RELATIVITY IN SPACETIMES WITH SHORT-DISTANCE STRUCTURE GOVERNED BY AN OBSERVER-INDEPENDENT (PLANCKIAN) LENGTH SCALE

I show that it is possible to formulate the Relativity postulates in a way that does not lead to inconsistencies in the case of spacetimes whose short-distance structure is governed by an observer-independent length scale. The consistency of these postulates proves incorrect the expectation that modifications of the rules of kinematics involving the Planck length would necessarily require the introduction of a preferred class of inertial observers. In particular, it is possible for every inertial observer to agree on physical laws supporting deformed dispersion relations of the type E²-c² p²-c⁴m² + f(E, p, m; L_p) =0, at least for certain types of f.