Quantum Particles from Classical Probabilities in Phase Space

Abstract

Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow, including interference or tunneling. The appropriate quantum observables for position and momentum contain a statistical part which reflects the roughness of the probability distribution. "Zwitters" realize a continuous interpolation between quantum and classical particles. Such objects may provide for an effective one-particle description of classical or quantum collective states as droplets of a liquid, macromolecules or a Bose-Einstein condensate. They may also be used for quantitative fundamental tests of quantum mechanics. We show that the ground state for zwitters has no longer a sharp energy. This feature permits to put quantitative experimental bounds on a small parameter for possible deviations from quantum mechanics.

From probabilistic mechanics to quantum theory

“…Since then, several other papers sharing this interpretation, but using a variety of different methods and assumptions, have been published. An incomplete list includes attempts to understand QT in terms of ensembles either in phase space [6][7][8][9][10] or in configuration space [11][12][13][14][15][16][17]. These works clarify several important aspects of QT.…”

“…Introducing for each A a complex-valued classical state variable, one obtains, after some manipulations, a theory which shares many structural properties with QT (see Sects. [7][8][9][10]. Certain phase space operatorsL A (introduced already in I), which are generalizations of Koopman-Neumann operators, represent the HLLK counterpart of quantum operatorsÂ.…”