Quantum free fall motion and quantum violation of weak equivalence principle

TL;DR

This paper investigates the quantum violation of the weak equivalence principle by constructing a time of arrival operator for a quantum particle in a gravitational field, revealing mass-dependent quantum corrections that violate classical equivalence.

Contribution

It introduces a novel approach using a time of arrival operator to demonstrate quantum violations of the weak equivalence principle, incorporating Weyl-quantization under key physical constraints.

Findings

Expectation value of TOA equals classical time plus quantum corrections

Quantum corrections depend on particle mass, indicating WEP violation

Time of arrival distribution shows explicit mass dependence

Abstract

The weak equivalence principle (WEP) in the quantum regime has been the subject of many studies with a broad range of approach to the problem. Here we tackle the problem anew through the time of arrival (TOA) operator approach by constructing the time of arrival operator for a non-relativistic and structureless particle that is projected upward in a uniform gravitational field with an intended arrival point below the classical turning point. The TOA-operator is constructed under the constraint that the inertial and gravitational masses are equivalent, and that Galilean invariance is preserved. These constraints are implemented by Weyl-quantization of the corresponding classical time of arrival function for the projectile. The expectation value of the TOA-operator is explicitly shown to be equal to the classical time of arrival plus mass-dependent quantum correction terms, implying incompatibility of the weak equivalence principle with quantum mechanics. The full extent of the violation of the WEP is shown through the mass dependence of time of arrival distribution for the projectile.