On the Measurement of the Speed of Light in a Cavity

Abstract

Nowadays the speed of light in vacuum is fixed by convention as a constant c, whose value has been chosen according to the results of the most precise measurements. We investigate from a purely theoretical point of view how precisely an observer can determine c when measuring the frequency of light inside a cubic cavity and calculating c through $c=\frac{\omega \lambda }{2\pi }$. The theoretical analysis is done by combining arguments from quantum parameter estimation theory and general relativity. This leads to a lower bound on the uncertainty depending on the size of the cavity, the measuring time and the number of measurements.