Effect of quantum statistics on the gravitational weak equivalence principle

We study the effect of quantum statistics on the arrival time distribution of quantum particles computed through the probability current density. It is shown that symmetrization or asymmetrization of the wave function affects the arrival time distribution for even freely propagating particles. In order to investigate the effect of statistics on the weak equivalence principle in quantum mechanics (WEQ), we then compute the mean arrival time for wave packets in free fall. The violation of WEQ through the effect of statistics on the mass-dependence of the mean arrival time is clearly exhibited. We finally evaluate the effect of spin on the violation of WEQ using a different approach by including an explicit spin-dependence in the probability current distribution, and compare it with the approach using particle statistics. Our results show WEQ re-emerges smoothly in the limit of large mass.