Speed of particles and a relativity of locality in $\kappa$-Minkowski quantum spacetime

TL;DR

This paper investigates the speed of massless particles in $$-Minkowski spacetime, resolving previous controversies by focusing on local event assessments, and finds that detection times depend linearly on particle momentum.

Contribution

It clarifies the momentum dependence of massless particle speeds in $$-Minkowski spacetime by avoiding issues with distant event coincidence assessments.

Findings

Detection times of massless particles depend linearly on momentum.

No momentum dependence of particle speed when local event assessments are used.

Supports the idea that $$-Minkowski spacetime exhibits a relativity of locality.

Abstract

The last decade of research on $\kappa$-Minkowski noncommutative spacetime has been strongly characterized by a controversy concerning the speed of propagation of massless particles. Most arguments suggested that this speed should depend on the momentum of the particle strongly enough to be of interest for some ongoing experimental studies. But the only explicit derivations of worldlines in $\kappa$-Minkowski predicted no momentum dependence for the speed of massless particles. We return to this controversy equipped with the recent understanding (arXiv:1006.2126, arXiv:1007.0718, arXiv:1008.2962, arXiv:1101.0931) that in some quantum spacetimes coincidences of events assessed by an observer who is distant from the events can be artifactual, and particularly Smolin's thesis (arXiv:1007.0718) that $\kappa$-Minkowski should be an example of such a spacetime. We therefore set up our investigation in such a way that we never rely on the assessment of coincidences of events by distant observers. This allows us to verify explicitly that in $\kappa$-Minkowski simultaneously-emitted massless particles of different momentum are detected at different times, and establish a linear dependence of the detection times on momentum.