A modification of Einstein-Schrodinger theory that contains both general relativity and electrodynamics
Abstract
We modify the Einstein-Schrodinger theory to include a cosmological constant z which multiplies the symmetric metric, and we show how the theory can be easily coupled to additional fields. The cosmological constant z is assumed to be nearly cancelled by Schrodinger's cosmological constant b which multiplies the nonsymmetric fundamental tensor, such that the total =z+b matches measurement. The resulting theory becomes exactly Einstein-Maxwell theory in the limit as |z|∞. For |z| 1/(Planck length)2 the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are <10-16 of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein-Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein-Infeld-Hoffmann (EIH) equations of motion match the equations of motion for Einstein-Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. This fixes a problem of the original Einstein-Schrodinger theory, which failed to predict a Lorentz force. An exact charged solution matches the Reissner-Nordstrom solution except for additional terms which are 10-66 of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein-Maxwell theory.