Gauge Theory of the Gravitational-Electromagnetic Field

TL;DR

This paper develops a gauge theory combining gravity and electromagnetism by extending the Poincaré group to include clock synchronization, revealing electromagnetic fields as local gauge fields of the synchrony group and linking invariance principles to the conventionality of simultaneity.

Contribution

It introduces a novel gauge-theoretic framework that unifies gravitational and electromagnetic fields through clock synchronization transformations, offering new insights into the invariance principles of physics.

Findings

Electromagnetic field interpreted as a gauge field of the synchrony group

Derived Einstein-Maxwell equations with additional coupling terms

Established invariance under clock synchronization as a fundamental principle

Abstract

We develop a gauge theory of the combined gravitational-electromagnetic field by expanding the Poincar\'e group to include clock synchronization transformations. We show that the electromagnetic field can be interpreted as a local gauge theory of the synchrony group. According to this interpretation, the electromagnetic field equations possess nonlinear terms and electromagnetic gauge transformations acquire a space-time interpretation as local synchrony transformations. The free Lagrangian for the fields leads to the usual Einstein-Maxwell field equations with additional gravitational-electromagnetic coupling terms. The connection between the electromagnetic field and the invariance properties of the Lagrangian under clock synchronization transformations provides a strong theoretical argument in favor of the thesis of the conventionality of simultaneity. This suggests that clock synchronization invariance (or equivalently, invariance under transformations of the one-way speed of light) is a fundamental invariance principle of physics.