A hidden variables model for non-relativistic quantum mechanics in terms of probabilities of particle paths

TL;DR

This paper introduces a non-local, stochastic hidden variables model for non-relativistic quantum mechanics that describes transition probabilities via particle paths with positive probabilities, offering an intuitive picture of quantum motion.

Contribution

It presents a novel hidden variables framework where particle paths have positive probabilities, differing from classical local action, and extends the understanding of quantum transition probabilities.

Findings

Transition probabilities can be described by particle paths with positive probabilities.

The model is non-local but stochastic, not deterministic.

Provides an intuitive particle motion picture in quantum mechanics.

Abstract

It is proved that in non-relativistic quantum mechanics (without spin) the transition probability may be described in terms of particle paths, every path having a (positive) probability. This leads to a stochastic hidden variables theory providing an intuitive picture of particle motion. The change of velocity at every time has a probability that depends on the potential over a large region, at a difference with the local action of classical dynamics. Thus the hidden variables theory is non-local like Bohm's, but not deterministic.