Matter and light wave interferometry in gravitational fields

We consider the problem of finding the quantum mechanical phase associated with the propagation of a particle in a given external gravitational field, and conclude that it ism∫ ds. In weak fieldsh _μυ this allows us to calculate the gravitationally induced phase on a freely traveling particle as 1/2 ∫h _μυ P ^υ dx ^μ whereP ^υ is the ordinary momentum. This formula has the expected Newtonian limit and is then used to calculate effects in matter wave interferometry such as those due to gravity waves and the “dragging of the ether frame” by rotating bodies. Light wave interferometry is then considered and is shown to be also described by 1/2 ∫h _μυ K ^υ dx ^μ , whereK ^υ is the wave vector of the light, and the integral is along the path of the ray. Matter and light wave interferometry are compared in various cases.