Maxwell-Heaviside theory electrodynamics

In U(l) electrodynamics, we recover the familiar 4-curl of Maxwell-Heaviside theory because the commutator [ ,Av] is zero. In 0(3) electrodynamics, Eq. (22) applies and each component G, G > and G is defined as... 

From the foregoing, U(l) electrodynamics was never a complete theory, although it is rigidly adhered to in the received view. It has been argued already that the Maxwell-Heaviside theory is a U(l) Yang-Mills gauge theory that discards the basic commutator A(1) x A(2). However, this commutator appears in the fundamental definition of circular polarity in the Maxwell-Heaviside theory through the third Stokes parameter... 

Thus the received view of normal reflection (1) in U(l) electrodynamics violates parity. This violation is not allowed in classical physics. For off-normal reflection (Fig. 1), projections on to the normal result in the same paradox using the empirical fact that the angle of reflection is equal to the angle of incidence. In the received view, Eq. (40) is held to rigidly, but is nevertheless in violation of parity. This is true if and only if Snell s law is true. In conclusion, ( - (oat ), which is Snell s law in Maxwell-Heaviside theory. 

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) ... 

The Maxwell-Heaviside theory seen as a U(l) symmetry gauge field theory has no explanation for the photoelectric effect, which is the emission of electrons from metals on ultraviolet irradiation [39]. Above a threshold frequency, the emission is instantaneous and independent of radiation intensity. Below the threshold, there is no emission, however intense the radiation. In U(l), electrodynamics energy is proportional to intensity and there is, consequently, no possible explanation for the photoelectric effect, which is conventionally regarded as an archetypical quantum effect. In classical 0(3) electrodynamics, the effect is simply... 

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 the Maxwell-Heaviside theory of electrodynamics, the electromagnetic phase is a product of two 4-vectors together with a random quantity a ... 

The explanation of the IFE in the Maxwell-Heaviside theory relies on phenomenology that is self-inconsistent. The reason is that A x A 2 is introduced phenomenologically [56] but the same quantity (Section III) is discarded in U(l) gauge field theory, which is asserted in the received view to be the Maxwell-Heaviside theory. In 0(3) electrodynamics, the IFE and third Stokes parameter are both manifestations of the 3 held proportional to the conjugate product that emerges from first principles [11-20] of gauge held theory, provided the internal gauge space is described in the basis ((1),(2),(3)). 

To consider magnetic flux density components of IAIV, Q must have the units of weber and R, the scalar curvature, must have units of inverse square meters. In the flat spacetime limit, R 0, so it is clear that the non-Abelian part of the field tensor, Eq. (6), vanishes in special relativity. The complete field tensor F vanishes [1] in flat spacetime because the curvature tensor vanishes. These considerations refute the Maxwell-Heaviside theory, which is developed in flat spacetime, and show that 0(3) electrodynamics is a theory of conformally curved spacetime. Most generally, the Sachs theory is a closed field theory that, in principle, unifies all four fields gravitational, electromagnetic, weak, and strong. 

There exist generally covariant four-valued 4-vectors that are components of q, and these can be used to construct the basic structure of 0(3) electrodynamics in terms of single-valued components of the quaternion-valued metric q1. Therefore, the Sachs theory can be reduced to 0(3) electrodynamics, which is a Yang-Mills theory [3,4]. The empirical evidence available for both the Sachs and 0(3) theories is summarized in this review, and discussed more extensively in the individual reviews by Sachs [1] and Evans [2]. In other words, empirical evidence is given of the instances where the Maxwell-Heaviside theory fails and where the Sachs and 0(3) electrodynamics succeed in describing empirical data from various sources. The fusion of the 0(3) and Sachs theories provides proof that the B(3) held [2] is a physical held of curved spacetime, which vanishes in hat spacetime (Maxwell-Heaviside theory [2]). 

In this short review, we have extended the topological considerations of Ranada and Trueba [1] to 0(3) electrodynamics [3] and therefore also linked these concepts to the Sachs theory reviewed elsewhere in this three-volume compilation [2]. In the same way that topology and knot theory applied to the Maxwell-Heaviside theory produce a rich structure, so does topology applied to the higher-symmetry forms of electrodynamics such as the Sachs theory and 0(3) electrodynamics. 

In general, all the off-diagonal elements of the quaternion-valued commutator term [the fifth term in Sachs Eq. (4.19)] exist, and in this appendix, it is shown, by a choice of metric, that one of these components is the Ba> field discussed in the text. The B<3) field is the fundamental signature of 0(3) electrodynamics discussed in Vol. 114, part 2. In this appendix, we also give the most general form of the vector potential in curved spacetime, a form that also has longitudinal and transverse components under all conditions, including the vacuum. In the Maxwell-Heaviside theory, on the other hand, the vector... 

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. 

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