Einstein-Schrodinger theory in the presence of zero-point fluctuations

TL;DR

This paper extends Einstein-Schrodinger theory to include zero-point fluctuation effects, deriving modified field equations that closely resemble Einstein-Maxwell theory with negligible deviations, and demonstrating the theory's consistency and ghost-free nature.

Contribution

It introduces a modified Einstein-Schrodinger theory incorporating zero-point fluctuations, deriving its field equations, and showing its near equivalence to Einstein-Maxwell theory with negligible deviations.

Findings

Field equations match Einstein-Maxwell with minimal deviations

Exact electric monopole solution similar to Reissner-Nordstrom

Theory remains ghost-free and consistent with known physics

Abstract

The Einstein-Schrodinger theory is modified by adding a cosmological constant contribution caused by zero-point fluctuations. This cosmological constant which multiplies the symmetric metric is assumed to be nearly cancelled by Schrodinger's ``bare'' cosmological constant which multiplies the nonsymmetric fundamental tensor, such that the total ``physical'' cosmological constant matches measurement. We first derive the field equations of the theory from a Lagrangian density. We show that the divergence of the Einstein equations vanishes using the Christoffel connection formed from the symmetric metric, allowing additional fields to be included in the same manner as with ordinary general relativity. We show that the field equations match the ordinary electro-vac Einstein and Maxwell equations except for additional terms which are $<10^{-16}$ of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. We also show that the theory avoids ghosts in an unusual way. We show that the Einstein-Infeld-Hoffmann (EIH) equations of motion for this theory match the equations of motion for Einstein-Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force. We derive an exact electric monopole solution, and show that it matches the Reissner-Nordstrom solution except for additional terms which are $\sim10^{-66}$ of the usual terms for worst-case radii accessible to measurement. Finally, we show that the theory becomes exactly electro-vac Einstein-Maxwell theory in the limit as the cosmological constant from zero-point fluctuations goes to infinity.