On the invariance of the relative rest in doubly special relativity

TL;DR

This paper demonstrates that in 1+1 dimensions, doubly special relativity can be formulated to keep the relative rest invariant using the standard velocity formula, without abandoning Minkowski space-time or energy independence.

Contribution

It shows that the velocity formula $dE/dp$ is consistent with invariance of relative rest in 1+1D doubly special relativity, preserving Minkowski space-time and standard boost transformations.

Findings

The velocity formula $dE/dp$ is consistent with invariance of relative rest in 1+1D.

Standard Minkowski space-time can be used without modifications in this framework.

The approach is compatible with superluminal propagation and linear energy addition.

Abstract

In the framework of the most-studied doubly special relativity models the use of the naive formula $v=dE/dp$ has been argued to lead to inconsistencies connected to different rules of transformation, under boosts, of particles with the same energy but with different masses. In this paper we show that, at least in 1+1 dimensions, doubly special relativity can be formulated in such a way that the formula $v=dE/dp$ is fully consistent with the invariance of the relative rest, easily fitting to the relativity principle. It is also argued that, always in 1+1d, is not necessary to renounce to the usual (commutative) Minkowski space-time endowed with energy-independent boost transformations. The compatibility of the approach with superluminal propagation, with linear addition rule for energy, and possible extensions to 3+1 dimensions are also discussed.