Quantum mechanics as an approximation of statistical mechanics for classical fields

TL;DR

This paper demonstrates that quantum mechanics can be viewed as an approximation of classical statistical mechanics, derived through a Taylor expansion, with quantum effects emerging from second-order terms.

Contribution

It introduces a novel perspective where quantum mechanics is an approximation of classical statistical mechanics, using Taylor expansion to connect the two frameworks.

Findings

Quantum mechanics can be derived as a second-order approximation of classical statistical mechanics.

The approach applies initially to finite-dimensional systems.

Predictions from quantum mechanics may have small deviations from actual experimental averages.

Abstract

We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical variables. The quantum contribution is given by the term of the second order. To escape technical difficulties, we start with the finite dimensional quantum mechanics. In our approach quantum mechanics is an approximative theory. It predicts statistical averages only with some precision. In principle, there might be found deviations of averages calculated within the quantum formalism from experimental averages (which are supposed to be equal to classical averages given by our model).