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I Quantum Collapse

  1. Sep 14, 2017 #1
    I am confused about the QM phenomenon of collapse. For example, if an electron is prepared by a magnetic field as spin right and then measured in a device determining whether it is spin up or down, it is said that the electron, which had been in a linear superposition of up and down will now collapse to up or down, with probability amplitudes (PAs) given by the inner product of appropriate bra and ket vectors and probabilities being the square of the PAs. In this case it has a 50% chance of being measured as up. OK, but I am told that post measurement it will always in future be measured as up. Why cannot the measurement that caused the collapse be considered another preparation of the particle in which case it would have a new set of linear superpositions? Or alternatively, what is magic about the preparation of the spin that gave it superposition?
     
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  3. Sep 14, 2017 #2

    PeterDonis

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    Collapse isn't a phenomenon, it's an interpretation. There are many interpretations of QM, and not all of them have collapse.

    Nothing. Superposition is basis dependent--in other words, whether or not a state is a superposition depends on what measurement you make on it. If you take an electron that was prepared as spin right and measure its spin in the left-right direction, it will always be measured as spin right--i.e., it is not in a superposition of spin left and spin right. But if you measure its spin in the up-down direction, there is a 50-50 chance of each outcome--i.e., it is in a superposition of spin up and spin down.

    If you measure its spin again in the up-down direction, yes. But if you take an electron that you just measured as spin up, and measure its spin in the left-right direction, there is a 50-50 chance of each outcome--i.e., the electron is in a superposition of spin left and spin right.
     
  4. Sep 14, 2017 #3

    atyy

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    It depends on what one means by collapse. Collapse is the informal term for state reduction. The only non-controversial interpretation of QM has state reduction, and hence has collapse.

    If by collapse, you mean "physically real collapse", them that is indeed an interpretation, since the standard interpretation is agnostic about the reality of the quantum state.
     
  5. Sep 15, 2017 at 3:18 AM #4

    vanhees71

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    The only non-controversial interpretation has no collapse. It's the minimal statistical interpretation, and what's called collapse or state reduction in some flavors of Copenhagen-type interpretations, is simply the update of the (statistical) information about the system due to a preparation procedure. One should not use the terms "collapse" or "state reduction" for this, because they are indeed associated with what @atyy calls "physically real collapse".

    In the minimal interpretation a particle has a determined spin component in direction of the magnetic field used to prepare it, because it has been prepared in this way. It's a tautology in the minimal interpretation! Indeed, if the particle's spin component is prepared to have a determined value a proper precise measurement of this spin component gives with 100% probability this prepared value, and that's what's observed. Otherwise QT would be self-contradictory and would have to be substituted by some better theory, but that's not the case!
     
  6. Sep 15, 2017 at 6:06 AM #5

    stevendaryl

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    To me, as it was with Einstein who proposed it, the most important experiment for understanding quantum mechanics (or understanding how little you understand it) is the EPR.

    We create a pair of spin-1/2 particles that have total spin zero. Alice measures the spin of one particle along the z-axis, and finds that it's spin-up. She immediately knows that if Bob far away measures the spin of the other particle along the axis, he'll measure spin-down. So Alice's measurement tells something about the result of a distant measurement by Bob. The "collapse" is a mathematical procedure: After Alice's measurement, she uses a "collapsed" wave function to predict the result of Bob's measurement. The fact that this procedure works is independent of interpretation.

    There are basically three ways of thinking about it, as far as I know:
    1. Alice's measurement affects Bob's measurement result. This is the physical interpretation of collapse.
    2. Alice's measurement just reveals something about Bob's particle that was true before she performed her measurement. This is the epistemic interpretation of collapse.
    3. Somehow, Alice's measurement puts her into a possible world in which Bob gets spin-down (there might be another possible world in which Bob gets spin-up, but that world is inaccessible to Alice). This is basically the Many-Worlds interpretation.
    All three possibilities raise more questions than they answer. Which I guess is a reason to stick to a minimal interpretation--that doesn't require you to understand what's going on, only to calculate predictions. (Shut up and calculate)

    It would seem to me that the minimalist interpretation says nothing about whether collapse is physical or epistemic. Claiming that it's epistemic is going beyond what's minimally needed to get on with doing quantum mechanics.
     
  7. Sep 15, 2017 at 6:15 AM #6

    vanhees71

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    This example clearly shows that there is no problem with QT and no EPR paradoxon if you take the view of the minimal statistical interpretation. When A measures her particle's polarization, she immediately known that of Bob's, and she updates the state. This is due to the preparation of the spin-entangled pair but not due to her measurement. B, to his knowledge, still has an unpolarized particle and finds with 50% probability either of the two possible spin-##z## values. Only when A and B note their registration times and compare their measurement protocols they can find that indeed their polarization states were 100% correlated although the single-particle polarization were maximally unknown before the measurement. The linked-cluster principle holds, and there is nowhere anything that hints at a "spooky action at a distance". Only the assumption of a collapse (as a physical process) leads to this errorneous conclusion, and of course EPR were right with the criticism against the spooky action at a distance conclusion implied by the collapse hypothesis, which however is an additional (and not needed!) assumption on top of the minimal interpretation.
     
  8. Sep 15, 2017 at 11:43 AM #7

    PeterDonis

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    Thread closed for moderation.
     
  9. Sep 15, 2017 at 3:17 PM #8
    This is a reply to peter donis, aty and others who answered my questions on the subject. Thank you very much. I have a much better understanding of the interpretation (not phenomenon, as I now understand)

    [Moderator's note: moved from separate thread.]
     
    Last edited by a moderator: Sep 15, 2017 at 3:54 PM
  10. Sep 15, 2017 at 3:55 PM #9

    PeterDonis

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    Since the OP has said his question has been answered, the thread will remain closed.
     
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