Quantum time-of-arrival expectation values for freely falling quantum particle as indicators of quantum violation of the weak equivalence principle

Abstract

The free fall of a quantum particle is considered where its time-of-arrival (TOA) is treated as a quantum dynamical variable using the theory advocated by one of the authors in [1]. It is shown here that the weak equivalence principle is violated at the quantum scale evident from the mass dependence of the TOA’s corresponding expectation values. This work provides actual predictions that are experimentally verifiable, and if confirmed positively it can also serve as a proof to the existence of time as a dynamical variable.