Distance Measurement and $κ$-Deformed Propagation of Light and Heavy Probes

Abstract

We investigate the implications for the measurability of distances of a covariant dimensionful ``$κ$'' deformation of D=4 relativistic symmetries, with quantum time coordinate and modified Heisenberg algebra. We show that the structure of the deformed mass-shell condition has significant implications for measurement procedures relying on light probes, whereas in the case of heavy probes the most sizeable effect is due to the nontrivial commutation relation between three-momenta and quantum time coordinate. We argue that these findings might indicate that $κ$-Poincaré symmetries capture some aspects of the physics of the Quantum-Gravity vacuum.