Rotating Frames in SRT: Sagnac's Effect and Related Issues

TL;DR

This paper rigorously analyzes rotating frames in Special Relativity, clarifying misconceptions about the Sagnac effect, light velocity measurement, and transformations between reference frames, emphasizing the importance of precise mathematical methods.

Contribution

It provides a rigorous mathematical framework for understanding rotating frames in Special Relativity, clarifying misconceptions and refuting claims about the Sagnac effect and related transformations.

Findings

Sagnac effect can be explained within Special Relativity.

Measurement of one-way light velocity in rotating frames is clarified.

Transformations between rotating and inertial frames are not limited to Lorentz-like forms.

Abstract

After recalling the rigorous mathematical representations in Relativity Theory (\emph{RT}) of (i): observers, (ii): reference frames fields, (iii): their classifications, (iv) naturally adapted coordinate systems (\emph{nacs}%) to a given reference frame, (v): synchronization procedure and some other key concepts, we analyze three problems concerning experiments on rotating frames which even now (after almost a century from the birth of \emph{RT}) are sources of misunderstandings and misconceptions. The first problem, which serves to illustrate the power of rigorous mathematical methods in \emph{RT}is the explanation of the Sagnac effect (\emph{SE}). This presentation is opportune because recently there are many non sequitur claims in the literature stating that the \emph{SE} cannot be explained by \emph{SRT}, even disproving this theory or that the explanation of the effect requires a new theory of electrodynamics. The second example has to do with the measurement of the one way velocity of light in rotating reference frames, a problem for which many wrong statements appear in recent literature. The third problem has to do with claims that only Lorentz like type transformations can be used between the \emph{nacs}associated to a reference frame mathematically moddeling of a rotating platform and the \emph{nacs} associated with a inertial frame (the laboratory). Whe show that these claims are equivocated.