Minimal uncertainty in momentum: The effects of IR gravity on quantum mechanics

The effects of the IR aspects of gravity on quantum mechanics is investigated. At large distances where, due to gravity, the space-time is curved, there appears nonzero minimal uncertainty $\Delta p_0$ in the momentum of a quantum mechanical particle. We apply the minimal uncertainty momentum to some quantum mechanical interferometry examples and show that the phase shift depends on the area surrounded by the path of the test particle. We also put some limits on the related parameters. This prediction may be tested through future experiments. The assumption of minimal uncertainty in momentum can also explain the anomalous excess of the mass of the Cooper pair in a thin, rotating, superconductor ring.