Synchronization Gauges and the Principles of Special Relativity

TL;DR

This paper re-examines the axiomatic foundations of Special Relativity, focusing on synchronization procedures and gauges, showing they do not alter the theory's predictions but offer different formal frameworks within Minkowski spacetime.

Contribution

It introduces a hierarchy of synchronization gauges in SRT, clarifies their implications, and demonstrates their consistency with empirical facts and the geometry of spacetime.

Findings

Synchronization gauges do not challenge SRT but provide alternative formalisms.

The hierarchy includes Selleri, Mansouri-Sexl, and Anderson-Vetharaniam-Stedman gauges.

Gauge freedom explains phenomena like the Sagnac effect without altering spacetime geometry.

Abstract

The axiomatic bases of Special Relativity Theory (SRT) are thoroughly re-examined from an operational point of view, with particular emphasis on the status of Einstein synchronization in the light of the possibility of arbitrary synchronization procedures in inertial reference frames. Once correctly and explicitly phrased, the principles of SRT allow for a wide range of `theories' that differ from the standard SRT only for the difference in the chosen synchronization procedures, but are wholly equivalent to SRT in predicting empirical facts. This results in the introduction, in the full background of SRT, of a suitable synchronization gauge. A complete hierarchy of synchronization gauges is introduced and elucidated, ranging from the useful Selleri synchronization gauge (which should lead, according to Selleri, to a multiplicity of theories alternative to SRT) to the more general Mansouri-Sexl synchronization gauge and, finally, to the even more general Anderson-Vetharaniam-Stedman's synchronization gauge. It is showed that all these gauges do not challenge the SRT, as claimed by Selleri, but simply lead to a number of formalisms which leave the geometrical structure of Minkowski spacetime unchanged. Several aspects of fundamental and applied interest related to the conventional aspect of the synchronization choice are discussed, encompassing the issue of the one-way velocity of light on inertial and rotating reference frames, the GPS's working, and the recasting of Maxwell equations in generic synchronizations. Finally, it is showed how the gauge freedom introduced in SRT can be exploited in order to give a clear explanation of the Sagnac effect for counter-propagating matter beams.