A note on the Sagnac effect and current terrestrial experiments

We focus on the Sagnac effect for light beams in order to evaluate if the higher-order relativistic corrections of kinematic origin could be relevant for actual terrestrial experiments. Moreover, we discuss to what extent the analogy with the Aharonov-Bohm effect holds true in a fully relativistic framework. We show that the analogy with the Aharonov-Bohm is not true in general, but is recovered in a suitable low-order approximation, and that even though the Sagnac effect is influenced by both the position of the interferometer in the rotating frame and its extension, these effects are negligible for current terrestrial experiments.