Minkowski spacetime electrodynamics

Physical optics, and interferometry in general, are described by the phase equation of 0(3) electrodynamics, Eq. (524). The round trip or closed loop in Minkowski spacetime is illustrated as follows ... 

The received view, in which the phase factor of optics and electrodynamics is given by Eq. (554), can describe neither the Sagnac nor the Tomita-Chiao effects, which, as we have argued, are the same effects, differing only by geometry. Both are non-Abelian, and both depend on a round trip in Minkowski spacetime using 0(3) covariant derivatives. 

Equation (482) is a simple form of the non-Abelian Stokes theorem, a form that is derived by a round trip in Minkowski spacetime [46]. It has been adapted directly for the 0(3) invariant phase factor as in Eq. (547), which gives a simple and accurate description of the Sagnac effect [44], A U(l) invariant electrodynamics has failed to describe the Sagnac effect for nearly 90 years, and kinematic explanations are also unsatisfactory [50], In an 0(3) or SU(2) invariant electrodynamics, the Sagnac effect is simply a round trip in Minkowski space-time and an effect of special relativity and gauge theory, the most successful theory of the late twentieth century. There are open questions in special relativity [108], but no theory has yet evolved to replace it. 

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