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Bohmian mechanics as 'complete' theory

  1. Jan 17, 2013 #1
    Hello, forum!

    I am puzzling my way through some interpretation. In the famous EPR paper, the authors ask whether quantum mechanics is a 'complete' theory in the sense of whether or not the wave function completely describes the physical circumstances in question. EPR conclude that it is not complete.

    Setting that aside, my question is: how would the same authors feel about Bohmian mechanics? Is it correct to say that, taken on its own terms, Bohmian mechanics would be accepted by Einstein as a 'complete' theory? After all, it expressly holds to nonlocality and 'spooky action at a distance'.
     
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  3. Jan 17, 2013 #2

    ZapperZ

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    May I suggest that you spend some time browsing through the Quantum Physics forum first? There have been a lot of threads on this very topic that have been discussed. I know that it may be tedious to weed through pages and pages of threads, but it shouldn't take you that long to discover a couple of them.

    Furthermore, the question of something being "complete" is often a philosophical question, especially when one has no physical evidence to support the argument one way or another. You will notice that, more often than not, such preferences for one or the other are based on TASTES. We need to try and limit such philosophical discussion and stick to just physics.


    Zz.
     
  4. Jan 17, 2013 #3
    How disappointing that this is the first reply I receive on this forum. I hope it does not reflect the overall quality of discussion here.

    You may note that the problem of completeness is not a 'philosophical' question as you say, but the very issue Einstein had with quantum mechanics. To wit:

    "In a complete theory there is an element corresponding to each element of reality."

    That is a scientific definition of 'completeness', and taken from the EPR paper. It is the definition of completeness put forward by Einstein himself.

    My question is not a philosophical one, but more a history-of-physics question, if anything. It asks: would Bohmian mechanics be considered 'complete' according to Einstein's definition given that it allows for non-locality?

    I am amazed that this scientific question (whether a theory is deterministic) would be put down as 'philosophical' by you and a 'matter of taste'.
     
  5. Jan 17, 2013 #4
    AFAIK there are no experiments that can separate Bohmian Mechanics from the more common interpretations of QM. Therefore it is a philosophical question. Either way, it's pretty difficult to say what Einstein would think. If he were frozen in his 30's until today, I bet he would be willing to accept whatever experiments show. He would probably struggle a little with both (all) interpretations the same way that most people do. That being said, he's dead... so you can't prove me wrong!
     
  6. Jan 17, 2013 #5
    My question is not whether Bohmian mechanics is preferable to quantum mechanics. It is not "Which one is better?"

    This may be the question appearing in other threads. My question is: is Bohmian mechanics regarded as a complete theory in the sense of EPR?

    As these forums seem more devoted to answering homework problems, I'll happily withdraw my question.
     
  7. Jan 17, 2013 #6
    Yes, as I understand it, Bohmian mechanics is complete as per EPR criteria but it involves non-locality and a hidden variable (position); that is, the wave function provides only a partial description of the system. In Bohmian mechanics, the description provided by a Schrödinger-evolving wave function is supplemented by the information provided by the configuration of the particles. Thus, the description is completed by the specification of the actual positions of the particles. Consider this quote:
    Bohmian Mechanics
    http://plato.stanford.edu/entries/qm-bohm/#com

    The Einstein-Podolsky-Rosen Argument in Quantum Theory
    http://plato.stanford.edu/entries/qt-epr/#CR

    If you haven't read it, you might want to read the Stanford piece on Bohmian mechanics written by Goldstein and the Stanford EPR argument to see if you're convinced of that.
     
    Last edited: Jan 17, 2013
  8. Jan 17, 2013 #7

    Demystifier

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    Yes it is.

    Nevertheless, Einstein did not like Bohmian mechanics (BM). (BM has appeared in 1952, while Einstein died in 1955.) The reason is the fact that, at that time, Einstein has been preoccupied with developing his radically new unification theory, so at that time he thought that BM was "too cheap".

    Had BM appeared in 1935 when the EPR paper appeared, Einstein would probably not call it "too cheap", but he would still not be satisfied with it because it was nonlocal, while locality was one of central assumptions in the EPR paper.

    Had the Bell theorem (which appeared in 1964) also known in 1935, according to which it is impossible to have both reality and locality, I believe that in such a context Einstein would like BM in 1935 very much.

    For an alternative hypothetical history of foundations of quantum mechanics see also
    http://arxiv.org/abs/physics/0702069 [Am.J.Phys.76:143-146,2008]
     
  9. Jan 17, 2013 #8
    Homework problems are actually not allowed in this part of the forum. Your OP sounded to me like one of the all-to-common questions that deify people such as Einstein. I apologize for misinterpreting.

    When it comes to observables in QM that have a classical analogue, I think Bohmian Mech. would easily be considered complete. My questions start to arise with spin. I have read that BM can explain spin, but I don't know much about it. The non-scientific sources that I have read haven't convinced me, but I really haven't had the time to devote to a full understanding. You would probably answer your question by pursuing this question. I don't know what you'll find.

    On this note, if anyone know of any good intros to BM that just present the theory instead of explaining why it isn't wrong, I would like to take the time to learn more at some point.
     
  10. Jan 17, 2013 #9
    Thanks all for your replies.

    The statistical mechanics connection is the one I have been looking for, I think. There seems little doubt that Einstein considered statistical mechanics 'complete' in the sense he was looking for in QM.

    I've come across that 'too cheap' quote elsewhere. I'd love to see the original German to perhaps get a better sense of what he was saying at that moment. Does anyone happen to know of any online resource with Einstein's letters to Born in the original German?

    Thanks again for all helpful replies.
     
  11. Jan 17, 2013 #10

    DrChinese

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    Welcome to PhysicsForums, ho.ho.cho!

    I would agree that in EPR terms, Bohmian class theories are "more" complete than QM - and possibly "complete".

    The sticking point might be whether the unknown/unknowable initial distribution within BM is more of a philosophical restriction or a practical one. At some point semantics enters the equation to settle this. So in that sense I agree with ZapperZ. By the way, I think over time you will come to realize that ZapperZ is quite knowledgeable. His words may be few, but there is plenty of wisdom* in there as well the occasional tart.

    *OK ZapperZ, you owe me for that plug. :smile:
     
  12. Jan 17, 2013 #11
    It seems to me that sometimes we may be too quick to ascribe to difficult problems the qualities of murkiness or 'taste' in order to escape them.

    In EPR, completeness is explicitly defined as a one-to-one correspondence between elements of a scientific description and elements of a physical situation. Whether completeness is an important or a meaningful criterion, of course, isn't important here.

    Given the above, anyone with a sufficient grasp of deBroglie-Bohm or Bohmian mechanics (not me) ought to be able to say: yes or no, one or the other is complete or incomplete in the sense of EPR.

    I'm more or less in agreement with what I've read above. But nailing it down, of course, is why I've presented it on the forum -- and why it's interesting.

    From what I've been reading, there's something of a distinction that could be made between deterministic and complete. Bell is quoted in the Stanford article as saying determinism was lurking in the background of EPR. But if Einstein's example of what he thought was a better situation for QM -- something along the lines of statistical mechanics in a classical context -- is true, it might be clear why EPR chose 'complete' rather than 'deterministic' as the name for what they perceived to be lacking. The problem might have been less about causality than it was about escaping complementarity.

    I think that BM is dubbed a 'hidden variables' theory only to the extent that it tries to avoid complementarity. When it comes to identifying the variables in it that are supposedly hidden, though, I don't see that they are truly hidden. Nothing new is introduced. I might be wrong here, but it seems to simply restate QM in a way that removes the observer/measurement problems, which is why it strikes so many as 'cheap' or trivial.

    (Thanks for the interesting/informative conversation.)
     
  13. Jan 17, 2013 #12
    Here's a simple question: is the guiding wave/pilot wave the 'hidden variable' in deBroglie-Bohm?

    Cheers!
     
  14. Jan 17, 2013 #13
    Also, I think there may be something wrong in what I wrote above.

    If 'deterministic' is taken to mean *non-probabilistic outcome*, then it could probably be said that EPR thought QM was incomplete to extent that it was not deterministic in its predictions.

    But then what about statistical mechanics? Does statistical mechanics yield deterministic, non-probabilistic outcomes?
     
  15. Jan 17, 2013 #14
    Yes, in a sense, the true "hidden" variable is actually the wave function as it is the wave function that cannot be measured. Having said that, with respect to the completeness argument, the position is usually considered as the hidden variable. To answer Bell's question:
    The deBroglie-Bohm theory takes the first option: the description provided by a Schrödinger-evolving wave function is supplemented by the information provided by the configuration of the particles. But in reality, it is actually the wave function that is hidden.
     
  16. Jan 17, 2013 #15
    So, it's 'hidden variable' vs. 'incomplete' in terms of the two charges both sides level at each other. EPR and Bohm would say QM is incomplete. Their positions all vary, but in general it might be said that they all hold a 'realist' position, i.e. what is down there, at bottom, must be ontologically real. Like in classical physics. So to escape the probabilistic outcomes of QM, they say there must be some theory that has enough variables (one for each component of the physical system) that the predictions are not just open probabilities.

    But here I ask again -- and happily show my ignorance -- how is this different than statistical mechanics? Does statistical mechanics really ever make predictions that are not rooted in probability but instead that are totally 'determined' by initial conditions? I suspect this is so, but would like confirmation.
     
  17. Jan 17, 2013 #16

    rubi

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    Your definition of completeness depends heavily on your definition of reality. If your definition of reality includes the fact that every particle should have a definite position, then of course QM is not complete and Bohmian mechanics might be. However it is not clear at all, why reality should be like this. It might as well be, that position is just not a property of a particle but merely a useful concept for physics. The wave function might already include everything we can possibly know about reality. With this definition of reality, QM is already complete (according to your definition) without any necessity for guiding waves and so on.

    With the methods of science, we can never find out what "reality" is really supposed to mean, because we can only know what we can actually measure. The concept of a definite position for every particle in every moment is only an idealistic idea with no scientific justification. What reality really is, is therefore a philosophical question and thus your definition of completeness, which depends on the question what reality is, is also mere philosophy. It is not at all a scientific criterion to classify theories of physics, because the answer depends on ones idealistic idea of reality, which is a question of philosophy or even religion.
     
  18. Jan 18, 2013 #17

    Demystifier

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    Yes it is.
    First, because it is not directly measurable, so is hidden.
    Second, because it is supposed to exist even when no measurement is performed.

    Note that particle positions are hidden variables in deBroglie-Bohm only by the second criterium.

    Finally, see
    https://www.physicsforums.com/blog.php?b=3077 [Broken]

    EDIT: Now I see that bohm2 already said something similar.
     
    Last edited by a moderator: May 6, 2017
  19. Jan 18, 2013 #18

    Demystifier

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    Statistical mechanics does not make non-probabilistic predictions. However, statistical mechanics is DERIVED from a theory which makes non-probabilistic predictions. In this sense, Bohmian mechanics is not like statistical mechanics, but like the theory from which statistical mechanics is derived.
     
  20. Jan 18, 2013 #19
    I keep hearing this. What is amusing about it is three-fold:

    1. The arbitrary distinction between science and philosophy. Most of Newton's written works dealt with theology. Einstein never erected any kind of firewall between his 'scientific' and 'religious' ideas, which meant he could make objections like "God does not play dice". The best minds in physics routinely mix what might be called 'scientific' and 'religious' lines of thought -- not when it comes to scientific proof or demonstration, but always at the level of personal imagination and thought. The idea therefore that there is 'mere philosophy' seems more something people on the lower rungs of the physics ladder repeat in a natural tendency to assert the importance of their own field.

    2. When it comes to questions like, for example, the 'completeness' of a given theory -- some of the best minds in physics dealt with this question on both sides of the debate. To therefore declare that the question of, in this case, the completeness of QM is a non-scientific one or 'mere philosophy' demonstrates an ignorance of what science is. Scientific demonstration always takes place within a broader conceptual and mental context. While the rules of demonstration and argument must always remain rigorous, the generation of scientific knowledge always takes place in a broader, less rigorous context of free thinking. I'll just note in passing that the EPR paper seems to reflect exactly this. The broader context dealt with the issue of completeness. The narrower context dealt with the so-called EPR paradox. According to Wikipedia:

    So at the heart of the EPR paper was a thought-experiment involving two entangled particles. This was the experimental side of the argument. The other side dealt with the 'completeness' of theories using a narrow definition. It was no less scientific just because it touched on matters not strictly undertaken within experimentation. It informed the creation of the thought-experiment.

    3.

    The above is already a philosophical interpretation, a philosophical conclusion derived from a certain reading of the EPR/QM dispute. There is nothing in the EPR paper, for example, that has to do with the ultimate meaning of reality. So where does the commenter above get this? It's introduced from the outside; in other words, it is philosophy. But it is also a kind of dogmatic assertion designed to compel belief. I would say that all leading physicists are concerned with what 'reality' is to the extent they are concerned with the truth of what they are saying. Even if they decide that the reality in question cannot be determined because for example the collapse of the wave function is an objectively real fact; or, if on the other hand, they think there is no objective collapse, but the true situation is unknowable. The point here is, though, that these differences in 'mere philosophy' drive the direction of research. Experiments are devised and performed in order to test these differing perspectives in 'mere philosophy'. Much of the work done in QM since the '30s has been undertaken precisely to resolve these disputes in order to find out the truth. So pooh-pooh 'mere philosophy' if you like. But all the great physicists are actively engaged in it to the extent that they interpret results and wonder what they might 'mean'.
     
  21. Jan 18, 2013 #20

    Demystifier

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    Bravo!!!! :approve:
     
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