On the validity of Einstein's Equivalence Principle in Quantum Mechanics

Abstract

Einstein’s Equivalence Principle (EEP) is a cornerstone in the development of General Relativity. Its validity implies that gravity is a geometrical phenomena. Several experiments have proven that EEP is valid in the classical regime. Nevertheless, its validity for quantum systems is still undergoing experimental tests. In this work we study, following two different approaches, the quantum free fall of quantum particles. Our results suggest that EEP is violated in the quantum regime, but naturally emerges as the energy/mass approaches macroscopic values. We first show that the transient current density of a suddenly released beam of quantum particles depends explicitly on the particle’s mass (thus contradicting the universality of free fall), but such dependence disappear as the mass increases (indicating the emerge of the EEP). We also consider the problem of a quantum particle bouncing above a mirror in the presence of the Earth’s gravitational field. By means of a simple method based on Fourier analysis, we show that the classical probability distribution (which is mass independent) emerges from its quantum-mechanical analogue in the limit of large quantum numbers (high energy regime), thus also supporting the emergence of the EEP from quantum mechanics.