Strong quantum violation of the gravitational weak equivalence principle by a non-Gaussian wave-packet

TL;DR

This paper demonstrates quantum violations of the weak equivalence principle using non-Gaussian wave packets, showing mass dependence in detection probabilities and arrival times, with violations diminishing at large masses.

Contribution

It introduces a novel analysis of quantum violations of the weak equivalence principle using non-Gaussian wave packets and quantifies how non-Gaussianity enhances these violations.

Findings

Position detection probabilities depend on mass, indicating violation.

Mean arrival time is mass-dependent, showing quantum effects.

Violations diminish as mass increases, restoring classical behavior.

Abstract

The weak equivalence principle of gravity is examined at the quantum level in two ways. First, the position detection probabilities of particles described by a non-Gaussian wave-packet projected upwards against gravity around the classical turning point and also around the point of initial projection are calculated. These probabilities exhibit mass-dependence at both these points, thereby reflecting the quantum violation of the weak equivalence principle. Secondly, the mean arrival time of freely falling particles is calculated using the quantum probability current, which also turns out to be mass dependent. Such a mass-dependence is shown to be enhanced by increasing the non-Gaussianity parameter of the wave packet, thus signifying a stronger violation of the weak equivalence principle through a greater departure from Gaussianity of the initial wave packet. The mass-dependence of both the position detection probabilities and the mean arrival time vanish in the limit of large mass. Thus, compatibility between the weak equivalence principle and quantum mechanics is recovered in the macroscopic limit of the latter. A selection of Bohm trajectories is exhibited to illustrate these features in the free fall case.