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Question on the probabilistic nature of QM

  1. Jun 3, 2012 #1
    Question on the "probabilistic" nature of QM

    I read very recently something that I interpreted as stating that certain quantum-mechanical phenomena are necessarily probability-based: for instance the exact path traversed by a photon/electron in the double-slit experiment.

    That's all well and good, but the material seemed to make an implication that I've been having a lot of difficulty reconciling or finding an appropriate analogy for in classical terms: that the phenomenon in question, whatever it may be, is genuinely random. That is to say, the exact, actual result has no identifiable cause.

    The notion of randomness, to me, has always seemed like an idealisation: we create a situation in which an event has no actual cause, and therefore the occurrence of which can't be exactly predicted, and apply this model to situations in which we have insufficient information or methodology to obtain a perfect prediction. I wouldn't call such a situation "genuine randomness" because we can identify factors which contribute to causing the result, but the model fits well enough I suppose.

    Problem is, I can't think of any classical situations in which this notion of genuine randomness actually applies. If you consider, for example, a computerised random number generator, it can generate numbers that are approximately genuinely random very well in many cases, but it always needs a seed of some kind: an example of the cause-and-effect logic I've come to believe is necessary at a classical level.

    So, finally, the question(s): a good place to start would certainly be, am I just interpreting the information wrong? Do we know for sure that quantum mechanics obeys this genuine-randomness-dependent behaviour? If not, then what do we suppose determines the behaviour of quantum mechanical phenomena? If so, then how is it that the behaviour is determined without a cause?

    As always, any insight would be much appreciated. This has me quite puzzled.
     
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  3. Jun 3, 2012 #2

    Hurkyl

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    Re: Question on the "probabilistic" nature of QM

    You are having trouble imagining "genuine randomness" because you insist on instead imaging "there's extra stuff that we don't know that determines what's going on".

    There's a class of theories called "hidden variable theories", which postulate that the state of a particle includes information beyond the quantum mechanical description, and that this extra information determines the results of measurement.

    The point of Bell's theorem is that it is a no-go theorem -- it proves that a vast class of hidden variable theories are mathematically incapable of reproducing the predictions of quantum mechanics even for very simple systems.

    Instead, if you want a deterministic version of quantum mechanics, you have to embrace quantum "weirdness" and go in directions such as MWI or Bohmian mechanics.
     
  4. Jun 3, 2012 #3

    bhobba

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    Re: Question on the "probabilistic" nature of QM

    The fundamental axiom of QM is the superposition principle which trivially shows the possible system states form a vector space. First thing to note is determinism is contained in a statistical theory - but it only allows probabilities of zero or one.

    Now there is a Theorem called Gleason's Theorem that shows there is really only one way to define probabilities on a vector space - that being the way QM does it. There is an out - the hidden assumption is states do not depend on other states it may part of a basis with - this is known as non-contextuality - that's how Bohmian Mechanics gets around it - its deliberately concocted to be contextual. Now if we try to only assign zero and one we find a contradiction - you can't do it - this is the celebrated Kochen-Specker Theorem - but it is a simple corollary to Gleason's Theorem. So classically probabilities are all you can have in QM - its implied by its fundamental axiom - the Superposition Principle - no way out of it unless you want to be really sneaky and introduce contextuality - which I personally find unnatural - but to each his/her own.

    Thanks
    Bill
     
  5. Jun 3, 2012 #4

    Jano L.

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    Re: Question on the "probabilistic" nature of QM

    Exactly. What is genuine randomness? As you point out, it is hard to find a clear example of it. Perhaps it can be defined mathematically?

    Or perhaps "true randomness" is just a belief that probability is the ultimate physical quantity and there is no better theory than Born's rule.

    I suspect that people proposing "true randomness" find searching for explanations too difficult but still want to appear as sage thinkers.
     
  6. Jun 3, 2012 #5
    Re: Question on the "probabilistic" nature of QM

    I tend to think all the opposite way. I tend to think that the universe is deterministic and that randomness is apparent and it appears because of insuficient information about the instrument which is making the measure. I gave some details of my point of view in the following link:

    https://www.physicsforums.com/showthread.php?t=609087

    but nobody said nothing about this. What do the experts think? Is it wrong? Is it against some experiment?

    Thanks!
     
  7. Jun 3, 2012 #6

    Ken G

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    Re: Question on the "probabilistic" nature of QM

    I have heard a lot of people who like "fundamental determinism" but hate "fundamental randomness." I find it curious that they don't see these two as simply opposite sides of the same coin-- the coin of what science has at its disposal with which to make working models. In other words, neither one of those phrases has any business including the word "fundamental" (or "genuine")-- what the heck does that mean anyway? I challenge anyone to supply a scientifically testable (not religious or philosphical) way of saying how you could tell if something is "fundamentally" random or deterministic. It's sheer nonsense, it all stems from an error in understanding what science does. Nothing that science does is "fundamental", never has, never will. Once you understand that, the whole problem just goes away-- some models invoke determinism, others invoke randomness, neither is the least bit "fundamental."

    Any who doubt that should answer this: what empirical tests has classical physics passed that showed it was "fundamentally deterministic", that I could not devise a "fundamentally random" version of classical physics that would pass all those same tests? What empirical tests has quantum physics passed that shows it is "fundamentally random", that I cannot supply a version that passes all the same tests yet is "fundamentally deterministic"?

    In other words, I see no justification at all to be bothered by models that are "fundamentally random" but happy with models that are "fundamentally deterministic." A model is what it is: just a model. We layer on interpretations for various reasons, but they are not unique to the theory, and we should not bother with worrying whether or not they conform to how we'd like the universe to be. That's just not the job of the scientist.
     
  8. Jun 3, 2012 #7

    bhobba

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    Re: Question on the "probabilistic" nature of QM

    Yes it can be defined mathematically - see the works of Kolmogorov for example.

    It's not a belief and its not that people find searching for explanations too difficult - some of the greatest minds in history tried and failed to get around it in QM. And indeed powerful mathematical theorems such as Gleason's Theorem exists showing it is pretty much impossible if the superposition principle holds - and many many experiments show it does.

    Thanks
    Bill
     
  9. Jun 3, 2012 #8

    Ken G

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    Re: Question on the "probabilistic" nature of QM

    Yet there are two problems that trouble me about the language that is often used, along the lines that quantum mechanics is "genuinely random" and classical mechanics is "genuinely deterministic":
    1) Things like Gleason's theorem apply to the postulates of some theory (or some version of some theory), not to the universe. Nor does it follow that, simply because our theory has not been falsified by experiment, it must be a correct way to say what the universe is actually doing. We always have to keep separate what the universe is doing, from how we construct our theories, or we fall into the unending fallacy of mistaking our own current best understanding with the way things actually are. Haven't we learned yet the error in doing that? The map is not the territory.
    2) Even once we recognize that we are discussing a particular model, not the universe itself, it still isn't clear if we can unambiguously label one theory as "determinstic" and another as "random." As you said yourself, quantum mechanics can be interpreted either way, because Gleason's theorem requires assumptions that go farther than what has actually been experimentally justified. Same for classical mechanics-- deterministic theorems in classical mechanics also invoke assumptions that go beyond what is necessary to get experimental confirmation of the theory, which is exactly the reason that people thought the Newtonian paradigm was correct long before we discovered quantum mechanics. It's high time we recognized that "is the universe random or deterministic" is simply not a scientific question, and nothing that science does ever gives us a definitive or unambiguous answer to that question. It will always be a matter of interpretation, or better yet, a question that is best dispensed with as being outside the purvey of scientific investigation.

    The real question for science is, "what mastery and understanding do we obtain by imagining the universe is deterministic, or random?" Anyone addressing that question would have a very hard time dismissing either one of those analysis tools, they are both quite essential to the everyday practice of science, no matter what interpretation we paint over it.
     
    Last edited: Jun 3, 2012
  10. Jun 3, 2012 #9

    zonde

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    Re: Question on the "probabilistic" nature of QM

    I believe the question is not about universe being deterministic, or random but about some rather limited part of the universe being deterministic, or random.
     
  11. Jun 4, 2012 #10

    zonde

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    Re: Question on the "probabilistic" nature of QM

    You have seen works of Kolmogorov, right? So can you provide mathematical definition for genuine randomness?

    Do you say there are many many experiments showing that QM applies to single particle?
     
  12. Jun 4, 2012 #11

    Ken G

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    Re: Question on the "probabilistic" nature of QM

    But is there any such thing as a "limited part of the universe"? Seems to me you are talking about models, not the universe-- it is only models that are limited, the universe just is.
     
  13. Jun 4, 2012 #12

    Jano L.

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    Re: Question on the "probabilistic" nature of QM

    They did not fail, they just did not explain everything satisfactorily yet. There were genuine developments in explanations of QT after the Bohr paper refuting EPR in 30's - Bohm's theory, stochastic QT, stochastic electrodynamics/optics, classical models of light detection con-incidence experiments. This development occurs mainly because there are physicists that are not satisfied by "true randomness".

    In my opinion, these are contributing to understanding of the phenomena that were before described merely as random quantum jumps. I would not call that a failure, but rather partial success. The quest, of course, continues.
     
  14. Jun 4, 2012 #13

    Ken G

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    Re: Question on the "probabilistic" nature of QM

    What's more, you can certainly like or hate the deBroglie-Bohm approach, but at least for nonrelativistic QM, it seems clear that this approach has refuted the claim that you must view QM as "fundamentally" random. So we now can pick and choose however we wish to think of QM-- whether random, or deterministic, or best of all in my view: not fundamentally either one, because neither are ever fundamental descriptions. Models just don't have "fundamental" descriptions, and the universe certainly doesn't-- all descriptions are both subjective and provisional to the current state of knowledge and cultural preferences.
     
  15. Jun 4, 2012 #14

    Jano L.

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    Re: Question on the "probabilistic" nature of QM

    My words, Ken G. Regarding your previous post, I am curious though, do you think it possible to simulate every known deterministic model by a probabilistic model? I think this is hard. Equation of diffusion is easily simulated by random walk process, but think of, say, Schroedinger's time dependent equation for a molecule. It would be great to replace such complicated PDE by some variation of the monte carlo method or so, but is this possible?
     
  16. Jun 4, 2012 #15

    Ken G

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    Re: Question on the "probabilistic" nature of QM

    It won't be formally the same model, but it can agree with all the same observations, so it will be an equivalent model. One can only use other kinds of ways to select models like that, subjective issues like preferred interpretations or different ways to apply Occam's razor. For example, many people are quick to point out that classical chaos theory is a deterministic model, but I say, how can you tell? The model achieves predictions that quickly become nondeterministic, so even if it is deterministic in some mathematical sense, it is functionally not deterministic whenever used as a physical theory, i.e, whenever tested by observation. This also means that a random model, like statistical mechanics, will achieve the same degree of agreement with observation, so the models cannot be distinguished by anything empirical when applied to general situations.

    Even pure Newtonian physics can be used to spawn a probabilistic theory by simply noting the highest precision that Newtonian physics has been tested with, even in situations of very high quantum numbers, and notice that the theory cannot be said to apply to exact inputs, since no such thing ever exists anywhere in physics. All theories must be able to work on inexact initial conditions, and have never been tested in any other context, so they are all statistical, automatically. No theory asserts or requires that the theory must still work if the input data uncertainty is reduced arbitrarily, that never happens in physics so it is no kind of requirement of any model. Purely deterministic models are simply a class of model that don't tell you the level of precision at which they become physically impossible to test.

    I would imagine that a Monte Carlo treatment of the Feynman path integral formulation would suffice nicely. The path integral can be viewed as a formally mathematical exact structure, but it doesn't need to be viewed that way, nor has it ever been tested to be so. Why should we assume that any "slop" in a theory based on path integrals could be arbitrarily reduced by arbitrarily more precise measurements? When is that ever possible to demonstrate, and when is it ever likely to be true? Determinism could easily be a complete illusion of insufficiently precise measurements, as any probabilistic theory can be made to look deterministic with poor enough resolution.
     
    Last edited: Jun 4, 2012
  17. Jun 4, 2012 #16

    bhobba

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    Re: Question on the "probabilistic" nature of QM

    This is well known to math students:
    http://en.wikipedia.org/wiki/Probability_axioms

    Thats not what I said - I said many many experiments support the superposition principle.

    Thanks
    Bill
     
  18. Jun 4, 2012 #17

    zonde

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    Re: Question on the "probabilistic" nature of QM

    Just to be sure that we are talking about the same thing. Do you mean "genuinely random" in the same sense as OP?

     
  19. Jun 4, 2012 #18

    zonde

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    Re: Question on the "probabilistic" nature of QM

    Well yes, I am talking about models. We can't meaningfully discuss reality (if that's what you mean with universe). It's always models.
     
  20. Jun 4, 2012 #19
    Re: Question on the "probabilistic" nature of QM

    in concise terms:


    how is it that the behaviour is determined without a cause?

    actual result has no identifiable cause.

    forget 'genuine determinism' 'fundamental' cos we need zero ramble.
     
  21. Jun 4, 2012 #20

    Ken G

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    Re: Question on the "probabilistic" nature of QM

    Yes, and that helps answer-- if we are talking about models, then it doesn't have to be an either/or proposition, deterministic or random is not necessarily uniquely specified, it might just be how we are interpreting our models. For example, the OP connects randomness with lacking a cause, but the concept of cause is also a kind of interpretation. The exact same physical phenomenon could be accurately predicted using language that avoids causation, or language that embraces it, and yet it's still the same "happening."
     
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