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What Does It Mean?. From the “Afterword” of D J Griffith’s Introduction to Quantum Mechanics. Da Big Question. Did the physical system “actually have” the eigenvalue in question prior to the measurement? ( REALIST ) OR - PowerPoint PPT Presentation

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  • What Does It Mean?From the Afterword of D J Griffiths Introduction to Quantum Mechanics

  • Da 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)

  • Realist 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!

  • Orthodox 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 mystical

  • Agnostic ResponseI refuse to answerI ignore these problems

  • EPR 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 positronp0->e- + e+The positron and electron fly off in opposite directions and the pion has spin=0

  • EPR ContdSince 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 cant tell you which you will get, but that they will be correlated

  • Movin 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!

  • The 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 dont have an opinion

  • EPR SaysOrthodox view is spooky action at a distanceErgo, 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 locality

  • Bells 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 doesnt matterJ. S. Bell proved that ANY hidden variable theory is INCOMPATIBLE with QM

  • The 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)abp0e-e+

  • The 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)

  • HoweverIf they are anti-parallel, then P(a,-a)=+1For any arbitrary orientation thenP(a,b)=-a bThis result is IMPOSSIBLE for any hidden variable theory

  • Why?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).

  • Lets 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 k

  • SoWhere rho is the probability density of k

    Now lets eliminate B(b,k) by using our correlation function

  • If c is an other unit vector thenBells Inequality:

  • |P(a,b)-P(a,c)|
  • But 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 Bells inequality: the results were compatible with QM and incompatible with Bells 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 influences

  • Supernaturally 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 dont get upset that geometric points move faster than lightSo is this influence casual or is just information like a geometric point?

  • Two types of influenceCausal: subluminal or luminalethereal: neither energy or information and for which the only evidence is a correlation in the data of two different subsystems

  • Here, kitty, kitty .What is a measurement and why is it so different from other physical processes? And how can we tell when a measurement has occurred?Schroedinger attempted to answer this in his famous thought experiment formally titled The cat paradox

  • The Cat ParadoxA cat is placed in steel chamber, together with the following hellish contraption: In a Geiger counter there is a tiny amount of radioactive material so tiny that maybe within 1 hour one of the atoms decays but equally probable none of them decays. If one decays then the counter triggers and via a relay activates a little hammer which breaks a container of cyanide. If one has let this entire system for one hour, then one would say the cat is living if no atom has decayed. The first decay would have poisoned it. The wave function of the entire system would express this by containing equal parts of the living and dead cat. At then end of an hour, the wave function of the cat has the form of

  • Its ALIVE! Its Dead! Etc. etc.So according to the paradox, the cat is trapped between life and death: a linear combination untilYou look! And the cat is:ALIVE: You saved it by measuring itDEAD: You killed it by measuring itSchroedinger thought this whole blame game was nonsense

  • Out of the ParadoxMost widely accepted answer: the Geiger counter is the measurer, not you and it will make the statistical determination, not youWigner and others say that it is the intervention of human consciousness that constitutes measurement in QMWigner was Diracs brother in law and was associated with the Maharishi Institute and the Natural Law party.Unfortunately, the term measurement seems to imply human intervention but it does is not necessarily so

  • My Answer to All These Difficult Dilemmas

    I refuse to answer.