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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 $\hbar\nabla_q \Im (\ln\psi(q,t))$.

Ruslan
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reza-ebadi
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2 Answers2

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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.

Gilbert
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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.

anna v
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