Photon under repeated transverse Lorentz boosts: An apparent paradox

TL;DR

This paper explores how repeated transverse Lorentz boosts can reverse a photon's momentum direction and demonstrates that an infinite sequence results in a Lorentz transformation involving a rotation, illustrating the counterintuitive nature of relativistic velocity transformations.

Contribution

It reveals how repeated transverse Lorentz boosts can lead to momentum reversal and connects this to the Wigner rotation, providing new insights into relativistic transformations.

Findings

Repeated transverse Lorentz boosts can reverse photon momentum.

Infinite infinitesimal boosts result in a Lorentz transformation with a rotation.

The effects are explained via the Wigner rotation concept.

Abstract

We investigate the effects of the repeated application of Lorentz-boosts to the four momentum of a photon in the transverse direction and observe that this can take us to a reference frame in which the direction of the photon's momentum is apparently reversed. We further extend this to an infinite succession of infinitesimal transverse Lorentz-boosts and show it amounts to a rotation of the photon's momentum, while the transformation is not a simple rotation but a Lorentz transformation. These possibly surprising results can be understood in light of the Wigner rotation: the combination of Lorentz-boosts along different directions amounts to a Lorentz-boost combined with a rotation. The presented exercises are some more illustrations of the counterintuitive behavior of Lorentz-boost combinations.