Discerned and Non-Discerned Particles in Classical Mechanics and Quantum Mechanics Interpretation

TL;DR

This paper introduces the concept of non-discerned particles in classical mechanics to explain the Gibbs paradox and investigates how quantum mechanics converges to classical mechanics as Planck's constant approaches zero, offering new interpretative insights.

Contribution

It extends classical mechanics with non-discerned particles and analyzes quantum-classical convergence, providing a fresh perspective on quantum mechanics interpretation.

Findings

Non-discerned particles explain Gibbs paradox.

Quantum mechanics converges to classical mechanics as hbar -> 0.

New interpretation of quantum mechanics suggested.

Abstract

We introduce into classical mechanics the concept of non-discerned particles for particles that are identical, non-interacting and prepared in the same way. The non-discerned particles correspond to an action and a density which satisfy the statistical Hamilton-Jacobi equations and allow to explain the Gibbs paradox in a simple manner. On the other hand, a discerned particle corresponds to a particular action that satisfies the local Hamilton-Jacobi equations. We then study the convergence of quantum mechanics to classical mechanics when hbar -> 0 by considering the convergence for the two cases. These results provide an argument for a renewed interpretation of quantum mechanics.