We show that the gravitational modification of the phase of a neutron
beam [the Colella-Overhauser-Werner (COW) experiment] has a classical
origin, being due to the time delay that classical particles experienc
e in traversing a background gravitational field. Similarly, we show t
hat classical light waves also undergo a phase shift in traversing a g
ravitational held. We show that the COW experiment respects the equiva
lence principle even in the presence of quantum mechanics. [S1050-2947
(98)03802-5].