  Any candidate theory of quantum gravity must address the breakdown of the
classical smooth manifold picture of space-time at distances comparable to the
Planck length. String theory, in contrast, is formulated on conventional
space-time. However, we show that in the low energy limit, the dynamics of
generally curved Dirichlet p-branes possess an extended local isometry group,
which can be absorbed into the brane geometry as an almost product structure.
The induced kinematics encode two invariant scales, namely a minimal length and
a maximal speed, without breaking general covariance. Quantum gravity effects
on D-branes at low energy are then seen to manifest themselves by the
kinematical effects of a maximal acceleration. Experimental and theoretical
implications of such new kinematics are easily derived. We comment on
consequences for brane world phenomenology.
