  We show that Dirac-Born-Infeld theory possesses a hidden invariance that
enhances the local O(1,p) Lorentz symmetry on a Dirichlet p-brane to an O(1,p)
x O(1,p) gauge group, encoding both an invariant velocity and acceleration (or
length) scale. This enlarged gauge group predicts consequences for the
kinematics of observers on Dirichlet branes, with admissible accelerations
being bounded from above. An important lesson beyond string theory is that a
fundamental length scale can be implemented into the kinematics of general
relativity, whilst preserving both space-time as a smooth manifold and local
Lorentz symmetry, contrary to common belief. We point out consequences for
string phenomenology, classical gravity and atomic physics.
