The maximal acceleration, Extended Relativistic Dynamics and Doppler type shift for an accelerated source

TL;DR

This paper proposes an extension to relativistic dynamics incorporating a universal maximal acceleration, predicts a Doppler-like shift for accelerated sources, and suggests experimental methods to measure this maximal acceleration.

Contribution

It introduces a Lorentz-type transformation for accelerated systems implying a maximal acceleration and extends relativistic dynamics accordingly.

Findings

Reanalysis of the K"undig experiment indicates the Clock Hypothesis is invalid.

Predicted maximal acceleration is approximately 10^{19} m/s^2.

Provides a method to experimentally measure the maximal acceleration with current technology.

Abstract

Based on the generalized principle of relativity and the ensuing symmetry, we have shown that there are only two possible types of transformations between uniformly accelerated systems. The first allowable type of transformation holds if and only if the Clock Hypothesis is true. If the Clock Hypothesis is not true, the transformation is of Lorentz-type and implies the existence of a universal maximal acceleration $a_m$. We present an extension of relativistic dynamics for which all admissible solutions will have have a speed bounded by the speed of light $c$ and the acceleration bounded by $a_m$. An additional Doppler type shift for an accelerated source is predicted. The formulas for such shift are the same as for the usual Doppler shift with $v/c$ replaced by $a/a_m$. The W. K\"{u}ndig experiment of measurement of the transverse Doppler shift in an accelerated system was also exposed to a longtitudal shift due to the acceleration. This experiment, as reanalyzed by Kholmetskii et al, shows that the Clock Hypothesis is not valid. Based on the results of this experiment, we predict that the value of the maximal acceleration $a_m$ is of the order $10^{19}m/s^2$. Moreover, our analysis provides a way to measure experimentally the maximal acceleration with existing technology.