The Real Quaternion Relativity

TL;DR

This paper introduces a quaternion-based framework for special relativity that extends its applicability to stationary, rotating, and moving frames, providing a unified mathematical approach to space-time, mass, and energy using quaternion algebra.

Contribution

It develops a quaternion time domain and space-time formulation, extending relativity beyond inertial frames and linking physical measurements to quaternion norms.

Findings

Quaternion time measurement depends on observer location.

Lorentz relations are recovered within the quaternion framework.

Quaternion conjugation models frame transitions, while norms represent physical measurements.

Abstract

In this work, we use real quaternions and the basic concept of the final speed of light in an attempt to enhance the standard description of special relativity. First, we demonstrate that it is possible to introduce a quaternion time domain where a coordinate point is described by a quaternion time. We show that the time measurement is a function of the observer location, even for stationary frames of reference. We introduce a moving observer, which leads to the traditional Lorentz relation for the time interval. We show that the present approach can be used in stationary, moving, or rotating frames of reference, unlike the traditional special relativity, which applies only to the inertial moving frames. Then, we use the quaternion formulation of space-time and mass-energy equivalence to extend the quaternion relativity to space, mass, and energy. We demonstrate that the transition between the particle and observer reference frames is equivalent to space inversion and can be described mathematically by quaternion conjugation. On the other hand, physical measurements are described by the quaternion norm and consequently are independent of the conjugation, which seems to be the quaternion formulation of the relativity principle.