Optical data implies a null simultaneity test theory parameter in rotating frames

TL;DR

This paper uses optical data and the Mansouri-Sexl test theory to analyze simultaneity in rotating frames, concluding that absolute simultaneity is supported and deriving a rotational Lorentz transformation.

Contribution

It demonstrates that the Mansouri-Sexl parameter $ extepsilon(v)$ is a physical descriptor of simultaneity, not just a convention, and derives a rotational Lorentz transformation from optical data.

Findings

The conventional Sagnac effect equation matches optical data.

$ extepsilon(v)$ is null in rotating frames, indicating absolute simultaneity.

The rotational Lorentz transformation accurately describes relativistic effects in rotation.

Abstract

The simultaneity framework describes the relativistic interaction of time with space. The two major proposed simultaneity frameworks are differential simultaneity, in which time is offset with distance in "moving" or rotating frames for each "stationary" observer, and absolute simultaneity, in which time is not offset with distance. We use the Mansouri and Sexl test theory to analyze the simultaneity framework in rotating frames in the absence of spacetime curvature. The Mansouri and Sexl test theory has four parameters. Three parameters describe relativistic effects. The fourth parameter, $\epsilon (v)$, was described as a convention on clock synchronization. We show that $\epsilon (v)$ is not a convention, but is instead a descriptor of the simultaneity framework whose value can be determined from the extent of anisotropy in the unidirectional one-way speed of light. In rotating frames, one-way light speed anisotropy is described by the Sagnac effect equation. We show that four published Sagnac equations form a relativistic series based on relativistic kinematics and simultaneity framework. Only the conventional Sagnac effect equation, and its associated isotropic two-way speed of light, is found to match high-resolution optical data. Using the conventional Sagnac effect equation, we show that $\epsilon (v)$ has a null value in rotating frames, which implies absolute simultaneity. Introducing the empirical Mansouri and Sexl parameter values into the test theory equations generates the rotational form of the absolute Lorentz transformation, implying that this transformation accurately describes rotational relativistic effects.