On multi-time correlations in stochastic mechanics

Abstract

We address a long-standing criticism of the stochastic mechanics approach to quantum theory by one of its pioneers, Edward Nelson: Multi-time correlations in stochastic mechanics differ from those in textbook quantum theory. We elaborate upon an answer to this criticism by Blanchard et al. (Phys Rev D 34(12):3732-3738, 1986), who showed that if the (derived) wave function in stochastic mechanics is assumed to collapse to a delta function in a position measurement, the collapse will change the stochastic process for the particles (because the stochastic process depends on derivatives of the wave function), and the resulting multi-time correlations will agree with those in textbook quantum theory. We show that this assumption can be made rigorous through the tool of ‘effective collapse’ familiar from pilot-wave theories, and we illustrate this with an example involving the double-slit experiment. Hence one of the major lingering objections to stochastic mechanics is dissolved. We finally show that in the case of multi-time correlations between multiple particles, effective collapse implies nonlocal influences between particles.