Gauge Theory of the Gravitational-Electromagnetic Field
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.
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Cite
@article{arxiv.1505.04133,
title = {Gauge Theory of the Gravitational-Electromagnetic Field},
author = {Robert D. Bock},
journal= {arXiv preprint arXiv:1505.04133},
year = {2015}
}