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Conceptual underpinning(s) of the QM projection postulate

  1. Jun 15, 2012 #1
    The title says it. I would like to see what knowledgeable people at PF have to say about the QM projection postulate -- primarily understandings of the conceptual reasoning underlying it. But anything anyone has to say about it is welcomed, including opinions that it shouldn't be a part of the basic axiomatic formulation of QM.
     
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  3. Jun 16, 2012 #2

    Demystifier

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    The projection postulate is a simplified description of a continuous physical process caused by decoherence and something else, where the "something else" is something we don't know what it is, but have a few ideas what it could be.
     
  4. Jun 16, 2012 #3
    Such as ... ?
     
  5. Jun 17, 2012 #4
    Since you're a Bohmian, id the "something else" you're referring to ignorance of which of the Everett many worlds is the "actual world"?
     
  6. Jun 17, 2012 #5

    bhobba

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    Well its basically the wavefuntion collapse issue. Decoherence is the usual explanation these days. I believe it resolves it and in a very elegant way but opinions vary.

    The conceptual reasoning behind it is its usually thought to be the only reasonable way you can define probabilities in a theory based on the principle of superposition eg see Gleasons Theorem. The reason you need probabilities is deterministic models turn out to be problematical eg see the Kochren Specker Theorem.

    Thanks
    Bill
     
    Last edited: Jun 17, 2012
  7. Jun 18, 2012 #6

    Demystifier

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    Bohmian particle trajectories are certainly one possibility.

    Another possibility are additional axioms needed for the many-world interpretation to work. (For example, an axiom from which the Born rule can be explained.)
     
  8. Jun 18, 2012 #7

    Demystifier

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    Most papers on decoherence these days admit that decoherence is important but not sufficient to explain the collapse.
     
  9. Jun 18, 2012 #8

    vanhees71

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    Well, I'm even more "heretic" (against the Copenhagen doctrine) and ask, what is the collapse assumption good for? It's not needed within the Minimal Interpretation, and I don't see, why I should assume more than necessary to apply the mathematical formalism to "reality" (which is of course simply what's observed in nature or in experiments in the lab)?

    The only interpretation I need to make the connection between the QT formalism and real-world observations is Born's probabilistic interpretation of states, and there is no need for a collapse! So, I don't need an "explanation" for a collapse.

    This is true in even stronger form for any additional elements in the formalism as in Bohm-de-Broglie pilot-wave interpretations. There I don't need to bother with unobservable trajectories; let alone any other esoterics like the "many-worlds" or "Princeton" interpretation.
     
  10. Jun 18, 2012 #9

    Demystifier

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    This is essentially the Ballentine statistical ensemble interpretation. It is indeed consistent, but still has some unappealing features which make it not universally accepted.
     
  11. Jun 18, 2012 #10

    Fredrik

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    All we need to make predictions about results of experiments, is the version of the Born rule that says for all observables A, and all pure states s, the average result in a long sequence of measurements of A, on systems that are all in the state |s>, will be <s|A|s>.

    But to test those predictions, we also need to know what state to associate with the preparation procedure we're using. We need a rule that assigns states to preparation procedures. I'm not aware of anything other than the projection postulate that can do that.


    Edit: I just need to make sure that we're talking about the same thing. What I just said is based on the assumption that the "projection postulate" is the rule that says that if we measure A and get the result a, and if the system wasn't destroyed by the measurement, then immediately after the measurement, it will be in an eigenstate of A with eigenvalue a. Let me know if you guys were actually talking about something else.

    Edit: 2 After reading Demystifier's post #2 again, I started thinking "Is decoherence another thing that can associate mathematical states with preparation procedures?". It seems to me that the answer is no. Decoherence is a prediction of the theory, but we don't even have a theory without the projection postulate.
     
    Last edited: Jun 18, 2012
  12. Jun 18, 2012 #11

    bhobba

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    That's because the wrong question was asked. It for all practical purposes does explain it - there is no way to observationally tell the difference between a mixed state where each state is an eigenstate and wavefunction collapse.

    Out of curiosity mind giving me some of those most papers - its not the view of the stuff I read such as Sholosshaurs book on decohrerence.

    Thanks
    Bill
     
  13. Jun 18, 2012 #12

    bhobba

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    All interpretations suck in some way - it a matter of personal preference which you think sucks the least - I think the ensemble interpretation does that combined with decoherence - not that Ballentine is a big fan of decoherence.

    Thanks
    Bill
     
  14. Jun 18, 2012 #13

    bhobba

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    Indeed. But it does allow us to skirt problematical issues. For example the ensemble interpretation has problems with accepting the actual reality of the ensembles because the Kochen-Specker theorem means it can not be in an actual state that observation selects - but with decoherence it can.

    Thanks
    Bill
     
  15. Jun 18, 2012 #14

    Demystifier

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    Fair enough! :approve:
     
  16. Jun 18, 2012 #15

    Demystifier

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    I disagree. Even without the projection postulate, even without the Born rule, even without the probabilistic interpretation, we can calculate "reduced density matrices" as abstract mathematical objects governed by the Schrodinger equation. This is sufficient to predict decoherence, even if we have no idea what it means physically.

    Of course, if you do have a probabilistic interpretation, then this further motivates you to calculate the reduced density matrix because then you know what is the meaning of it. But the point is - you can calculate it even without knowing about the probabilistic interpretation.

    Besides, Bohmian interpretation is an example demonstrating that we can even have a full physical interpretation without the projection postulate.
     
  17. Jun 18, 2012 #16

    Fredrik

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    I'm a little confused about what we disagree about. My main point was that if we take the usual assumptions that define QM, and simply drop the projection postulate from that list, what we have left isn't a theory. I suspect that you will agree with that.

    I certainly didn't mean to suggest that the theory is guaranteed to remain broken even if we replace the projection postulate with something else. I don't know what that would be in Bohmian mechanics, but it has to be something. Every theory needs a rule that associates preparation procedures with mathematical things that can represent them.

    The only thing I said (or rather inadvertently suggested, by my precise choice of words) that your argument seems to refute is that we need the full theory (=mathematics+correspondence rules) to find decoherence. I agree of course that decoherence is present in the purely mathematical part of the theory.
     
  18. Jun 18, 2012 #17
    In my opinion the only reasonable interpretation is the "Mind makes collapse" interpretation.
    I explained this starting with introductions of metaphysics, noting that purely mathematical laws of physics can only describe a mathematical universe, with a merely mathematical existence.
    There needs to be something beyond mathematical laws to both provide for existence beyond mere mathematical existence, and for non-algorithmicity.
    Because the mind's behavior cannot be purely algorithmic, for at least 2 reasons:

    One is that, again, a purely algorithmic behavior cannot account for the notion that we "really exist" (that we have an authentic feeling of our existence, that morality makes real sense), because otherwise our existence would be purely mathematical, making any concept of probability devoid of any sense (since all possibilities equally exist mathematically, none of them can meaningfully be said more probable than another) and therefore in contradiction with the fact that such probability laws exist and have been verified.

    The other is that the reasoning power of the mathematician can know things such as the consistency of ZF, that cannot be proven out of any formal system that can be reasonably assumed to be his. I am planning to soon add this point to my site on set theory and the foundations of mathematics - this will come after the many also very important things already there that you will surely not finish reading before I add it.

    I observe that once started from these ideas and formalized them on the case of Markov processes, the principles of quantum physics can appear much more natural and intuitive, less paradoxical, than otherwise; and also the thermodynamical time orientation that comes from apparently nowhere is quite well explained in this view.
     
  19. Jun 18, 2012 #18

    bhobba

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    Here we go again with its only math stuff. What don't you get about system states being mapped to stuff out there like a particles position, momentum, spin, or whatever, and because of that is not purely mathematics? Do you believe the same thing about the points and lines of Euclidean Geometry? That's just math as well under your view. But suggest that to a surveyor and you are likely to get some weird looks.

    That's not to denigrate the mind makes collapse view - Von Neumann thought so (so does Roger Penrose who goes a step further and believes he has found processes in the brain that do it) - its perfectly valid - just a bit too over determined for my tastes and not at all necessary. IMHO. However all interpretations suck in some way and its a matter of personal preference which one sucks the least.

    Here is a Link about Penrose's views:
    http://www.quantumconsciousness.org/penrose-hameroff/orchor.html [Broken]

    BTW Markov processes can not be used as a model for QM - fundamental theorems show they always converge to a single state or cycle.

    That is the essence of Quantum weirdness - in order to allow continuous transformations between states you must go to complex numbers - if not you get funny behavior like those of Markov chains. In fact a Wiener process (itself a Markov process) models QM if you do a Wick Rotation into complex numbers. Many people have been struck by this and have tried to figure out a way it can be used as an interpretation of QM but it has not proved successful.

    Thanks
    Bill
     
    Last edited by a moderator: May 6, 2017
  20. Jun 19, 2012 #19

    Demystifier

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    Then I probably misunderstood you, because I agree with the above. :approve:
     
  21. Jun 20, 2012 #20
    I suggest you read the information interpretation (Zeilinger 1999+). In this interpretation, what we would usually call "the system" in physics is considered an amount of information (in the most existential sense) and is only considered a particle, an amount of energy, mass, etc. in a secondary sense. This changes everything. What you're calling "the projection postulate" or "the measurement problem" is nothing more than a consequence of the rules that govern information theory, which governs quantum mechanics (or at least in the information interpretation).
     
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