I recently discovered the stochastic interpretation of quantum mechanics, which is different from the De Broglie-Bohm theory The best article I found on it was very much a comparison of the two by Bohm himself: here (which is probably not accessible to everyone).
Therefore, a short summary:
- quantum particles perform random walks (Wiener process)
- the theory is non-local, the particles random walk is guided by the drift velocity $\nabla\Psi/\Psi$ in contrast to the quantum potential $\nabla^2\Psi/\Psi$ of De Broglie-Bohm theory.
- in contrast to De Broglie-Bohm theory, the stochastic trajectories can cross
- in contrast to path integral formulation, there is a definite trajectory, which we can however not know.
- in contrast to the Kopenhagen interpretation, particles are already at a certain position/in a certain state before measurement, we just can't know in which one (due to the stochastic nature). There is thus no collapse of wave function. (i.e. Schrödingers cat is either dead or alive, even before the measurement, we just can't know.)
I think, this interpretation is quite elegant as it avoids two concepts, that seem quite absurd: the wave function collapse of the Kopenhagen interpretation as well as the bizarre non-crossing paths of the De Broglie-Bohm theory. Furthermore, the correspondence principle is quite elegantly resolved: the stochastic fluctuations of the random walk become negligible for large systems. I see that some objections to the De Broglie-Bohm theory apply as well (the need for a guiding wave), but I don't really see them as a problem.
Alors: Why is this interpretation not more popular/well known?
Thanks in advance for any answer!
Edit: There has already been this question here with some instructive answers.