Adherence and violation of the equivalence principle from classical to quantum mechanics

Abstract

Investigation into the applicability of the equivalence principle in quantum mechanics has taken many forms, with varying conclusions. Here, a dynamical semi-classical description of a wave packet in terms of its center of mass and higher quantum fluctuations is applied to the case of a quantum particle in gravitational free fall. The analysis provides an intuitive account of the origin of mass-dependence in quantum-gravitational dynamics through an effective potential that enforces the uncertainty principle. This potential has two implications: (i) The lowest order quantum fluctuations encoding the width and spreading of the wave packet obey an uncertainty relation whose observance is mass-dependent. (ii) In an inhomogeneous gravitational field tidal effects couple the center of mass motion to the quantum fluctuations. The combined effect results in a clear demonstration of how some conceptions of the weak equivalence principle, based on mass dependence, are violated. The size of this violation is within sensitivities of current Eotvos and clock-based return time experiments.