Quantum particles from coarse grained classical probabilities in phase space

TL;DR

This paper demonstrates that quantum particles and their characteristic behaviors can emerge from classical probability distributions in phase space through coarse graining, classical dynamics, and observable choices.

Contribution

It shows how quantum phenomena like interference and tunneling can be derived from classical statistics with appropriate coarse graining and evolution.

Findings

Quantum features emerge from classical phase space distributions.

Interference and tunneling are reproduced in the classical framework.

Uncertainty relations are derived from classical probabilities.

Abstract

Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of the classical probabilities and choice of observables all features of a quantum particle in a potential follow from classical statistics. This includes interference, tunneling and the uncertainty relation.