# How does the photon's spin affect Gravitational Wave measurements?

## TL;DR

This paper investigates how photon polarization influences gravitational wave measurements by analyzing photon trajectories under different spin conditions, revealing tiny polarization-dependent effects on time delay in gravitational wave experiments.

## Contribution

It introduces a detailed analysis of photon spin effects on gravitational wave measurements using the Mathisson-Papapetrou-Dixon equations with different spin supplementary conditions.

## Key findings

- Photon polarization can cause tiny deviations in measured time delays.
- Null geodesic assumption neglects spin effects, which are present under certain conditions.
- Spin effects depend on the choice of spin supplementary condition.

## Abstract

We study the effect of the polarization of light beams on the time delay measured in Gravitational Wave experiments. To this end, we consider the Mathisson-Papapetrou-Dixon equations in a gravitational wave background, with two of the possible spin supplementary conditions: by Frenkel-Pirani, or by Tulczyjew. In the first case, photons follow a null geodesic and thus no spin effect is present. The second case shows a deviation of the photons from the null geodesic, resulting in a tiny effect on the measured time delay of photons depending on their polarization state.