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Bohmian Mechanics

  1. Dec 10, 2004 #1
    Recently, I read Bohm's articles explaining his interpretation of Quantum Mechanics. I did not find anything "bad" with it, so why didn't anybody pursue it further? Any experimental evidence against its predictions?
  2. jcsd
  3. Dec 10, 2004 #2
    Did you not notice the central role of the position representation ? In Copenhagen interpretation, there is no well-defined trajectory, because one cannot speak about objects by themselves outside measurement. Bohm attempts to keep classical concepts valid, which is very questionable ! Do you not think that QM teach us that the microworld is very different from the macroworld ? In the same context, the process of decoherence is well understood in Copenhagen interpretation, but quite artificial in Bohm's theory. The worse IMHO, is the fact that this interpretation is in conflict with elementary Lorentz invariance (which is due to the central role of non-locality. In Copenhagen interpretation, non-locality is also here but limited to EPR-like phenomena). Bohmian mechanics cannot be formulated in a Lorentz-invariant way, which is not the case for Copenhagen interpretation.

    For instance : http://en.wikipedia.org/wiki/Bohm_interpretation
  4. Dec 10, 2004 #3

    Doc Al

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    Staff: Mentor

    There's still quite a bit of interest in it. You might want to take a look at Shelly Goldstein's review article (Stanford Encyclopedia of Philosophy) here:
  5. Dec 10, 2004 #4
    Yes, Doc Al is right. Plus the fact that Stanford Encycl. Phil. is such a great ressource. Actually it is quoted in the wikipedia link. Wikepedia is more scientific : less discussion (which is bad) but more equations (which is useful)

    I also wanted to add a welcome for you George Isaac :smile:
  6. Dec 10, 2004 #5


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    Staff: Mentor

    As I recall, Bohm's version of QM doesn't make any experimental predictions that distinguish it from "standard" QM, so there isn't even a possibility of experimental evidence one way or the other.
  7. Dec 10, 2004 #6
    What's your opinions about Landau's work on QM?
  8. Dec 11, 2004 #7
    BM is only an equivalent model of QM (formally). Only the interpretations of BM are questionable (as well as the QM interpretations ;).

    BM is the explicit display of the QM statistics through the Q observable. we replace the schroedinger equation (evolution of the state |psi(t)>) by 2 equations : the rho(q,t) time evolution (probability conservation law) and the v(q,t) time evolution (the Hamilton-jacobi equation).
    As long as we stay with these two variables, we always recover the QM results (including the measurement postulate). However, to solve the rho(q,t) and v(q,t), we almost always need to solve the schroedinger equation first. Thus, this model is not much useful to get initial results. This may explain why this model is not much used today (even if some experts are using it).

    The questionable interpretation of BM concerns the v(q,t) field: you can attach an extra equation "the bohmian particle path": dq/dt=v(q,t). However, this path cannot be measured (included in the statement of the BM). Therefore, it is quite a philosophy to accept or not its "reality" (no testable results of QM depends on the existence of this path).

    The Lorentz invariance is more hidden in BM but we still have it as a formally equivalent QM model. It is analogue to the Lorentz invariance of EM field with either the coulomb gauge (you have an instantaneous V pontential) or the lorenz gauge (we can view BM as QM with “the coulomb gauge”, ie the Q observable).

    However, in my humble opinion, BM model is a very interesting tool to understand how QM works. It also helps in demystifying the measurement problem of QM and some paradoxes.

  9. Dec 11, 2004 #8
    Dear George:
    I think Bohm's Mechanics is the last resort to those who needs particle trajectory. I would like to show you (one of these papers in that directory http://hume.iet.unipi.it/iannaccone/publications/ ) in which the author finally says if one needs to calculate the tunelling time without the debate about larmor times then turn your sight to BM in which you can navigate the electron in defined path with a defined propagation time. Unfortunately (as you know about me from myself my friend) I do not practice BM so I do not "know" how to calculte such thing in BM. I hope someone else give us more info
    Last edited by a moderator: Apr 21, 2017
  10. Dec 11, 2004 #9
    The decoherent histories interpretation actually allows you to describe paths for any particles at any times in the history of the universe from just after the big bang. There are some restrictions, however, that distinguish the paths from classical ones.

    If you choose to describe particle positions, then you can't describe particle momenta at the times you describe positions, and you need to course-grain these fine-grained particle descriptions by only looking at some particles at some times to get useful probabilities. Also, if a particle lacks sufficient entanglement with the rest of the universe then the particle histories interfere, as in the two particle paths in the two-slit experiment.

    Other than that, you can talk of a particle going from here to there in almost a classical sense.
  11. Dec 15, 2004 #10
    And he said ... what? would you explain or give link(s) to what the legendary Landau said?
  12. Dec 15, 2004 #11
    AFAIK, the work of Landau in his famous lectures is a (very good) restatement of Bohr's work and the Copenhagen interpretation.
  13. Dec 15, 2004 #12
    In Bohm's words ...

    Here are Bohm's own words on the subject, written around the time of his retirement in 1987:
  14. Dec 15, 2004 #13
    IMHO, BM is just another interpetation of QM. Personally, I like the idea that in time, particle trajectories then to collapse. That theory, using time as a parameter, can vary all the way from the Copenhagen Interpetation to the Bohm Interpetation.
    I should find that reference- about 6 months ago in www.arXiv.com.

    Personally, I think it just points out how little we are really sure about in physics. Avtually that just justifies how little I know.

  15. Dec 16, 2004 #14
    Today www.arXiv.org has posted a reasoned paper review by Oliver Passon of BM. Turns out that there are two relevant equations: the potential equation and the guidance equation. Bohm and his followers emphasized the potential equation as fundamental; whereas Durr and his school emphasized the guidance equation as fundamental, and called that approach "Bohmian Mechanics"-- hence some confusion about what BM means.

    An essential part of BM is a distribution of initial particle positions given by the squared modulus of the eigenfunctions. Given that, then Passon concludes that there is no experimental way to discern BM from ordinary QM.

    Here is the link to the paper:
    http://www.arxiv.org/PS_cache/quant-ph/pdf/0412/0412119.pdf [Broken]

    Ten pages long, it is the most concise review I am aware of.

    Last edited by a moderator: May 1, 2017
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