Exploring quaternion framework for subluminal to superluminal space transformations in particle dynamics

TL;DR

This paper develops a quaternionic framework to unify subluminal and superluminal space transformations, extending Lorentz transformations and analyzing relativistic effects across different spacetime regimes.

Contribution

It introduces generalized quaternionic Lorentz transformations for both subluminal and superluminal spaces, providing a unified approach to relativistic phenomena.

Findings

Quaternionic length contraction and time dilation are formulated for mixed space regimes.

The transformation between two superluminal spaces reduces to a subluminal space.

Tachyonic behavior emerges when frames are in different spacetime regimes.

Abstract

The present study explores the behavior of quaternionic four-space algebra for subluminal and superluminal spaces. We formulate the generalized Lorentz transformations for quaternionic subluminal, superluminal, and their combined Minkowski spaces. Furthermore, we have studied the relativistic phenomenon of quaternionic length contraction, time dilation, velocity addition, and the Doppler effect for the combination of subluminal and superluminal space. We claim that the transformation between two superluminal spaces is ultimately a subluminal space; the tachyonic behavior reveals itself in the consequences when the two frames are in different spaces (i.e., generalized subluminal-superluminal spaces).