The Lorentz factor in a reverse coordinate system

TL;DR

This paper derives an alternative Lorentz factor using a reverse coordinate system, which confirms relativistic isotropy and allows for superluminal frame velocities, challenging traditional limits.

Contribution

It introduces a novel transformation factor that aligns with the Lorentz factor but permits reference frames to move faster than light.

Findings

The alternative transformation matches Lorentz factor results at all angles.

It confirms the isotropy of space in Minkowski spacetime.

It allows for superluminal frame velocities.

Abstract

In the present study, we have derived the Lorentz factor using a coordinate system with antiparallel X-axes. Using a thought experiment, common in relativistic literature, we have used the case of a pulse of light moving along the X-axis. Next, we have argued that, consequently with the isotropy of space, the result must be the same if the trajectory of the light pulse is any angle $\alpha>0^{\circ}$, thus obtaining an alternative transformation factor that generates the same results as the Lorenz factor at any angle of the trajectory of the light pulse, therefore confirming the relativistic isotropy of space in the context of the Minkowski spacetime. Nevertheless, a particularly important novelty is that the derived alternative transformation factor allows the reference frames involved to move at speeds greater than that of light.