Quantum particles from classical statistics

TL;DR

This paper demonstrates that quantum particles can be described within a classical statistical framework, unifying their description with classical particles and deriving quantum phenomena like interference and tunneling.

Contribution

It constructs a unified formalism where quantum and classical particles are described using classical statistical ensembles, enabling derivation of quantum features from classical probabilities.

Findings

Quantum particles are represented in classical statistical ensembles.

Quantum phenomena such as interference and tunneling are derived from classical probabilities.

A common formalism for classical and quantum particles is established.

Abstract

Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs, however, between quantum and classical particles. We describe position, motion and correlations of a quantum particle in terms of observables in a classical statistical ensemble. On the other side, we also construct explicitly the quantum formalism with wave function and Hamiltonian for classical particles. For a suitable time evolution of the classical probabilities and a suitable choice of observables all features of a quantum particle in a potential can be derived from classical statistics, including interference and tunneling. Besides conceptual advances, the treatment of classical and quantum particles in a common formalism could lead to interesting cross-fertilization between classical statistics and quantum physics.