New subluminal and superluminal spacetime measures

TL;DR

This paper introduces a novel set of spacetime measures applicable to both subluminal and superluminal regimes, avoiding divergence at the speed of light and defining separate causality cones, with implications for crossing the light speed barrier.

Contribution

The work proposes a new framework of spacetime measures that remain finite at the speed of light and allow discrete transitions across it, expanding the understanding of relativistic motion.

Findings

Measures do not diverge at light speed

Distinct light-like cones for each regime

Possibility of discrete superluminal transitions

Abstract

In present work the author presents a new set of spacetime measures for both, subluminal and superluminal motion regimes, which do not diverge for the speed of light in the former case and each regime has its own light-like cone which warrants causality to each regime. For events located in the vicinity of the light cone and inside it, there exists the possibility to transit across the speed of light value in a discrete way, in terms of the very small constant which we introduce here to prevent the divergence of our spacetime measures at the speed of light.