Doubly Special Relativity

I give a short non-technical review of the results obtained in recent work on “Doubly Special Relativity”, the relativistic theories in which the rotation/boost transformations between inertial observers are characterized by two observer-independent scales (the familiar velocity scale, c, and a new observer-independent length/momentum scale, naturally identified with the Planck length/momentum). I emphasize the aspects relevant for the search of a solution to the cosmic-ray paradox. Galilei/Newton Relativity was abandoned because of the conflicting results of the Michelson-Morley experiments and because of its incompatibility with the mathematical structure of the successful Maxwell theory of electromagnetism. After a century of successes, Einstein’s Special Relativity, the theory that replaced Galilei/Newton Relativity, could now be questioned for similar reasons. A key Special-Relativity prediction appears to be violated by certain observations of ultra-high-energy cosmic rays [1], and some Quantum-Gravity arguments appear to encourage a modification of Special Relativity. I argued in Ref. [2] that this situation can provide motivation for considering a change in the Relativity postulates somewhat analogous to the one needed for the transition from Galilei/Newton Relativity to Einstein’s Relativity: the introduction of a new absolute observer-independent scale. I analyzed in detail a first illustrative example of relativity postulates with an observer-independent length(momentum) scale, in addition to the familiar observer-independent velocity scale c, and I showed that there is no in principle obstruction for the construction of such new relativistic theories. That illustrative example of new relativistic theory also predicts some new effects of a type that could explain the observations of ultra-high-energy cosmic rays, but the predicted magnitude of these effects turns out to be too weak for a description of the data. For nearly a year, follow-up studies [3] focused on the example of new relativistic The published version was edited and shortened. The title was changed to “Special Treatment”, with “Relativity” as subject heading, and a figure (with elementary description of cosmic-ray observations) was added.