Observer-independent quanta of mass and length

TL;DR

This paper proposes a modification to special relativity to incorporate observer-independent mass and length scales, suggesting that at the Planck scale, the universe may behave non-relativistically due to altered dispersion relations.

Contribution

It introduces a framework where mass and length scales are invariant for all inertial observers by modifying the principles of special relativity using quantum $ppa$-Poincare9 symmetry.

Findings

Invariance of mass and length scales for all observers.

At the Planck scale, the universe may exhibit non-relativistic behavior.

Modified dispersion relations imply infinite light speed at finite momentum.

Abstract

It has been observed recently by Giovanni Amelino-Camelia \cite{gac1, gac2} that the hypothesis of existence of a minimal observer-independent (Planck) length scale is hard to reconcile with special relativity. As a remedy he postulated to modify special relativity by introducing an observer-independent length scale. In this letter we set forward a proposal how one should modify the principles of special relativity, so as to assure that the values of mass and length scales are the same for any inertial observer. It turns out that one can achieve this by taking dispersion relations such that the speed of light goes to infinity for finite momentum (but infinite energy), proposed e.g., in the framework of the quantum $\kappa$-Poincar\'e symmetry. It follows that at the Planck scale the world may be non-relativistic.