Sagnac effect

In a rotating interferometer, fringe shifts have been observed between light beams that propagate parallel and antiparallel with the direction of rotation [4]. This Sagnac effect requires an unconventional explanation. 

The group space of 0(3) is doubly connected (i.e., non-simply connected) and can therefore support an Aharonov-Bohm effect (Section V), which is described by a physical inhomogeneous term produced by a rotation in the internal gauge space of 0(3) [24]. The existence of the Aharonov-Bohm effect is therefore clear evidence for an extended electrodynamics such as 0(3) electrodynamics, as argued already. A great deal more evidence is reviewed in this article in favor of 0(3) over U(l). For example, it is shown that the Sagnac effect [25] can be described accurately with 0(3), while U(l) fails completely to describe it. 

The Sagnac effect cannot be described by U(l) electrodynamics [4,43] because of the invariance of the U(l) phase factor under motion reversal symmetry (T) ... 

The explanation of interferometric effects in U(l) electrodynamics is in general self-inconsistent, and sometimes, as in the Sagnac effect, nonexistent. In this... 

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... 

C) Sagnac loop from the counterclockwise (A) loop [17]. It follows that the phase difference observed with platform at rest in the Sagnac effect [47] cannot be described by U(l) electrodynamics. This result is also consistent with the fact that the traditional phase of U(l) electrodynamics is invariant under T as discussed already in Section (III). The same result applies for the Michelson-Gale experiment [48], which is a Sagnac effect. 

The Sagnac effect with a platform at rest [47] is explained as the phase factor ... 

When the platform is rotated in the Sagnac effect, there is an additional rotation in the internal gauge space described by... 

This result is true for all matter waves and also in the Michelson-Gale experiment, where it has been measured to a precision of one part in 1023 [49]. Hasselbach et al. [51] have demonstrated it in electron waves. We have therefore shown that the electrodynamic and kinematic explanation of the Sagnac effect gives the same result in a structured vacuum described by 0(3) gauge group symmetry. 

The Maxwell-Heaviside theory of electrodynamics has no explanation for the Sagnac effect [4] because its phase is invariant under 7 as argued already, and because the equations are invariant to rotation in the vacuum. The d Alembert wave equation of U(l) electrodynamics is also 7 -invariant. One of the most telling pieces of evidence against the validity of the U(l) electrodynamics was given experimentally by Pegram [54] who discovered a little known [4] cross-relation between magnetic and electric fields in the vacuum that is denied by Lorentz transformation. 

It can be shown straightforwardly, as follows, that there is no holonomy difference if the phase factor (154) is applied to the problem of the Sagnac effect with U(l) covariant derivatives. In other words, the Dirac phase factor [4] of U(l) electrodynamics does not describe the Sagnac effect. For C and A loops, consider the boundary... 

The Sagnac effect caused by the rotating platform is therefore due to a rotation in the internal gauge space ((1),(2),(3)), which results in the frequency shift in Eq. (171). The frequency shift is experimentally the same to an observer on and off the platform and is independent of the shape of the area Ar. The holonomy difference (172) derived theoretically depends only on the magnitudes and ff, and these scalars are frame-invariant, as observed experimentally. There is no shape specified for the area Ar in the theory, and only its scalar magnitude enters into Eq. (172), again in agreement with experiment. 

The Lehnert equations are a great improvement over the Maxwell-Heaviside equations [45,49] but are unable to describe phenomena such as the Sagnac effect and interferometry [42], for which an 0(3) internal gauge space symmetry is needed. 

In the Sagnac effect, for example, the closed loop and area can be illustrated as follows ... 

There is no Sagnac effect in U(l) electrodynamics, as just argued, a result that is obviously contrary to observation [44]. In 0(3) electrodynamics, the Sagnac effect with platform at rest is given by the phase factor [44]... 

The Sagnac effect is therefore due to a gauge transformation and a closed loop in Minkowski spacetime with 0(3) covariant derivatives. 

If we attempt the same exercise in U(l) electrodynamics, the closed loop gives the Maxwell-Heaviside equations in the vacuum, which are invariant under T and that therefore cannot describe the Sagnac effect [44] because one loop of the Sagnac interferometer is obtained from the other loop by T symmetry. The U(l) phase factor is oof kZ + a, where a is arbitrary [44], and this phase factor is also "/ -invariant. The Maxwell-Heaviside equations in the vacuum are... 

It can be shown that the Sagnac effect with platform at rest is the rotation of the plane of linearly polarized light as a result of radiation propagating around a circle in free space. Such an effect cannot exist in the received view where the phase factor in such a round trip is always the same and given by Eq. (554). However, it can be shown as follows that there develops a rotation in the plane of polarization when the phase is defined by Eq. (553). It is now known that the phase must always be defined by Eq. (553). Therefore, proceeding on this inference, we construct plane polarized light as the sum of left and right circularly polarized components ... 

The round trip of the Sagnac effect in a given—say, clockwise—direction produces the effect... 

Therefore, the Tomita-Chiao effect reduces to the Sagnac effect under the condition... 

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