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Bohm trajectories and protective measurements?

  1. Sep 10, 2012 #1
    Bohm trajectories and "protective" measurements?

    I'm having trouble understanding the arguments presented in these papers. They seem to be both arguing against the de Broglie-Bohm theory bassed on the concept of "protective measurements". Is this just a rehash of the problems with the meaning of "weak measurements" described in previous threads and summarized in Demystifier's blog on that topic?
    Protective measurements and Bohm trajectories
    http://www.tau.ac.il/~yakir/yahp/yh26
    Meaning of the wave function
    http://arxiv.org/ftp/arxiv/papers/1001/1001.5085.pdf
     
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  3. Sep 11, 2012 #2

    Demystifier

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    Re: Bohm trajectories and "protective" measurements?

    The conclusion of the first paper is a variant of the so-called surrealistic Bohmian trajectories. They conclude that "Either the particle’s Bohm trajectory and its position are unrelated, or the particle’s position is irrelevant for its participation in local interactions." But this is almost the same as saying that either Bohm's trajectories are not real or they interact with other particles non-locally. Indeed, it is well known and accepted that Bohm's particles have non-local influences on each other, and the present paper just rediscovers it.

    However, this type of nonlocality is slightly softer than nonlocality needed for violation of Bell inequalities. Unlike violation of Bell inequalities, thys type of nonlocality CAN be explained in classical terms without superluminal velocities.

    Essentially, this is like arguing in the following way: "Bohmians claim that president Obama is a local object moving only within America. However, there is experimental evidence that Obama's decisions leave trace in Iraq and Afganistan. Therefore, the experiments show that Obama is present in Iraq and Afganistan and hence Bohmians are wrong." I think I don't need to explain why this argument is incorrect. But I have to say that the argument in the first paper is incorrect for exactly the same reason.

    Indeed, it is well known that Obama's decisions have a global impact and that, to understand THAT, it does not help much to think of Obama as a local object moving only within America. And yet, it is perfectly consistent, and even helpful to explain some OTHER phenomena, to think of Obama as a local object moving within America. The Bohmian particle trajectories are just like Obama - they are local and move under certain trajectories, but have some impacts far from their trajectories.
     
    Last edited: Sep 11, 2012
  4. Sep 11, 2012 #3

    Demystifier

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    Re: Bohm trajectories and "protective" measurements?

    Another good and relatively neutral paper (by Lev Vaidman who is NOT a strong supporter of the Bohm interpretation) on this subject is this:
    http://xxx.lanl.gov/abs/1207.0793
     
    Last edited: Sep 11, 2012
  5. Sep 25, 2012 #4
    Re: Bohm trajectories and "protective" measurements?

    This was a recent paper trying to combine aspects of Everett and Bohmian:
    But I think this part discussing the empty branches in Bohm's and what it implies is inaccurate:
    Combining Bohm and Everett: Axiomatics for a Standalone Quantum Mechanics
    http://lanl.arxiv.org/pdf/1208.5632.pdf

    As T. Maudlin points out:
    Remarks on flat-footed ontolgy
    www.math.rutgers.edu/~tumulka/shellyfest/maudlin.ppt

    Similar remarks were made in this paper by Peter J. Lewis:

    Empty Waves in Bohmian Quantum Mechanics
    http://philsci-archive.pitt.edu/2899/
     
    Last edited: Sep 25, 2012
  6. Sep 26, 2012 #5

    Demystifier

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    Re: Bohm trajectories and "protective" measurements?

    Many-world people argue that decoherence provides dynamical branching of the wave function which is sufficient to explain the illusion of collapse, and that Bohmian trajectories (as entities the only role of which is to fill up one particular branch) are superfluous.

    In a recent paper
    http://arxiv.org/abs/1209.5196
    I argue that Bohmian trajectories are more than that. I argue that they are needed even to explain the decoherence and branching itself. Namely, in a closed system (e.g., the whole Universe) in a state with definite total energy, the wave function governed by the Schrodinger equation does not depend on time at all. Without time dependence, there is no no change in the system, so there is no decoherence and no branching. One needs some additional time dependence not described by the Schrodinger equation. Bohmian formulation provides such a needed time dependence in a natural way in terms of conditional wave functions.

    For a closed system in a state with definite total energy it is not impossible to explain the time dependence with the many-world interpretation, but this requires a redefinition of the concept of time itself. (See Appendix A of the paper above.) Bohmian formulation explains it more naturally than the many-world interpretation, without any redefinition of the concept of time.
     
  7. Sep 26, 2012 #6
    Re: Bohm trajectories and "protective" measurements?

    Thanks, Demystifier. I had already seen your paper and I'm looking forward to reading it. There was another previous paper taking a different, more critical argument of Bohmian trajectories. I'm still trying to understand it and haven't read it fully but I'm thinking you have already read it but just in case you haven't:
    Are Bohmian trajectories real? On the dynamical mismatch between de Broglie-Bohm and classical dynamics in semiclassical systems
    http://arxiv.org/pdf/quant-ph/0609172.pdf
     
  8. Sep 27, 2012 #7

    Demystifier

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    Re: Bohm trajectories and "protective" measurements?

    Semiclassical is not classical, so a mismatch is expected. I don't see a problem with it.
     
  9. Sep 28, 2012 #8
    Re: Bohm trajectories and "protective" measurements?

    Demystifier:

    Could you explain in a bit more layman terms what this parsimony with time dependence and why it's not as natural in MWI?
    I've never heard anyone else mention any "time" problems for MWI, so this was intriguing.
     
  10. Sep 28, 2012 #9

    Demystifier

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    Re: Bohm trajectories and "protective" measurements?

    MWI says that there is nothing else except the wave function and that its evolution is always given by the Schrodinger equation. In this respect MWI is unique, because all other interpretations say that either there is something else except the wave function, or that the wave function does not always evolve according to the Schrodinger equation. I guess you already know that.

    Now consider the total wave function for the whole Universe. It is reasonable to expect that the total energy of the whole Universe has some definite value E. But then it is a simple consequence of the Schrodinger equation that the wave function does not depend on time. On the other hand, we see that the Universe does depend on time. This is not a problem for other interpretations, because either there is something else which depends on time, or the wave function itself depends on time because it does not really evolve according to the Schrodinger equation. But it is a problem for MWI, because MWI rejects both possibilities.

    I hope it is layman enough.
     
  11. Sep 28, 2012 #10
    Re: Bohm trajectories and "protective" measurements?

    Ok, makes sense, but isn't this then a well-known "problem" ?
    What would be a MWI'ers response?
     
  12. Sep 28, 2012 #11

    kith

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    Re: Bohm trajectories and "protective" measurements?

    How do we see this? The state of the universe can't be observed by an observer who is part of the universe.
     
  13. Sep 28, 2012 #12

    Demystifier

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    Re: Bohm trajectories and "protective" measurements?

    This problem is known, but perhaps not sufficiently well. I suspect that most MWI'ers would not know how to respond. Nevertheless, those who do know will say the following: The time independent wave function psi(x1,...,xn) depends, among other things, on positions which represent readings of clocks. So even if wave function does not depend on the evolution time t, it does depend on the clock time. In other words, there is no time without a clock. Of course, not everybody is satisfied with it, but this seems to be the best what can be done within MWI.
     
  14. Sep 28, 2012 #13

    Demystifier

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    Re: Bohm trajectories and "protective" measurements?

    We certainly see that a part of the Universe depends on time, which is sufficient to conclude that Universe as a whole depends on time as well. I don't see how a part of the Universe could depend on time if the whole Universe did not depend on time.
     
  15. Sep 28, 2012 #14

    kith

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    Re: Bohm trajectories and "protective" measurements?

    It just isn't immediately clear to my, why it can't depend on time.

    Lets say the universe is in an eigenstate of the full Hamiltonian H = Hobserver + Heverything else + Hinteraction. Now we know for the full state that ∂tρ = 0. Why does this imply that already ∂t(trobserver{ρ}) = 0? Maybe I'm overlooking something really obvious here. ;-)
     
    Last edited: Sep 28, 2012
  16. Sep 29, 2012 #15

    kith

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    Re: Bohm trajectories and "protective" measurements?

    I got it. Tracing and differentiating commute. D'oh ;-)
     
  17. Sep 29, 2012 #16
    Re: Bohm trajectories and "protective" measurements?


    Could you expand a little? I feel like I have missed a very important point in the fundamentals debate.
    Is this tied to the preferred basis ( position basis ) ? Is this how they "get away" with the issue?

    Is there any litterature on this? I can not recall ever hearing this objection raised or adressed by either proponents or opponents of MWI
     
  18. Sep 30, 2012 #17

    Demystifier

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    Re: Bohm trajectories and "protective" measurements?

    See the references in the paper, especially 13, 16, and 17. The most explicit referring to MWI is in Ref. 17, Sec. 6.2.3.
     
  19. Sep 30, 2012 #18
    Re: Bohm trajectories and "protective" measurements?

    Ok that became quite complicated quick. But I noticed all the papers were from the early 90s.
    Are you sure this issue hasn't been dealt with in tmore modern times? E.G. Wallace's FAPP etc?
     
  20. Oct 1, 2012 #19

    Demystifier

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    Re: Bohm trajectories and "protective" measurements?

    As far as I know, there was no much progress since then.

    Note also that most people who use MWI don't say it explicitly. They just use Schrodinger equation to describe everything they talk about, but they rarely mention the existence of "many worlds".

    Similarly, people who use textbook QM, rarely mention the fact that they use "Copenhagen" interpretation. Instead, they simply and carelessly talk about collapse, observers, and classical macro world, as if the meaning of these terms is self-evident.
     
  21. Oct 1, 2012 #20
    Re: Bohm trajectories and "protective" measurements?

    Yes, I am aware of this, but what about those that really do?
    The people who has done the most work on MWI claim it's almost inevitably true; Deutsch, Wallace, Zeh, Joos, Tegmark etc.
    I can't find anything about this in any of their papers.
     
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