Fuzzy dimensions and Planck$apos$s uncertainty principle for p-branes

The explicit form of the quantum propagator of a bosonic p-brane, previously obtained by the authors in the quenched-minisuperspace approximation, suggests the possibility of a novel, unified description of p-branes with different dimensionality. The background metric that emerges in this framework is a quadratic form on a Clifford manifold. Substitution of the Lorentzian metric with the Clifford line element has two far-reaching consequences. On the one hand, it changes the very structure of the spacetime fabric since the new metric is built out of a minimum length below which it is impossible to resolve the distance between two points; on the other hand, the introduction of the Clifford line element extends the usual relativity of motion to the case of relative dimensionalism of all p-branes that make up the spacetime manifold near the Planck scale.