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PBR theorem question

  1. Apr 12, 2013 #1
    I read some blog on the PBR theorem which asserts that : any ontic (being reality itself) model which wants to reproduce qm results should be psi-ontic. The latter means that the wf should be considered as having a physical reality hence that the particle can really be in more than one place simultaneously. Since this seems barely tenable can we then conclude that PBR in fact lead to the abandon of the quest for ontic models of qm ?
  2. jcsd
  3. Apr 13, 2013 #2

  4. Apr 13, 2013 #3
    The theorem assumes that nonorthogonal quantum states correspond to probability distributions over overlapping sets of ontic states. i.e. it assumes that if psi0, psi1 are two quantum states such that <psi0|psi1> ≠ 0, then there must be ontic states that are possible under both psi0 and psi1. This assumption is already false for Bohmian mechanics, and it is also false for a theory like Maxim Raykin's, which reproduces the Bohmian trajectories without needing a pilot wave. So the existence of the wavefunction is not a requirement of realism.
  5. Apr 14, 2013 #4
    So these hidden variable theory (Bohmian) consider the wavefunction not as being real (for example it's complex valued), but uses it as a mathematical tool to build the trajectories which on the other hand are real ?
    Does this mean that the wavefunction were a kind of average over classical chaotic random motion ?

    Wrt to dBB I had a question in another thread : https://www.physicsforums.com/showthread.php?t=685269
  6. Apr 14, 2013 #5
    No, in Bohm's theory, you usually say that the wavefunction is a physical thing; it's the cause of how the particles move. But many people, maybe even most people, who work on Bohmian mechanics don't regard it as the final theory, they see it as just one step beyond quantum mechanics towards some better theory. Raykin's work is an example of a step beyond Bohm, because he gets the same particle motions as Bohm, but he doesn't get them from a wavefunction, he just has particles interacting.

    What you describe is like a cone balanced exactly on its tip. Even if it's just slightly off-center, it will fall over. So mathematically you can write an equation for a cone that doesn't fall over, or a Bohmian particle that never moves, but it requires infinite finetuning.

    Also, in practical quantum mechanics (or practical Bohmian mechanics), you never just talk about a particle at an exact position anyway. In quantum mechanics, infinite exactness of position means infinite uncertainty of momentum, so if you start with a wavefunction concentrated entirely at a point (which is called a Dirac delta function), in the very next moment the wavefunction will spread out across space. Real particle physics always uses wavepackets, that may be bunched up, but they won't be concentrated completely into a point, so they will evolve more smoothly.

    In Bohmian mechanics, you have wavefunction plus particle, and you treat the particle as having an unknown position. The difference with quantum mechanics is that the position is always definite, and it's following a definite deterministic trajectory, you just don't know what the exact position is. So it's like quantum mechanics but completed in a common-sense way - you still have the uncertainty, but the uncertainty is just due to human ignorance.

    So returning to your scenario, if the particle happened to exactly be at a stationary point in the Bohmian wavefunction, then yes, it would sit there without moving. But in fact it is infinitely unlikely to be exactly at the stationary point, and if it is anywhere else, it will move. And the Bohmian trajectories do give you the same behavior for position as in ordinary quantum mechanics.

    One more comment on PBR theorem: it seems to be irrelevant for all the ontic theories that have any sort of popularity among physicists. Bohm, many worlds, transactional interpretation, the PBR theorem is irrelevant to all of them. They all have the same features and the same problems that they ever had. None of those theories is invalidated by it or affected by it. The people who care about the PBR theorem are "quantum foundations" people and what they do is very abstract and maybe not very useful.
  7. Apr 15, 2013 #6
    May it be the case for foundations.
    In the case given for dBB the position 0 is a stable point for the guiding equation. This prob. Density is like a hole not a hill, since if the particle moves a bit off let say in positive direction then the speed is negative hence pushing it towards the 0 position again, bringing it to a more probable position. In this sense it does not look like a cone on its tip ?
    Last edited: Apr 15, 2013
  8. Apr 15, 2013 #7


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    Reality of wf does NOT imply that particle can be in more than one place simultaneously. For example, in dBB theory wf is real and yet particle has only one position.

    Not at all. For example, dBB and many-world interpretations are perfectly consistent with PBR theorem and ontological wf.

    For a simple explanation of the PBR theorem see also
    https://www.physicsforums.com/blog.php?b=4330 [Broken]
    Last edited by a moderator: May 6, 2017
  9. Apr 15, 2013 #8


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    That's simply not true. Or if you think it is, try to support it with an explicit calculation of the velocity.
  10. May 7, 2013 #9
    not necessarily, is just inaccessible, we just have a epistemic view.

    Last edited: May 7, 2013
  11. May 11, 2013 #10
    stated recently by rudolph (epistemic proponent)

    "Even though it seems very abstract, what we're saying in some sense is tied to space and time,"

    "I prepare this, and then I measure that, and so on. So although it comes in very implicitly, I think that ultimately what we will understand is that space and time are just part of what this particular primate has evolved to find a use for – that what's actually going on in the universe doesn't care about space and time."
    Last edited: May 11, 2013
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