On the Stochastic-Quantum Correspondence

TL;DR

This paper clarifies the Stochastic-Quantum correspondence, deriving quantum axioms from stochastic laws, exploring implications for space discreteness, and addressing measurement and classical limits within a unified stochastic framework.

Contribution

It introduces a novel approach deriving quantum mechanics from stochastic laws and extends the framework to continuous bases and classical-quantum fields.

Findings

Quantum axioms derived from a single stochastic law

Indication of space being discrete at fundamental level

Explanation of wavefunction collapse and classical limit

Abstract

This paper aims to first explain, somewhat more clearly, the Stochastic-Quantum correspondence put forward in by Barandes in 2023. Specifically, the quantum-mechanical bra-ket notation is used, illuminating some results of previous results. With this, we prove the six axioms of textbook quantum mechanics from a single axiom: every physical system evolves according to a, generally indivisible, stochastic law. Afterwards, we generalise the treatment to continuous bases, which showcases a problem with them, indicating that space (and other physical variables) may be discrete in nature. Some concrete examples are also given, including the generalisation to classical and quantum fields. Then, we treat some practical issues of this new stochastic approach, regarding the solving of problems in physics, which turns out to still be most tractable in the traditional way. Finally, we explain the classical limit, where a system of many particles is found to behave classically according to Newton's second law. Along with that, we present a way of solving the measurement problem, characterising what is an environment and a measuring device and explaining how the wavefunction collapse comes about. Specifically, it is found that what distinguishes an environment is its number of degrees of freedom, while a measuring device is a low-entropy type of environment.