A local phase space stochastic quantization?

TL;DR

This paper explores whether Nelson's stochastic approach to quantum mechanics can be derived from a local phase space process with colored noise, potentially leading to a local hidden variable theory that challenges traditional nonlocality assumptions.

Contribution

It proposes a novel derivation of stochastic quantum mechanics from a phase space process with colored noise, suggesting a local hidden variable interpretation.

Findings

Colored noise smoothing can produce a local phase space stochastic process.

Such a process could lead to a local hidden variable theory of quantum mechanics.

The approach may extend to field quantization and has implications for gravity-related noise.

Abstract

I examine whether Nelson's stochastic formulation of Schr\"{o}dinger equation could be derived from a phase space process through a colored noise smoothing. If this conjecture is true, it would yield a local stochastic hidden variable theory. I discuss how this does not necessarily contradict Bell type theorems as general local stochastic theories can violate local causality assumptions. I also discuss the generalization to quantization of fields and speculate about the gravitational origins of noise.