CLASSICAL GENERAL RELATIVITY AND GAUGE THEORY

There is a long history of attempts to demonstrate a connection between gravity and electromagnetics. Soon after Einstein's revolutionary general relativity (GR) paper in 1915, Weyl proposed a geometrically based connection between EM and GR that eventually led to today's standard model of particle physics.

"Weyl's geometry can be described as follows. First, the space-time manifold M is equipped with a conformal structure, i.e., with a class [g] of conformally equivalent Lorentz metrics g (and not a definite metric as in GR). This corresponds to the requirement that it should only be possible to compare lengths at one and the same world point. Second, it is assumed, as in Riemannian geometry, that there is an affine (linear) torsion-free connection which defines a covariant derivative, and respects the conformal structure. Differentially this means that for any the covariant derivative should be proportional to. So "

-- O’Raifeartaigh & Straumann

While such an affine connection was not found, it is remarkably close to gravitational self-field theory (GSFT) where it is found that a differential connection between function (EMSFT) and gradient (GSFT) exists. This is demonstrated via the forces existing between charged particles compared with the forces existing between dipoles (dipolar particles, atoms). This shows however that while the orbital rotations for both EM and gravitation are in the same radial direction, the cyclotron rotation for the dipole is orthogonal to that due to charged particles. A similar effect can be applied to the subsequent differentials and this may be validated by observation at both galactic and super-cluster domains. What Weyl needed perhaps was some input from the physics of EM as well as his geometric (mathematical) insights.