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I Understanding the Born rule

  1. Jan 12, 2017 #1
    i have been trying to obtain a schema for the Born rule and have got to this result.
    The incidence of detection at a point (x,t) = the incidence of the particle being at point (x,t) multiplied by the incidence of the detector being at point (x,t) on detection. The incidence of the second term is proportional to the probability of the the particle being at (x,t). Is this justifiable?
     
  2. jcsd
  3. Jan 12, 2017 #2
    Diagram?
     
  4. Jan 12, 2017 #3
    Yes please, if you can it would be helpful.
     
  5. Jan 12, 2017 #4

    bhobba

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  6. Jan 15, 2017 #5

    vanhees71

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    To put it less complicated. The justification for Born's rule simply is that it works. Today, there's seems to be no way to derive Born's rule from the other postulates of QT, and that's why it's taken as an independent postulate. To a certain extent, Gleason's theorem, mentioned by bhobba above shows that it's the only way to define probabilities in terms of a (rigged) Hilbert space as used in QT as the mathematical foundation of quantum theory. The meaning of states is given by Born's probabilistic rule and in my opinion nothing else and also nothing else is needed to do physics. You can browse this forum to find gigantic threads on "interpretation", leading to no conclusion. The good thing is that these debates are unnecessary for physics. It's about philosophy and epistemology, not about the hard observable facts described by QT as a physical theory, and that's just the minimal statistical interpretation. So far there's no observational fact hinting at something missing in QT.

    The only fundamental physical problem concerning QT is that we are still lacking a consistent description of gravity within QT, but I don't think that the solution will be an issue about interpretation. One needs a new ingenious physical idea and/or new observations hinting in the right direction of model/theory building, not philosophical pseculations, which never have lead to any results in the history of physics.
     
  7. Jan 15, 2017 #6

    ShayanJ

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    I appreciate your good post but this sentence doesn't seem right to me! If there was no EPR, there was no Bell's theorem either! At their time, EPR were doing philosophical speculations and years later, with Bell's theorem, it was revealed that there was a little physics there. How can you be sure that there is no physics in things that you now call philosophy?(Of course, people can go too far in that direction!)
    Sure, you see no problem with QM, but it was the same with EPR. People were ok with QM but still EPR led to new insights!
     
  8. Jan 15, 2017 #7
    This is not quite what I am asking. Would it not be correct to interpret the probability of detection being In part due to the location of the particle and in part due to the location of the detector?
     
  9. Jan 15, 2017 #8

    ShayanJ

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    What does "being in part due to" even mean?
    Quantum mechanics is contextual which means what you measure depends on your process of measurement but I don't think simply moving your detector non-trivially changes anything!
     
  10. Jan 15, 2017 #9
    Well if you move the detector to a region where the amplitude of the particle is low there is less chance of detection.
     
  11. Jan 15, 2017 #10

    ShayanJ

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    Yeah, but I said "non-trivially", and that's what I call a trivial change. Because of course that happens, whether we're talking about classical or quantum physics.

    You haven't answered my question!
     
  12. Jan 15, 2017 #11
    Sure, but doesn't the Born rule also apply to macroscopic entities?
     
  13. Jan 15, 2017 #12

    ShayanJ

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    If you don't use quantum mechanics to describe them, no!
    What's your point anyway?
     
  14. Jan 15, 2017 #13
    But can't they also be described by QM?
     
  15. Jan 15, 2017 #14

    ShayanJ

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    Yes, but then you have to consider the interaction of your measurement device with its environment which induces decoherence and makes things complicated.
    I'm not sure where you're going with this but I'm sure you need to learn more before you can continue.
     
  16. Jan 15, 2017 #15

    bhobba

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    What location of the particle? Why do you think in QM a particle has the property of location independent of measurement?

    Thanks
    Bill
     
  17. Jan 16, 2017 #16
    The unmeasured location as a probability distribution as specified by the wave function. The measured location is a function of both.
     
  18. Jan 16, 2017 #17

    bhobba

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    That's an error in your reasoning. Without being measured the formalism says nothing - it may not even have the property of location. Think of a spinning coin when you toss it - it doesn't even have the property of heads up or down until it is 'measured' ie hits the ground. BTW is just an analogy - one side is still heads and the other tales - it isn't like that in QM - it literally may not have the property of head's or tales until measured in QM. Unmeasured location is an interpretive assumption you are making. Once you understand in QM whats going on when not measured is the area of interpretations and not the QM formalism things will be a lot clearer - weirder - yes - but clearer.

    To understand QM better studying actual interpretation's IMHO will help a lot.

    Consistent histories is a good place to start - but its just a start:
    http://quantum.phys.cmu.edu/CHS/histories.html

    Thanks
    Bill
     
  19. Jan 16, 2017 #18
    Thanks Bill, it looks like in CH the Born rule is also a postulate.
     
  20. Jan 16, 2017 #19

    vanhees71

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    The EPR paper is clearly a physics paper, not philosophy. However, even Einstein himself didn't like it too much, and he wrote a much better one with him as single author to make his point of view clear. His issue was the "inseparability" of far-distant parts of a quantum system described by entanglement. Bell's great achievement was to make the philosophical assumption that the world should be separable in Einstein's sense a physically decidable question by showing that any deterministic local hidden-variable theory implies his famous inequality, which is violated by QT, and all corresponding "Bell tests" show that the inequality is violated and that the predictions of QT prevail. This rules out the validity of any deterministic local hidden-variable theory.

    Einstein's paper is unfortunately in German, and I don't know, whether there is an English translation:
    A. Einstein, Quantenmechanik und Realität, Dialectica 2, 320 (1948)
     
  21. Jan 16, 2017 #20
    Well, that is kind of pertinent to my original question. Would not the correlations between the observations have as much to do with the correlations between the detectors as between the states of the particles?
     
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