Discussion of Claverie and Diner’s Paper: The Classical Limit in the Framework of Stochastic Mechanics

Abstract

In sharp contrast with usual Quantum Mechanics (hereafter abreviated as Q.M.), Stochastic Mechanics (hereafter abreviated as S.M.) exhibits the pleasant feature of providing a clear and qualitatively understandable picture of physical systems, and not only a mathematical algorithm for the quantitative evaluation of various properties. It could be objected that Q.M. does not reduce to a set of mathematical algorithms and contains a variety of new qualitative concepts (stationary state, quantification of some observables, and so on); but as it has been exemplified by Diner in his lecture, a thorough qualitative understanding of microphysical phenomena is not really obtained by usual Q.M., and S.M. appears able to bring in substantial conceptual progress. The purpose of this contribution is to describe these conceptual improvements in another (and rather obscure) area of Quantum Mechanics, namely the so-called ‘transition to Classical Mechanics’. I shall first describe briefly the difficulties which appear in the framework of usual Q.M., and then show how they would disappear in the framework of S.M., provided that appropriate dynamical laws may be found such that, by using them, S.M. actually gives the main results of Q.M. (position and velocity probability distributions, mean values of energy, angular momentum…). The search for such appropriate dynamical laws is presently investigated by several workers [14–18].