Implementing Mach's Principle Using Gauge Theory

TL;DR

This paper reformulates Mach's principle using gauge theory, connecting particle models with Yang-Mills theories and proposing a modified approach that could influence understanding of gravitational gauge properties.

Contribution

It introduces a gauge theory-based reformulation of Mach's principle applicable to arbitrary symmetry groups, linking particle models to Yang-Mills theories and geometrodynamics.

Findings

Reformulation of Mach's principle using gauge theory techniques.

Equivalence of the modified and original BB methods.

Potential implications for understanding gravitational gauge properties.

Abstract

We reformulate an approach fist given by Barbour and Bertotti (BB) for implementing Mach's principle for nonrelativistic particles. This reformulation can deal with arbitrary symmetry groups and finite group elements. Applying these techniques to U(1) and SU(N) invariant scalar field theories, we show that BB's proposal is nearly equivalent to defining a covariant derivative using a dynamical connection. We then propose a modified version of the BB method which implements Mach's principle using gauge theory techniques and argue that this modified method is equivalent to the original. Given this connection between the particle models and Yang-Mills theories, we consider the effect of dynamic curvature as a possible generalization of the BB scheme. Since the BB method can be used as a novel way of deriving geometrodynamics, the connection with gauge theory may shed new light on the gauge properties of the gravitational field.