  In this article we examine a Generalized Uncertainty Principle which differs
from the Heisenberg Uncertainty Principle by terms linear and quadratic in
particle momenta, as proposed by the authors in an earlier paper. We show that
this affects all Hamiltonians, and in particular those which describe low
energy experiments. We discuss possible observational consequences. Further, we
also show that this indicates that space may be discrete at the fundamental
level.
