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Optical Data describing Structure of Spacetime:

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The following is an article and paper I came across. Can a relativist/physicist please explain in simpler detail, if possible? particulalry the following..."There are four distinct rotational relativistic transformations in the literature: the Langevin metric; Post transformation; Franklin transformation; and the absolute Lorentz transformation (ALT) in its rotational form." and how is validates or otherwise relativity.

Researchers use optical data to reveal the basic structure of spacetime in rotating frames:

One of the most basic structural aspects of relativistic spacetime is the description of how time and distances are altered by motion. The theory of special relativity describes a spacetime framework for linear constant motion in which time dilates and lengths contract in response to motion. This framework is described by the Lorentz transformation, which encompasses mathematical formulas that describe how time and distance are altered between moving reference frames. The Lorentz transformation also describes how a stationary observer views time in the moving frame to be offset with distance. The offsetting of time with distance between reference frames generates differential simultaneity, in which events that are simultaneous for one observer will not be simultaneous for a second observer moving relative to the first observer.

more at link....

the paper:

Abstract

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 Lorentz transformation. 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.

Edited by beecee
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Quote

Conclusions
...
The kinematic rTs have simple structures with descriptions using peripheral velocity and polar coordinates. Despite this simple structure, the ALT rT produces exact solutions that include the empirically-validated conventional Sagnac effect equation and the isotropic two-way speed of light (see Secs. 4 and 5). Both of these have been confirmed to the resolutions of the experiments. Additionally, the ALT rT generates a time dilation relation (shared with the Franklin rT) that has also been experimentally confirmed. Thus, the ALT rT can accurately describe relativistic observations without incorporating non-inertial effects or utilizing co-moving linear transformations.
...
The rTs can be distinguished based on their predictions on the ability of rotating-frame observers to determine their rotational motion using light propa-gation. The ALT rT predicts that rotating-frame observers can determine their rotational velocity based on anisotropic one-way speeds of light, but cannot de-termine their rotational velocity using the isotropic two-way speed of light. The Langevin metric and Post rT predict that rotational velocity can be determined by both anisotropic one-way and anisotropic two-way speeds of light. The Franklin rT predicts that rotational velocity cannot be determined by either isotropic one-way or isotropic two-way speeds of light. Significantly, only the ALT rT predictions match observations.

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The difference between ALT and the other 3 is given in the paper. Essentially it uses a preferred (absolute) reference frame based on gravitational centers.

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