Exact Rotational Space-time Transformations, Davies-Jennison Experiments and Limiting Lorentz-Poincar\'e Invariance

TL;DR

This paper derives exact rotational space-time transformations based on limiting Lorentz-Poincaré invariance, supporting Jennison's radius contraction and aligning with Davies-Jennison experiments, proposing new tests for these transformations.

Contribution

It introduces exact rotational transformations forming a pseudo-group, differing from Lorentz transformations, and validates them against experimental results.

Findings

Supports Jennison's radius contraction in rotational frames

Aligns with Davies-Jennison experimental results

Proposes new experimental tests for rotational transformations

Abstract

Jennison deduced from the rotational experiments that a rotating radius $r_r$ measured by the rotating observer is contracted by $r_r = r(1-\om^2 r^2/c^2)^{1/2}$, compared with the radius $r$ measured in an inertial frame. This conclusion differs from the result based on Lorentz transformations. Since rotational frames are not equivalent to inertial frames, we analyze the rotational experiments by using the exact rotational space-time transformations rather than the Lorentz transformations. We derive exact rotational transformations on the basis of the principle of limiting Lorentz-Poincar\'e invariance. The exact rotational transformations form a pseudo-group rather than the usual Lie group. They support Jennison's contraction of a rotating radius and are consistent with two Davies-Jennison experiments. We also suggest new experimental tests for the exact rotational transformations.