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What is the wave function about?

  1. Sep 16, 2011 #1
    Does the wave function represent the physical state of the system (MW) or merely our information about the system (orthodox interpretation)? If it represents something in between (Bohmian), what does that imply? Furthermore, if QM is supposed to be more “fundamental” than classical physics, does this suggest that configuration space is more "fundamental" than normal 3-space or (4 dimensional space-time)? If it’s more fundamental, why does the world appear to evolve in 3-space or (4 dimensional space-time)? I mean what is the nature of this configuration space where the wave function lives in? Goldstein writes:

    A second point is that for a multi-particle system the wave function (q) = (q1 ,..., qN ) is not a weird field on physical space, its a weird field on configuration space, the set of all hypothetical configurations of the system. For a system of more than one particle that space is not physical space. What kind of thing is this field on that space?


    http://philsci-archive.pitt.edu/1272/
    http://users.ox.ac.uk/~sfop0257/papers/Finding.pdf [Broken]


    If one takes the quasi-objective (in between) view as in the Bohmian model, what does the necessary non-locality/non-separability imply? Moreover, how is it possible that the wave function acts upon the positions of the particles but it is not acted upon by the particles? So that in,

    Bohmian mechanics there’s no back action, no effect in the other direction, of the configuration upon the wave function, which evolves autonomously via Schrodinger’s equation, in which the actual configuration Q does not appear.

    Furthermore, there are problems with treating the wave function as nomological (denoting a law of nature) as in Bohm's model because, "laws aren’t supposed to be dynamical objects, (as) they aren’t supposed to change with time, but the wave function of a system typically does...(since), we can in (a) sense control the wave function of a system. But we don’t control a law of nature. This makes it a bit difficult to regard the wave function as nomological."

    http://math.rutgers.edu/~oldstein/papers/rrwf.pdf
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Sep 17, 2011 #2
    Last edited: Sep 17, 2011
  4. Sep 17, 2011 #3
    This is a false dichotomy. The wave function represents what we observe and the latest theories imply what we observe depends on the context.
     
  5. Sep 17, 2011 #4
    It's in Russian? Is there a full English version?

    This should read one of the Bohmian models as originally presented by Durr, D., Goldstein, S. and Zanghi, N. (1992):

    We propose that the reason, on the universal level, that there is no action of configurations upon wavefunctions, as there seems to be between all other elements of physical reality, is that the wavefunction of the universe is not an element of physical reality. We propose that the wave function belongs to an altogether different category of existence than that of substantive physical entities, and that its existence is nomological rather than material. We propose, in other words, that the wavefunction is a component of physical law rather than of the reality described by the law.

    But this version of the pilot wave seems to have been abandoned. In the present form of pilot-wave theory, ψ is regarded as ontological treated as "a new kind of causal agent acting in confguration space." I think this is how Bohm originally interpreted it.

    http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/valentini_2008_denial.pdf
     
  6. Sep 18, 2011 #5
    There is the old English version (http://www.ptep-online.com/index_files/2008/PP-13-18.PDF [Broken] ). But there are not wave function. There are only complex probability density function.
     
    Last edited by a moderator: May 5, 2017
  7. Oct 1, 2011 #6
    If you try to give quantum mechanics a naive realist interpretation, like Bohm or Everett, you find yourself contorting yourself beyond belief with things that are unobservable, bring forth no new results and still have gaping big holes. But these girls tell it better than I can:



    On a more serious note, this short paper in Physics Today by Asher Peres and Chris Fuchs might be interesting:

    http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.77.8442&rep=rep1&type=pdf

    Skippy
     
    Last edited by a moderator: Sep 25, 2014
  8. Oct 1, 2011 #7
    I'm not sure I would describe Bohm's or Everett's version as "naive". One can argue that there is nothing naive about the concepts of non-locality/non-separability or multiple universes/branches. Moreover, I think the epistemic view argued for by Peres and Fuchs is, in the final analysis, also just another interpretation. And there's arguably even less motivation to take their interpretation any more seriously than any of the others. In fact, one might have less motivation because to view physics as the "science of meter reading" doesn't look particularly rewarding, I think.
     
  9. Oct 1, 2011 #8
    For that matter viewing physics as the "science of long shots" doesn't look particularly rewarding either. After 85 years of producing nothing useful Bohmian mechanics are about as big a long shot as they get.
     
  10. Oct 1, 2011 #9
    Perhaps "naive" was a poor choice of words. I should have said "clever and sophisticated theories desperately clinging to a naive classical reality".

    I also don't think "science of meter reading" is an accurate description of searching for understanding of the universe without the baggage of accepting unobservable entities as a matter of faith.

    Skippy
     
  11. Oct 3, 2011 #10

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  12. Oct 3, 2011 #11
  13. Oct 3, 2011 #12

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    Let me quote from the introduction of the book:
    "... we believe that Bohmian mechanics can help us make progress with our real problems.
    There are, at least, three clear reasons why one could be interested in studying quantum
    problems with Bohmian mechanics:

    (1) Bohmian explaining: Even when the Copenhagen mathematical machinery is
    used to compute observable results, the Bohmian interpretation ofently offers
    better interpretational tools. We can find descriptions of electron dynamics
    such as “an electron crosses a resonant tunneling barrier and interacts with another
    electron inside the well”. However, an electron crossing a tunneling region is not
    rigourously supported within orthodox quantum mechanics, but it is within
    the Bohmian picture. Thus, in contrast to the Copenhagen formulation, the
    Bohmian interpretation allows for an easy visualization of quantum phenomena
    in terms of trajectories that has important demystifying or clarifying consequences.
    In fact, Bohmian mechanics allows for a simultaneous description
    and interpreation of quantum mechanics within the same theoretical framework.
    In particular, it provides a single-event description of the experiment,
    while Copenhagen quantum mechanics accounts for its statistical or ensemble
    explanation. We will present several examples in chapters 2 and 3 emphasizing
    all these points.

    (2) Bohmian computing: Although the predictions of the Bohmian interpretation
    reproduce the ones of the orthodox formulation of quantum mechanics, its
    mathematical formalism is different. In some systems, the Bohmian equations
    might provide better computational tools than the ones obtained from the orthodox
    machinery, resulting in a reduction of the computational time, an increase
    in the number of degrees of freedom directly simulated, etc. We will
    see examples of these computational issues in quantum chemistry in chapters
    4 and 5, as well as in quantum electron transport in Chap. 6.

    (3) Bohmian thinking: From a more fundamental point of view, alternative formulations
    of quantum mechanics can provide alternative routes to look for the
    limits and possible extensions of the quantum theory. As we will discuss later,
    the work of John Bell on non-locality is a clear example of the unquestionable
    utility of understanding quantum phenomena with Bohmian mechanics.
    In particular, Chap. 7 presents the route to connect Bohmian mechanics with
    geometrical optics and beyond opening the way to apply the powerful computational
    tools of quantum mechanics to classical optics, and even to electromagnetism.
    The natural extension of Bohmian mechanics to the relativistic
    regime and to quantum field theory are presented in Chap. 8, while Chap. 9
    discusses its application to cosmology."

    For more details, you need to get the book itself.
     
  14. Oct 3, 2011 #13
    Sorry, not interested in what people believe might be possible. After 85 years of speculation its not unreasonable to demand some concrete results.
     
  15. Oct 4, 2011 #14
    They're naive in the sense that they involve/entail nonempirical fantasies.

    Or one can argue that there is. And ultimately they offer no demonstrable insights about the underlying reality that can't be inferred from standard QM.

    Yes, the most sophisticated one.

    I like it because I think that, despite what some might see as apparent superficiality, it's actually deeper than either the Bohmian or Everettian interpretations. I think that's why, imo, most physicists would agree with Peres' and Fuchs' take on QM, as opposed to the alternatives.

    Bohmians and MWIers are reading the same meters and predicting the same probabilities as standard 'uninterpreted' QMers. They're just carrying some unwarranted philosophical baggage along with that.
     
  16. Oct 4, 2011 #15

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    The results in item (2) of my post above are very concrete. In some cases, Bohmian trajectories are a much more efficient method (but equivalent to the standard method) to compute some measurable predictions of QM.
     
  17. Oct 4, 2011 #16
    Yes, there is that. As well as some other aspects of BM that make it attractive. But then there's BM's nonlocality.
     
  18. Oct 4, 2011 #17
    Being more efficient in some cases without making any new predictions just isn't terribly useful. I'm sure we could say the same thing about any number of other theories including phlogiston theory. It needs to prove itself uniquely useful in some significant way.
     
  19. Oct 4, 2011 #18
    I have to admit, I couldn't help but enjoy the humour (and truth?) about this statement by Fuchs:

    Whatever it is, it cannot be for want of a self-ordained solution: Go to any meeting, and it is like being in a holy city in great tumult. You will find all the religions with all their priests pitted in holy war—the Bohmians, the Consistent Historians, the Transactionalists, the Spontaneous Collapseans, the Einselectionists, the Contextual Objectivists, the outright Everettics, and many more beyond that. They all declare to see the light, the ultimate light. Each tells us that if we will accept their solution as our savior, then we too will see the light.But there has to be something wrong with this! If any of these priests had truly shown the light, there simply would not be the year-after-year conference. The verdict seems clear enough: If we—i.e., the set of people who might be reading this paper—really care about quantum foundations, then it behooves us as a community to ask why these meetings are happening and find a way to put a stop to them.

    http://perimeterinstitute.ca/personal/cfuchs/VaccineQPH.pdf
     
  20. Oct 4, 2011 #19

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    And then there is the Bell theorem saying that any hidden variable theory (compatible with QM) MUST be nonlocal.
     
    Last edited: Oct 4, 2011
  21. Oct 4, 2011 #20

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    First you indicate that you would be satisfied with something useful. Then, when I show that there is something useful you want terribly useful, and later you want even more - uniquely useful. What will be next? Absolutely useful? Ultimatively useful?
     
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