What Does It Mean?Da Big QuestionRealist ViewOrthodox PositionAgnostic ResponseEPR ParadoxEPR Cont’dMovin’ On Up to the Big Time, the Deluxe Apartment in the Sky!The 3 views againEPR SaysBell’s ThmThe GedunkenThe Results of the ExperimentHoweverWhy?Let’s do some mathSoIf c is an other unit vector then|P(a,b)-P(a,c)|<= 1+P(b,c)But What does it Mean?Supernaturally SuperluminalTwo types of influenceHere, kitty, kitty ….The Cat ParadoxIt’s ALIVE! It’s Dead! Etc. etc.Out of the ParadoxMy Answer to All These Difficult Dilemmas1What Does It Mean?From the “Afterword” of D J Griffith’s Introduction to Quantum Mechanics2Da Big QuestionDid the physical system “actually have” the eigenvalue in question prior to the measurement? (REALIST)OR Did the act of measurement “create” the eigenvalue (constrained by the wavefunction)? (ORTHODOX)ORCan we completely duck the question? (AGNOSTIC)3Realist ViewIf the realist view is true, QM is an incomplete theory because:Even if you know everything that QM has to tell you about the system, you STILL cannot determine all of its features!4Orthodox PositionMeasurement forces the system to “make a stand” helping create an attribute that was not there previouslySince repeated measurements yield the same result, the act of measurement collapses the wavefunctions.This is strange but not mystical5Agnostic ResponseI refuse to answerI ignore these problems6EPR Paradox1935- Einstein, Podolsky, and Rosen came up with the EPR ParadoxDesigned to prove that the realist postion is the only possible oneA simplified version goes like this:Assume that a pion at rest decays into an electron and positron0->e- + e+The positron and electron fly off in opposite directions and the pion has spin=07EPR Cont’dSince pion is spin 0, then electron and positron are in singlet configuration |00>So if the positron is spin up then electron must be down or vice versa.QM can’t tell you which you will get, but that they will be correlated 218Movin’ On Up to the Big Time, the Deluxe Apartment in the Sky!Now move the electron far apart (pick one)10 meters10 light yearsNow say you measure electron spin down, then IMMEDIATELY you know that the positron is spin upBTW, this is an INSTANTANEOUS knowledge!9The 3 views againRealist: This is not surprising, the positron was always up since the decayOrthodox: Hmmm… electron was neither up or down until measurement. The measurement caused the wave function to collapse and that “knowledge” was transmitted instantaneously across the gulf to the corresponding particle.Agnostic: I don’t have an opinion10EPR SaysOrthodox view is “spooky action at a distance”Ergo, says EPR, the realist have it correct and the spins were predetermined at the decayOf course, this is all predicated on the argument that nothing, not even information, can go faster than the speed of light– called the principle of locality11Bell’s ThmEPR did not doubt that QM is correct, just incompleteSome other “hidden variable” is needed to completely quantify the system.The hidden variable could be a single number or a whole collection of numbers; it doesn’t matterJ. S. Bell proved that ANY hidden variable theory is INCOMPATIBLE with QM12The GedunkenInstead of having the electron and positron detectors along the same direction, allow them to be rotated independentlyThe first detector measures the component of the electron spin in the direction of unit vector a and the second along the direction of bFor simplicity, we will record the spins as +1 (up) and -1(down)a be-e+13The Results of the ExperimentBell proposed to calculate the average value of the product of the spins called P(a,b) If detectors are parallel, then we have original EPR configuration so always +1 and -1 and therefore P(a,a)= -1 (and so is the average)electron positron product+1 -1 -1+1 +1 +1-1 +1 -1+1 -1 -1-1 -1 +1… … …14HoweverIf they are anti-parallel, then P(a,-a)=+1For any arbitrary orientation thenP(a,b)=-a ·bThis result is IMPOSSIBLE for any hidden variable theory15Why?Assume, that the hidden variable is called kk varies in some way that we neither understand nor control from one decay to the nextSuppose that the outcome of the electron measurement is independent of the orientation (b) of the positron detector. b is chosen after the decay but before measurement of electron and thus is hindered by speed of light (locality condition).16Let’s do some mathSo there is a function A(a,k) which gives the result of the electron measurement and B(b,k) which gives the result of the positron measurementA(a,k)=+/- 1 and B(b,k)=+/-1 When detectors are aligned, the results are perfectly anti-correlated A(a,k)=-B(b,k) for all k17So dkkbBkaAkbaP ),(),()(),(Where rho is the probability density of kNow let’s eliminate B(b,k) by using our correlation function dkkaAkaAkbaP ),(),()(),(18If c is an other unit vector then),(1),(),()],(),(1)[(),(),(0)],(),(1)[(1)],(),([1),(),()],(),(1)[(),(),(:1)],([)],(),(),(),()[(),(),(2cbPcaPbaPdkkcAkbAkcaPbaPkcAkbAkandkbAkaASincedkkbAkaAkcAkbAkcaPbaPkbASincedkkcAkaAkbAkaAkcaPbaPBell’s Inequality:19|P(a,b)-P(a,c)|<= 1+P(b,c)It is easy to show that P(a,b)=-a·b (the QM prediction) is incompatible with Bell’s InequalitySuppose all three vectors, a, b, and c lie in a plane with c at 450 to a and b (a perpendicular to b)Then P(a,b)=0 and P(a,c)=P(b,c)=-.707Obviously .707 is not greater than 1-0.707 (.293)20But What does it Mean?If EPR is correct, then QM is completely WRONG!On the other hand, NO hidden variable is going to rescue us from the nonlocality that Einstein considered preposterousMany experiments were performed to test Bell’s inequality: the results were compatible with QM and incompatible with Bell’s InequalityIn other words, the realists are wrong and there is spooky action at a distance Or in the lingo: there is the possibility of superluminal influences21Supernaturally SuperluminalA causal influence that propagates faster than light is bad newsBecause relativity says that anything going faster than light is going backward in time!Faster than light things: any geometric pointWe don’t
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