  The computation of the phase shift in a symmetric atom interferometer in the
presence of a gravitational field is reviewed. The difference of action-phase
integrals between the two paths of the interferometer is zero for any
Lagrangian which is at most quadratic in position and velocity. We emphasize
that in a large class of theories of gravity the atom interferometer permits a
test of the weak version of the equivalence principle (or universality of free
fall) by comparing the acceleration of atoms with that of ordinary bodies, but
is insensitive to that aspect of the equivalence principle known as the
gravitational redshift or universality of clock rates.
