Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction

TL;DR

This paper derives quantum and classical statistical mechanics within a unified axiomatic framework, revealing how quantum features like entanglement and uncertainty emerge from an ontic extension and epistemic restriction.

Contribution

It introduces a novel axiomatic approach that unifies quantum and classical mechanics, highlighting the roles of an ontic extension and epistemic restriction in quantum phenomena.

Findings

Quantum entanglement arises from the ontic extension.

Uncertainty relations follow from the epistemic restriction.

Wave function is interpreted as epistemic, not ontic.

Abstract

Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic framework, allowing an unambiguous account of how one theory is the limit of the other. Here we derive nonrelativistic quantum mechanics and classical statistical mechanics within a common framework. The common axioms include conservation of average energy and conservation of probability current. But two axioms distinguish quantum mechanics from classical statistical mechanics: an "ontic extension" defines a nonseparable (global) random variable that generates physical correlations, and an "epistemic restriction" constrains allowed phase space distributions. The ontic extension and epistemic restriction, with strength on the order of Planck's constant, imply quantum entanglement and uncertainty relations. This framework suggests that the wave function is epistemic, yet it does not provide an ontic dynamics for individual systems.