On the Conventionality of Simultaneity

TL;DR

This paper explores how the isotropy of light speed can be seen as a matter of convention, showing that different gauge choices lead to the same physical theory and linking simultaneity conventions to gauge theories.

Contribution

It demonstrates the consistency of anisotropic and inhomogeneous conventions and connects simultaneity choices with gauge theory frameworks.

Findings

All conventions yield the same physical predictions.

A Euclidean space with the L/c law results in Minkowskian causal structure.

The choice of simultaneity is a gauge choice in the theory.

Abstract

Starting from the experimental fact that light propagates over a closed path at speed c (L/c law), we show to what extent the isotropy of the speed of light can be considered a matter of convention. We prove the consistence of anisotropic and inhomogenous conventions, limiting the allowed possibilities. All conventions lead to the same physical theory even if its formulation can change in form. The mathematics involved is that of gauge theories and the choice of a simultaneity convention is interpreted as a choice of the gauge. Moreover we prove that a Euclidean space where the L/c law holds, gives rise to a spacetime with Minkowskian causal structure, and we exploit the consequences for the causal approach to the conventionality of simultaneity.