Introduction: what is DSR?

The definition of doubly special relativity (DSR) (see for review) is deceptively simple. Recall that Special Relativity is based on two postulates: the relativity principle for inertial observers and the existence of a single observer independent scale associated with the velocity of light. In this DSR replaces the second postulate by assuming the existence of two observer-independent scales: the old one of velocity plus the scale of mass (or of momentum, or of energy). That's it.

Adding a new postulate has consequences, however. The most immediate one is the question: what does the second observer-independent scale mean physically? Before trying to answer this question, let us recall the concept of an observer-independent scale. It can be easily understood, when contrasted with the notion of dimensionful coupling constant, like the Planck constant ħ or the gravitational constant G. What is their status in relativity? Do they transform under Lorentz transformation? Well, naively, one would think that they should because they are given by dimensional quantities. But of course they do not. The point is that there is a special operational definition of these quantities. Namely each observer, synchronized with all the other observers, by means of the standard Einstein synchronization procedure, measures their values in an identical quasi-static experiment in her own reference frame (like the Cavendish experiment).