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In Bohmian QM, the wave function $\psi$ is moving a classical point particle around. Without effort, it could also move a large ensemble of particles (since there is no back reaction).
Is there a name for this specific interpretation of QM?!

A natural and interesting choice would be an ensemble with the density equal to $|\psi^2|$. That case would be interesting because:

  1. The wave function would determine the ensemble. ($|\psi^2|$ the density, and Bohm's piloting mechanism the velocity).
  2. The ensemble (if large enough) would determine the wave function: $|\psi|$ from density and its phase from the collective movement because by Bohm's mechanism that is equal to the probability current $\text{Im}(\psi^* \nabla\psi)$, which then only leaves a total phase factor unknown.
  3. So it looks like a direct one-to-one correspondence between QM and a classical multiverse.

Generalization to multi-particle states, quantum-field wave functionals, and even fermion fields may be a problem, or it may be possible, but as already stated, the question here is simply: What is the name of this QM interpretation? (I don't find anything like "Bohm ensemble theory" or "classical many-worlds" when searching.)

NB: The many states in the ensemble here are already needed for a one-particle wave function, an $N$-particle wave function would of course need a big ensemble of $N$-tuples of particles.

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  • $\begingroup$ The issue with this is that you then need to write down some equations describing the dynamics of your particles. And when you try to do this, I suspect that the first thing you do is to write down Bohmian mechanics, as classically reproducing a (probability) density of $|\psi|^2$ was exactly what it was designed to do. But this obviously just gets you back where you started, so you will need something cleverer. It is also not obvious what this is gaining you. Why is an ensemble of unobservable particles that teleport nonlocally preferable to an unobservable wavefunction that changes nonlocaly $\endgroup$
    – By Symmetry
    Commented May 4 at 13:57
  • $\begingroup$ As I wrote I'm not asking about the usefulness, but only about the name! (Nevertheless, what you gain, if the wave function and the ensamble are indeed equivalent, is at least an additional method for analysis, or visualization, as for instance in: en.wikipedia.org/wiki/… In the text there they use the phrase "the Bohmian trajectories for an electron" but that is not really a name that singles out this interpretation, I'm afraid...) $\endgroup$
    – Jos Bergervoet
    Commented May 4 at 15:13

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