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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.
Giovanni Amelino-Camelia (Fri,) studied this question.