Physical Optics, the Sagnac Effect, and the Aharonov-Bohm Effect in the Evans Unified Field Theory

Abstract

A generally covariant and gauge invariant description of physical optics, the Sagnac effect, and the Aharonov-Bohm (AB) effect is developed using the appropriate phase factor for electrodynamics. The latter is a generally covariant development of the Dirac-Wu-Yang phase factor based on the generally covariant Stokes theorem. The Maxwell-Heaviside (MH) field theory fails to describe physical optics, interferometry, and topological phase effects in general because the phase factor in that theory is under-determined. A random number from a U(1) gauge transformations can be added to the MH phase factor. The generally covariant phase factor of the Evans unified field theory is gauge invariant and has the correct property under parity inversion to produce observables such as reflection, interferograms, the Sagnac and AB effects, the Tomita-Chao effect and topological phase effects in general. These effects are described simply and self consistently with the generally covariant Stokes theorem in which ordinary exterior derivative is replaced by the covariant exterior derivative of differential geometry.