Pilot-wave quantum theory in discrete space and time and the principle of least action

TL;DR

This paper develops a pilot-wave quantum theory on a discrete lattice with discrete time, deriving particle motion from a least-action principle and illustrating it with a double-slit experiment example.

Contribution

It introduces a novel discrete-space, discrete-time pilot-wave model using a least-action principle to determine stochastic particle trajectories.

Findings

Particle motion described by a $| ext{Psi}|^2$-distributed Markov chain

Stochastic matrices derived from a discrete least-action principle

Application demonstrated with a double-slit experiment simulation

Abstract

The idea of obtaining a pilot-wave quantum theory on a lattice with discrete time is presented. The motion of quantum particles is described by a $|\Psi|^2$-distributed Markov chain. Stochastic matrices of the process are found by the discrete version of the least-action principle. Probability currents are the consequence of Hamilton's principle and the stochasticity of the Markov process is minimized. As an example, stochastic motion of single particles in a double-slit experiment is examined.