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)...

2 Special relativity 4 2.1 Motivation for special relativistic kinematics in place of Newtonian kinematics . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Axiomatization Specrel of special relativity in first-order logic 15 2.4 Characteristic differences between Newtonian and special relativistic kinematics . . . ...