Propagation of pulsed light in an optical cavity in a gravitational field

All modern theories of gravitation, starting with Newton's, predict that gravity will affect the speed of light propagation. Einstein's theory of General Relativity famously predicted that the effect is twice the Newtonian value, a prediction that was verified during the 1919 solar eclipse. Recent theories of vector gravity can be interpreted to imply that gravity will have a different effect on pulsed light versus continuous-wave (CW) light propagating between the two mirrors of an optical cavity. Interestingly, we are not aware of any previous experiments to determine the relative effect of gravity on the propagation of pulsed versus CW light. In order to observe if there are small differences, we use a 6 GHz electro-optic frequency comb and low-noise CW laser to make careful measurements of the resonance frequencies of a high-finesse optical cavity. Once correcting for the effects of mirror dispersion, we determine that the cavity resonance frequencies for pulsed and CW light are the same to within our experimental error, which is on the order of $10^{-12}$ of the optical frequency, and one part in 700 of the expected gravitational shift.