A new relativistic kinematics of accelerated systems

TL;DR

This paper develops a relativistic framework for accelerated systems without the Clock Hypothesis, predicting a maximal acceleration, acceleration-induced time dilation, and Doppler shifts, supported by reanalysis of experimental data.

Contribution

It introduces a new linear Lorentz-type transformation for accelerated systems using proper velocity-time variables, challenging traditional assumptions.

Findings

Predicts a maximal acceleration limit.

Explains experimental results with reanalyzed data.

Identifies acceleration-induced time dilation and Doppler effects.

Abstract

We consider transformations between uniformly accelerated systems, assuming that the Clock Hypothesis is false. We use the proper velocity-time description of events rather than the usual space-time description in order to obtain linear transformations. Based on the generalized principle of relativity and the ensuing symmetry, we obtain transformations of Lorentz-type. We predict the existence of a maximal acceleration and time dilation due to acceleration. We also predict a Doppler shift due to acceleration of the source in addition to the shift due to the source's velocity. Based on our results, we explain the W. K\"{u}ndig experiment, as reanalyzed by Kholmetski \textit{et al}, and obtain an estimate of the maximal acceleration.