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

TL;DR

This paper demonstrates that relativity principles can be extended to space-times with a fundamental length scale, like the Planck length, without requiring a preferred inertial frame, thus maintaining observer independence.

Contribution

It formulates a consistent version of relativity accommodating an observer-independent length scale, challenging the belief that such modifications imply preferred frames.

Findings

Relativity postulates can be consistent with a Planckian length scale.

Deformed dispersion relations can be compatible with observer-independent physics.

No preferred inertial observers are necessary for these modifications.

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 $f$.