Relativity of superluminal observers in $1+3$ spacetime

TL;DR

This paper extends special relativity to include superluminal observers in 1+3 spacetime, demonstrating that such an extension necessitates a field-theoretic framework over particle mechanics.

Contribution

It introduces a relativistic framework accommodating superluminal observers, linking extended relativity to the necessity of field theory for consistent dynamics.

Findings

Superluminal observers cannot be described by point particles within this framework.

Extended relativity excludes conventional particle dynamics, favoring a field-theoretic approach.

Field theory emerges naturally from the extended relativistic principles.

Abstract

We develop an extension of special relativity in $1+3$ dimensional spacetime to account for superluminal inertial observers and show that such an extension rules out the conventional dynamics of mechanical point-like particles and forces one to use a field-theoretic framework. Therefore we show that field theory can be viewed as a direct consequence of extended special relativity.