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I don't understand why some people argue that Bohmian quantum mechanics is just an interpretation of quantum mechanics. In addition to the usual Schrödinger equation, we have the following deterministic equation (in 1d): $$ m\dot q=\hbar\nabla_q \Im (\ln\psi(q,t)). $$

And we have more information than standard quantum mechanics. If we solve the Schrödinger equation, the paths of particles are known.

The above equation has not an intrinsic importance in quantum mechanics and we may crudely write the current as $J\sim m\dot q$ which is equal to $\hbar\nabla_q \Im (\ln\psi(q,t))$.

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    $\begingroup$ I agree with this sentiment, but I am not sure this question has an answer that wouldn't be an opinion. To me, an "interpretation" simply means trying to assign semantic values to the various terms in the theory. I would call Bohmian mechanics a "model" of quantum theory, instead, or an "extension" of quantum theory, but someone else will inevitably have a different opinion. $\endgroup$ Jul 9, 2022 at 20:17
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    $\begingroup$ I consider many worlds and Copenhagen interpretations as different interpretations of quantum mechanics, because they have the same mathematical structure and there are not extra equations rather than the Schrodinger equation in these interpretations. $\endgroup$
    – reza-ebadi
    Jul 9, 2022 at 20:32
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    $\begingroup$ it depends if it could eventually be shown to add new/different predictions. The answer is still unclear to me. physics.stackexchange.com/questions/410242/… $\endgroup$
    – user338734
    Jul 9, 2022 at 21:20
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    $\begingroup$ physics.stackexchange.com/questions/460388/… $\endgroup$
    – alanf
    Jul 9, 2022 at 21:50

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What qualifies as an ”interpretation” of QM or not is a matter of semantics, and this question is only as well-defined as the meaning of the word “interpretation.”

My take is: An interpretation is a self-consistent description of how to understand the mathematics of a theory, with the intention to guide our physical intuition. This could include language to describe the quantities in the equations, narratives to describe interactions and dynamics that result from the equations, and auxiliary equations which reinforce the self-consistency of the whole thing. As long as the auxiliary equations make no new testable predictions (even in principle), then they are truly of the interpretation rather than of the mathematical structure of the theory.

If the auxiliary equations result in testable predictions, then the interpretation is an interpretation of an extension of the theory.

As far as I can tell, in this light, Bohmian mechanics is an interpretation of QM and does not extend QM in any testable way.

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  • $\begingroup$ Thank you so much, I believe that the auxiliary equation can produce some new predications. According to this equation, we may distinguish particles by their paths, so some phenomena such as Bose-Einstein condensation which is based on symmetrization of wave function are not so justifying for me. You can find my question in physics.stackexchange.com/questions/709213/… $\endgroup$
    – reza-ebadi
    Jul 10, 2022 at 7:02
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In my vocabulary an interpretation, an extended deterministic theory , should reproduce the mathematics of quantum mechanics as accepted by mainstream physics, so that the successes of quantum mechanics to fit and predict data are reproduced.

In that sense the non relativistic Bohm theory is an interpretation of mainstream QM. It fails in relativistic quantum mechanics to be an interpretation. From the link:

Like nonrelativistic quantum theory, of which it is a version, Bohmian mechanics is not compatible with special relativity, a central principle of physics: Bohmian mechanics is not Lorentz invariant. Nor can it easily be modified to accommodate Lorentz invariance.

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  • $\begingroup$ Is symmetrization(or antisymmetrization) necessary for identical particles in Bohmian mechanics? Particles can be distinguished by their paths, Is this a new prediction of Bohmian mechanics? $\endgroup$
    – reza-ebadi
    Jul 10, 2022 at 7:06
  • $\begingroup$ @reza-ebadi sorry, it is not my field of work. I just have the general framework from papers as the one I link. look at paragraph 15 for symmetrization and anti. $\endgroup$
    – anna v
    Jul 10, 2022 at 8:01
  • $\begingroup$ The disfavour which the Bohmian approach to QM has received, corresponds with the disfavour that the Lorentzian approach to relativity has received, and I would suspect that any reconciliation would require both of these approaches to be adopted simultaneously. $\endgroup$
    – Steve
    Jul 10, 2022 at 8:12
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    $\begingroup$ @Steve unless it stops being an interpretation and can give predictions for new observations it is jut a mathematically more complex method of getting the same fits to data. $\endgroup$
    – anna v
    Jul 10, 2022 at 8:44
  • $\begingroup$ @annav, the only way it will give any new predictions is if physicists buckle down and develop a theory that makes additional predictions. Most of them, wrongly, behave as if the Bohmian or Lorentzian interpretations have been somehow already falsified. Also, additional predictiveness is not the only test of the quality of a theory - reconciliation of explanation can be another important criteria. One general theory may explain no more than what is already explained by two conceptually-incompatible special theories, but by being general in scope it is regarded as better. $\endgroup$
    – Steve
    Jul 10, 2022 at 9:06

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