Density Relaxation in de Broglie-Bohm Mechanics

TL;DR

This paper provides a Lagrangian analysis explaining how particle densities in de Broglie-Bohm mechanics relax to the Born rule through coarse-graining, supporting the statistical interpretation of quantum mechanics.

Contribution

It introduces a Lagrangian framework to explain density relaxation in de Broglie-Bohm mechanics, extending previous numerical findings.

Findings

Particle density relaxes to the Born density under coarse-graining.

Lagrangian analysis clarifies the relaxation process.

Supports the statistical interpretation of quantum mechanics.

Abstract

A Lagrangian analysis explains the numerical results of Valentini and Westman (2005) which demonstrate that an initially arbitrary particle density, stirred by the field of de Broglie velocities associated with a Schrodinger wave function, relaxes to the Born probability density provided both densities are coarse-grained.