Distance Measurement and $\kappa$-Deformed Propagation of Light and Heavy Probes

TL;DR

This paper explores how a $mbda$-deformed relativistic symmetry affects the measurement of distances using light and heavy probes, revealing potential links to quantum gravity effects.

Contribution

It analyzes the impact of $mbda$-deformation on distance measurement procedures and highlights differences between light and heavy probes in this context.

Findings

Deformed mass-shell condition affects light probe measurements

Nontrivial commutation relations influence heavy probe measurements

Potential connection to quantum gravity phenomena

Abstract

We investigate the implications for the measurability of distances of a covariant dimensionful ``$\kappa$'' 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 $\kappa$-Poincar\'e symmetries capture some aspects of the physics of the Quantum-Gravity vacuum.