Curvature, Torsion and the Qubit Spinor Pre-Geometry
Commentary on the Penrose-Rindler Formalism
Jack Sarfatti
Abstract
The physics of spacetime and matter fields is unified by the principle of local gauge invariance applied to symmetry groups of different kinds of frame transformations that leave the global dynamical classical actions invariant. Indeed, the geometrodynamic field embodied in the spin 1 gravity tetrads can be looked at as simply another dynamical field on a formal global Minkowski spacetime that is not generally directly observable since the behavior of clocks and measuring rods is controlled by the geometrodynamical field in a universal way consistent with the strongest form of Einstein’s equivalence principle. The most fundamental quantity here is the connection field that is always a non-tensor field relative to the global symmetry group it localizes. Einstein’s 1916 General Relativity (GR) is, from this point of view, simply the localization of the universal globally rigid abelian 4-parameter translation Lie group T4 whose Lie Algebra is the total energy-momentum 4-vector of the matter fields on the globally flat Minkowski spacetime of Einstein’s 1905 Special Relativity (GR). The electromagnetic-weak and strong sub-nuclear forces are essentially the connections for parallel transport of tensors and spinors in the internal fiber spaces of the U1, SU2, & SU3 groups with projections onto world lines (in the point particle low energy limit) in 4D spacetime. Unlike T4, U1, SU2, SU3 are not universal. The connections for the internal symmetry groups are essentially the gauge potentials with their covariant “curvature” curls as the “forces”. The situation is qualitatively different in the case of Einstein’s 1916 GR where the T4-based torsionless Levi-Civita Christoffel Symbol connection is Newton’s “gravity force” that is locally equivalent to the inertial g-force of an accelerating detector (aka LNIF). For example, we standing still on the surface of the Earth, must accelerate in order not to move in curved spacetime. The inability of even some PhD physicists to really understand this has led to a lot of confusion especially among naïve high-energy particle physicists attempting to unify the “four forces” as well as some relativists and philosophers of physics who try to argue that Einstein was wrong in the way he formulated the equivalence principle.