  We present the explicit solution to the geodesic equations in a warped de
Sitter space-time proposed by Randall-Sundrum. We find that a test particle
moves in the bulk and is not restricted on a 3-brane (to be taken as our
universe). On the 3-brane, the test particle moves with uniform velocity,
giving the appearance that it is not subject to a force. But computing the
particle's energy using the energy-momentum tensor yields a time-dependent
energy that suggests a time-dependent mass. Thus, the extra force, which is the
effect of the warped extra dimension on the particle's motion on the 3-brane,
does not change the velocity but the mass of the particle. The particle's
motion in the bulk also results in a time-dependent modification of the
Heisenberg uncertainty principle as viewed on the 3-brane. These two results
show that the classical physics along the extra dimension results in the
time-dependence of particle masses and the uncertainty principle. If the
particle masses are time-independent and the Heisenberg's uncertainty principle
is to remain unchanged, then there must be a non-gravitational force that will
restrict all particles on the 3-brane. Finally, we just note that although
classically, these time-dependent corrections on the 3-brane can be removed,
quantum mechanical corrections along the extra dimension will restore back the
problem.
