  Some of the possible consequences of a generalized uncertainty principle
(which emerges in the context of string theory and quantum gravity models as a
consequence of fluctuations of the background metric) are analyzed considering
the case of a quantum particle immersed in a homogeneous gravitational field.
It will be shown that the expectation value of the momentum operator depends in
a novel way on the mass of the involved particle. This kind of physical
characteristics could be, in principle, detected. In other words, one way of
confronting against the experiment some of the models around quantum gravity is
given by the detection of the dependence upon the mass parameter of the
expectation value of the momentum operator.
