Relational Entropic Dynamics of Particles

TL;DR

This paper develops a relational quantum dynamics framework using entropic measures and information geometry, enabling a new approach to gauge theories and Mach's principles in physics.

Contribution

It introduces an entropic version of best matching for relational quantum dynamics, extending classical techniques with information geometry tools.

Findings

Formulates a relational quantum dynamics using entropic measures.

Demonstrates the approach with a system of particles with translational symmetry.

Provides a foundation for handling gauge theories within an informational framework.

Abstract

The general framework of entropic dynamics is used to formulate a relational quantum dynamics. The main new idea is to use tools of information geometry to develop an entropic measure of the mismatch between successive configurations of a system. This leads to an entropic version of the classical best matching technique developed by J. Barbour and collaborators. The procedure is illustrated in the simple case of a system of N particles with global translational symmetry. The generalization to other symmetries whether global (rotational invariance) or local (gauge invariance) is straightforward. The entropic best matching allows a quantum implementation Mach's principles of spatial and temporal relationalism and provides the foundation for a method of handling gauge theories in an informational framework.