On the Stochastic Origin of Quantum Mechanics

TL;DR

This paper explores the statistical and stochastic foundations of quantum mechanics, extending classical phase space methods to relativistic regimes and proposing an imaginary stochastic process as its origin.

Contribution

It introduces a relativistic extension of the Wigner-Moyal equation and proposes an imaginary stochastic process as the fundamental origin of quantum mechanics.

Findings

Derived a relativistic mass expression in quantum phase space.

Analyzed the quantum Liouville equation via Kramers-Moyal expansion.

Discussed diffusion with an imaginary coefficient as a quantum phenomenon.

Abstract

The quantum Liouville equation, which describes the phase space dynamics of a quantum system of fermions, is analyzed from statistical point of view as a particular example of the Kramers-Moyal expansion. Quantum mechanics is extended to the relativistic domain by generalizing the Wigner-Moyal equation. Thus, an expression is derived for the relativistic mass in the Wigner quantum phase space presentation. The diffusion with an imaginary diffusion coefficient is also discussed. An imaginary stochastic process is proposed as the origin of quantum mechanics.