The status and programs of the New Relativity Theory

Abstract

A review of the most recent results of the New Relativity Theory is presented. These include a straightforward derivation of the Black Hole Entropy-Area relation and its $logarithmic$ corrections; the derivation of the string uncertainty relations and generalizations ; ; the relation between the four dimensional gravitational conformal anomaly and the fine structure constant; the role of Noncommutative Geometry, Negative Probabilities and Cantorian-Fractal spacetime in the Young's two-slit experiment. We then generalize the recent construction of the Quenched-Minisuperspace bosonic $p$-brane propagator in $D$ dimensions ($AACS$ [18]) to the full multidimensional case involving all $p$-branes : the construction of the Multidimensional-Particle propagator in Clifford spaces ($C$-spaces) associated with a nested family of $p$-loop histories living in a target $D$-dim background spacetime . We show how the effective $C$-space geometry is related to $extrinsic$ curvature of ordinary spacetime. The motion of rigid particles/branes is studied to explain the natural $emergence$ of classical spin. The relation among $C$-space geometry and ${\cal W}$, Finsler Geometry and (Braided) Quantum Groups is discussed. Some final remarks about the Riemannian long distance limit of $C$-space geometry are made.