A time-symmetric soliton dynamics \`a la de Broglie

TL;DR

This paper develops a time-symmetric soliton model inspired by de Broglie and Bohm, using a nonlinear Klein-Gordon equation to replicate quantum phenomena like entanglement and nonlocality.

Contribution

It introduces a novel time-symmetric soliton framework that reproduces key quantum behaviors within a nonlinear Klein-Gordon theory, extending pilot-wave concepts.

Findings

Reproduces main results of pilot-wave interpretation for non-interacting particles.

Explains quantum entanglement through soliton interactions.

Reproduces de Broglie-Bohm nonlocality phenomena.

Abstract

In this work we develop a time-symmetric soliton theory for quantum particles inspired from works by de Broglie and Bohm. We consider explicitly a non-linear Klein-Gordon theory leading to monopolar oscillating solitons. We show that the theory is able to reproduce the main results of the pilot-wave interpretation for non interacting particles in a external electromagnetic field. In this regime, using the time symmetry of the theory, we are also able to explain quantum entanglement between several solitons and we reproduce the famous pilot-wave nonlocality associated with the de Broglie-Bohm theory.