Relativistic contraction and related effects in noninertial frames

TL;DR

This paper offers a corrected analysis of relativistic effects in rotating frames, resolving the Ehrenfest paradox by considering noninertial frames and demonstrating that observers see equal lengths and isotropic light speed.

Contribution

It introduces a novel approach using noninertial frames to accurately describe relativistic effects in rotating systems, challenging standard assumptions.

Findings

Tensile stresses are consistent with the corrected model.

Observers on the rim see equal lengths of differently moving objects.

Light speed remains isotropic and equal to c in local measurements.

Abstract

Although there is no relative motion among different points on a rotating disc, each point belongs to a different noninertial frame. This fact, not recognized in previous approaches to the Ehrenfest paradox and related problems, is exploited to give a correct treatment of a rotating ring and a rotating disc. Tensile stresses are recovered, but, contrary to the prediction of the standard approach, it is found that an observer on the rim of the disc will see equal lengths of other differently moving objects as an inertial observer whose instantaneous position and velocity are equal to that of the observer on the rim. The rate of clocks at various positions, as seen by various observers, is also discussed. Some results are generalized for observers arbitrarily moving in a flat or a curved spacetime. The generally accepted formula for the space line element in a non-time-orthogonal frame is found inappropriate in some cases. Use of Fermi coordinates leads to the result that for any observer the velocity of light is isotropic and is equal to $c$, providing that it is measured by propagating a light beam in a small neighborhood of the observer.