The statistical origins of gauge coupling and spin

TL;DR

This paper derives Schrödinger's equation, gauge coupling, and spin effects from statistical assumptions, providing a unified statistical foundation for quantum mechanics, gauge fields, and spin phenomena.

Contribution

It generalizes a statistical derivation to include gauge fields and spin, linking these features to underlying statistical assumptions and providing new insights into their origins.

Findings

Derivation of gauge coupling terms from statistical assumptions

Introduction of spin as a statistical response to gauge fields

Connection of classical limit to quantum formalism interpretation

Abstract

A previous one-dimensional derivation of Schr\"odinger's equation from statistical assumptions is generalized to three spatial dimensions, gauge fields, and spin. It is found that the same statistical assumptions that imply Schr\"odinger's equation determine also the form of the gauge coupling terms, and the form of the corresponding local (Lorentz) forces. An explanation for the role of the electrodynamic potentials, as statistical representatives of the Lorentz force, is given. Spin one-half is introduced as the property of a statistical ensemble to respond to an external gauge field in two different ways. A generalized calculation, using the twofold number of variables, leads to Pauli's equation. The new spin term is again the statistical representative of the corresponding local force. The classical limit $\hbar \to 0$ of Schr\"odinger's equation and closely related questions of interpretation of the quantum mechanical formalism are discussed.