Quantum Gravity Phenomenology, Lorentz Invariance and Discreteness

TL;DR

This paper argues that fundamental spacetime discreteness can be compatible with Lorentz invariance, introduces a causal set model for particle propagation, and explores potential implications for high-energy cosmic rays.

Contribution

It demonstrates that causal set discreteness does not violate Lorentz invariance and presents a phenomenological model of particle diffusion in this framework.

Findings

Causal set discreteness is locally Lorentz invariant.

Particles undergo Lorentz invariant phase space diffusion.

Potential connection to high energy cosmic ray origins.

Abstract

Contrary to what is often stated, a fundamental spacetime discreteness need not contradict Lorentz invariance. A causal set's discreteness is in fact locally Lorentz invariant, and we recall the reasons why. For illustration, we introduce a phenomenological model of massive particles propagating in a Minkowski spacetime which arises from an underlying causal set. The particles undergo a Lorentz invariant diffusion in phase space, and we speculate on whether this could have any bearing on the origin of high energy cosmic rays.