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Relationship between Bohmian trajectories and Feynman paths ?

  1. Aug 20, 2012 #1
    Relationship between "Bohmian trajectories" and "Feynman paths"?

    Can someone summarize what (if any) relationship there is between these two? I've read that Bohmian trajectories are very different than Feynman paths but I've also come across papers suggesting that "Feynman method of summing over all paths can be constructed with the de Broglie-Bohm theory at its basis". It seems that these two views are incompatible.
     
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  3. Aug 21, 2012 #2

    Demystifier

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    Re: Relationship between "Bohmian trajectories" and "Feynman paths"?

    I would like to see those papers suggesting that "Feynman method of summing over all paths can be constructed with the de Broglie-Bohm theory at its basis", even if they are not (yet) published in peer reviewed journals. I know moderators do not like links on unpublished papers, in which case you can send me a PM.
     
  4. Aug 21, 2012 #3
    Re: Relationship between "Bohmian trajectories" and "Feynman paths"?

    I've sent you the link (PM) as I doubt that the journal "The Waterloo Mathematics Review" would be deemed acceptable as per forum guidelines. Looking forward to your input (if any).
     
  5. Aug 21, 2012 #4

    Demystifier

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    Re: Relationship between "Bohmian trajectories" and "Feynman paths"?

    Thanks, bohm2. I have three negative comments on the paper.

    First, the deBroglie-Bohm path integral (8.1) is not new.

    Second, equation (8.1) is also quite useless. Namely, to calculate psi by this equation you must know L_q and v^psi, which is essentially the same as knowing psi. In other words, (8.1) can be used to calculate psi only if psi is already known.

    Third, their derivation of Feynman path integral from deBroglie-Bohm path integral (8.1) is wrong. Namely, in 3th-4th line of page 29 they say that mv^psi=p is constant. But in fact it is not constant. It is constant only for a plane wave, but not for a superposition of plane waves in (8.2). Due to that error, their "proof" is incorrect.
     
  6. Aug 21, 2012 #5

    Demystifier

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    Re: Relationship between "Bohmian trajectories" and "Feynman paths"?

    To conclude, Feynman-path formulation of QM and deBroglie-Bohm path formulation of QM are quite independent. Some relations between them exist (after all, they are observationally equivalent), but these relations do not seem very interesting.

    What I find more interesting is the fact that Feynman at one place uses Bohmian equations of motion in a totally different context:
    https://www.physicsforums.com/showthread.php?t=448366
     
    Last edited: Aug 21, 2012
  7. Nov 14, 2012 #6
    Re: Relationship between "Bohmian trajectories" and "Feynman paths"?

    While I haven't read the piece or watched the video yet, I found a paper and this Perimeter video lecture suggesting some link between the two. I'm not sure if one would consider the relations between the two as interesting (assuming his arguments are meaningful):
    Bohm Trajectories, Feynman Paths and Subquantum Dynamical Processes
    http://www.math.ryerson.ca/~gord/abstracts/PiQudos/PiQudoswebH/index.html

    http://streamer.perimeterinstitute.ca/Flash/01a99ea2-1d23-4eb9-b7f0-b5dc3ae3cd13/viewer.html [Broken]

    I'm not sure if this paper suggests a link also:

    Bohmian trajectories and the Path Integral Paradigm. Complexified Lagrangian Mechanics.
    http://arxiv.org/pdf/0808.1245.pdf

    But these seem inconsistent with this argument by Tumulka or am I mistaken:
    Feynman’s Path Integrals and Bohm’s Particle Paths
    http://arxiv.org/pdf/quant-ph/0501167.pdf
     
    Last edited by a moderator: May 6, 2017
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