Emergent universality of free fall from quantum mechanics

Abstract

Classical and quantum mechanical descriptions of motion are fundamentally different. The Universality of Free Fall (UFF) is a distinguishing feature of the classical motion (which has been verified with astonishing precision), while quantum theory tell us only about probabilities and uncertainties thus breaking the UFF. There are strong reasons to believe that the classical description must emerge, under plausible hypothesis, from quantum mechanics. In this paper, we show that the UFF is an emergent phenomenon: the coarse-grained quantum distribution for high-energy levels leads to the classical distribution as the lowest order plus quantum corrections. We estimate the size of these corrections on the Eötvös parameter and discuss the physical implications.