The equivalence principle in classical mechanics and quantum mechanics ∗

We discuss our understanding of the equivalence principle in both classical mechanics and quantum mechanics. We show that not only does the equivalence principle hold for the trajectories of quantum particles in a background gravitational field, but also that it is only because of this that the equivalence principle is even to be expected to hold for classical particles at all. While the equivalence principle stands at the very heart of general relativity, there appear to be some aspects of it that are not quite as secure as they might be. In particular, while there is no disputing the fact that classical geodesics in a background gravitational field exhibit the equivalence principle, the question of whether the motions of real physical systems can explicitly be associated with such geodesics is actually a logically independent issue. Moreover, so also is the further question of what is supposed to happen when the physical systems are to be described by quantum mechanics, a situation which has actually been explored experimentally in the landmark Colella-Overhauser-Werner (COW) study [1, 2, 3, 4] of a quantum-mechanical beam of neutrons traversing an interferometer located in an external gravitational