From light-speed state to the rest: new representation for energy-momentum

TL;DR

This paper introduces a novel 'counter-rapidity' concept to redefine energy and momentum in relativity, linking hyperbolic geometry with particle velocity quantization near light speed.

Contribution

It proposes a new rapidity framework, extending relativistic dynamics and providing insights into particle behavior at light speed and zero-mass limits.

Findings

Correctly limits to Dirac equation at zero mass

Explains parity violation at zero mass

Predicts quantized velocities near light speed

Abstract

In this paper, we introduce a new concept of rapidity and define formulae for energy and momentum as functions of the new rapidity, we denominate "counter-rapidity". The correspoding velocity is measured from the state of light speed in direction to the rest state. This theory admits correct limit of Dirac equation at the zero-mass point and explain violation of the parity at this point. We show that the velocity of the particle near light-speed is quantized. With the new concept of rapidity are related a new group of transformations and new link between relativistic dynamics and hyperbolic geometry.