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

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 stationaryobserver, 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.

Assessment of the relativistic rotational transformations

Rotational transformations describe relativistic effects in rotating frames. There are four major kinematic rotational transformations: the Langevin metric; Post transformation; Franklin transformation; and the rotational form of the absolute Lorentztransformation. The four transformations exhibit different combinations of relativistic effects and simultaneity frameworks, and generate different predictions for relativistic phenomena. Here, the predictions of the four rotational transformations are compared with recent optical data that has sufficient resolution to distinguish the transformations. We show that the rotational absolute Lorentz transformation matches diverse relativistic optical and non-optical rotational data. These include experimental observations of length contraction, directional time dilation, anisotropic one-way speed of light, isotropic two-way speed of light, and the conventional Sagnac effect. In contrast, the other three transformations do not match the full range of rotating-frame relativistic observations.