Thomas Precession by Uniform Acceleration

TL;DR

This paper explores the effects of uniform acceleration on physical phenomena, deriving analogues of relativistic effects and examining the role of Thomas precession in physics and cosmology.

Contribution

It introduces nonlinear transformations for uniformly accelerated frames and analyzes their impact on mass, length, time, and relativistic effects, including Thomas precession.

Findings

Derived acceleration-dependent formulas for mass, length, and time.

Established an analogy between acceleration effects and special relativity phenomena.

Discussed potential implications of Thomas precession in cosmology.

Abstract

We determine the nonlinear transformations between coordinate systems which are mutually in a constant symmetrical accelerated motion. The maximal acceleration limit follows from the kinematical origin and it is an analogue of the maximal velocity in special relativity. We derive the dependence of mass, length, time, Doppler effect, Cherenkov effect and transition radiation angle on acceleration as an analogue phenomena in special theory of relativity. The last application of our method is the Thomas precession by uniform acceleration with the possible role in the modern physics and cosmology. The comparison of derived results with other relativistic methods is necessary.