On the definition of velocity in theories with two observer-independent scales

TL;DR

This paper discusses how to define particle velocity consistently in theories with two observer-independent scales, emphasizing the need for definitions that are mass-independent, and evaluates existing proposals.

Contribution

It clarifies the criteria for defining velocity in doubly special relativity and assesses the validity of various proposed definitions.

Findings

The velocity should be independent of particle mass.

The standard definition v_i=∂p_0/∂p_i is inconsistent.

Alternative definitions are compatible with the criteria.

Abstract

We argue that a consistent definition of the velocity of a particle in generalizations of special relativity with two observer-independent scales should be independent from the mass of the particle. This request rules out the definition $v_i=\partial p_0/\partial p_i$, but allows for other definitions proposed in the literature.