On the time delay between ultra-relativistic particles

TL;DR

This paper explains that the time delay between ultra-relativistic particles emitted simultaneously can be understood through a simple physical interpretation, highlighting a kinematical property of general relativity related to tidal forces.

Contribution

It demonstrates that the previously derived formula for time delay has a straightforward physical interpretation involving constant relative velocity.

Findings

The relative velocity between ultra-relativistic particles remains constant.

Tidal forces along the particles' motion are negligible compared to orthogonal directions.

The formula's interpretation simplifies understanding of particle time delays in curved spacetime.

Abstract

The time delay between the receptions of ultra-relativistic particles emitted simultaneously is a useful observable for both fundamental physics and cosmology. The expression of the delay when the particles travel through an arbitrary spacetime has been derived recently by Fanizza et al., using a particular coordinate system and self-consistent assumptions. The present article shows that this formula enjoys a simple physical interpretation: the relative velocity between two ultra-relativistic particles is constant. This result reveals an interesting kinematical property of general relativity, namely that the tidal forces experienced by ultra-relativistic particles in the direction of their motion are much smaller than those experienced orthogonally to their motion.