Discerned and non-discerned particles in classical mechanics and convergence of quantum mechanics to classical mechanics

Michel Gondran (1) , Alexandre Gondran (2)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 ENAC - Ecole Nationale de l'Aviation Civile

We introduce into classical mechanics the concept of nondiscerned 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. On the other hand, a discerned particle corresponds to a particular action that satisfies the special Hamilton-Jacobi equations. We then study the convergence of quantum mechanics to classical mechanics when ~ tends to 0 by considering two cases : the convergence to non-discerned classical particles and the convergence to a classical discerned particle. Based on these convergences, we propose an updated interpretation of quantum mechanics.

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Michel Gondran, Alexandre Gondran. Discerned and non-discerned particles in classical mechanics and convergence of quantum mechanics to classical mechanics. Annales de la Fondation Louis de Broglie, 2011, 36, pp 117-135. ⟨hal-00934664⟩