General Relativity, Maxwell's Electrodynamics, and the Foundations of the Quantum Theory of Gravitation and Matter
Abstract
The formalism of electric - magnetic duality, first pioneered by Reinich and Wheeler, extends General Relativity to encompass non-Abelian fields. Several energy Tensors Tuv with non-vanishing trace matter are developed solely as a function of the field strength tensor Fuv, including the Euler tensor, and tensors for matter in flux, pressure in flux, and stationary pressure. The spacetime metric guv is not only a solution to the second-order Einstein equation based on Tuv, but is also constrained by a third-order equation involving the Bianchi identity together with the gravitational energy components kappau for each Tuv. The common appearance of Fuv in all of the Tuv and kappav makes it possible to obtain quantum solutions for the spacetime metric, thereby geometrizing quantum physics as a non-linear theory.
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