Energy-momentum diffusion from spacetime discreteness

TL;DR

This paper investigates how the fundamental discreteness of spacetime could cause observable energy-momentum diffusion in particles, deriving equations and setting bounds based on cosmic microwave background data.

Contribution

It introduces Lorentz invariant diffusion models for massive and massless particles arising from spacetime discreteness, with derived equations and phenomenological parameter bounds.

Findings

Energy-momentum diffusion described by a single parameter for massive particles.

Derived the most general Lorentz invariant diffusion equation for massless particles.

Set bounds on diffusion and drift parameters from cosmic microwave background observations.

Abstract

We study potentially observable consequences of spatiotemporal discreteness for the motion of massive and massless particles. First we describe some simple intrinsic models for the motion of a massive point particle in a fixed causal set background. At large scales, the microscopic swerves induced by the underlying atomicity manifest themselves as a Lorentz invariant diffusion in energy-momentum governed by a single phenomenological parameter, and we derive in full the corresponding diffusion equation. Inspired by the simplicity of the result, we then derive the most general Lorentz invariant diffusion equation for a massless particle, which turns out to contain two phenomenological parameters describing, respectively, diffusion and drift in the particle's energy. The particles do not leave the light cone however: their worldlines continue to be null geodesics. Finally, we deduce bounds on the drift and diffusion constants for photons from the blackbody nature of the spectrum of the cosmic microwave background radiation.