Approaching Space Time Through Velocity in Doubly Special Relativity

TL;DR

This paper investigates how velocity definitions in Doubly Special Relativity impact the possibility of constructing a consistent space-time framework with an invariant length scale, finding that certain definitions prevent such a construction.

Contribution

It demonstrates that under various velocity definitions in DSR, a compatible space-time cannot be derived, highlighting limitations in current formulations.

Findings

Velocity as dE/dp can match dx/dt in DSR

Space-time consistent with DSR principles cannot be derived with certain velocity definitions

Invariant length scale challenges the construction of compatible space-time in DSR

Abstract

We discuss the definition of velocity as dE/dp, where E,p are the energy and momentum of a particle, in Doubly Special Relativity (DSR). If this definition matches dx/dt appropriate for the space-time sector, then space-time can in principle be built consistently with the existence of an invariant length scale. We show that, within different possible velocity definitions, a space-time compatible with momentum-space DSR principles can not be derived.