Maxwell-Heaviside equations 0 electrodynamics

A simple example in classical electrodynamics of what is now known as gauge invariance was introduced by Heaviside [3,4], who reduced the original electrodynamical equations of Maxwell to their present form. Therefore, these equations are more properly known as the Maxwell-Heaviside equations and, in the terminology of contemporary gauge field theory, are identifiable as U(l) Yang-Mills equations [15]. The subj ect of this chapter is 0(3) Yang-Mills gauge theory applied to electrodynamics and electroweak theory. 

More than a century later, Lehnert [7] introduced and developed [7-10] the concept of vacuum charge on the classical level, and showed [7-10] that this concept leads to advantages over the Maxwell-Heaviside equations in the description of empirical data, for example, the problem of an interface with a vacuum [7-10,15]. The introduction of a vacuum charge leads to axisymmetric vacuum solutions akin to the B(3> vacuum component of 0(3) electrodynamics... 

Beltrami fields have been advanced [4] as theoretical models for astrophy-sical phenomena such as solar flares and spiral galaxies, plasma vortex filaments arising from plasma focus experiments, and superconductivity. Beltrami electrodynamic fields probably have major potential significance to theoretical and empirical science. In plasma vortex filaments, for example, energy anomalies arise that cannot be described with the Maxwell-Heaviside equations. The three magnetic components of 0(3) electrodynamics are Beltrami fields as well as being complex lamellar and solenoidal fields. The component is identically nonzero in Beltrami electrodynamics if is so. In the Beltrami... 

Since the present standard U(l) electrodynamics model forbids electrical power systems with COP > 1.0, my colleagues and I also studied the derivation of that model, which is recognized to contain flaws due to its > 136-year-old basis. We particularly examined how it developed, how it was changed, and how we came to have the Lorentz-regauged Maxwell-Heaviside equations model ubiquitously used today, particularly with respect to the design, manufacture, and use of electrical power systems. 

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... 

The inverse Faraday effect depends on the third Stokes parameter empirically in the received view [36], and is the archetypical magneto-optical effect in conventional Maxwell-Heaviside theory. This type of phenomenology directly contradicts U(l) gauge theory in the same way as argued already for the third Stokes parameter. In 0(3) electrodynamics, the paradox is circumvented by using the field equations (31) and (32). A self-consistent description [11-20] of the inverse Faraday effect is achieved by expanding Eq. (32) ... 

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... 

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. 

In this final section, it is shown that the three magnetic field components of electromagnetic radiation in 0(3) electrodynamics are Beltrami vector fields, illustrating the fact that conventional Maxwell-Heaviside electrodynamics are incomplete. Therefore Beltrami electrodynamics can be regarded as foundational, structuring the vacuum fields of nature, and extending the point of view of Heaviside, who reduced the original Maxwell equations to their presently accepted textbook form. In this section, transverse plane waves are shown to be solenoidal, complex lamellar, and Beltrami, and to obey the Beltrami equation, of which B is an identically nonzero solution. In the Beltrami electrodynamics, therefore, the existence of the transverse 1 = implies that of , as in 0(3) electrodynamics. 

This argument shows again that Maxwell-Heaviside electrodynamics is incomplete, because B(3) is zero. General solutions are given in this section of the Beltrami equation, which is an equation of 0(3) electrodynamics. Therefore these solutions are also general solutions of 0(3) electrodynamics in the vacuum. 

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