Interferometry 0 electrodynamics

Finally, in this section, we develop the concept of electromagnetic phase from U(l) to 0(3). This is a nontrivial development [4] that has foundational consequences for interferometry and physical optics for example. In U(l) electrodynamics, the electromagnetic phase is defined up to an arbitrary factor... 

Michelson interferometry is dependent on normal reflection from two mirrors at right angles, and so the same foundational argument as just given can be used to show that U(l) electrodynamics does not describe Michelson interferometry self-consistently. Without loss of generality, we can write Eq. (38) as... 

VI. EXPLANATION OF INTERFEROMETRY AND RELATED PHYSICAL OPTICAL EFFECTS USING 0(3) ELECTRODYNAMICS... 

In U(l) electrodynamics in free space, there are only transverse components of the vector potential, so the integral (158) vanishes. It follows that the area integral in Eq. (157) also vanishes, and so the U(l) phase factor cannot be used to describe interferometry. For example, it cannot be used to describe the Sagnac effect. The latter result is consistent with the fact that the Maxwell-Heaviside and d Alembert equations are invariant under T, which generates the clockwise... 

Equations leading to Eq. (162) apply in general in 0(3) electrodynamics and to interferometry and physical optics in general. They imply the existence of the quantity... 

The principle of interferometry in 0(3) electrodynamics follows from the fact that it is caused by a rotation in the internal gauge space... 

VIII. Empirical Testing of 0(3) Electrodynamics Interferometry and the Aharonov-Bohm Effect... 

VIII. EMPIRICAL TESTING OF 0(3) ELECTRODYNAMICS INTERFEROMETRY AND THE AHARONOV-BOHM EFFECT... 

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 ... 

Therefore, it has been shown convincingly that electrodynamics is an 0(3) invariant theory, and so the 0(3) gauge invariance must also be found in experiments with matter waves, such as matter waves from electrons, in which there is no electromagnetic potential. One such experiment is the Sagnac effect with electrons, which was reviewed in Ref. 44, and another is Young interferometry with electron waves. For both experiments, Eq. (584) becomes... 

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