01577121950685978, 0.011178215965628624, -0.02968447655439377, 0.010516969487071037, 0.05153033137321472, -0.0051328400149941444, 0.06395033001899719, 0.025432143360376358, 0.023665418848395348, -0.0274044256657362, -0.06379494071006775, 0.04725567623972893, 0.006003791466355324, 0.03167058154940605, -0.03205329552292824, 0.04701116308569908, 0.051100943237543106, 0.018890853971242905, 0.0038831119891256094, -0.06130573898553848, -0.011891359463334084, -0.04242371767759323, 0.0024140356108546257, -0.031130967661738396, -0.1127219945192337, -0.01802138239145279, 0.055961597710847855, -0.032738104462623596, 0.10349875688552856, -0.02162351831793785, -0.0605149008333683, -0.05624230578541756, -0.015891866758465767, -0.0002158408024115488, 0.024460434913635254, -0.02567906305193901, 0.021470557898283005, 0.011982055380940437, 0.009679388254880905, 0.01142559852451086, 0.039354581385850906, -0.05848046764731407, -0.003600285155698657, -0.03708677366375923, 0.014763119630515575, -0.03073517046868801, 0.0173106100410223, -0.007066889200359583, 0.011999759823083878, 0.06685400009155273, 0.016111982986330986, 0.08340170979499817, -0.018661638721823692, -0.018991151824593544, -0.039398327469825745, -0.04692283272743225, 0.08781319856643677, 0.015512711368501186, 0.01948942430317402, 0.02726753242313862, 0.00625280337408185, 0.012048101052641869, -0.02233191579580307, 0.07274990528821945, 0.012903526425361633, 0.005155410151928663, -0.00537854665890336, -0.01838146336376667, 0.004369262605905533, 0.028741613030433655, 0.030805889517068863, -0.015929315239191055, -0.010879285633563995, 0.0023094327189028263, 0.008456462994217873, -0.028351837769150734, 0.06907277554273605, 0.018352137878537178, -0.023600028827786446, 0.02925446629524231, 0.023035811260342598, 0.009637256152927876, 0.042993832379579544, -0.025868568569421768, 0.010266497731208801, -0.06349194049835205, -0.028689811006188393, -0.017495349049568176, -0.029945213347673416, -0.009374203160405159, 0.04113655909895897, -0.07157860696315765, -0.007955120876431465, -0.00787444319576025, 0.02510087564587593, -0.018492883071303368, -0.02690052054822445, 0.00247327983379364, -0.022310834378004074, -0.03049083985388279, -0.08497043699026108, -0.024971676990389824, 0.0030092166271060705, 0.011029611341655254, 0.04457738995552063, 0.00847726222127676, 0.06434645503759384, 0.010617098771035671, 0.05269136652350426, -0.010061969980597496, 0.026882827281951904, 0.02991572581231594, -0.05457251891493797, 0.014606737531721592, -0.08355765789747238, -0.025660105049610138, -0.08923730999231339, -0.008052565157413483, 0.03389056399464607, 0.002698687370866537, -0.0023293166887015104, -0.03593796119093895, 0.03915420547127724, 0.03858784958720207, -0.005094105843454599, 0.01748490519821644, 0.143218994140625, 0.02491891197860241, 0.007562285754829645, -0.003693211358040571, -0.044006772339344025, -0.03350266069173813, 0.005417604930698872, 0.04328927397727966, -0.006010528653860092, 0.0036216226872056723, 0.0030914642848074436, -0.05015124753117561, 0.02425316534936428, -0.0031259702518582344, -0.0397304892539978, 0.011630772612988949, 0.010829785838723183, 0.0167072843760252, -0.015729233622550964, 0.05101712420582771, 0.013834111392498016, 0.10147694498300552, -0.0028223281260579824, -0.03418463468551636, 0.05945466086268425, 0.0363798663020134, -0.022927049547433853, 0.011152133345603943, 0.030465563759207726, -0.04543709009885788, -0.0024394027423113585, -0.030481643974781036, -0.022027023136615753, 0.025755183771252632, 0.04277825355529785, 0.038080181926488876, -0.0685458704829216, 0.01027972437441349, 0.027052903547883034, -0.04285375028848648, 0.05396560579538345, 0.010279525071382523, 0.014462346211075783, -0.01936889998614788, 0.004611027892678976, -0.09027735143899918, -0.007858514785766602, -0.010996798984706402, 0.006905755493789911, 0.0021551453974097967, 0.027018733322620392, 0.01860359124839306, -0.05535941570997238, 0.001300316071137786, 0.01136690005660057, -0.07566303014755249, -0.0011584882158786058, -0.0016450253315269947, -0.04833317548036575, -0.00870975200086832, 0.06678979843854904, 0.012690609320998192, -0.0007465027738362551, 0.04739570990204811, -0.015597982332110405, 0.037083737552165985, 0.02649587020277977, 0.06909633427858353, 0.018322382122278214, 0.008610615506768227, -0.057253532111644745, -0.0742805227637291, -0.03125203400850296, -0.03259749338030815, 0.06675267219543457, -0.05347539484500885, -0.037428807467222214, -0.020947961136698723, -0.052823152393102646, 0.02148887887597084, 0.02736576646566391, -0.00008719444304006174, 0.011491219513118267, -0.003355109365656972, -0.026357319205999374, -0.019543085247278214, 0.03595832362771034, -0.013595935888588428, -0.022549087181687355, 0.03893444314599037, -0.04598293453454971, 0.013089265674352646, -0.008790860883891582, 0.03768011927604675, -0.03922488912940025, 0.029585331678390503, 0.03845854848623276, -0.04745405912399292, -0.020867405459284782, -0.033080801367759705, -0.01687350496649742, 0.042491842061281204, 0.04240502789616585, -0.003917239140719175, 0.0068399193696677685, -0.016540134325623512, 0.00519216526299715, -0.019999023526906967, -0.04027194902300835, 0.038738008588552475, 0.056673500686883926, 0.020731372758746147, 0.00019503707881085575, -0.03945087268948555, 0.03108995221555233, -0.03832538425922394, -0.039728593081235886, 0.01790499873459339, -0.07938554883003235, -0.04865000396966934, 0.030633004382252693, 0.006522015668451786, -0.03954372555017471, -0.0395524837076664, -0.03277895227074623, 0.016686681658029556, -0.06947272270917892, -0.017398355528712273, -0.00039598142029717565, 0.029381705448031425, 0.0026143311988562346, -0.031084321439266205, -0.07337804138660431, 0.029088327661156654, -0.028322460129857063, -0.0006583444192074239, -0.012012145482003689, -0.019511044025421143, -0.037375591695308685, -0.034272450953722, -0.0424870066344738, -0.0248381569981575, -0.03282255679368973, 0.060733359307050705, -0.006724969483911991, -0.002857108600437641, 0.018567964434623718, -0.06996166706085205, -0.023045886307954788, 0.018363749608397484, 0.003382895141839981, 0.022075919434428215, -0.02583819441497326, 0.018257249146699905, 0.04764115437865257, 0.051549073308706284, 0.038117364048957825, 0.002018395811319351, 0.0007546839769929647, -0.004461805801838636, 0.017675403505563736, -0.054312948137521744, 0.0036917461548000574, -0.050674498081207275, -0.008260520175099373, -0.07731999456882477, 0.017617831006646156, -0.040540121495723724, 0.02327180840075016, 0.009987880475819111, 0.0019094666931778193, 0.04656306281685829, 0.01702549122273922, -0.051113639026880264, 0.026522671803832054, -0.018780797719955444, -0.003321633208543062, 0.04164144769310951, 0.0037136010359972715, -0.04041166231036186, -0.047083575278520584, -0.024433551356196404, -0.00781339406967163, 0.03416905179619789, -0.0031406746711581945, -0.03004409745335579, 0.04295496270060539, -0.01953493244946003, -0.026981819421052933, -0.02734467387199402, 0.0011876089265570045, 0.033302903175354004, 0.03754973039031029, 0.021205492317676544, -0.029340246692299843, -0.01141873374581337, -0.013122000731527805, -0.01461090613156557, -0.04462401941418648, 0.0361708328127861, 0.0793565884232521, 0.0363425612449646, -0.03901124373078346, -0.008388538844883442, -0.015323675237596035, 0.040290143340826035, -0.008682318963110447, -0.006641997490078211, -0.034133829176425934, -0.004030590411275625, -0.04189331457018852, -0.030039168894290924, 0.013108354061841965, -0.02454543486237526, 0.08313070982694626, -0.024330751970410347, 0.009786148555576801, -0.03286414593458176, -0.017048170790076256, -0.003560982644557953, -0.02795044146478176, -0.013086538761854172, 0.01032609399408102, 0.03668573126196861, -0.0061887349002063274, 0.015686672180891037, -0.04359624534845352, -0.053778838366270065, 0.0036865847650915384, -0.05346417799592018, -0.02509802021086216, 0.029648223891854286, 0.08214134722948074, -0.021904900670051575, 0.06699594855308533, -0.033495884388685226, -0.04964558407664299, 0.015011089853942394, -0.02092001959681511, -0.008310050703585148, 0.000793140847235918, 0.03211212158203125, -0.04270967096090317, 0.002748191123828292, 0.005957980174571276, -0.08194474875926971, 0.015951359644532204, -0.026361722499132156, -0.004843299742788076, 0.04148247092962265, -0.0021020479034632444, 0.00043258597725071013, 0.005522570572793484, -0.05097653716802597, 0.020004021003842354, -0.009108362719416618, -0.044526033103466034, 0.025336427614092827, 0.05630066990852356, 0.004452214110642672, 0.011870117858052254, -0.054154690355062485, -0.0192004032433033, 0.02472091279923916, -0.053057603538036346, -0.0374467670917511, 0.028772329911589622, 0.028904106467962265, 0.035991132259368896, -0.004713678732514381, -0.0036963026504963636, 0.022296825423836708, 0.009647892788052559, -0.02996373176574707, -0.01115429401397705, -0.06396690011024475, 0.016867808997631073, 0.07322463393211365, -0.04082034155726433, -0.04591540992259979, 0.0355154313147068, -0.04807748273015022, 0.0019122213125228882, -0.03227914869785309, 0.008128090761601925, -0.029587818309664726, -0.01762731373310089, -0.004675538744777441, 0.011641223914921284, 0.045809775590896606, -0.004450817126780748, -0.001244636019691825, 0.010915422812104225, 0.007955277338624, -0.011044920422136784, -0.026005782186985016, -0.03098146989941597, 0.0394161157310009, 0.027961842715740204, -0.011729534715414047, -0.020087946206331253, 0.09809233248233795, -0.008820686489343643, 0.018654972314834595, -0.04274238646030426, 0.0034355667885392904, 0.01171800959855318, -0.003303905948996544, 0.02444133535027504, 0.04926684871315956, 0.008711585775017738, 0.04243571683764458, -0.019472647458314896, 0.059318166226148605, 0.07032408565282822, 0.005177241750061512, -0.02834068052470684, 0.06824863702058792, -0.04308899864554405, 0.07650099694728851, -0.047053445130586624, 0.016794972121715546, 0.03031608834862709, -0.03986620157957077, -0.006639739032834768, 0.020069530233740807, 0.018398258835077286, -0.004740078933537006, -0.005937438923865557, -0.013251686468720436, -0.02832190692424774, 0.011092188768088818, 0.010018419474363327, 0.036830734461545944, 0.01666998863220215, -0.006170759443193674, 0.02356453239917755, -0.033038459718227386, 0.01499463152140379, -0.006042770575731993, 0.03629857674241066, 0.001057931687682867, -0.015205223113298416, 0.0061956788413226604, -0.026983555406332016, 0.026033276692032814, -0.009954579174518585, -0.022904787212610245, 0.014532090164721012, 0.04880965128540993, 0.06399058550596237, -0.018010707572102547, -0.030647138133645058, 0.002550118835642934, -0.00319468230009079, 0.007403973489999771, 0.040680043399333954, 0.01594259776175022, 0.008915425278246403, -0.0024295574985444546, 0.058573536574840546, -0.0045286682434380054, 0.00971674919128418, 0.005531537812203169, 0.0736708790063858, 0.04240376502275467, 0.02307872660458088, 0.032021451741456985, 0.004333135671913624, -0.012686725705862045, 0.023560842499136925, 0.019214311614632607, 0.03828605264425278, -0.08062088489532471, 0.028593117371201515, 0.03771619871258736, -0.017700770869851112, -0.05229362100362778, 0.03914446756243706, 0.03249996900558472, 0.055395182222127914, 0.0676766112446785, -0.05862574279308319, -0.02106594853103161, 0.028132902458310127, 0.006418675649911165, 0.012163824401795864, -0.05522793158888817, -0.0500607043504715, 0.0378236323595047, 0.0406322106719017, 0.025291413068771362, -0.01341861393302679, -0.04693511128425598, 0.003953698091208935, -0.01923799142241478, -0.020906079560518265, -0.010620697401463985, -0.04954153299331665, 0.036883529275655746, 0.03727724775671959, -0.04309970512986183, 0.030984684824943542, 0.0358392670750618, 0.007898199371993542, -0.008610687218606472, 0.06635569781064987, 0.020416487008333206, -0.05183042585849762, 0.06826431304216385, 0.10245002061128616, -0.019689273089170456, 0.04416684806346893, -0.03870067000389099, -0.02552757039666176, -0.005524247884750366, -0.05253709852695465, 0.0047902450896799564, 0.01133472565561533, 0.019291343167424202, -0.0129143837839365, 0.0241995919495821, -0.008372291922569275, 0.0030568598303943872, -0.04796367511153221, 0.002274321625009179, 0.04820048063993454, 0.022315265610814095, -0.06054988130927086, -0.017946582287549973, 0.006510549690574408, -0.0015534869162365794, -0.032081060111522675, 0.04109666496515274, 0.021622763946652412, -0.04901546612381935, 0.03109586238861084, -0.044614847749471664, -0.007088532671332359, 0.03476445749402046, -0.035823360085487366, -0.005248755216598511, -0.01082419790327549, 0.06431295722723007, 0.0053948755376040936, -0.08413830399513245, 0.0111935343593359, 0.014958695508539677, -0.05488782748579979, -0.008594322018325329, 0.030216561630368233, -0.010193835943937302, -0.0279049314558506, 0.010781100019812584, -0.0061964672058820724, -0.03264911100268364, 0.03819890692830086, 0.07612840086221695, -0.02298158034682274, -0.05466008931398392, -0.004972598981112242, -0.012039611116051674, 0.009739921428263187, -0.08377354592084885, 0.013812790624797344, 0.004209162667393684, -0.021187588572502136, -0.022057056427001953, 0.024850858375430107, 0.043215904384851456, 0.019129032269120216, 0.023868611082434654, -0.09247713536024094, 0.0004416915471665561, 0.006770187523216009, -0.015097488649189472, 0.010418878868222237, 0.05682496726512909, 0.03176135942339897, 0.019046492874622345, -0.04173988848924637, -0.061953797936439514, 0.0333186537027359, 0.010750941000878811, -0.09463053941726685, -0.0010193013586103916, 0.016810273751616478, 0.05169185623526573, 0.04184776544570923, -0.026394983753561974, 0.0037008130457252264, 0.021988140419125557, 0.03586897999048233, 0.0228000245988369, -0.10757198184728622, 0.010139990597963333, 0.035262349992990494 ]
<p>I saw this in an art museum: <img src="http://i.stack.imgur.com/LLO24.jpg" alt="Floating Rock"></p> <p>How is this possible? The materials used to make this were foam, wood, stone dust, paint, electromagnets, and metal. I would like to know how this was make and how I could make something similar.</p> <p>Thank You.</p>
g5461
[ 0.06176302954554558, 0.036050084978342056, -0.001060565235093236, -0.07233066111803055, 0.05345442518591881, 0.11289317905902863, 0.00027329963631927967, -0.0013279903214424849, -0.04359037056565285, -0.052051346749067307, -0.02327764593064785, 0.02140752784907818, 0.06817150115966797, -0.007078520487993956, -0.004116994794458151, 0.01590096205472946, 0.042285289615392685, 0.013522441498935223, -0.005419977940618992, 0.0036395075730979443, 0.029445715248584747, 0.009486284106969833, 0.01890108920633793, 0.0025838566944003105, -0.040008578449487686, -0.057712655514478683, -0.014604895375669003, -0.007646462414413691, -0.01162173692137003, -0.041585955768823624, 0.010674870572984219, -0.008680718950927258, -0.03472353518009186, 0.015398060902953148, -0.02176257036626339, -0.06694066524505615, 0.016453852877020836, 0.010535522364079952, -0.011189750395715237, 0.022477375343441963, -0.05327419564127922, -0.020191052928566933, 0.011554552242159843, -0.02426324225962162, -0.04198503494262695, -0.004079281818121672, 0.022108687087893486, -0.025357456877827644, -0.030189212411642075, -0.006631182041019201, -0.02459139935672283, 0.03148597106337547, 0.038968898355960846, -0.010097324848175049, -0.03819917514920235, -0.031400274485349655, 0.011122320778667927, -0.008582144044339657, 0.0663309097290039, 0.009063772857189178, -0.04720541089773178, -0.052028145641088486, -0.015859130769968033, 0.07284092158079147, -0.00989298615604639, 0.012181643396615982, -0.010226784273982048, 0.03009478561580181, 0.03674279525876045, 0.012748234905302525, 0.029845789074897766, 0.022641621530056, 0.020636212080717087, -0.025639621540904045, -0.03713999688625336, 0.07070141285657883, 0.028340723365545273, 0.03829594701528549, -0.003586790058761835, 0.015191609039902687, 0.006158130243420601, 0.014495923183858395, -0.040142741054296494, -0.020872529596090317, 0.0395544059574604, -0.006481787655502558, -0.05422912910580635, -0.0283025112003088, -0.02509341388940811, -0.008827075362205505, -0.03911370784044266, -0.03863942250609398, 0.06550119817256927, 0.018292643129825592, 0.015023264102637768, -0.03821013867855072, -0.042538970708847046, 0.011149046942591667, -0.04696187376976013, -0.016680503264069557, -0.03392383083701134, -0.0544302873313427, 0.04239187762141228, 0.025147410109639168, 0.008169340901076794, 0.020185329020023346, 0.004333706572651863, -0.0014401841908693314, -0.057907626032829285, 0.02190331183373928, 0.018481314182281494, -0.018592504784464836, -0.013700309209525585, 0.023273756727576256, 0.02719203382730484, -0.02050708420574665, 0.04088396206498146, 0.029427556321024895, 0.022431716322898865, 0.014058358035981655, 0.0735292136669159, -0.025441346690058708, 0.04175418242812157, 0.035095106810331345, -0.05692183971405029, 0.02440580539405346, 0.08002173155546188, -0.015615327283740044, 0.0024489888455718756, -0.008804325945675373, 0.014437521807849407, 0.02250760793685913, 0.040044303983449936, -0.03559589758515358, 0.012454843148589134, 0.03307555615901947, 0.03785025328397751, -0.023105064406991005, 0.02278638631105423, -0.02298686094582081, 0.0033918400295078754, -0.05644812434911728, -0.03119262121617794, 0.011401341296732426, 0.021245380863547325, -0.0189385786652565, 0.0020518044475466013, 0.036435481160879135, -0.0063371979631483555, 0.004237373825162649, 0.007640975061804056, 0.058692291378974915, 0.005145092029124498, -0.024265065789222717, 0.06132765859365463, -0.04158621281385422, 0.0721362829208374, 0.010703399777412415, 0.032919663935899734, -0.0061543183401227, 0.0687553882598877, 0.008231966756284237, 0.03656316548585892, -0.030168704688549042, -0.04174153879284859, 0.030288411304354668, 0.04329635947942734, 0.02632017433643341, 0.010447457432746887, -0.005014208611100912, -0.01654904894530773, -0.016979720443487167, -0.03305891901254654, 0.065529964864254, 0.03612694516777992, 0.0018948892829939723, 0.05112721025943756, -0.05813043937087059, 0.058170560747385025, -0.01850523240864277, 0.0033800131641328335, -0.043810248374938965, -0.05174442380666733, 0.006234992761164904, -0.006752985995262861, 0.02506091445684433, 0.0282348170876503, 0.005032237619161606, -0.009444957599043846, -0.0025571503210812807, -0.0026706133503466845, -0.03575163707137108, -0.08823508024215698, 0.011194171383976936, 0.04503506422042847, -0.017114872112870216, 0.05460958927869797, -0.030341628938913345, -0.00280615477822721, -0.00280999718233943, 0.07321164757013321, 0.05969730764627457, 0.04205624386668205, -0.007714367471635342, 0.010057767853140831, -0.023069346323609352, -0.04203850403428078, -0.007947491481900215, -0.011840828694403172, -0.007043879479169846, 0.01320149190723896, 0.05204082652926445, -0.001981977839022875, 0.008977314457297325, -0.034947559237480164, 0.03838535025715828, 0.013094929046928883, -0.011446011252701283, -0.010146290063858032, -0.020345143973827362, 0.004029609262943268, 0.04396514967083931, -0.008741278201341629, -0.000925658387131989, 0.06252525746822357, -0.012403665110468864, 0.0015383027493953705, 0.017269210889935493, 0.02320423163473606, 0.00014833625755272806, 0.0033245545346289873, -0.02662343531847, 0.020503045991063118, 0.009472128935158253, -0.002789041493088007, 0.06003488972783089, -0.053537867963314056, 0.038368526846170425, -0.035951562225818634, -0.028765210881829262, -0.0334278829395771, -0.02011513151228428, 0.007435951381921768, -0.11287754029035568, 0.019148029386997223, 0.027292415499687195, -0.012017600238323212, 0.02947120927274227, 0.020923558622598648, 0.07050907611846924, 0.07989797741174698, -0.07096847891807556, -0.04933380335569382, 0.005999376997351646, -0.004244956187903881, 0.004129794891923666, -0.05605536326766014, 0.03462134674191475, 0.011686193756759167, -0.02723284251987934, 0.03803635761141777, -0.05964858829975128, 0.0005818130448460579, 0.04548759385943413, 0.0020605719182640314, -0.04184555262327194, -0.06264597922563553, 0.036456864327192307, 0.004423556849360466, 0.03588934242725372, -0.04330787435173988, -0.05110074579715729, 0.02921999804675579, 0.025528712198138237, -0.05827655643224716, -0.02665693685412407, 0.03980367258191109, -0.005224296823143959, -0.0030253143049776554, -0.024590009823441505, 0.053179580718278885, 0.018875421956181526, -0.004819577559828758, 0.012552241794764996, -0.027926992624998093, 0.013495640829205513, 0.005333380773663521, 0.02244519256055355, -0.03194179758429527, 0.05292418599128723, -0.025290191173553467, -0.017962701618671417, -0.008505427278578281, -0.05031543970108032, -0.05338187888264656, 0.054646797478199005, -0.02458258531987667, 0.029931049793958664, -0.037797749042510986, 0.03138551115989685, 0.04459888115525246, -0.029224932193756104, 0.05692443624138832, 0.046260248869657516, -0.02305932156741619, 0.009192898869514465, 0.07071778923273087, -0.006233568303287029, -0.00006177186878630891, -0.04076497256755829, -0.04420214146375656, 0.025467239320278168, 0.0031726134475320578, 0.03020227700471878, -0.02443893440067768, 0.07333160191774368, 0.004288843832910061, -0.005269242450594902, 0.025816168636083603, -0.04169018194079399, 0.015160854905843735, -0.014089521951973438, 0.050206173211336136, 0.05180547386407852, 0.05270746722817421, 0.03444640338420868, -0.06140400469303131, -0.012134047225117683, -0.07825987786054611, -0.013647177256643772, 0.04115268960595131, 0.0015008342452347279, -0.0708579272031784, -0.05768607184290886, -0.057300325483083725, 0.022036012262105942, -0.005885245278477669, 0.0050866915844380856, -0.010657236911356449, -0.03782760351896286, -0.04795263707637787, 0.005283186677843332, -0.019997576251626015, -0.021293675526976585, -0.009825168177485466, 0.03868023678660393, -0.0193925928324461, -0.031210854649543762, -0.032487671822309494, 0.006865296512842178, -0.003992015030235052, 0.006072969641536474, 0.04318389669060707, -0.0338345542550087, 0.041643813252449036, 0.05005195364356041, 0.03832824528217316, 0.03007342666387558, 0.0372568741440773, -0.03887343406677246, 0.012421658262610435, -0.07732193917036057, 0.04989945515990257, -0.05614643543958664, 0.0025088663678616285, -0.003024059347808361, 0.03968029469251633, 0.028763161972165108, 0.012795897200703621, 0.04134177416563034, 0.0450982004404068, -0.006196967326104641, -0.017152510583400726, -0.04700389876961708, 0.04641753435134888, -0.04328637197613716, 0.02944977767765522, 0.03433635085821152, -0.004311350639909506, 0.01918892376124859, -0.006111738737672567, 0.027459224686026573, 0.03613628074526787, -0.04105285555124283, -0.03280152752995491, 0.05185982212424278, -0.03572015464305878, 0.0156538225710392, 0.00739766051992774, -0.10440735518932343, -0.022078687325119972, 0.0066688708029687405, -0.07459699362516403, 0.015634093433618546, -0.015636535361409187, -0.03478705510497093, 0.01836114563047886, -0.009641039185225964, -0.03504440560936928, -0.012317853979766369, -0.002684452570974827, 0.043750468641519547, -0.015022823587059975, 0.025151439011096954, 0.043921440839767456, -0.014633283019065857, 0.0420105941593647, -0.05202934518456459, 0.021600786596536636, -0.08841978013515472, -0.0032354972790926695, 0.01271122507750988, -0.012553373351693153, -0.004800502676516771, 0.01948150061070919, -0.0304118525236845, 0.028975501656532288, 0.10069812089204788, 0.025896839797496796, 0.001452332129701972, -0.04465357959270477, 0.05403910577297211, 0.03362242132425308, 0.008373497053980827, 0.05392666533589363, 0.036448147147893906, 0.0004749561776407063, 0.010068078525364399, -0.03051077388226986, -0.03063347004354, 0.030784662812948227, 0.003591756569221616, -0.03499343991279602, -0.04797564446926117, -0.03443117067217827, 0.008643490262329578, -0.03180408477783203, -0.03519398719072342, 0.043648991733789444, 0.05563153699040413, 0.044819001108407974, -0.014487636275589466, 0.035112474113702774, 0.03511745110154152, 0.029088009148836136, 0.046859558671712875, -0.03379138186573982, 0.01582304947078228, -0.004328836686909199, 0.0016709082992747426, -0.0384092777967453, -0.0708443820476532, -0.028929995372891426, -0.013251959346234798, 0.03264094516634941, 0.016477016732096672, 0.012483836151659489, 0.02311166375875473, -0.023909632116556168, 0.009434187784790993, -0.0403377003967762, -0.017279919236898422, -0.0023850335273891687, -0.011368289589881897, -0.004286360926926136, -0.008141221478581429, -0.025711247697472572, -0.07867734134197235, -0.003781453939154744, -0.03421866148710251, 0.010973680764436722, -0.003915899898856878, -0.0069331219419837, 0.06188005954027176, -0.010640601627528667, -0.028355946764349937, -0.0035286860074847937, -0.049218758940696716, -0.033948495984077454, -0.07232173532247543, 0.02773062139749527, 0.0895686224102974, -0.019941015169024467, -0.03849004581570625, -0.009642550721764565, 0.0170978382229805, -0.0896046981215477, 0.04171697422862053, 0.02914867177605629, 0.020073287189006805, -0.014636208303272724, -0.01566542498767376, 0.017115535214543343, 0.002929618349298835, 0.017511028796434402, -0.03207497298717499, -0.05617893487215042, 0.0027232568245381117, 0.003919332288205624, 0.033987194299697876, 0.03160829842090607, -0.02007569558918476, 0.005184590350836515, 0.02157856523990631, 0.02234758622944355, 0.013275311328470707, 0.008443504571914673, -0.03296384960412979, 0.04435281082987785, 0.0901731327176094, -0.017177946865558624, -0.059036318212747574, -0.04353142902255058, -0.02420342154800892, 0.06304555386304855, -0.020310712978243828, -0.010066267102956772, -0.009134925901889801, 0.012416067533195019, 0.039220042526721954, -0.010732664726674557, -0.022627733647823334, -0.015393266454339027, -0.012983860448002815, -0.0571105033159256, -0.008641577325761318, -0.08145862072706223, -0.07973576337099075, 0.02615308202803135, 0.08508184552192688, -0.012527473270893097, -0.039949823170900345, 0.0256416704505682, -0.04561861976981163, -0.0013637017691507936, 0.0012897447450086474, 0.039035312831401825, -0.004098477773368359, 0.043697208166122437, 0.08099224418401718, 0.013402215205132961, -0.07426390051841736, 0.020649129524827003, 0.04746779426932335, 0.058484409004449844, -0.012658070772886276, 0.007239037659019232, 0.006527280900627375, 0.06108001619577408, 0.005823406390845776, -0.025138501077890396, 0.03855171799659729, 0.04759000241756439, 0.042482614517211914, -0.008501194417476654, -0.013506329618394375, -0.09774520248174667, -0.05405721440911293, 0.02356886677443981, -0.004729748237878084, 0.07820352911949158, -0.029995393007993698, 0.0225047804415226, -0.041575606912374496, 0.02819189243018627, -0.04685309901833534, 0.020878896117210388, 0.028773313388228416, 0.023347461596131325, 0.02152738720178604, -0.013936049304902554, 0.017632395029067993, -0.042702510952949524, -0.01808476448059082, -0.015739740803837776, -0.02585940808057785, -0.015579450875520706, 0.03596245124936104, -0.027632849290966988, 0.03956051170825958, 0.025309359654784203, 0.06389524042606354, 0.014861599542200565, -0.0075896489433944225, -0.018369460478425026, 0.009046695195138454, -0.03436746448278427, -0.011767049320042133, -0.03981499373912811, -0.061663974076509476, -0.07217585295438766, 0.05768631771206856, -0.05718076229095459, -0.006300034001469612, -0.028486404567956924, -0.034212492406368256, -0.007406443823128939, 0.05408009886741638, 0.029498398303985596, -0.001350640319287777, -0.06440896540880203, -0.029268136247992516, -0.028330251574516296, 0.0098185483366251, 0.006542407441884279, 0.019526520743966103, 0.010351903736591339, 0.05219098553061485, 0.01016822550445795, -0.0037371155340224504, -0.047222837805747986, 0.029774105176329613, -0.04849306866526604, -0.001356996246613562, -0.041677650064229965, -0.030848555266857147, 0.009487047791481018, -0.024702560156583786, 0.014443804509937763, 0.0013315418036654592, -0.008533863350749016, 0.0037619827780872583, -0.009729735553264618, -0.03984395042061806, 0.0011562382569536567, -0.03382975980639458, -0.03794055059552193, 0.026530664414167404, 0.013063236139714718, 0.0029610623605549335, -0.03931881859898567, -0.026577571406960487, 0.020297149196267128, 0.000885159766767174, 0.017129022628068924, 0.05384830757975578, 0.005227530375123024, 0.001335074077360332, 0.039154861122369766, 0.0403987392783165, -0.027451854199171066, 0.009847231209278107, -0.006660250946879387, 0.051995083689689636, -0.032839011400938034, 0.0061536733992397785, 0.013269283808767796, -0.059132497757673264, -0.03531308099627495, -0.024637209251523018, 0.05374389886856079, -0.02496887557208538, -0.007830786518752575, 0.0038272857200354338, -0.07541856169700623, 0.02016647905111313, 0.018943119794130325, -0.0012874320382252336, -0.0067162769846618176, -0.05081510171294212, -0.025483453646302223, -0.013424934819340706, 0.028529785573482513, -0.0517808198928833, -0.0036659063771367073, 0.027444856241345406, -0.07484117150306702, 0.029556432738900185, -0.010082252323627472, -0.013213053345680237, 0.00427274452522397, 0.01601424254477024, 0.024579133838415146, 0.0296269990503788, -0.04466954246163368, -0.034929804503917694, 0.003831401700153947, 0.037928346544504166, 0.05002070590853691, 0.028167590498924255, -0.01459395419806242, 0.07354111224412918, -0.015085422433912754, -0.04076043888926506, -0.01636766828596592, -0.012683418579399586, -0.0005045804427936673, 0.08128085732460022, -0.014249847270548344, -0.003944327589124441, 0.005773627664893866, 0.05358356982469559, 0.00007203678978839889, 0.025425974279642105, -0.013635656796395779, -0.030100906267762184, 0.015378306619822979, -0.0029767730738967657, 0.06177524849772453, -0.03578174114227295, -0.03456808254122734, -0.027685238048434258, -0.0035011260770261288, -0.036320872604846954, -0.01515036728233099, -0.021275686100125313, -0.0003939464222639799, 0.02299145609140396, -0.04664904996752739, -0.016490204259753227, 0.04800968989729881, 0.012893077917397022, 0.03493931517004967, -0.03346851095557213, 0.020028920844197273, 0.09754355251789093, -0.016695037484169006, 0.07165912538766861, -0.03927150368690491, -0.019654080271720886, -0.10505361109972, 0.05759879946708679, -0.021557847037911415, -0.06311456859111786, -0.010265653021633625, 0.02259187586605549, 0.02658359333872795, -0.0004358124569989741, -0.01337692141532898, 0.015706922858953476, -0.03287070244550705, -0.006303730420768261, -0.014326727017760277, 0.011958491057157516, -0.02047801949083805, -0.040911439806222916, 0.010683778673410416, -0.02283228188753128, 0.06828358769416809, -0.03173444792628288, -0.009364224970340729, 0.014691228978335857, -0.06412440538406372, -0.027489928528666496, 0.00820524338632822, -0.004195142537355423, -0.07495925575494766, 0.09689151495695114, -0.06720533221960068, -0.052953775972127914, -0.00001989177144423593, 0.016712628304958344, 0.0002255619183415547, -0.04239529371261597, 0.07308042049407959, -0.06367852538824081, -0.04250891134142876, 0.03942791000008583, 0.06190991774201393, 0.006942778825759888, -0.023625776171684265, 0.04542537033557892, 0.02151787281036377, 0.03066903166472912, -0.021736081689596176, -0.023205703124403954, 0.028126226738095284, 0.0024240980856120586 ]
<p>In this <a href="http://arxiv.org/abs/1108.3003v1" rel="nofollow">article</a> it is claimed that certain type of string theory called EGBd allows for traversable wormhole solutions that do not require exotic matter.</p> <p>What is this EGBd model and how it fits in the grand scheme of things of string theory? is this fringe science or is serious? (i know that there might be fringe authors in ArXiv). But my main concern is how general or realistic is this result?</p>
g5462
[ -0.01683172769844532, 0.08987922221422195, 0.013362007215619087, -0.0534287765622139, 0.02688462659716606, 0.04187870770692825, 0.014779575169086456, -0.014383296482264996, 0.004051778931170702, 0.0019556498154997826, 0.0646999403834343, -0.009571523405611515, 0.030820293352007866, -0.00857956800609827, -0.05909024551510811, 0.009319036267697811, -0.004110043402761221, -0.0040173716843128204, 0.020106397569179535, -0.026960063725709915, 0.024243641644716263, 0.038676925003528595, -0.011118033900856972, 0.01034209318459034, -0.021927913650870323, -0.04849813133478165, 0.06323017925024033, 0.03375948220491409, 0.048014428466558456, -0.03190694376826286, 0.04380457475781441, 0.03636876493692398, 0.00899503193795681, 0.0037338989786803722, -0.059825196862220764, 0.014149390161037445, -0.015545560978353024, 0.02233210951089859, 0.04650935158133507, 0.06178482249379158, -0.01551027037203312, -0.006177481729537249, -0.02982846274971962, -0.014776390045881271, -0.034851569682359695, 0.0008656796417199075, 0.00437466986477375, 0.02753159962594509, 0.04353714361786842, -0.046606045216321945, 0.0024427687749266624, 0.04683545604348183, 0.04119923710823059, -0.04769783839583397, -0.01810343749821186, 0.036578647792339325, -0.006103801541030407, 0.01839018240571022, 0.04995543509721756, 0.04413047432899475, 0.02452000603079796, 0.03419385850429535, 0.01362071093171835, 0.0074047064408659935, 0.04503631591796875, -0.012837426736950874, -0.010795374400913715, -0.03158777207136154, 0.03369120508432388, -0.05338815972208977, 0.0588151253759861, -0.037952978163957596, -0.0021622220519930124, -0.06219581514596939, -0.05423492193222046, 0.05335519462823868, -0.016697585582733154, 0.022567791864275932, -0.012708021327853203, -0.006353376433253288, -0.04948435723781586, -0.031123580411076546, -0.04712808132171631, 0.005514080636203289, 0.07749788463115692, -0.02282029204070568, -0.02647358551621437, 0.029277129098773003, 0.018854288384318352, -0.010874869301915169, 0.05480843782424927, -0.08553516864776611, 0.005785488523542881, -0.02135901153087616, 0.02134189009666443, -0.04459323361515999, -0.02216341719031334, 0.04602691903710365, -0.044895850121974945, -0.032258935272693634, -0.0024631319101899862, 0.039793793112039566, 0.010972704738378525, 0.014881602488458157, -0.04240185022354126, 0.003998355474323034, -0.017378928139805794, 0.031341101974248886, 0.026208966970443726, 0.016842195764183998, -0.006233920343220234, 0.021918736398220062, -0.01717210002243519, -0.05634034052491188, 0.00016976112965494394, 0.008382365107536316, -0.039217106997966766, 0.024217763915657997, -0.010903234593570232, 0.0482029989361763, 0.0414426252245903, 0.006695229560136795, -0.01313950214534998, 0.06119459122419357, -0.0777459517121315, -0.015214867889881134, -0.005633044522255659, -0.058202244341373444, -0.01869550161063671, -0.004756537731736898, 0.0037692757323384285, 0.025570081546902657, 0.04471132531762123, 0.07214770466089249, 0.040708813816308975, 0.03620276227593422, 0.013895225711166859, 0.044541094452142715, -0.019551608711481094, 0.031677745282649994, -0.0027493475936353207, -0.06939489394426346, 0.005692125763744116, 0.00180301652289927, 0.001560093485750258, -0.021085606887936592, 0.027179889380931854, 0.050858549773693085, -0.02086012251675129, -0.007796065881848335, 0.008677345700562, 0.15039534866809845, 0.013921748846769333, -0.034426167607307434, 0.023598235100507736, 0.020557232201099396, 0.09135656803846359, -0.028552833944559097, -0.026376938447356224, 0.036688461899757385, -0.00012717396020889282, -0.0058775730431079865, 0.010723424144089222, 0.01269723754376173, -0.03529569134116173, -0.013453494757413864, -0.003216288983821869, -0.07989393919706345, -0.04531079903244972, -0.013673395849764347, -0.047658972442150116, 0.05027695372700691, 0.05448860302567482, 0.06916303187608719, 0.029888702556490898, 0.0026997134555131197, 0.011100636795163155, -0.02736256644129753, 0.0015099199954420328, -0.06909170746803284, -0.0012230968568474054, -0.03472258895635605, -0.0011752797290682793, 0.02519102394580841, 0.022127576172351837, 0.046197861433029175, -0.008456412702798843, -0.016140399500727654, 0.06808141618967056, 0.04056273400783539, -0.012379403226077557, -0.045438822358846664, 0.03190955892205238, 0.009217789396643639, -0.0033016325905919075, 0.012405399233102798, 0.0523504912853241, -0.024865921586751938, 0.015216820873320103, 0.012754496186971664, -0.03201649710536003, 0.09293524920940399, -0.03162643313407898, -0.03505551442503929, 0.04753371328115463, 0.013814096339046955, -0.022509025409817696, 0.005117825232446194, 0.03490198776125908, -0.01868266984820366, 0.07393871992826462, 0.00022093765437602997, -0.02268633246421814, 0.01448184996843338, -0.03177686408162117, -0.0807853639125824, -0.032317522913217545, -0.008841189555823803, 0.00481607299298048, 0.03484984487295151, 0.014772140420973301, -0.021599868312478065, -0.031742971390485764, 0.0038784481585025787, 0.025961682200431824, 0.037272535264492035, -0.06195582449436188, -0.04570523276925087, 0.014909440651535988, 0.0035520712845027447, -0.0038951323367655277, -0.04822850972414017, -0.015718258917331696, -0.06595543771982193, 0.06779302656650543, 0.014401618391275406, 0.011813832446932793, -0.021260034292936325, 0.0222618505358696, 0.00017324196232948452, 0.043381039053201675, -0.0001893190637929365, -0.013951579108834267, -0.034210994839668274, 0.045585114508867264, -0.017598306760191917, 0.018368873745203018, -0.0037783035077154636, -0.012156616896390915, -0.020464597269892693, 0.046619292348623276, -0.055866871029138565, 0.04616471379995346, 0.059030309319496155, 0.03439095616340637, 0.019393688067793846, 0.07168138027191162, 0.036723338067531586, 0.014437191188335419, -0.011350936256349087, -0.026833999902009964, -0.007224836852401495, -0.008108312264084816, 0.03515242412686348, -0.08979405462741852, -0.0162802841514349, -0.055812589824199677, -0.033977705985307693, -0.048628050833940506, 0.0031269709579646587, -0.02788914367556572, -0.04753879830241203, -0.0513191856443882, -0.026419930160045624, -0.00010057476174551994, 0.011704038828611374, -0.004866787698119879, 0.046847399324178696, -0.011658410541713238, -0.034191686660051346, -0.009952099062502384, -0.019863516092300415, -0.016958462074398994, 0.02210954762995243, 0.0326240248978138, -0.02314949408173561, -0.046367887407541275, -0.0014650600496679544, 0.0056211925111711025, 0.06781361997127533, -0.0009588297107256949, -0.06210250407457352, 0.008466518484055996, 0.022792521864175797, 0.0070383925922214985, 0.09354936331510544, -0.05966288596391678, 0.014906059019267559, -0.013973066583275795, -0.003363658208400011, -0.06157238781452179, 0.015017388388514519, 0.0004201540432404727, 0.05214603245258331, -0.044320788234472275, 0.022792508825659752, -0.06187741085886955, -0.0357481949031353, -0.012633705511689186, -0.011506525799632072, -0.013569271191954613, 0.06615155190229416, 0.02514665201306343, 0.014384491369128227, 0.024937128648161888, 0.009739541448652744, 0.018156560137867928, 0.022309433668851852, 0.04139500856399536, -0.013776491396129131, -0.04573681578040123, 0.00379472435452044, 0.019785573706030846, 0.0017986017046496272, 0.0031873604748398066, 0.011247072368860245, -0.04598351567983627, -0.062249694019556046, -0.07135796546936035, 0.05179319530725479, 0.013885462656617165, -0.042853135615587234, -0.024833301082253456, 0.007741194684058428, -0.03588498383760452, 0.01659397967159748, 0.032443441450595856, 0.07299364358186722, 0.04307316243648529, 0.03455641493201256, -0.0629127025604248, -0.09801222383975983, -0.017314640805125237, 0.006710859946906567, -0.03148377314209938, 0.043681126087903976, -0.03025875985622406, -0.023187652230262756, 0.0352255143225193, 0.007698152679949999, 0.04122878238558769, -0.002541778376325965, 0.012146441265940666, 0.006021733861416578, 0.008063491433858871, 0.040927089750766754, 0.06308647245168686, 0.02490939386188984, 0.0614042729139328, 0.012443981133401394, 0.029334835708141327, -0.004825955256819725, 0.015930578112602234, -0.017382051795721054, 0.03754114732146263, -0.03445626050233841, 0.01535650435835123, -0.018535587936639786, 0.020999925211071968, 0.0009070755331777036, -0.030912505462765694, 0.017421886324882507, -0.015447722747921944, 0.0021256685722619295, 0.034976422786712646, 0.015405931510031223, -0.01819669082760811, -0.0011615175753831863, -0.007908446714282036, 0.006278420332819223, 0.04522049054503441, 0.04871834069490433, 0.013809827156364918, -0.007277661934494972, 0.015446081757545471, 0.014873573556542397, -0.005196366459131241, 0.0068827965296804905, -0.03309283405542374, -0.01040200237184763, -0.03127847611904144, -0.014917016960680485, -0.014892932958900928, -0.07649820297956467, -0.03479655086994171, 0.03227697312831879, -0.051520999521017075, -0.0033084601163864136, 0.005585400853306055, -0.04360920935869217, 0.05668581649661064, 0.001978545682504773, -0.0006197690381668508, 0.05479684844613075, -0.06559909135103226, -0.012419451959431171, -0.007665019482374191, -0.04818877950310707, -0.0015233714366331697, -0.07862632721662521, 0.05540723353624344, 0.007544760126620531, -0.027842076495289803, 0.01609741896390915, -0.024571746587753296, -0.010142550803720951, -0.013055996969342232, -0.06504771113395691, 0.022089416161179543, 0.0019092726288363338, 0.01275327056646347, 0.014359516091644764, 0.052360013127326965, -0.005107685923576355, -0.05478762090206146, 0.07073961198329926, -0.047283634543418884, 0.0193466916680336, -0.012829350307583809, 0.027783850207924843, -0.01641036383807659, -0.009621251374483109, -0.05948764458298683, 0.02287578023970127, -0.05397813022136688, 0.09957628697156906, -0.032071344554424286, 0.025697967037558556, 0.0037373623345047235, -0.027853379026055336, 0.06209772452712059, -0.019130757078528404, -0.0017612723167985678, -0.028719879686832428, -0.002568302908912301, 0.053227245807647705, -0.0026676564011722803, -0.012723894789814949, 0.010385074652731419, 0.016368616372346878, -0.002975569339469075, -0.026709305122494698, 0.008991464041173458, -0.001953369239345193, -0.03372672200202942, 0.00998824555426836, -0.016727467998862267, 0.05249250680208206, -0.01575375348329544, -0.027736591175198555, -0.10336443781852722, 0.032166626304388046, 0.04215250909328461, 0.054753657430410385, 0.027664106339216232, -0.009019285440444946, -0.013422121293842793, -0.03698783740401268, 0.004853604827076197, -0.029963649809360504, -0.0017267413204535842, -0.03185608983039856, 0.05761510878801346, 0.005413231439888477, -0.004268726333975792, -0.005426985677331686, -0.01921047642827034, 0.00543432729318738, -0.04001281410455704, -0.08367574959993362, -0.03706055134534836, -0.008156304247677326, 0.05053655058145523, 0.03534276783466339, 0.04781292378902435, -0.000585985544603318, -0.017076455056667328, 0.06449758261442184, -0.045511312782764435, 0.06143765524029732, -0.02191164903342724, -0.01163503248244524, -0.00026981817791238427, 0.01776394248008728, -0.018989674746990204, 0.014876008033752441, 0.01948849856853485, -0.04887063428759575, -0.053235672414302826, 0.05859300121665001, -0.03544961288571358, -0.02009599469602108, 0.07130388915538788, -0.01532069407403469, -0.002299646381288767, 0.045465633273124695, 0.0473199263215065, 0.003144599962979555, -0.018840281292796135, -0.03991756588220596, -0.02166196145117283, -0.04927967116236687, -0.0682370662689209, 0.006830400321632624, 0.007386120036244392, -0.0506158247590065, -0.05931223928928375, -0.052123021334409714, 0.011661478318274021, -0.0005128917400725186, -0.024810411036014557, 0.016815360635519028, 0.015160943381488323, 0.01002536341547966, 0.04014452546834946, 0.029465949162840843, -0.02222205512225628, 0.0076878988184034824, -0.02167247049510479, 0.04944094642996788, 0.027646584436297417, -0.011126771569252014, 0.06752270460128784, -0.003937841393053532, 0.02586578018963337, 0.021463656798005104, 0.028901012614369392, 0.026102595031261444, 0.020709587261080742, -0.05014226213097572, -0.03520075976848602, -0.003951935563236475, 0.037384290248155594, 0.020656852051615715, 0.021665381267666817, -0.031872302293777466, -0.02347169630229473, 0.0465216189622879, 0.037605028599500656, -0.07530645281076431, -0.016486790031194687, -0.028614243492484093, -0.029505208134651184, 0.07423843443393707, -0.0010317167034372687, 0.004845192190259695, -0.036496352404356, -0.015368258580565453, 0.030891017988324165, 0.010417575016617775, -0.021153423935174942, 0.04310254752635956, -0.005736215505748987, 0.012837762013077736, 0.001462878892198205, -0.026371749117970467, 0.018240293487906456, 0.02568204514682293, 0.0513431616127491, 0.06045936048030853, -0.07614795863628387, 0.08035876601934433, -0.01457189116626978, 0.017118986696004868, 0.007358262315392494, -0.04917231947183609, -0.053300078958272934, -0.06794014573097229, -0.034978318959474564, -0.026147808879613876, -0.00913334172219038, 0.01920785754919052, 0.05865835025906563, -0.02827443741261959, -0.014597064815461636, -0.03951411694288254, -0.045013997703790665, 0.006131230387836695, 0.005945733282715082, 0.031953759491443634, -0.03385843709111214, 0.08379195630550385, -0.003083638148382306, 0.006074287462979555, -0.028516860678792, 0.02512597106397152, 0.008699259720742702, -0.005529077723622322, -0.0493726022541523, -0.003943532705307007, 0.04078855365514755, -0.008671501651406288, -0.01035598386079073, 0.04811912402510643, 0.05821577087044716, -0.006749829743057489, -0.05718463286757469, 0.005674383603036404, -0.009378507733345032, -0.021183118224143982, 0.02345983497798443, 0.013033353723585606, -0.005719585344195366, -0.06560684740543365, -0.02722514234483242, 0.007514217868447304, -0.052840180695056915, -0.021746443584561348, 0.006066088564693928, 0.049096859991550446, -0.01179376058280468, -0.010016016662120819, 0.030780404806137085, -0.02144423872232437, 0.006896901410073042, 0.06105539947748184, -0.03374634310603142, -0.021439025178551674, 0.029505187645554543, -0.004868095740675926, -0.0743679404258728, -0.02029413916170597, 0.07063104957342148, -0.010267947800457478, 0.010541449300944805, 0.0021070577204227448, -0.1105726957321167, -0.04785427451133728, -0.02287357859313488, 0.011238407343626022, -0.020506346598267555, -0.000711748085450381, 0.07548685371875763, -0.044325634837150574, -0.04050148278474808, 0.035404205322265625, 0.03158951178193092, -0.011255999095737934, -0.015649249777197838, -0.03210383653640747, 0.013463643379509449, -0.051677703857421875, -0.054231882095336914, 0.030294252559542656, 0.006918079219758511, -0.04202090948820114, -0.010173500515520573, 0.022691527381539345, -0.021994292736053467, 0.009803314693272114, -0.03243174031376839, 0.038025155663490295, 0.05866672843694687, 0.010659299790859222, -0.0072641572915017605, 0.005478420294821262, 0.005565297789871693, -0.07023463398218155, 0.021355057135224342, 0.007460585795342922, -0.012840635143220425, -0.027436740696430206, -0.0473933219909668, -0.009175771847367287, 0.013651116751134396, -0.07742132991552353, -0.015042035840451717, -0.014485154300928116, -0.05417323112487793, -0.010025371797382832, 0.033687837421894073, 0.055948302149772644, 0.018769361078739166, 0.025399405509233475, -0.07329719513654709, 0.05767997354269028, 0.014769896864891052, 0.018453199416399002, -0.02504727989435196, 0.014488477259874344, 0.045758575201034546, 0.06833405792713165, -0.014953500591218472, -0.050977643579244614, 0.0060098739340901375, 0.0025302518624812365, -0.03239748626947403, 0.04379844292998314, -0.0024356835056096315, 0.01643335446715355, -0.010084685869514942, -0.01648959144949913, -0.05534278228878975, -0.037567637860774994, 0.020751403644680977, -0.0454515665769577, 0.02308935672044754, -0.001983064226806164, -0.056676823645830154, -0.009147959761321545, -0.0021943035535514355, -0.005027375649660826, -0.03508380055427551, 0.08045005798339844, -0.003618411021307111, -0.02496727555990219, -0.02110946550965309, -0.01771417073905468, -0.018407754600048065, 0.03808855265378952, 0.0091524887830019, 0.01289639063179493, -0.023924032226204872, 0.02175358682870865, -0.009347299113869667, -0.008179093711078167, -0.0434882789850235, -0.04848466441035271, 0.0002171476517105475, -0.02735377475619316, -0.004043147433549166, -0.03151226043701172, 0.0060805510729551315, 0.025728436186909676, -0.033976517617702484, -0.010688013397157192, -0.007904907688498497, -0.08236344158649445, 0.016014566645026207, 0.006651213858276606, 0.02440362609922886, 0.021647054702043533, -0.014053158462047577, -0.06298473477363586, -0.011794419959187508, 0.05681588873267174, -0.05493463948369026, -0.006913784891366959, 0.005904556252062321, 0.054645851254463196, 0.05754823237657547, 0.023325899615883827, -0.0071138353087008, 0.052676010876894, 0.06144452095031738, -0.020200878381729126, 0.012585468590259552, -0.0045774769969284534, -0.025885358452796936, 0.045472804456949234, -0.020924020558595657, -0.0222861859947443, 0.002978753298521042, 0.009193838573992252, -0.04135917127132416, -0.04312973842024803, 0.03906266391277313, 0.08629044890403748 ]
<p>The following blue-cone <a href="http://en.wikipedia.org/wiki/Metric_expansion_of_space#Understanding_the_expansion_of_Universe" rel="nofollow">Wikipedia diagram</a> confuses me.</p> <p><img src="http://upload.wikimedia.org/wikipedia/commons/3/32/Embedded_LambdaCDM_geometry.png" alt=""></p> <p>At any point of cosmological time the encircling horizontal lines in the diagram are of finite circumference. That is indicative of a closed model of the universe.</p> <p>Queries: 1. Why does the author use a closed model of the universe to explain his point?</p> <p>2.Can we conclude "It is also possible for a distance to exceed the speed of light times the age of the universe, which means that light from one part of space generated near the beginning of the Universe........." if we draw the same diagram on a flat sheet of paper[instead of using the cone we take a flat surface],remembering that the null geodesics are always straight lines in the flat spacetime context? </p>
g5463
[ 0.008399778977036476, 0.03555397316813469, -0.0007850148249417543, -0.05392605811357498, 0.0421903133392334, 0.06558027118444443, 0.019062301144003868, -0.046307388693094254, -0.034078728407621384, -0.07842514663934708, 0.0717381089925766, -0.06821804493665695, 0.1134318858385086, 0.05935101583600044, 0.01597740687429905, -0.002555681159719825, 0.03652449697256088, -0.043150436133146286, 0.03648122027516365, -0.009144337847828865, 0.014403685927391052, -0.03789608180522919, 0.013501778244972229, -0.04058502987027168, -0.04151789844036102, -0.045703254640102386, 0.07158606499433517, -0.022026846185326576, -0.056754570454359055, -0.0036724170204252005, 0.0372406430542469, 0.03594550862908363, 0.07079920172691345, -0.015289204195141792, 0.00900192465633154, 0.016178227961063385, 0.013097723014652729, 0.022449064999818802, 0.06334029883146286, -0.009167241863906384, 0.01712034083902836, 0.011982208117842674, 0.0028150237631052732, -0.009783942252397537, 0.025955084711313248, -0.029913529753684998, -0.05994888022542, 0.04288803040981293, 0.03967234119772911, -0.04188342019915581, -0.0371919721364975, 0.0228462852537632, 0.04714229330420494, -0.02222898043692112, 0.01447715237736702, 0.053558100014925, 0.02230031043291092, -0.048894286155700684, 0.054732490330934525, 0.04156143590807915, -0.05929411202669144, 0.007967628538608551, 0.09978894144296646, 0.010470843873918056, 0.04139120131731033, 0.008815659210085869, 0.011124045588076115, -0.0778847262263298, 0.04865981638431549, -0.016948578879237175, 0.03640376031398773, -0.07232680916786194, -0.0068782055750489235, -0.06331058591604233, -0.032635413110256195, 0.09932669997215271, 0.00022733287187293172, 0.01213887333869934, -0.01570068672299385, 0.00613340875133872, -0.05891980603337288, 0.04533633962273598, -0.03258197754621506, -0.004158276133239269, 0.08002455532550812, 0.003626143094152212, -0.012759460136294365, -0.02471137046813965, -0.022037362679839134, 0.02464686892926693, -0.0055448017083108425, -0.029348991811275482, 0.0594925582408905, -0.03167423978447914, 0.004941087681800127, 0.0013769861543551087, -0.014118164777755737, 0.01276211254298687, -0.027218328788876534, 0.0011687707155942917, -0.07089699804782867, -0.004339487757533789, 0.041375529021024704, -0.030055787414312363, 0.035925764590501785, 0.02327321656048298, 0.002371643902733922, -0.026814917102456093, -0.0017466876888647676, -0.06429498642683029, -0.06852734088897705, -0.01331793237477541, -0.057465605437755585, -0.029222017154097557, -0.0012967509683221579, -0.052151765674352646, 0.035169146955013275, 0.06720201671123505, 0.03596147149801254, 0.016663460060954094, -0.012952810153365135, 0.01697431690990925, 0.0005363088566809893, 0.010321962647140026, -0.06658068299293518, -0.03658691793680191, -0.016757842153310776, -0.047615718096494675, -0.03678883612155914, -0.024598371237516403, -0.03283176198601723, 0.05258462205529213, -0.017080487683415413, 0.0736500695347786, 0.031885258853435516, -0.001180910738185048, 0.022012218832969666, -0.008753876201808453, -0.009031585417687893, 0.020769191905856133, -0.03727337718009949, -0.0562770813703537, 0.007193855941295624, -0.052470892667770386, 0.002046031877398491, 0.027881896123290062, 0.015304423868656158, -0.0014044466661289334, 0.02767208404839039, -0.022753823548555374, -0.028754210099577904, 0.11650712788105011, -0.0016053421422839165, 0.044552844017744064, -0.013319486752152443, -0.013849946670234203, 0.024991478770971298, -0.002759138122200966, -0.011831927113234997, -0.05901973322033882, 0.04372323304414749, 0.00012783956481143832, 0.00388898397795856, -0.014570953324437141, -0.02607899159193039, 0.04649164527654648, -0.04099110886454582, -0.1018807664513588, 0.010722202248871326, -0.0666327178478241, -0.07368350774049759, 0.0074414461851119995, 0.01154281571507454, 0.013862513937056065, 0.024608762934803963, -0.001491196220740676, 0.045891813933849335, 0.02271399274468422, -0.015453748404979706, -0.016313467174768448, -0.051328182220458984, -0.053941261023283005, 0.010815375484526157, 0.025021838024258614, -0.03297458589076996, -0.02774159610271454, 0.005973985884338617, -0.05427926778793335, -0.02405761182308197, -0.019901907071471214, 0.038332000374794006, -0.06805781275033951, 0.010197321884334087, 0.049823638051748276, 0.03274993970990181, 0.01833365298807621, 0.10290762037038803, -0.013241168111562729, -0.03156430274248123, -0.042631201446056366, -0.0018013966036960483, 0.05242297425866127, 0.043087027966976166, 0.0006289549637585878, -0.03098677471280098, -0.004530437756329775, 0.0027468963526189327, 0.0708729550242424, 0.02831554412841797, 0.04561322182416916, 0.008175568655133247, -0.0036364439874887466, 0.0285103227943182, -0.0002258889435324818, -0.04459865391254425, -0.02794426679611206, -0.037570636719465256, 0.018005838617682457, -0.023337580263614655, 0.042715635150671005, 0.017442487180233, -0.02760036662220955, 0.032570067793130875, -0.0397917702794075, 0.015262575820088387, -0.027968082576990128, -0.016188696026802063, -0.05625235289335251, -0.0127469627186656, 0.04795311018824577, -0.05028214305639267, -0.051021069288253784, 0.00019903275824617594, 0.02194058895111084, 0.044095780700445175, -0.041602037847042084, -0.0038212155923247337, 0.052998606115579605, -0.01960195228457451, 0.0051685213111341, 0.037144288420677185, -0.014242991805076599, -0.027628211304545403, -0.05842248350381851, 0.004093837458640337, -0.10329940915107727, -0.00465101795271039, -0.08103553205728531, -0.0384204164147377, 0.04124409705400467, 0.04739447683095932, 0.03189040347933769, 0.03229019418358803, 0.028143148869276047, 0.03605008125305176, -0.01198187842965126, -0.015051950700581074, 0.052020423114299774, -0.13040760159492493, -0.047578904777765274, 0.01700051873922348, -0.05174794793128967, -0.05290065333247185, -0.02705635130405426, -0.010587125085294247, 0.023230530321598053, -0.1082436665892601, -0.031089460477232933, -0.015753047540783882, -0.031546451151371, -0.035238053649663925, 0.029289469122886658, 0.01797007955610752, 0.03841486573219299, -0.00718814367428422, -0.023566804826259613, 0.024561207741498947, -0.02132367715239525, 0.002995199291035533, -0.017014576122164726, 0.020345507189631462, -0.011778953485190868, -0.038839906454086304, 0.048051707446575165, 0.025061314925551414, -0.04731401801109314, -0.03826018050312996, 0.014369196258485317, -0.010830201208591461, 0.01637442782521248, -0.0019329208880662918, 0.047536808997392654, -0.009661119431257248, 0.028330953791737556, -0.0011376147158443928, 0.04032599925994873, -0.029370440170168877, 0.025984201580286026, -0.035386234521865845, -0.028291165828704834, -0.034291353076696396, -0.018131742253899574, 0.009750664234161377, 0.018637025728821754, -0.0036993215326219797, 0.04508062079548836, 0.020962269976735115, -0.03161991760134697, -0.016078928485512733, -0.0023327008821070194, 0.008846325799822807, 0.006578958127647638, 0.012499014846980572, 0.023335177451372147, 0.020736418664455414, 0.015221631154417992, -0.020113129168748856, 0.0022291960194706917, 0.00412230147048831, 0.061674412339925766, 0.018356826156377792, 0.03948044031858444, -0.04225089028477669, 0.047441910952329636, -0.0093685919418931, -0.003988112322986126, -0.004383424762636423, -0.042222268879413605, -0.025684082880616188, 0.031275469809770584, 0.003961015027016401, -0.06519521027803421, 0.0060680946335196495, 0.024825898930430412, -0.06161891296505928, -0.009779214859008789, -0.029461251571774483, -0.02896936424076557, 0.06701298803091049, 0.018905870616436005, -0.035072118043899536, 0.012404181994497776, -0.030041221529245377, 0.024179385975003242, 0.04189252108335495, 0.036301083862781525, 0.0013434282736852765, -0.00278864661231637, -0.014109060168266296, -0.02192976325750351, 0.04456426948308945, 0.011089029721915722, -0.028376208618283272, -0.06626607477664948, 0.017074262723326683, 0.03850267454981804, -0.007561829406768084, 0.05412467569112778, -0.007637697737663984, -0.04022951424121857, 0.07430294156074524, 0.04836844280362129, 0.0017529679462313652, 0.008569932542741299, -0.022890480235219002, 0.03528938442468643, 0.01590554416179657, 0.0001768582296790555, -0.00040660944068804383, 0.009021257050335407, -0.005950912833213806, -0.034640874713659286, -0.051693785935640335, 0.048244018107652664, 0.05485738068819046, 0.0361526794731617, 0.018666908144950867, -0.022501055151224136, -0.0014637884451076388, 0.0650995746254921, 0.050838906317949295, 0.011790171265602112, 0.030290191993117332, 0.0020291288383305073, 0.00977501180022955, 0.043755922466516495, -0.05850593000650406, -0.057800427079200745, -0.003186867106705904, -0.06167123466730118, 0.07217077165842056, -0.034880563616752625, -0.005310630891472101, -0.013025025837123394, 0.009029899723827839, -0.036390483379364014, -0.025931892916560173, 0.010600090958178043, -0.009792102500796318, -0.008992251940071583, 0.033304162323474884, 0.001309136743657291, -0.012184467166662216, 0.005842913407832384, -0.032334815710783005, -0.05483127012848854, 0.020578274503350258, -0.0017737688031047583, 0.03305472061038017, -0.03753199055790901, 0.023931749165058136, 0.06012580543756485, -0.0036727602127939463, -0.06130043417215347, 0.09436299651861191, -0.004847344942390919, 0.050405167043209076, -0.07574234902858734, -0.0184890478849411, 0.04389260709285736, 0.013683597557246685, 0.04259549081325531, -0.012006552889943123, -0.004154092166572809, 0.03798980265855789, 0.04387441650032997, -0.006989053916186094, -0.03549275919795036, -0.01418452337384224, 0.007174760103225708, 0.021276718005537987, 0.022793719545006752, 0.0012725245906040072, 0.07580776512622833, -0.031357914209365845, 0.04953046143054962, 0.010466584004461765, 0.0950879380106926, -0.00953498762100935, -0.03768995404243469, 0.04459952563047409, -0.03666990250349045, 0.051047176122665405, -0.0479770265519619, -0.002441100310534239, 0.03539715334773064, -0.02855014055967331, -0.03639545291662216, -0.010903079062700272, -0.03804032877087593, -0.0148264579474926, 0.0227174274623394, 0.03015502169728279, -0.014318212866783142, 0.046746134757995605, -0.05994920805096626, 0.023339632898569107, 0.037918731570243835, 0.018292754888534546, 0.07680016756057739, -0.03772003576159477, 0.009639384225010872, -0.0024750656448304653, 0.01525199506431818, 0.05000091344118118, -0.0016127163544297218, -0.0312701053917408, -0.011382587254047394, -0.010921589098870754, -0.017648713663220406, -0.0012650408316403627, 0.021297773346304893, 0.03161873295903206, -0.003573762718588114, -0.059114668518304825, 0.06006445735692978, -0.03276011720299721, 0.01731047034263611, -0.0496540367603302, -0.02151102013885975, -0.004714551847428083, -0.017723452299833298, 0.03495701774954796, 0.006452696397900581, 0.04712069407105446, 0.036339569836854935, 0.01276442687958479, 0.015287481248378754, -0.014525864273309708, -0.001933342544361949, 0.03743808716535568, -0.07302502542734146, 0.03477175161242485, 0.023642992600798607, -0.019616249948740005, -0.003938630688935518, 0.06903932988643646, 0.003961475566029549, 0.0013610278256237507, -0.02237502858042717, 0.001550226821564138, 0.04287627339363098, 0.039880551397800446, -0.029555097222328186, -0.016024546697735786, 0.04478096961975098, 0.005495220888406038, -0.020838342607021332, -0.007563575636595488, -0.0016569975996389985, 0.012819255702197552, -0.013867503963410854, 0.009288539178669453, 0.07128830999135971, 0.03469173610210419, -0.05300431326031685, -0.05469633266329765, -0.0005584656028077006, 0.01313192117959261, -0.03284190967679024, -0.022811248898506165, 0.02140721306204796, 0.03800209239125252, -0.00179377687163651, 0.0481390543282032, 0.054067134857177734, -0.0273380558937788, -0.02183692343533039, 0.050876837223768234, 0.024760419502854347, 0.008721529506146908, 0.040775999426841736, -0.0016507209511473775, -0.05075782537460327, -0.012664617039263248, 0.027850838378071785, 0.023075824603438377, 0.018244614824652672, 0.08770971745252609, -0.05875866115093231, 0.013680698350071907, -0.03802609071135521, -0.0056184870190918446, 0.041193436831235886, 0.03514004126191139, 0.0343300960958004, -0.03412840515375137, 0.004415161907672882, 0.01566537655889988, -0.03723413869738579, -0.028604280203580856, -0.020238172262907028, 0.02227676659822464, 0.024393443018198013, -0.0514228418469429, 0.02415742725133896, 0.016578122973442078, 0.00004736783739645034, -0.048478517681360245, -0.02371988259255886, -0.00102661841083318, 0.054824817925691605, 0.01179847028106451, 0.002257696585729718, -0.03390691056847572, -0.047210805118083954, -0.013884777203202248, 0.020853634923696518, 0.08893393725156784, -0.027887269854545593, 0.03132003918290138, -0.0034301115665584803, 0.03402886167168617, 0.0423918291926384, 0.0128174414858222, 0.035113949328660965, 0.03471110388636589, -0.0022089025005698204, -0.06640616804361343, -0.005462222266942263, -0.02147730253636837, -0.055493079125881195, 0.060773689299821854, -0.03942093253135681, 0.030470656231045723, 0.019389407709240913, -0.03948908671736717, -0.022117165848612785, 0.034005776047706604, -0.04792698472738266, 0.0004858927277382463, -0.010591669008135796, 0.019415345042943954, -0.00002606812813610304, -0.032001081854104996, -0.008487165905535221, -0.01784227043390274, 0.025944950059056282, -0.0934232696890831, -0.017493871971964836, -0.051661115139722824, 0.017444990575313568, 0.013491945341229439, -0.03159668669104576, 0.06092843785881996, 0.012603565119206905, -0.040476713329553604, -0.003984787967056036, 0.025196710601449013, -0.05960806831717491, 0.03077777288854122, 0.050235893577337265, -0.00878371112048626, 0.029689565300941467, -0.01076437346637249, -0.018386729061603546, 0.00023229360522236675, -0.030294639989733696, -0.031051013618707657, 0.003488717135041952, 0.00772405369207263, 0.012835236266255379, 0.035708118230104446, -0.0007489495328627527, -0.028625845909118652, 0.022971926257014275, -0.025937912985682487, 0.04155859351158142, 0.006484870333224535, 0.0347696952521801, -0.01073574647307396, 0.01858210563659668, -0.03637906163930893, 0.030727609992027283, 0.010109423659741879, 0.04024280235171318, -0.028623970225453377, 0.03347715362906456, 0.03226480260491371, 0.02173013985157013, -0.005655896849930286, 0.0022104450035840273, 0.04919237643480301, 0.04592490941286087, -0.02628994546830654, -0.03259194269776344, 0.009256433695554733, -0.05669170618057251, -0.015225900337100029, -0.008092383854091167, 0.009395363740622997, -0.042749203741550446, -0.07541138678789139, -0.021060338243842125, -0.002518970984965563, -0.0007332543027587235, -0.055766187608242035, 0.008989435620605946, -0.02817065641283989, -0.07322821766138077, 0.008540446870028973, -0.019895005971193314, 0.00872028898447752, -0.010167978703975677, -0.026855165138840675, 0.02173628658056259, 0.009118052199482918, -0.012632605619728565, -0.0465543270111084, -0.04342977702617645, -0.04526285082101822, 0.02227061800658703, -0.02407931163907051, -0.0005959462141618133, 0.03515378385782242, 0.004132989794015884, -0.04397544637322426, -0.0012665950926020741, 0.04234711080789566, -0.04380248859524727, 0.014689117670059204, 0.06076756492257118, -0.030453171581029892, 0.02305332012474537, -0.03482476994395256, 0.021386243402957916, 0.018609996885061264, -0.0010041672503575683, -0.03655525669455528, -0.017312729731202126, 0.03181757032871246, 0.026995060965418816, -0.047024764120578766, -0.020370565354824066, 0.09896964579820633, -0.014138519763946533, 0.0053899153135716915, 0.04651927947998047, 0.00921622198075056, -0.03703221678733826, 0.0050734528340399265, -0.033723898231983185, -0.06106318160891533, 0.0005148054915480316, 0.03011508658528328, -0.031114261597394943, -0.018922453746199608, 0.01472350861877203, -0.026976563036441803, -0.05282498896121979, -0.001253166003152728, 0.0057504489086568356, -0.017513304948806763, 0.00476647075265646, -0.021521277725696564, 0.031476330012083054, 0.03230191022157669, -0.013783779926598072, -0.03198256343603134, -0.03762968257069588, -0.024080224335193634, -0.059145234525203705, -0.0017788374098017812, -0.03773149847984314, -0.005810493603348732, 0.013288024812936783, -0.018556633964180946, 0.02574971504509449, -0.015454129315912724, -0.002444277983158827, -0.01891883835196495, 0.0044694580137729645, -0.021838918328285217, 0.007616071030497551, -0.07963500916957855, 0.01797335036098957, -0.009468906559050083, -0.017511481419205666, 0.006416902877390385, 0.0013275444507598877, -0.07314374297857285, -0.02925545908510685, 0.0094878189265728, 0.032512687146663666, -0.009505867026746273, -0.0483635812997818, -0.06141401454806328, 0.005964762531220913, 0.05964723974466324, 0.0352344810962677, 0.02461392432451248, 0.013788474723696709, 0.025381339713931084, 0.011584551073610783, 0.04163634404540062, -0.014466400258243084, 0.01104777492582798, -0.041612476110458374, 0.031210729852318764, -0.01688665896654129, -0.004957299679517746, -0.0011428927537053823, 0.04815591126680374, 0.03315300866961479, 0.013565012253820896, -0.019546516239643097, -0.02655463106930256, 0.03477957099676132 ]
<p>Some authorities have stated publicly and without explanation that if the theories of Special and General Relativity were not taken into account in the design of the <a href="http://en.wikipedia.org/wiki/Global_Positioning_System#History" rel="nofollow">GPS</a> (by building the satellite clocks to run 38us/day slower than GPS time before launch aka 'the factory offset), the position indicated by an earthbound GPS user device would drift by about 11km/day. I've considered this for various GPS models but can only predict much smaller effects. That multiplying the 38us/day uncorrected difference from GPS time by the speed of light yields 11.6km/day, does not for me seem to relate to GPS receiver function. Please reply with references if possible. I'd be very glad for any pointers.</p>
g5464
[ -0.021484877914190292, 0.06425606459379196, -0.02547004260122776, 0.03504767268896103, 0.00508167315274477, 0.008085466921329498, 0.08290524780750275, 0.0256350040435791, 0.010778076015412807, -0.02843744494020939, 0.03205939754843712, -0.016425246372818947, 0.05451975017786026, -0.001518990145996213, 0.008273422718048096, 0.034355055540800095, 0.0829223245382309, 0.01224310602992773, 0.036762136965990067, 0.032820407301187515, 0.07748188823461533, 0.023635299876332283, -0.03638627752661705, -0.007515975274145603, -0.029884377494454384, -0.028234459459781647, 0.065187469124794, -0.029068272560834885, -0.06671769917011261, 0.026157421991229057, 0.02266796864569187, -0.03812169283628464, -0.005569394677877426, -0.05112042650580406, 0.011023705825209618, 0.007735102437436581, -0.010543493553996086, 0.027816159650683403, -0.04308715835213661, 0.004787364974617958, 0.00786811113357544, -0.029346121475100517, -0.010231236927211285, 0.015161984600126743, 0.03158248960971832, -0.0002526536991354078, 0.02023313008248806, 0.004049751441925764, -0.00455770967528224, -0.011570136994123459, -0.06660955399274826, 0.05153599753975868, 0.005161557346582413, 0.03081645257771015, 0.03232412412762642, 0.014911537058651447, -0.009532887488603592, 0.0421660952270031, -0.017571335658431053, 0.019652044400572777, 0.02801012247800827, -0.03375103324651718, 0.018933437764644623, 0.0031467897351831198, 0.02474880963563919, -0.025521311908960342, -0.008936436846852303, -0.04602774232625961, -0.013193143531680107, 0.005169372074306011, 0.00944572500884533, 0.0476868599653244, -0.06351135671138763, -0.03253643587231636, 0.047850437462329865, 0.03521998971700668, 0.034788861870765686, -0.015119170770049095, 0.010475657880306244, 0.0730801448225975, -0.01976613700389862, 0.031210143119096756, -0.01817350648343563, 0.0312078595161438, 0.05712493136525154, 0.018968870863318443, -0.026939883828163147, 0.05796894058585167, 0.06837987899780273, 0.02285296469926834, 0.02334349974989891, -0.029588406905531883, 0.07083403319120407, 0.027328265830874443, -0.04982035979628563, 0.0004125487757846713, -0.029971716925501823, 0.024750331416726112, -0.021938472986221313, 0.047393277287483215, -0.04361584410071373, 0.031620897352695465, -0.03729650005698204, 0.014349422417581081, -0.026057135313749313, -0.03406751528382301, 0.00200700294226408, 0.026215532794594765, -0.010452987626194954, -0.02096235752105713, 0.0625605657696724, -0.060229647904634476, 0.012727651745080948, -0.015950964763760567, -0.018673313781619072, -0.05422038212418556, -0.019910456612706184, -0.04242553934454918, -0.010254624299705029, -0.03852808475494385, -0.020025234669446945, 0.02565782703459263, -0.05612878128886223, 0.05788491293787956, -0.037272658199071884, -0.003291283966973424, -0.0153763797134161, 0.00441559124737978, -0.020357713103294373, 0.08117348700761795, -0.02502451464533806, -0.05522069334983826, -0.01983344368636608, 0.028377695009112358, -0.044836778193712234, 0.004478130955249071, 0.04622666910290718, -0.0037558304611593485, -0.0351497046649456, 0.02979285642504692, 0.010678138583898544, -0.06226074695587158, 0.07020778208971024, -0.06906851381063461, -0.034180525690317154, 0.05374213680624962, 0.016976505517959595, 0.026776010170578957, 0.007305905222892761, 0.039403285831213, -0.012266133911907673, 0.03697013109922409, 0.05147261917591095, 0.04920252785086632, 0.024485042318701744, -0.004933807998895645, -0.009437136352062225, 0.009273438714444637, -0.011365328915417194, -0.00028859174926765263, 0.06269823759794235, -0.03311934322118759, 0.029898984357714653, -0.009147305972874165, -0.07238417863845825, -0.029807094484567642, 0.021408600732684135, -0.04630783945322037, -0.01841898448765278, -0.07451055198907852, -0.01490714866667986, -0.012092890217900276, 0.020449236035346985, 0.027428098022937775, -0.027991270646452904, 0.04651626944541931, 0.04972386732697487, -0.004604119807481766, -0.029050283133983612, 0.025345753878355026, -0.0037086252123117447, -0.03835488483309746, -0.01208218652755022, -0.005406707059592009, -0.02368718758225441, -0.020476752892136574, -0.030536489561200142, -0.08717581629753113, -0.08891643583774567, 0.022096766158938408, -0.01749144308269024, 0.01803925260901451, 0.007805997040122747, 0.04554930701851845, -0.0381353422999382, 0.023493679240345955, -0.0324832946062088, -0.030732301995158195, 0.007364931516349316, 0.07470304518938065, -0.023123232647776604, 0.0342356339097023, 0.042976606637239456, -0.010311892256140709, 0.04318629205226898, -0.0650637075304985, 0.03068704716861248, -0.003482494270429015, 0.030190087854862213, -0.042094193398952484, -0.001344427466392517, 0.008652384392917156, 0.027079368010163307, 0.00542782386764884, 0.051094260066747665, -0.005568261723965406, -0.006093049421906471, 0.007246026769280434, 0.03678435459733009, 0.03520181030035019, -0.016278542578220367, 0.04907415062189102, 0.00557253323495388, 0.029253605753183365, -0.0044135223142802715, -0.023507894948124886, 0.001227047061547637, -0.009398909285664558, 0.0023602975998073816, 0.00039923327858559787, 0.021742992103099823, -0.00538224121555686, -0.05474020913243294, -0.04878060892224312, 0.04965713620185852, 0.056837718933820724, 0.005421856418251991, -0.00763244554400444, 0.061195116490125656, 0.050975434482097626, 0.010973101481795311, 0.0014628262724727392, -0.01967746578156948, -0.02047910913825035, -0.002545539988204837, -0.06117093190550804, 0.003582388162612915, -0.014130836352705956, -0.056654173880815506, 0.002956296317279339, -0.0034254472702741623, 0.006342421285808086, 0.011300218291580677, -0.06687232106924057, 0.0004922735970467329, 0.03577468544244766, -0.00883398111909628, 0.008791333064436913, -0.06855084002017975, -0.018097080290317535, -0.09250039607286453, 0.0016810576198622584, 0.0324917808175087, 0.045268163084983826, 0.023131513968110085, -0.04584571719169617, -0.025582635775208473, 0.012402360327541828, -0.028505565598607063, -0.018974650651216507, 0.04587792605161667, -0.05449090898036957, 0.035403989255428314, 0.07640654593706131, -0.026298362761735916, -0.003604779951274395, 0.025540001690387726, -0.027042977511882782, -0.00045721212518401444, 0.045035094022750854, 0.005914854351431131, 0.010643926449120045, -0.0794534757733345, -0.03313031047582626, 0.026559455320239067, -0.06079355627298355, -0.0033981071319431067, 0.047863710671663284, 0.019901324063539505, -0.005821261089295149, -0.01510505098849535, 0.04516594856977463, 0.08574485778808594, 0.01102789118885994, 0.04359068349003792, 0.06113739311695099, -0.0030864435248076916, -0.03283194079995155, -0.010181893594563007, -0.006169519387185574, 0.0993894636631012, 0.0018448643386363983, 0.0024483713787049055, -0.010832640342414379, -0.030064690858125687, -0.02104613371193409, -0.01540630217641592, -0.009952087886631489, -0.03715626150369644, -0.06295537203550339, 0.0685555636882782, 0.04625499248504639, -0.002728378167375922, -0.02768799103796482, 0.003441323060542345, -0.03483051434159279, -0.034782830625772476, 0.03742124140262604, 0.009927192702889442, 0.016496358439326286, 0.029189331457018852, -0.05761510506272316, -0.02816525660455227, -0.02968461439013481, 0.02453489974141121, 0.05981633812189102, 0.024662917479872704, 0.015522352419793606, -0.013026275672018528, 0.043459367007017136, -0.0016745642060413957, 0.028943046927452087, -0.04500634968280792, -0.015693211928009987, -0.03519900515675545, 0.010938792489469051, 0.06005989760160446, 0.05472546070814133, -0.020185960456728935, 0.036165136843919754, -0.04501618072390556, -0.0056826649233698845, -0.020360048860311508, 0.001550159533508122, -0.016290612518787384, 0.028892653062939644, 0.00969650037586689, -0.018623534590005875, -0.051069822162389755, 0.01781490072607994, 0.05231030285358429, -0.098530612885952, -0.022008301690220833, 0.010786542668938637, 0.029917748644948006, 0.05534464865922928, -0.014084245078265667, 0.06866317242383957, -0.01651795022189617, -0.02667362429201603, 0.012373559176921844, 0.04665973410010338, 0.024612538516521454, 0.04818343371152878, 0.02861134521663189, 0.048580415546894073, -0.01733335107564926, 0.041039466857910156, -0.017316604033112526, -0.029845884069800377, -0.022052576765418053, 0.03299498185515404, 0.0190135445445776, -0.06151757389307022, 0.06570882350206375, 0.015379922464489937, 0.041300997138023376, -0.012040014378726482, -0.019633788615465164, 0.037562888115644455, 0.02082044631242752, 0.03782813251018524, -0.0303095243871212, -0.04558071494102478, 0.04877359792590141, -0.05256448686122894, 0.007956566289067268, -0.012101645581424236, -0.03845498338341713, -0.020528379827737808, -0.054782550781965256, -0.005619743838906288, -0.00936286710202694, -0.010787567123770714, -0.012704446911811829, 0.04206949844956398, 0.041772834956645966, 0.03141054883599281, 0.027742773294448853, 0.016583958640694618, 0.012355944141745567, 0.03800107538700104, -0.013532052747905254, 0.022685807198286057, -0.026000751182436943, -0.038797445595264435, -0.002816258929669857, -0.04000917449593544, -0.049230463802814484, 0.02231547050178051, -0.03880222141742706, 0.020015578716993332, -0.033490657806396484, -0.04461795836687088, 0.05528923124074936, 0.0879453495144844, 0.0026609008200466633, -0.01120784506201744, 0.07077383249998093, 0.03535708785057068, -0.010390108451247215, 0.10812631249427795, 0.04107359051704407, -0.02150597609579563, -0.006038305815309286, 0.03463118523359299, -0.003784686326980591, 0.003116304986178875, 0.022531144320964813, -0.00041751048411242664, 0.03405972197651863, 0.004727581515908241, 0.0264135729521513, 0.10323860496282578, -0.07089655101299286, 0.02921023964881897, 0.06244128197431564, 0.04341062903404236, 0.0747593566775322, 0.0438765250146389, 0.0035147019661962986, -0.01082407683134079, 0.01774435117840767, 0.01831492967903614, -0.024879800155758858, 0.07746994495391846, -0.058022502809762955, -0.03995047137141228, 0.014224277809262276, -0.01307788398116827, 0.01007079053670168, -0.002188589423894882, 0.004916094709187746, 0.0032637338154017925, -0.019184336066246033, 0.06042914092540741, -0.010987462475895882, 0.024642763659358025, 0.0405692420899868, 0.004120541270822287, -0.02207208424806595, -0.036354340612888336, -0.010809632949531078, 0.019227635115385056, -0.02924509160220623, 0.00354627869091928, 0.00922772940248251, 0.006811080034822226, -0.0483650304377079, 0.012575059197843075, -0.025022262707352638, -0.039363984018564224, 0.01773812808096409, 0.0794067308306694, 0.012055536732077599, 0.014789953827857971, 0.0034541974309831858, -0.021151626482605934, 0.029030239209532738, 0.008345427922904491, -0.04600454866886139, 0.051285624504089355, 0.031350113451480865, -0.04768376424908638, 0.02690552920103073, -0.008110352791845798, -0.03675337880849838, -0.014849887229502201, -0.018851373344659805, -0.0461433045566082, 0.0015702522359788418, -0.09531524777412415, 0.006948044989258051, -0.0631905272603035, -0.005136057734489441, 0.02454613335430622, 0.030729172751307487, 0.040206968784332275, -0.029541583731770515, -0.07338336855173111, -0.077372707426548, 0.015654927119612694, 0.040508512407541275, -0.02352592535316944, -0.01994231902062893, 0.07260721921920776, 0.08749232441186905, -0.01017762254923582, -0.03308947756886482, 0.025610532611608505, -0.04829707741737366, 0.044245023280382156, -0.04172839596867561, -0.03410322591662407, 0.012007927522063255, -0.07432548701763153, -0.02832983061671257, 0.024220937862992287, 0.036719657480716705, -0.0499734953045845, -0.005440852604806423, -0.012201504781842232, 0.0622236430644989, 0.04631936177611351, 0.000004763307970279129, -0.00006956674042157829, 0.009489844553172588, -0.04880870506167412, -0.028305210173130035, -0.013173215091228485, 0.012942347675561905, 0.017287010326981544, -0.011586888693273067, -0.003676280379295349, 0.02399703674018383, -0.009795933030545712, 0.05297804996371269, -0.007683834061026573, 0.05151328071951866, -0.06469357758760452, -0.07181302458047867, 0.02065209113061428, 0.031969454139471054, 0.050355780869722366, -0.03574535995721817, -0.04897724837064743, -0.07171637564897537, 0.02663048729300499, 0.026121417060494423, -0.07225559651851654, -0.04360928386449814, -0.015527577139437199, -0.01614336296916008, 0.0456693060696125, -0.034677717834711075, 0.029219064861536026, 0.002829623408615589, 0.06123580038547516, -0.05027105286717415, -0.04104353114962578, 0.0004924843087792397, 0.024454861879348755, 0.027885688468813896, 0.03701024875044823, 0.04099978134036064, -0.0526493676006794, 0.01581397093832493, -0.010164078325033188, 0.06463859975337982, 0.019500667229294777, 0.014643009752035141, -0.02951720729470253, -0.04350176081061363, 0.016252310946583748, -0.05089961737394333, -0.018791647627949715, 0.01918017864227295, -0.0770459994673729, -0.044463206082582474, -0.008091898635029793, -0.04326126351952553, -0.03824487328529358, 0.011176418513059616, -0.03391997143626213, -0.005491210613399744, 0.013017692603170872, -0.03459921106696129, -0.016735533252358437, -0.036784280091524124, -0.013317647390067577, 0.02344079129397869, 0.03311844542622566, 0.0106831518933177, -0.00039111924706958234, -0.06056330353021622, -0.04104049131274223, -0.013255958445370197, 0.019472969695925713, -0.02494303323328495, -0.02925514243543148, -0.024104535579681396, 0.012107277289032936, 0.06924568861722946, -0.018087616190314293, 0.07032330334186554, 0.01945059560239315, -0.03893887251615524, -0.02122398652136326, 0.07461576163768768, -0.0510585680603981, 0.03315063193440437, 0.003946399781852961, 0.036439355462789536, -0.000626835273578763, -0.042086418718099594, -0.04694921150803566, 0.029066573828458786, 0.04070266708731651, -0.02887664921581745, -0.011248080059885979, 0.05809057503938675, 0.03636512905359268, -0.026844913139939308, 0.01359875500202179, -0.0009700441733002663, 0.03540817275643349, 0.008215773850679398, -0.06543699651956558, -0.017805112525820732, 0.00242939917370677, -0.005641041789203882, -0.018790051341056824, -0.029769282788038254, -0.029062271118164062, 0.02937537431716919, 0.02580271102488041, -0.01787152886390686, -0.0013676909729838371, -0.04699498787522316, -0.021781401708722115, -0.025408003479242325, -0.05557265505194664, -0.03618071228265762, 0.011844497174024582, -0.048270415514707565, -0.014718741178512573, -0.012495129369199276, 0.010470344685018063, 0.0626998245716095, 0.005957744549959898, -0.04877076670527458, -0.08418157696723938, -0.010171160101890564, 0.0029833370354026556, 0.03276641666889191, 0.00034268060699105263, 0.0065662916749715805, 0.04564176872372627, 0.007231913506984711, -0.04076734557747841, -0.033345744013786316, -0.007041239179670811, -0.00618578540161252, 0.018750926479697227, -0.015892012044787407, -0.004543917719274759, -0.03898334875702858, -0.04886818304657936, -0.03534112870693207, 0.02003190852701664, -0.030271101742982864, -0.011742020957171917, -0.03453449159860611, -0.005158238112926483, 0.017704380676150322, 0.00646202452480793, -0.05818704143166542, -0.0850701555609703, -0.053792040795087814, 0.0321318581700325, 0.022975824773311615, 0.03805208578705788, -0.01733514666557312, -0.01321946457028389, -0.027507036924362183, 0.04604591056704521, -0.06615111976861954, 0.018898729234933853, 0.03102908656001091, -0.023285428062081337, -0.02572403848171234, 0.03209865838289261, -0.04460681602358818, -0.014513920061290264, -0.020431188866496086, 0.022639837116003036, -0.009966879151761532, 0.02207411825656891, 0.003180956933647394, -0.026411045342683792, 0.00246423645876348, -0.009288112632930279, 0.03733423352241516, 0.017245711758732796, 0.022361064329743385, 0.016156615689396858, -0.018843790516257286, -0.04585561901330948, -0.030731869861483574, -0.01699305698275566, -0.008320961147546768, -0.01379642728716135, -0.05324956402182579, -0.0029540539253503084, 0.01470478530973196, -0.021045193076133728, 0.010174121707677841, -0.02733745239675045, -0.022792762145400047, -0.03778041899204254, -0.018553026020526886, -0.023624463006854057, 0.010385341010987759, -0.06897171586751938, -0.0002832497702911496, -0.018159765750169754, -0.001545248436741531, -0.05384884029626846, 0.0096428906545043, -0.0600568987429142, 0.02376505360007286, -0.004490587394684553, -0.022516202181577682, -0.012537595815956593, 0.025948816910386086, 0.014092023484408855, -0.008648951537907124, -0.043013084679841995, -0.06657186150550842, 0.020337609574198723, -0.02468128874897957, -0.031382083892822266, -0.017548037692904472, 0.024993110448122025, -0.02144787646830082, 0.005571736954152584, 0.028158677741885185, 0.07241564244031906, -0.00959856528788805, -0.029529500752687454, 0.020846420899033546, 0.11842755228281021, -0.017221471294760704, -0.02470448985695839, -0.01667039282619953, -0.011850560083985329, -0.0034550444688647985, 0.005382869858294725, 0.02924245409667492, -0.009007485583424568, -0.011358465068042278, -0.019003797322511673, 0.012990262359380722, 0.02880747988820076, 0.01360364630818367, -0.04175294563174248, 0.04755937680602074, 0.009076817892491817 ]
<p>I was running the washing up water this morning, and started to think about why the cold tap isn't hot, and why the water doesn't get hotter the faster it is flowing (if anything, the cold tap gets colder the faster it flows).</p> <p>From my understanding</p> <p>$K.E = \frac{mv^2}{2}$</p> <p>and temperature is directly proportional to kinetic energy.</p> <p>I know that the $v$ in the above equation is really the mean speed of the particles and therefore some are moving backwards and some moving forwards, it is the speed that is used. But surely the particles of water in the tap are all moving faster, therefore they should all be hotter. Perhaps the particles in the stream are moving at a much higher mean speed than the water is flowing, so the temperature increase is negligible... Am I correct in thinking this? or otherwise, why doesn't the cold tap get hot the more you turn it on?</p>
g5465
[ 0.0649079903960228, -0.010388835333287716, -0.006248839199542999, 0.03809528052806854, 0.044108662754297256, 0.02707487903535366, 0.048856232315301895, 0.04442053660750389, -0.037080999463796616, -0.048996683210134506, 0.011217067018151283, 0.0491337776184082, 0.047034528106451035, 0.07794506847858429, -0.057021062821149826, -0.011857355013489723, 0.054402291774749756, -0.013038577511906624, 0.03143377974629402, 0.0769224762916565, -0.020845143124461174, -0.023031996563076973, -0.004101867321878672, -0.040330905467271805, 0.027937965467572212, 0.001187097979709506, -0.027262357994914055, 0.014119021594524384, -0.029064515605568886, -0.005598363000899553, 0.03797968849539757, 0.03966400399804115, -0.040872689336538315, -0.016595520079135895, -0.02485242299735546, -0.022871948778629303, 0.060422204434871674, -0.012597513385117054, -0.012181439436972141, -0.03340590000152588, 0.019652077928185463, 0.04430525749921799, 0.052960798144340515, 0.03401371091604233, -0.02155277319252491, 0.010899675078690052, -0.017512788996100426, 0.02565675415098667, -0.09946814924478531, -0.007241419050842524, -0.050938930362463, -0.037409745156764984, -0.004239244386553764, 0.07473606616258621, -0.03346193581819534, -0.01252358965575695, -0.034045737236738205, -0.014270124025642872, 0.008747607469558716, 0.09004777669906616, 0.016468985006213188, -0.004765321034938097, 0.0024228799156844616, -0.008931268006563187, -0.023696117103099823, -0.006368906702846289, 0.009697223082184792, -0.01509644091129303, 0.03031068481504917, 0.030563989654183388, -0.0369669534265995, -0.03805437684059143, -0.07282346487045288, -0.04575687274336815, 0.022087987512350082, -0.030482947826385498, -0.02339472807943821, -0.048950064927339554, 0.03589819371700287, -0.036303192377090454, 0.006633854936808348, 0.04588986560702324, -0.013741634786128998, -0.011082399636507034, 0.00946294330060482, -0.00586998276412487, -0.03574592247605324, 0.06391764432191849, 0.020405208691954613, 0.02211279794573784, 0.0007901567732915282, -0.034570131450891495, 0.10019179433584213, 0.015696438029408455, -0.04029986634850502, -0.06215020641684532, -0.04603217914700508, -0.0025624691043049097, -0.04035428911447525, 0.015543882735073566, 0.007792027201503515, -0.04016292467713356, 0.07347207516431808, -0.014534994028508663, 0.013188911601901054, -0.020472902804613113, -0.0187041275203228, 0.0029541808180510998, -0.04446105286478996, -0.022584812715649605, -0.0007682870491407812, -0.08504462987184525, -0.04839543253183365, -0.007526758126914501, 0.009845779277384281, -0.012249751016497612, -0.0039664930664002895, 0.04187251254916191, -0.018661800771951675, 0.05693453177809715, -0.025709092617034912, 0.05140310898423195, -0.07976104319095612, 0.04601433873176575, -0.01232899446040392, 0.013492199592292309, 0.0083009023219347, 0.019920751452445984, -0.016719495877623558, 0.0009320047684013844, -0.05573028698563576, 0.05776691809296608, 0.0028996316250413656, 0.007584766484797001, 0.03484974056482315, 0.034062329679727554, -0.012000124901533127, 0.008375423960387707, 0.01622278057038784, -0.00843651033937931, 0.044667426496744156, -0.025028323754668236, -0.007069764658808708, -0.028205066919326782, -0.08830410987138748, 0.07027582079172134, -0.08204422891139984, -0.05150409787893295, 0.044934775680303574, 0.033504560589790344, 0.007899969816207886, 0.005253656301647425, 0.034839652478694916, -0.046073682606220245, 0.057543348520994186, 0.009309821762144566, 0.040691107511520386, -0.06026130169630051, 0.025020534172654152, -0.005107314791530371, 0.014066416770219803, -0.016470691189169884, 0.05986397713422775, 0.00564105249941349, -0.06235808506608009, -0.013366042636334896, 0.00584307499229908, -0.025051282718777657, -0.019385749474167824, -0.004009847994893789, -0.05236365646123886, 0.013882257044315338, -0.05633765086531639, 0.023021144792437553, 0.005952958017587662, -0.037730395793914795, 0.027174945920705795, -0.005679178051650524, -0.020873991772532463, 0.005508045665919781, -0.03272456303238869, -0.008995584212243557, 0.01685217209160328, -0.06078378111124039, 0.023569488897919655, 0.007460348308086395, -0.07156861573457718, 0.007984313182532787, -0.017146367579698563, -0.05311448872089386, -0.00465985294431448, 0.007726745214313269, 0.0130566181614995, 0.07207734137773514, 0.014228194952011108, -0.02754346840083599, -0.0743422582745552, -0.012918121181428432, -0.028572341427206993, 0.017832720652222633, -0.0013038974720984697, 0.0010093257296830416, -0.0010352479293942451, -0.009374711662530899, 0.05437026917934418, 0.02288724109530449, -0.03427218645811081, -0.026029251515865326, -0.019998569041490555, -0.04147900640964508, 0.0059515079483389854, 0.038243673741817474, -0.016894573345780373, -0.012665453366935253, -0.008106624707579613, 0.047395989298820496, 0.01466601062566042, 0.004812730010598898, -0.027275996282696724, 0.016749124974012375, -0.04064536094665527, -0.005031997803598642, 0.028047651052474976, 0.0027770770248025656, -0.09325195848941803, -0.019558288156986237, -0.06351236999034882, -0.0414535216987133, -0.03232806548476219, 0.09490067511796951, -0.024193160235881805, 0.03654411807656288, -0.013245537877082825, -0.0008038189262151718, 0.0187555942684412, 0.024688176810741425, 0.010925529524683952, 0.024303244426846504, 0.048454318195581436, 0.033072564750909805, 0.0008948954637162387, -0.05348683148622513, 0.004587207920849323, 0.046600136905908585, -0.0007644169381819665, -0.02400312013924122, 0.050242822617292404, -0.042537249624729156, 0.0025611126329749823, -0.003358958289027214, 0.04774438962340355, -0.018941709771752357, -0.031232090666890144, 0.0023385595995932817, 0.013060948811471462, -0.033668432384729385, -0.022416939958930016, 0.0737413763999939, -0.02249300107359886, -0.06193522736430168, -0.007390868850052357, -0.023366674780845642, -0.0009847318287938833, 0.0059009213000535965, -0.0261272881180048, 0.06234797090291977, -0.06742234528064728, 0.021713124588131905, -0.01018046960234642, 0.022916361689567566, 0.004534950014203787, 0.01962415501475334, -0.040276847779750824, 0.013955429196357727, -0.04844869673252106, -0.028380541130900383, 0.031252775341272354, 0.00040030290256254375, 0.06728915125131607, -0.06357726454734802, -0.04743725061416626, 0.018117841333150864, -0.018883168697357178, -0.04122218117117882, 0.054898910224437714, -0.02710329182446003, -0.021632490679621696, -0.0209139883518219, 0.0001155359495896846, -0.024310113862156868, 0.020421670749783516, 0.004013440106064081, 0.05635193735361099, 0.023824818432331085, 0.012115933001041412, 0.017471661791205406, 0.06437661498785019, -0.0825422927737236, 0.010226228274405003, 0.024515671655535698, 0.04872848838567734, 0.009685168042778969, 0.0016417251899838448, -0.025249363854527473, 0.025469264015555382, 0.03513568639755249, -0.05076690390706062, -0.056997932493686676, -0.038190629333257675, -0.0334097295999527, 0.08428674191236496, 0.02527540922164917, -0.02928563579916954, -0.0035606110468506813, -0.01795019581913948, -0.01505490392446518, -0.05835220590233803, 0.046605173498392105, 0.04880315810441971, 0.01901821605861187, -0.03172548487782478, 0.0335199199616909, 0.016892729327082634, 0.003559206845238805, -0.0036342127714306116, -0.00990771409124136, -0.0040735239163041115, -0.01088804192841053, 0.01218518614768982, -0.003401718335226178, -0.009226411581039429, -0.0021488789934664965, 0.025248989462852478, -0.007376058027148247, -0.019032415002584457, -0.0327913872897625, 0.027272682636976242, 0.024689221754670143, 0.03466576710343361, 0.03557124733924866, 0.023708274587988853, -0.0017673029797151685, -0.05049324408173561, 0.004551129415631294, -0.030039412900805473, 0.027608228847384453, -0.014814967289566994, 0.020393988117575645, -0.006612922064960003, -0.002526148222386837, 0.04646454378962517, 0.002158472081646323, -0.026583323255181313, 0.009550792165100574, -0.025517530739307404, -0.002935159718617797, 0.0317770279943943, 0.020883463323116302, -0.007036182563751936, 0.037977296859025955, 0.051260337233543396, 0.03463991731405258, 0.05298348516225815, -0.01311789732426405, -0.030481737107038498, 0.0695122480392456, -0.024085069075226784, 0.017881326377391815, -0.04640607535839081, 0.010476913303136826, -0.04120568931102753, -0.0183718241751194, -0.014627759344875813, 0.052378565073013306, 0.046228788793087006, 0.045761264860630035, 0.031470298767089844, -0.016016187146306038, 0.01634213887155056, 0.020898625254631042, 0.021784881129860878, -0.03702139854431152, -0.01717245578765869, 0.03770947828888893, 0.02964669093489647, 0.03560667484998703, -0.04079482704401016, -0.029812848195433617, 0.02469034492969513, -0.06148621439933777, 0.06462276726961136, 0.031083950772881508, 0.025025786831974983, -0.010115917772054672, -0.007468694355338812, 0.04547414183616638, 0.06500949710607529, 0.0036793674807995558, 0.02318497747182846, -0.029322965070605278, -0.024332718923687935, -0.004311467986553907, 0.007876561023294926, -0.051060281693935394, -0.03443628177046776, 0.010177010670304298, 0.06891860067844391, -0.024411452934145927, -0.01499766856431961, -0.08794204890727997, -0.028574442490935326, 0.0003947332443203777, 0.010219325311481953, -0.029961520805954933, -0.017758021131157875, -0.010589277371764183, -0.0706649050116539, 0.020085401833057404, 0.026148773729801178, -0.0016550540458410978, 0.011889970861375332, -0.06674917042255402, -0.02817346714437008, -0.026520676910877228, 0.049555253237485886, 0.06782516092061996, 0.05238480865955353, 0.04128625616431236, -0.039521731436252594, -0.05139817297458649, -0.001233790535479784, 0.013754156418144703, -0.013922082260251045, 0.0346638560295105, 0.019312428310513496, 0.07191520929336548, 0.033013246953487396, -0.010208366438746452, -0.017666002735495567, 0.06204307824373245, 0.03928178548812866, 0.04922889173030853, -0.05466265231370926, 0.0462968572974205, 0.013417836278676987, 0.04179766774177551, -0.02063307724893093, 0.000592115567997098, -0.02641388587653637, -0.03087013028562069, -0.04431522637605667, 0.05114009976387024, -0.03213350847363472, 0.0018484385218471289, 0.010867973789572716, 0.012526455335319042, 0.0017821918008849025, 0.022950654849410057, -0.04023135453462601, 0.026894373819231987, -0.029100611805915833, 0.07536371797323227, 0.041583992540836334, -0.008407380431890488, -0.030741482973098755, -0.04745331406593323, 0.03170154616236687, -0.029811479151248932, -0.043332844972610474, 0.040683336555957794, 0.03613976389169693, 0.06681325286626816, -0.04946180433034897, 0.06584189832210541, 0.04115458205342293, 0.0031779110431671143, 0.010656819678843021, 0.016278821974992752, 0.0506688617169857, -0.0036135027185082436, 0.0006295905914157629, -0.001410816446878016, 0.038366593420505524, 0.03801312297582626, 0.0022523868829011917, -0.019743531942367554, -0.051697324961423874, 0.1060948446393013, -0.022239714860916138, -0.026289962232112885, 0.046559080481529236, 0.046633441001176834, 0.008096776902675629, -0.013092650100588799, 0.012874621897935867, 0.05486039072275162, 0.03165373206138611, 0.008244631811976433, 0.013264531269669533, 0.002389565110206604, -0.03549477458000183, -0.010307240299880505, -0.07366254180669785, -0.017357926815748215, 0.0283963643014431, 0.030396007001399994, 0.03685608133673668, -0.06569928675889969, -0.010132905095815659, 0.0689944326877594, 0.02256724052131176, -0.033482830971479416, 0.0311416108161211, -0.03805572912096977, 0.08816678822040558, -0.037470459938049316, 0.0011572465300559998, -0.042820949107408524, 0.0616844967007637, -0.0016539308708161116, 0.05807119607925415, -0.03056998923420906, 0.024837782606482506, -0.014263602904975414, -0.05020028352737427, -0.004440035205334425, -0.08730049431324005, 0.008379296399652958, 0.008636708371341228, 0.036253657191991806, 0.026362590491771698, 0.00904194638133049, 0.010251094587147236, -0.02024095319211483, 0.0003245493571739644, -0.020240886136889458, 0.02549854665994644, -0.007228953763842583, 0.045791953802108765, 0.07379724085330963, -0.014083408750593662, 0.022655729204416275, -0.004145497921854258, 0.010581311769783497, 0.022640511393547058, -0.00029720779275521636, 0.020960800349712372, -0.05035676807165146, 0.07001940160989761, -0.030871927738189697, -0.03379998356103897, 0.0023556705564260483, 0.006181622389703989, -0.04871705174446106, -0.008779178373515606, -0.005402321461588144, 0.034185148775577545, 0.04436546564102173, -0.016727065667510033, -0.030573876574635506, -0.021856583654880524, 0.014113212004303932, 0.03174872323870659, 0.0537969172000885, 0.05039871856570244, -0.06823613494634628, -0.07722780108451843, 0.014772610738873482, 0.028620703145861626, 0.04645947739481926, 0.013779371045529842, 0.028247378766536713, 0.0077277133241295815, -0.03841220587491989, -0.021653912961483, 0.029758386313915253, -0.030261650681495667, -0.04433769732713699, -0.030779460445046425, -0.01378235500305891, -0.005635863170027733, -0.018748924136161804, -0.07240021228790283, -0.013087146915495396, 0.0533745214343071, -0.012454787269234657, -0.023140212520956993, 0.010819871909916401, 0.021278025582432747, 0.02912960574030876, -0.022225206717848778, 0.040086641907691956, -0.024732021614909172, 0.02734191156923771, 0.044365305453538895, -0.08636700361967087, -0.023650718852877617, 0.01208616141229868, -0.03983868286013603, -0.020673489198088646, 0.0005545355379581451, 0.0057047950103878975, 0.04462284967303276, -0.02470233105123043, -0.010385802015662193, 0.019490336999297142, -0.001047239056788385, 0.031518034636974335, -0.009613283909857273, -0.006584541872143745, 0.019740484654903412, 0.010673041455447674, 0.003942611627280712, 0.011309824883937836, -0.010443329811096191, -0.04695802554488182, 0.03005051240324974, 0.011975600384175777, 0.02959827147424221, 0.041102372109889984, 0.04897547513246536, -0.001793818548321724, 0.04722756892442703, -0.09420081973075867, 0.04805383086204529, 0.0032411173451691866, -0.01983642391860485, 0.050163254141807556, 0.05138492211699486, -0.014458601363003254, 0.0019796984270215034, -0.00899446476250887, -0.08488163352012634, 0.03197186067700386, 0.030713114887475967, 0.015124278143048286, 0.0004817766894120723, 0.03438984602689743, 0.02016051858663559, 0.03673094883561134, -0.05749206244945526, -0.007584291975945234, 0.006616790313273668, 0.019359391182661057, -0.022583406418561935, 0.015191353857517242, 0.011469152756035328, 0.023811202496290207, -0.07813335210084915, 0.012189055792987347, -0.05543665215373039, -0.03716425970196724, -0.01778654009103775, 0.006281817797571421, 0.01011040061712265, -0.015612617135047913, -0.031078234314918518, 0.04639653116464615, 0.030102502554655075, -0.04250851646065712, 0.006815342232584953, -0.001732811564579606, -0.04137874394655228, 0.009577128104865551, 0.057536590844392776, 0.07797534018754959, -0.002877539722248912, 0.024282988160848618, 0.05233022943139076, -0.05168122798204422, 0.013363578356802464, -0.013515632599592209, 0.002539522247388959, -0.029192717745900154, 0.04927404224872589, 0.023901959881186485, -0.0008841040544211864, 0.006641606334596872, -0.03299390897154808, 0.020629944279789925, 0.007950766943395138, -0.029879609122872353, 0.00339071499183774, -0.03395574912428856, -0.04665621742606163, -0.024678559973835945, -0.10903121531009674, -0.03379299119114876, 0.010763137601315975, -0.005431571509689093, 0.026644272729754448, 0.014567265287041664, 0.013296149671077728, 0.0011625814950093627, 0.007219045422971249, 0.04861513525247574, -0.0418359637260437, -0.02737516351044178, 0.05418790131807327, -0.01964498683810234, 0.059449050575494766, 0.00446173083037138, 0.01650414802134037, 0.04310048744082451, 0.0028876331634819508, 0.013502862304449081, -0.0029643827583640814, -0.03406771644949913, -0.081464983522892, -0.04550393670797348, -0.05631889030337334, 0.02380329929292202, -0.01840013824403286, -0.020350627601146698, -0.02396223321557045, -0.06949871778488159, -0.03212714567780495, 0.016567721962928772, -0.042074885219335556, -0.05841219052672386, -0.04980941489338875, 0.015260860323905945, -0.035468678921461105, -0.06964338570833206, 0.0005714252474717796, 0.0006952207768335938, -0.014699006453156471, 0.008586077950894833, -0.04998410493135452, 0.004729259293526411, -0.03303231671452522, -0.003428542520850897, -0.006484998390078545, -0.035654954612255096, -0.07394905388355255, 0.014454692602157593, 0.009483115747570992, -0.027725044637918472, 0.00026336059090681374, 0.038914021104574203, 0.042497288435697556, -0.019850611686706543, 0.025222236290574074, -0.03187531605362892, -0.02912140265107155, -0.05556380748748779, -0.000044748994696419686, 0.024423688650131226, 0.0017513317288830876, 0.034485917538404465, 0.05087432637810707, 0.017178276553750038, -0.09004142880439758, -0.0033557105343788862, 0.03457920625805855, 0.005497310776263475, 0.012417671270668507, 0.04796561598777771, -0.04820217564702034, -0.01925334706902504, -0.04100022837519646, -0.009651033207774162, -0.01023584883660078, -0.0021178689785301685, 0.048065148293972015, -0.054487504065036774, -0.025266878306865692, 0.006104404106736183 ]