On Multi-Time Correlations in Stochastic Mechanics

TL;DR

This paper demonstrates that multi-time correlations in stochastic mechanics can be made consistent with quantum theory through an effective collapse mechanism, addressing longstanding criticisms and revealing nonlocal influences between particles.

Contribution

It provides a rigorous framework for effective collapse in stochastic mechanics, reconciling multi-time correlations with quantum theory and highlighting nonlocal effects.

Findings

Multi-time correlations can match quantum predictions with effective collapse.

Effective collapse introduces nonlocal influences between particles.

The approach resolves major objections to 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. (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. We also show that in the case of multi-time correlations between multiple particles, effective collapse implies nonlocal influences between particles. Hence one of the major lingering objections to stochastic mechanics is dissolved.