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 $\mathcal{W}$, Finsler Geometry and (Braided) Quantum Groups is discussed. Some final remarks about the Riemannian long distance limit of $C$-space geometry are made.

Tex file, 21 pages

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• Algebraic and Dirac-Hestenes Spinors and Spinor Fields
• Spin Gauge Theory of Gravity in Clifford Space: A Realization of Kaluza-Klein Theory in 4-Dimensional Spacetime
• Higher Derivative Gravity and Torsion from the Geometry of C-spaces
• Kaluza-Klein Theory without Extra Dimensions: Curved Clifford Space
• How the Geometric Calculus Resolves the Ordering Ambiguity of Quantum Theory in Curved Space
• Finsler-Lagrange Geometries and Standard Theories in Physics: New Methods in Einstein and String Gravity
• On Negative Energies, Strings, Branes, and Braneworlds: A Review of Novel Approaches
• Quantum Field Theories in Spaces with Neutral Signatures
• An Elementary Derivation of the Black-Hole Area-Entropy Relation in Any Dimension
• Nonholonomic Ricci Flows: I. Riemann Metrics and Lagrange-Finsler Geometry
• Branes and Quantized Fields
• Extended Relativity: Beyond
• Comments on the Riemann conjecture and index theory on Cantorian fractal space-time