Geometric Quantum Mechanics
Since the advent of quantummechanics, there have been many attempts to provide it with a classical interpretation. Two approaches have received great attention in recent years: the Madelung-Bohm hydrodynamical formulation1 and the Feynès-Nelson stochastic formulation2 Unfortunately, notwithstanding their conceptual appeal, these approaches raised more problems than they resolved and failed in their principal intent: to shed some light on the physical mechanism responsible of the wavelike properties of matter. An odd mechanism, in fact, is inherent to both theories eliciting “a mysterious dependence of the individual on the statistical ensemble of which it is a member”3. This feed-back mechanism has no analog in newtonian mechanics nor in the theory of stochastic processes and has a purely quantum origin. It is evident, therefore, that both the Madelung-Bohm and the Feynès-Nelson “classical” formulations are more of appearance than substance.