The Extended Relativity Theory in Born-Clifford Phase Spaces with a Lower and Upper Length Scales and Clifford Group Geometric Unification

We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper and lower length scales (infrared/ultraviolet cutoff ). The invariance symmetry leads naturally to the real Clifford algebra Cl(2, 6, R) and complexified Clifford ClC(4) algebra related to Twistors. We proceed with an extensive review of Smith’s 8D model based on the Clifford algebra Cl(1, 7) that reproduces at low energies the physics of the Standard Model and Gravity; including the derivation of all the coupling constants, particle masses, mixing angles, ....with high precision. Further results by Smith are discussed pertaining the interplay among Clifford, Jordan, Division and Exceptional Lie algebras within the hierarchy of dimensions D = 26, 27, 28 related to bosonic string, M,F theory. Two Geometric actions are presented like the Clifford-Space extension of Maxwell’s Electrodynamics, Brandt’s action related the 8D spacetime tangent-bundle involving coordinates and velocities ( Finsler geometries ) followed by a discussion ( based on results by Cho et al ) why Einstein’s gravity in m + n dimensions is equivalent to an m-dim Yang-Mills-like theory of diffemorphisms of an internal n-dim space which admits a holographic reduction to lower dimensions in the case of AdSm×S and dSm×H backgrounds. Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit.