Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale

Abstract

I show that it is possible to formulate the Relativity postulates in a way that does not lead to inconsistencies in the case of space-times 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 $E^2- c^2 p^2- c^4 m^2 + f(E,p,m;L_p)=0$, at least for certain types of $f$.