Violation of the weak equivalence principle via the time of arrival operator
The weak equivalence principle for quantum systems states that particles with the same velocity wavefunction behave identically in free fall implying that the TOA distribution of different particles should be identical regardless of mass as long as they have the same initial momentum p0. This leads us to study the distribution of the first time of arrival for spinless particles fired upward using the theory of quantum time of arrival operators. We start by constructing an appropriate time of arrival operator that is conjugate with the system Hamiltonian using Weyl quantization. The time of arrival distribution was then constructed and shown to be mass-dependent, implying violation of the weak equivalence principle.