  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 rotating thin
superconductor ring.
