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Quantum Mechanics and Determinism

  1. Sep 12, 2007 #1
    Greetings,

    I'm an undergrad physics student currently taking a course in QM.

    There is, however, something that's been bothering me that's not exactly technical or mathematical in nature, but more of a matter of interpretation.

    As far as I've gone into QM, everything is dominated by probability. I'm satisfied with that and can understand that when a measurement is made regarding a physical property (in QM terms, an observable), multiple results can be obtained from the same system.

    Where it gets more complicated (in my mind, at least) is when one poses the question of whether defining things in terms of probability is an attempt to define a system that is truly random or making the best possible "educated guess" into the likely outcomes. Let me try and illustrate with an example (although I fear I'm getting metaphysical):

    Say you're measuring the spin of a particle in the Z axis, and you get +h/2. Now, suppose you could somehow manage to achieve exactly the same conditions that existed just before you performed the first measurement. With this I mean basically rewinding time, not just the experimental conditions, but absolutely the same exact version of the universe that existed before your last measurement.

    Do you still have a chance of getting -h/2 for the spin value? Is it a matter of interpretation? Or is this question beyond the scope of QM/Physics in general?

    Another question along those lines would be:

    Is there a chance that the probabilistic interpretation of QM is in reality a model for making crude predictions out of underlying physics that are not yet understood? Or is it clear that there is no room for hidden physics "under the hood"?

    Hoping to hear some answers so I can sleep well again. :D
     
  2. jcsd
  3. Sep 12, 2007 #2

    malawi_glenn

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    Well this was Einsteins argument against QM, that it must exist a hidden variable, that we are not aware of. However, Bells inequality is not satisfied in QM. If you want to learn more about the triumph of QM read about Bells inequality in QM, also "Einsteins locality principle" and "Einstein-Podolsky-Rosen paradox" are keywords. I know that Sakurai "Modern Quantum mechanics" 2nd ed has a good tutorial about this in chapter 3.9
     
  4. Sep 12, 2007 #3
    Yes, it is a matter of interpretation.

    If you take a traditional view (it's just a mathematical tool for the monkey to explain observations) then the wave-collapse is non-deterministic, so replaying would change things.

    If you're horrified by QM, you'll assume (against all evidence) that there is some kind of hidden variable, i.e., that the result was determined (just unknown) before you measured it.

    If you like time-symmetry, you might treat QM as a boundary value problem (the arbitrary predetermined start/end states of the universe determines everything else between, or maybe a superposition thereof?) and rewinding part-way wouldn't give a different result). If you like the "sliders" sci-fi, then "different you" measured all possible different values the first time anyway..
     
  5. Sep 12, 2007 #4
    It is an experimental fact that if you prepare exactly the same particle state many times, then sometimes you'll measure spin +h/2 and other times you'll measure spin -h/2. There is no known way to predict the exact outcome of each measurement. Quantum mechanics doesn't try to explain this apparent randomness of nature. QM accepts this probabilistic character of measurements as a given fact and simply formulates the rules by which we can calculate the probabilities.

    Many prominent physicists (beginning with Einstein) believed that this probabilistic character of quantum mechanics is a sign of weakness (incompleteness) of the theory. Their philosophy didn't allow random unpredictable behavior of nature (God doesn't play dice). They believed that some "hidden variables" will be discovered, which will allow us to return to a deterministic classical view of nature. However, no progress in this direction was made in more than 70 years. One cannot prove that "hidden variables" are impossible, but there is a lot of evidence that they are unlikely.

    Eugene.
     
  6. Sep 12, 2007 #5
    But then there is, of course, Bohmian mechanics...
     
  7. Sep 12, 2007 #6

    Demystifier

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    There is some room, but such hypothetic hidden physics must have some unusual properties. For example, it must be nonlocal. See e.g.
    http://xxx.lanl.gov/abs/quant-ph/0609163 (to be published in Found. Phys.)
    especially Secs. 4, 5 and 6.
     
  8. Sep 12, 2007 #7
    It is wrong impression. Try to study the QM content (P.A.M.Dirac “The Principles of QM”, fourth edition, Oxford, (1958)). I don’t believe that everything but the statistical interpretation is already clear for you.

    M.Born assumption that the observable quantity psybar*psy describes the statistical distribution even for the single particle system so far had no any experimental confirmation. Those that discuss the deterministic evolution of the probabilities or loudly claim that the highly regular three parameters picture of single photon/electron waveform in double slit has the statistical nature don’t know neither statmech, nor mathematics and I personally consider them mentally handicapped. And why it is important how you call it, particle field density or probability amplitude?

    Good night, Dany.
     
    Last edited: Sep 12, 2007
  9. Sep 12, 2007 #8

    ZapperZ

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    Then how exactly do you interpret the electronic wavefunction for the Hydrogenic atoms and the single-particle spectral function in Fermi Liquid theory? Or do you also consider those systems to have "no any experimental confirmation"?

    Zz.
     
  10. Sep 12, 2007 #9
    See, for example, E. Schrödinger, Phys.Rev., 1926, 28, 1049.

    Zz, sorry. I will present the detailed discussion next few days. The New Year will start within six hours. I should prepare myself to meet it properly.

    Do you mean the QM many-body system? The quantum statistics emerged similarly as it is in the classical statmech. M.Born statistical interpretation (single particle physical system) has nothing to do with that.

    Regards, Dany.
     
  11. Sep 12, 2007 #10

    Demystifier

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    From the Abstract of this classic paper:
    "... The wave-function physically means and determines a continuous distribution of electricity in space ..."
    Today we know that, if the wave function satisfies the Schrodinger equation, then this interpretation is not correct. It could be correct only if a collapse of the wave function also takes place, but in this case the wave function does not really satisfy the Schrodinger equation.
     
  12. Sep 12, 2007 #11

    ZapperZ

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    I don't see it. Schrodinger's paper was a reformulation of QM which is different than the Bohr model. He essentially is introducing the "Schrodinger Equation" and solving it for H-atom, which every school children majoring in physics would solve in class. How is this relevant to your point? In fact, if you look towards the end, he stated this:

    It clearly shows that Schrodinger is interpreting that conjugate product as the weighting function, which is what we all use it as when we call it the probability density! Thus, I don't see how this reference has anything that supports your displeasure at such usage.

    Huh? I'd like to see you use classical statmech to derive the single-particle spectral function. Till you can do that, please stop making such claim.

    Zz.
     
  13. Sep 12, 2007 #12
    E. Schrödinger and A.Einstein never accepted M.Born statistical interpretation.

    Zz, calm down and read what I wrote. See you next year! Shana Tova!

    Regards, Dany.
     
    Last edited: Sep 12, 2007
  14. Sep 12, 2007 #13

    Demystifier

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    I would not say that they did not accept it. It would be more correct to say that they believed that it cannot be the final answer.

    By the way, what calendar do you use?
     
  15. Sep 12, 2007 #14
    It was demonstrated by A.Einstein that the collapse is necessary to maintain the SR.

    Dem, please stop reformulating Physics from Resheet. And the measurement is “R-process” (J. von Neumann). See you next year! Shana Tova!

    Regards, Dany.
     
  16. Sep 12, 2007 #15

    ZapperZ

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    That's what you say. Look at what HE said in that paper itself.

    And this is supposed to be an explanation? I did read what you wrote. And read what *I* wrote.

    Zz.
     
  17. Sep 12, 2007 #16
    But is Bohmian mechanics capable of predicting whether the spin of a particular electron will be +h/2 or -h/2? I don't think so. It doesn't change the fact that behavior of micro-particles remains random and unpredictable.

    Eugene.
     
  18. Sep 13, 2007 #17

    Demystifier

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    Not in practice. But yes in principle.
     
  19. Sep 13, 2007 #18
    But no Non-Local theory like BM, QM, or Schrodinger Equations makes that prediction for a particular electron. They all have some Born Probabilistic element related to the measurement angle used for up/down; and can only be evaluated in real life by graphing the results of large numbers of events.
    Don’t be confused by “BM Local” based on Determinism. It is not the same as “Einstein Local” or “Bell Local” that people usually have in mind when they use the term “Local”.
    See Thread: “Is BM “Bohmian Local” actually Local

    RB
     
  20. Sep 13, 2007 #19
    Thanks for the replies, I should have probably read more on EPR before asking. That part is clearer now.

    The only issue that remains right now is time symmetry...

    Say you once again make a spin measurement for a single particle and get +h/2. From my understanding, this is interpreted as the collapse of the wave function, becoming non-zero only around the measurement obtained. Having done that, you somehow invert the direction of time.

    My question is... does the wave function return to its previous state, or can it remain collapsed, or at least altered in a way? Since, in theory, you already know what the measured value is going to be if you measure at that particular instant (assuming time is symmetrical).
     
  21. Sep 14, 2007 #20
    I want to reply to the following assertion which was posted a couple of days ago:

    >Originally Posted by meopemuk
    >It is an experimental fact that if you prepare exactly the same particle state many >times, then sometimes you'll measure spin +h/2 and other times you'll measure spin -h/2

    It is hard to prepare the same particle in the exact same state twice. This is the whole problem. You can prepare a beam of electrons which are spin-polarized sideways (that is actually what it means for them to be half the time spin up and half the time spin down). But each electron in the beam has a phase, and you don't know what the phase is. More to the point, the DETECTORS (there are two of them, one for each spin orientation) in some sense have a phase and you have no experimental way of preparing the beam so that you control the relative phases of the beam and the detectors. In other words, the experiment can't be done.
     
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