  In previous work we have developed a formulation of quantum mechanics in
non-inertial reference frames. This formulation is grounded in a class of
unitary cocycle representations of what we have called the Galilean line group,
the generalization of the Galilei group that includes transformations amongst
non-inertial reference frames. These representations show that in quantum
mechanics, just as is the case in classical mechanics, the transformations to
accelerating reference frames give rise to fictitious forces. A special feature
of these previously constructed representations is that they all respect the
non-relativistic equivalence principle, wherein the fictitious forces
associated with linear acceleration can equivalently be described by
gravitational forces. In this paper we exhibit a large class of cocycle
representations of the Galilean line group that violate the equivalence
principle. Nevertheless the classical mechanics analogue of these cocycle
representations all respect the equivalence principle.
