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General Relativity, Maxwell's Electrodynamics, and the Foundations of the Quantum Theory of Gravitation and Matter

Jay R. Yablon
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Abstract

The formalism of electric - magnetic duality, first pioneered by Reinich and Wheeler, extends General Relativity to encompass non-Abelian fields. Several energy Tensors T^uv with non-vanishing trace matter are developed solely as a function of the field strength tensor F^uv, including the Euler tensor, and tensors for matter in flux, pressure in flux, and stationary pressure. The spacetime metric g_uv is not only a solution to the second-order Einstein equation based on T^uv, but is also constrained by a third-order equation involving the Bianchi identity together with the gravitational energy components kappa_u for each T^uv. The common appearance of F^uv in all of the T^uv and kappa_v makes it possible to obtain quantum solutions for the spacetime metric, thereby geometrizing quantum physics as a non-linear theory.

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Jay R. Yablon. 2005-11-10. General Relativity, Maxwell's Electrodynamics, and the Foundations of the Quantum Theory of Gravitation and Matter. https://arxiv.org/abs/gr-qc/0511050

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