Derivation and New Interpretation of the Lorentz Transformations and Einstein's Theorem of Velocity Addition

TL;DR

This paper demonstrates that Lorentz transformations and Einstein's velocity addition theorem can be derived from classical mechanics if a universal speed limit is imposed, challenging the traditional view that they are exclusively relativistic.

Contribution

It introduces a derivation of Lorentz transformations and Einstein's velocity addition from classical kinematics with a speed limit, offering a new interpretation.

Findings

Lorentz transformations can be derived from classical mechanics with a speed limit.

Einstein's velocity addition theorem is obtainable within classical kinematics.

The universal speed limit can coincide with the speed of light in vacuum.

Abstract

It is traditionally believed that the Lorentz transformations (LT) and Einstein's theorem of velocity addition (ETVA), underlying special relativity, cannot be obtained from non-relativistic (classical) mechanics. In the present paper it is shown, however, that both the LT and the ETVA are derivable within the framework of classical kinematics if the speeds of material points are bounded above by a certain universal limit $c_+$ which can coincide with the speed of light $c$ in a vacuum.