A generalization of Jaynes' principle: an information-theoretic interpretation of the minimum principles of quantum mechanics and gravitation

TL;DR

This paper interprets the minimum principles of quantum mechanics and gravitation as information measures, unifying their conceptual foundations and extending to non-Riemannian geometries with new field equations.

Contribution

It offers an information-theoretic interpretation of minimum principles in quantum mechanics and gravity, extending to non-Riemannian spaces with novel torsion field equations.

Findings

Entropy and kinetic energy as correlation measures

Shared properties in quantum and relativistic principles

Extension to non-Riemannian geometries with new torsion equations

Abstract

By considering the "kinetic-energy" term of the minimum principle for the Schr\"{o}dinger equation as a measure of information, that minimum principle is viewed as a statistical estimation procedure, analogous to the manner in which Jaynes ({\it Phys. Rev.},{\bf 106}, 620, 1957) interpreted statistical mechanics. It is shown that the entropy formula of Boltzmann and Jaynes obey a property in common with the quantum-mechanical kinetic energy, in which both quantities are interpreted as measures of correlation. It is shown that this property is shared by the key terms in the minimum principles of relativistic quantum mechanics and General Relativity. It is shown how this principle may be extended to non-Riemannian nonEuclidean spaces, which leads to novel field equations for the torsion.