Quantum particles from classical probabilities in phase space

TL;DR

This paper proposes a framework where quantum particles are described by classical probabilities in phase space, reproducing quantum phenomena and allowing interpolation between classical and quantum states, with implications for fundamental tests.

Contribution

It introduces a time evolution law for classical probability distributions that reproduces quantum effects and defines zwitters as interpolations between classical and quantum particles.

Findings

Quantum phenomena like interference and tunneling are derived from classical probabilities.

Zwitters can interpolate continuously between quantum and classical particles.

Ground state energy of zwitters is not sharp, enabling experimental bounds on deviations from quantum mechanics.

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.