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Some Bohm questions

  1. Jul 28, 2008 #1

    Hurkyl

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    Or "what are particles good for?"


    Particles (as defined in the Bohm interpretation) exist, have well-defined positions and momentums, and get pushed around by the wave-function. However, they do not actually have any sort of effect on anything at all -- in fact it appears that their role seems more like the hypothetical test particles one commonly uses when analyzing a force field or space-time geometry, rather than corresponding to actual, 'physical' particles. This spawns two questions:

    (1) As a purely analytical question, what sorts of problems are this sort of 'test particle' good at describing?

    (2) If I want to consider Bohm interpretation as being the 'correct' description of reality, how do I reconcile the test-particle nature of Bohm particles with the fact that physical particles really do interact with with stuff? (Or... was I not supposed to make such a correspondence in the first place?)
     
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  3. Jul 28, 2008 #2

    The particles are ultimately all we see in experiments. For example in the single or double slit experiment with one electron or photon at a time being emitted, you see only small scintillation points, which we infer to be particles. And it is from these particles that we eventually infer a wavefunction because the particle positions on the detector screen build up as a wavelike pattern. From this, deBB theory just makes the very simple inference that those point particles exist in the world even before measurements, and sets out to write down the equation of motion for those particles for all times. The particles are also necessary for solving the measurement problem, namely, the preferred basis problem and problem of definite outcomes. For a clear discussion of how deBB solves the measurement problems with the particles, please see section 3.3 "How the deBB theory solves the measurement problem" of this paper by Passon:

    http://arxiv.org/PS_cache/quant-ph/pdf/0611/0611032v1.pdf
    Journal-ref. Physics and Philosophy 3 (2006)

    The particles are also where the mass of the electron is located in nonrelativistic QM, as indicated by the N-particle guiding equation. Also, in the field theoretic extensions of deBB theory, the particle is also where charge is localized. Hope this helps.
     
    Last edited: Jul 28, 2008
  4. Jul 28, 2008 #3
    I would still like to see in details how gluons fit into dBB.
     
  5. Jul 28, 2008 #4
    It's not that hard in principle, as it goes much along the same lines as formulating a Bohmian QED (recall that QED and QCD only differ by a few extra terms in basically the same Lagrangian). In fact, I think it is more easily doable within the context of Light-front QCD. Currently, I am working on a draft for eventual publication on light-front Bohmian QCD. For now, please have a look at the work from an equal-time approach. See sections 5, 7, and 8 of Struyve's paper:

    Field beables for quantum field theory
    Authors: W. Struyve
    to be published in Physics Reports
    http://arxiv.org/PS_cache/arxiv/pdf/0707/0707.3685v1.pdf
     
    Last edited: Jul 29, 2008
  6. Jul 28, 2008 #5
    I would certainly not agree with your only, like if it were trivial ! A light quark is not exactly an electron, plus a few extra feature. And a gluon is even worse.

    But thank you for the reference. It is very interesting.
    As I said, I'd like to see that in details. Remember Gribov copies ? I'll wait till they get to the "topological problems".
    This may indeed take a lot of work :
     
    Last edited: Jul 28, 2008
  7. Jul 28, 2008 #6

    Hurkyl

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    This appears to contradict the fact that the particles defined by the Bohm interpretation have absolutely no influence on anything whatsoever, which seemingly makes them completely unobservable.
     
    Last edited: Jul 28, 2008
  8. Jul 28, 2008 #7

    By "only" I just meant that QED and QCD are formally very similar theories (which they are), not that the differences are computationally trivial.

    But I would point out however that light-front QCD considerably simplifies the problems Struyve mentions, so that formulating a Bohmian QCD is much more straightforward, I would claim.
     
    Last edited: Jul 29, 2008
  9. Jul 28, 2008 #8
    The particles just don't act back on their own guiding wavefunctions. Furthermore, it is quite straightforward to see from the guiding equation that the particle is located at the scintillation point (which is where the electron particle of the detector is ejected and radiates). Bohmian QED explains this more precisely.
     
    Last edited: Jul 28, 2008
  10. Jul 29, 2008 #9

    vanesch

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    Eh, that's not true, right ? Although the particles do not influence the dynamics of the wavefunction, they do influence the dynamics of the other particles (and even in an "action-at-a-distance" way). The quantum force on particle 1 depends on the wavefunction and the positions of particles 2, 3, ...
     
  11. Jul 29, 2008 #10
    Yes exactly true. That's the origin of the nonlocality for particle velocities in deBB. It's just that particle 1 is influencing the velocity of particle 2 (and vice versa) indirectly via the wavefunction or quantum potential.
     
    Last edited: Jul 29, 2008
  12. Jul 29, 2008 #11

    Hurkyl

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    Hrm -- I think I see the problem. BM is not about "particles and a wavefunction" as I was led to believe. Instead, it's a theory of "particles and other stuff", where the data representing the particles and the other stuff can be assembled into a wavefunction which is not intended to correspond to a physical entity.
     
  13. Jul 29, 2008 #12
    Why do you say that? The fundamental postulates of nonrelativistic deBB-QM are that the complete state of the world are defined by two things, the wavefunction, psi, and particle position configuration, Q, or, (psi, Q). Then you can write down the Schroedinger equation for the wave, psi, and deduce the guiding equation for the particle configuration, Q. If the theory is take "as is", the wavefunction must then be interpreted as a physical entity ("ontological" in the words of Bohm or "beable" in the words of Bell) like the EM field (of course it propagates through configuration space as opposed to 3-space) otherwise it doesn't make any sense. But this is enough to specify all of nonrelativistic deBB-QM. The quantum potential is a somewhat extraneous object of the theory that comes in from constructing the second order dynamics of the theory and in defining the quantum-classical limit. The particle dynamics however is completely defined by the first-order guiding equation alone.

    If on the other hand you wanted to assume that deBB-QM is an approximation to, say, a stochastic mechanical theory, then, yes, the wavefunction is no longer a physically real field but rather a compact and convenient mathematical expression for the time evolution of the Madelung fluid dynamics with micro-stochastic fluctuations, and the deterministic Bohm particle velocities are macroscopic statistical averages of microphysical stochastic particle trajectories.
     
  14. Jul 29, 2008 #13

    Demystifier

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    Exactly!
    Another point that needs to be stressed is that Bohmian mechanics assumes that only particles are objects that are really observed, while wave function is an object with an auxiliary role. For an analogy in everyday life, see
    https://www.physicsforums.com/blog.php?b=6
     
  15. Jul 29, 2008 #14

    vanesch

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    This is the delicate point in BM. Although at first sight, BM looks like classical mechanics with "just another force field", the wave function is nevertheless a genuine part of it, and is not some "helper function". If you only have the dynamical state of the particles, you cannot do BM, you need the wavefunction too.

    I guess you can somehow compare (it's just an analogy, which fails at a certain point of course) the wavefunction with the EM field in classical electrodynamics. What "counts" are the charged particles of course, but you cannot obtain the dynamics of just the charged particles if you don't have the electromagnetic field *with its own dynamics*. So even if you don't care about the EM field, you still need it, and it is not a helper function.

    However, this analogy fails in 2 respects:
    - the particles DO have an influence on the EM field.
    - most of the time, the particles even *determine* the EM field, that is, if you really want to, you can eliminate the EM field from the dynamics (we don't keep EM modes that "came from infinity).

    It fails in even a 3rd respect: the EM field lives in spacetime, while the wavefunction doesn't: it lives in Hilbert space.
     
  16. Jul 29, 2008 #15

    Hurkyl

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    The problem with the wavefunction being a physical entity is that it leads to what I was saying in my opening post: particles don't contribute to the evolution of the wavefunction, and the evolution of particles is entirely determined by the wavefunction. In particular, the particles do not have any influence on one another, and cannot be observed. If Bohm particles are meant to be more than mere test particles, then I simply don't see how the wavefunction can be taken as corresponding to a physical entity.

    I would like to point out that I did not say we need to take only particles as physical entities -- I would presume there is something weaker than the wave function (i.e. "other stuff") one can postulate as real, and have it and the particles all on equal footing. But I don't know what that something actually is.


    Incidentally, the classical EM field doesn't live in space-time: it lives in the sheaf of continuous (or differentiable, or whatever) tangent vector fields on space-time.
     
  17. Jul 29, 2008 #16

    Demystifier

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    Yes they do. First, by classical forces. Second, because not every particle has its own wave function, but one wave function describes a collection of many particles (entanglement), so they influence each other by a quantum force. This is exactly why they can be observed.
     
  18. Jul 29, 2008 #17

    vanesch

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    Sorry but they do. The particles do influence one another (through the wavefunction). You cannot obtain the dynamics of particle 1 by just knowing the wavefunction: you need to know also the positions of the other particles. If you give the other particles other initial positions, then particle 1 will follow a different worldline.

    I don't think you can do with less than the wavefunction, as it usually follows entirely the unitary evolution: the wavefunction part is exactly that of standard quantum mechanics (without projection). I might be wrong, but I'd guess that if you can do with "less than the wavefunction", then this reduction should also apply to standard quantum theory.

    You're a mathematician, right ? :grumpy:

    "living in spacetime" to me is living on spacetime and all its tangent and cotangent backgardens :redface:
     
  19. Jul 29, 2008 #18
    Hello everyone...

    I think it is necessary here to precise that it is wrong to say that there is only one unique bohmian way of understanding quantum mechanics. It is possible to distinguish a large amount of different interpretations of the wave function, with more or less "substance" in the wave function. Talking about bohmian mechanics in general leads to misunderstanding, one asks something about one interpretation and the other answers about another...
    If you are interested in an account of these possibilities, you can read Belousek. He mostly distinguises two axes of interpretation, causal vs. guidance view and monistic vs. dualistic ontologies. The tension between causal and guidance view is also discussed by Baubliz.
    I personally think that a monistic approach is the best one, but it would be too long to argue here (I'm writing my MA dissertation in philo of physics about this right now...).


    PS. The references :
    @article{Belousek:2003,
    Author = {Darrin W. Belousek},
    Journal = {Foundations of Science},
    Pages = {109-172},
    Title = {Formalism, Ontology and Methodology in Bohmian Mechanics},
    Volume = {8},
    Year = {2003}}

    @incollection{Baublitz:1996,
    Author = {Millard Baublitz and Abner Shimony},
    Booktitle = {Bohmian Mechanics and Quantum Theory: An Appraisal},
    Editor = {James T. Cushing and Arthur Fine and Sheldon Goldstein},
    Pages = {251-264},
    Publisher = {Kluwer Academic Publishers},
    Series = {Boston Studies in the Philosophy of Science},
    Title = {Tension in Bohm's Interpretation of Quantum Mechanics},
    Volume = {184},
    Year = {1996}}
     
  20. Jul 29, 2008 #19
    I realize I don't have answered the question just given some references...
    So to be short, you're right to say that the corpuscle is useless in the case of a certain interpretation of the wave function. If the wave function does everything, the corpuscle is just here as a pointer. Note that the other version of the problem is to wonder why the wave function, if understood as a field similar to the EM field has no source...

    But as soon as you give another interpretation to the wave function, things are different. For instance, Bohm and Hiley interpret the wave function as a information field (with a meaning for information which neither the usual meaning nor Shannon meaning). In this case, the special interpretation that they have explains this asymmetry.
    The interpretation Dürr et al. propose is different. They consider the wave function as part of the law (like an Hamiltonian) and, the corpuscle is the only material part of the theory and therefore does all the job (whatever this mean).

    Ok I've tried to be short, I hope I have made myself clear


    PS1. Sorry for the grammar mistakes and the strange sentences composition, but my first language isn't English
    PS2. If someone wants further references about these different theories I can give them...
     
  21. Jul 29, 2008 #20
    << I would like to point out that I did not say we need to take only particles as physical entities -- I would presume there is something weaker than the wave function (i.e. "other stuff") one can postulate as real, and have it and the particles all on equal footing. But I don't know what that something actually is. >>

    As I explained earlier, this can indeed be done in the context of stochastic mechanical derivations of the Hamliton-Jacobi-Madelung (the equations of deBB) equations.
     
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