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

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 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.

Domaines: Physique Quantique [quant-ph]

Michel Gondran, Alexandre Gondran. Discerned and Non-Discerned Particles in Classical Mechanics and Quantum Mechanics Interpretation. 2010. ⟨hal-00507106⟩