Relativistic Theory of Superluminal Particles

TL;DR

This paper proposes a relativistic framework accommodating superluminal particles, suggesting modifications to inertial reference systems and the principle of relativity while maintaining Lorentz symmetry.

Contribution

It introduces a theoretical model for superluminal particles within relativity, proposing two sets of inertial frames and revising the principle of relativity accordingly.

Findings

Superluminal particles have distinct energy-momentum relations.

Two types of inertial reference systems are proposed for subluminal and superluminal particles.

The principle of relativity is revised to account for superluminal reference systems.

Abstract

Since some experiments have found superluminality, we assume that the particles in the universe are divided into three classes: the subluminal, luminal and superluminal particles by the speed of light, their energy-momenum relations are E2 = m2c4 + c2p2, E2 = c2p2, and E2 + m2c4 = c2p2, respectively. The Einstein's theory of relativity still holds and is consummated by the existence of superluminal particles, and the Lorentz symmetry of the spacetime is also not violated. There should have two sets of inertial reference systems: subluminal and superluminal reference systems. Two inertial reference systems in each set are linked by Lorentz transformations, but superluminal coordinate transformations between the two sets do not exist in the 1+3 dimensional spacetime. So the physical laws have different expressions in the two sets of inertial reference systems, the principle of special relativity should be revised.