Interesting examples of violation of the classical equivalence principle but not of the weak one

Abstract

The equivalence principle (EP), as well as Schiff's conjecture, are discussed (en passant), and the connection between the EP and quantum mechanics is then briefly analyzed. Two semiclassical violations of the classical equivalence principle (CEP) but not of the weak one (WEP), i.e. Greenberger gravitational Bohr atom and the tree-level scattering of different quantum particles by an external weak higher-order gravitational field, are thoroughly investigated afterwards. Next, two quantum examples of systems that agree with the WEP but not with the CEP, namely COW experiment and free fall in a constant gravitational field of a massive object described by its wave-function $\Psi$, are discussed in detail. Keeping in mind that among the four examples focused on this work only COW experiment is based on an experimental test, some important details related to it, are presented as well.