Elements of sub-quantum thermodynamics: quantum motion as ballistic diffusion

TL;DR

This paper models quantum motion as a form of ballistic diffusion arising from sub-quantum thermodynamics, providing a classical physics explanation for quantum wave packet decay and trajectories.

Contribution

It introduces a classical sub-quantum thermodynamics framework that reproduces quantum motion as ballistic diffusion, offering a micro-causal explanation for quantum phenomena.

Findings

Quantum wave packet decay results from sub-quantum diffusion.

Quantum trajectories are derived from classical physics.

Quantum motion in potentials also follows ballistic diffusion.

Abstract

By modelling quantum systems as emerging from a (classical) sub-quantum thermodynamics, the quantum mechanical "decay of the wave packet" is shown to simply result from sub-quantum diffusion with a specific diffusion coefficient varying in time due to a particle's changing thermal environment. It is thereby proven that free quantum motion strictly equals ballistic diffusion. The exact quantum mechanical trajectory distributions and the velocity field of the Gaussian wave packet are thus derived solely from classical physics. Moreover, also quantum motion in a linear (e.g., gravitational) potential is shown to equal said ballistic diffusion. Quantitative statements on the trajectories' characteristic behaviours are obtained which provide a detailed "micro-causal" explanation in full accordance with momentum conservation.