Quantum mechanics in noninertial reference frames: Violations of the nonrelativistic equivalence principle

•A formulation of Galilean quantum mechanics in non-inertial reference frames is given.•The key concept is the Galilean line group, an infinite dimensional group.•A large class of general cocycle representations of the Galilean line group is constructed.•These representations show violations of the equivalence principle at the quantum level.•At the classical limit, no violations of the equivalence principle are detected.

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.