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Schrödinger local and deterministic?

  1. Mar 19, 2010 #1
    There have been many QM Interpretation thread, but I haven't found this question answered:

    Taking aside the fact that a complex probability amplitude is not something we can picture, is the Schrödinger equation local and deterministic at once?
     
  2. jcsd
  3. Mar 19, 2010 #2
    Yes, the Schrodinger equation and the evolution of the wavefunction that follows from it is local and unitary. Unitary means that the time evolution of the wavefunction is unique and completely determined by the initial conditions. It is therefore deterministic.

    There is, however, a major practical obstruction that prevents us from actually calculating this time evolution for any macroscopic system. This is partically because it is practically impossible to determine the initial state of a macroscopic system. But even if we did know this state or if we are somehow able to finetune it, the time-evolution itself is a many-body problem which is, again, computationably intractable.

    We therefore always need to resort to some form of approximation, e.g. a statistical description of the system or ignoring a large number of degrees of freedom. Such a statistical description automatically introduces a degree of 'uncertainty' which manifests itself as a non-determinstic description of the system.

    So even if you put the whole measurement problem aside, you still end up with a non-deterministic description of macroscopic systems due to practical limitations.
     
  4. Mar 19, 2010 #3
    So how does that compare to the saying "QM can't be local and deterministic" by Bell's theorem and similar ones?
     
  5. Mar 19, 2010 #4

    jtbell

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    Bell's theorem plus the results of experiments testing it (insofar as one accepts those results and/or the validity of Bell's theorem with respect to those experiments, which is the source of the vigorous arguments here about the subject :smile:) support the statement that "QM can't be local and realistic", which is not the same thing as deterministic.
     
  6. Mar 19, 2010 #5
    Yes sure. And I do not wish to start yet another Bell discussion.

    But what's wrong about saying the Schrödinger equation is local and deterministic?
    Mathematically it does look so.
     
  7. Mar 19, 2010 #6
    I believe you said it, "...the fact that a complex probability amplitude is not something we can picture..." is the reason. Well, if it can only exist as math, it's not physics, just math. So, from the perspective of a mathematician... it is as you say. From the perspective of a Physicist... it is too, but it's not useful if it can't be made to do work. Hence all of the rest... so I'd say to answer your question: To avoid confusion.
     
  8. Mar 19, 2010 #7
    I guessed so. Now I'm trying to get some ideas to understand how determinism gets lost.... :)
     
  9. Mar 19, 2010 #8
    See, that's not too hard, because Determinism is lost when we have to calculate positions, velocities, etc... as probabilites. It all comes from the Heisenberg Uncertainty Principle (HUP), now backed up by the CMB surveys.
     
  10. Mar 21, 2010 #9
    I don't agree that the UP supports an external indeterminism in events; The UP does highlight however our lack of knowledge on a system. Just because there is a lack of knowledge from our behalf should not suggest that the universe is not deterministic.
     
  11. Mar 21, 2010 #10
    The CMB would beg to differ, barring a superdeterministic uneven distribution of "stuff" at 360K years post-BB...
     
  12. Mar 21, 2010 #11
    Calculating probabilities is fine. The problem comes in when someone tries to make a theory that works with probabilities alone.

    So if ppl wouldn't try to squeeze QM into basic probability theories, then QM would be local, deterministic and even linear?

    Maybe some sophisticated ingredient can make even the probabilities logical again.
     
  13. Mar 21, 2010 #12
    Time to start building the AI's that can find that... maybe they'll even be nice enough to try and explain it to us! :wink:
     
  14. Mar 21, 2010 #13
    No i beg to differ, because the UP is in light of what we can know - its a limitation of knowledge which does not impede determinism.
     
  15. Mar 21, 2010 #14
    Ok... then how is it that something which is a limitation on KNOWLEDGE managed to effect the (should-have-been-EVEN) distribution of "stuff" in the early universe? The HUP explains that nicely, as does SUPERdeterminism. The HUP + Determinism = Horse****.
     
  16. Mar 22, 2010 #15
    Wasn't the fundamental problem that the equation didn't properly model the interaction between particle and wave as de Broglie envisioned? (It rather just models "some wave" of unknown origin and constitution)
     
  17. Mar 22, 2010 #16
    Yeah... sadly yes... and the Bohmian interpretation replaces that issue with a Pilot wave of "unknown origin and constitution" as you put it so well. Welcome to QM... I need some aspirin. :wink:

    EDIT: Hence us left with 50-50 chances, or worse, 50-50-1! Never good when you get 101% in a physical theory...
     
  18. Mar 22, 2010 #17
    You do realize that particles are simply statistical averages right? Physics in general is a statistical theory at best yes? It's statistical because we don't have all the knowledge on a quanum system, but this is because of our lack of knowledge, not because there needs to be an indeterministic world externally of our limited knowledges.
     
  19. Mar 22, 2010 #18

    DrChinese

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    You keep saying this, but this is generally rejected as a viewpoint. The HUP is not about lack of knowledge, although at one time that was a common belief. It is generally held that particles have attributes only within the context of a measurement.
     
  20. Mar 22, 2010 #19
    To paraphrase DrChinese in my own words, representing my own opinion, "No, I don't realize that, because observational data has shown the HUP is a physical law, not merely a statistal event horizon for observers."
     
  21. Mar 22, 2010 #20
    Classical determinism: Repeating the same experiment many times always has the same result. Classical mechanics allows us to determine that result.
    Quantum determinism: Repeating the same experiment many times yields a unique probability distribution of all possible results. Quantum mechanics allows us to determine that probability distribution.
    Quantum mechanics does not predict the experimental result; it is not deterministic in the classical sense.

    Locality is a property of the space-time of classical physics. It is classical in nature. The wavefunction (probability amplitude) is defined in a Hilbert space. It seems to me that locality is an issue only if the wavefunction propagates in space-time, as many believe.

    In the classical sense, quantum mechanics is neither deterministic nor local.
     
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