Reconciling and Validating the Ashworth-Davies Doppler Shifts of a Translating Mirror

TL;DR

This paper simplifies the Ashworth-Davies relativistic theory for a translating mirror at arbitrary angles, confirms its accuracy through experiments, and compares it with a more intuitive approach in the non-relativistic limit.

Contribution

The paper provides a simplified derivation of the Ashworth-Davies theory and experimentally validates its predictions using phase-insensitive frequency measurements.

Findings

Good agreement between simplified theory and experiments

Experimental validation using liquid crystal light valve

Non-relativistic limit matches intuitive derivation

Abstract

We simplify the Ashworth-Davies special relativistic theory of a uniformly translating mirror with an arbitrary angle of incidence and direction of propagation in the non-relativistic limit. We show that it is in good agreement with a more intuitive derivation that only considers the constancy of the speed of light. We experimentally confirm the theory predictions with phase-insensitive frequency measurements using a liquid crystal light valve.