Reply to comment by E. Comay on the longitudinal magnetic field of circularly polarized electromagnetic waves

The argument presented by E. Comay in Ref. 1 is in error precisely at the point where he uses the Cartesian form of Stokes' theorem. His Comment is therefore erroneous and inconsequential.     

Experimental observation of the B(3) field: A reply to Raja et alia

The recent claims by Rajaet al. [1,2] are corrected in this reply. It is shown that there is no Faraday induction due toB ⁽³⁾in vacuo, as observed by these authors. The observation of the inverse Faraday effect by these authors is an observation of theB ⁽³⁾field at second order. Their data, correctly interpreted, constitute strong support for the existence and predicted properties of theB ⁽³⁾field.     

Reply to criticisms of theB (3) field

The confusion and self-contradiction among recent critics of theB ⁽³⁾ (Evans-Vigier) field are analysed. Barron [17] and Buckingham [18] assert that the field is zero by symmetry. Grimes [21] asserts that the field isnon-zero butfortuitous. Lakhtakia in one paper [19] asserts thatB ⁽³⁾ isnon-zero butnot fundamental, and in a second paper that it isunknowlable and therefore may as well be zero. A rebuttal is given of each the individual papers, and it is shown that the Evans-Vigier field is the fundamental magnetizing field of electromagnetic radiation.     

Charge Conjugation and the B(3) Field: A Reply to Comay

The argument for non-existence of the B ⁽³⁾ field proposed by E. Comay is based on adding radians to the phase of a plane wave. This is trivially incorrect because B ⁽³⁾ is a vacuum component of a C conserving Yang-Mills gauge field theory.     

Reply to A. Lakhtakia: Experimental measurement ofB (3)

In answer to the assertion by Lakhtakia [1] thatB ⁽³⁾ isunknowable, presumably unmeasurable, the experimental conditions for its measurement are defined.     

Optical NMR from the Dirac equation: A reply to Buckingham and Parlett

The Dirac equation of the fermion in a circularly polarized electromagnetic field produces optical NMR shifts of the same order of magnitude as observed in the recent experiments of Warrenet al. By decreasing the frequency of the irradiation field the Dirac equation shows that electromagnetically induced NMR lines can be observed in the infrared or visible range in theory. A recent paper by Buckingham and Parlett [9] is criticized in detail.     

On the observability of the fieldB (3): Relativistic effects in magneto-optics

It is shown that the novel vacuum fieldB ⁽³⁾ is an experimental observable, and several methods of observation are suggested: these include the pulsed microwave magnetization of a plasma, the optical Aharonov-Bohm effect, and the microwave frequency optical Faraday effect. The effect ofB ⁽³⁾ is presented in the form of relativistically corrected semi-classical theory.     

Reply to comay’s "relativity versus the longitudinal magnetic field of the photon"

Poincaré group electrodynamics is {ie255-1} conserving and Lorentz covariant under all conditions by definition. Examples are given of these properties. Comay’s comment is incorrect: any {ie255-2} conserving field theory that is Lorentz covariant is consistent with special relativity, whose underlying group is the Poincaré group.     

The evans-vigier field,B (3): Derivation of the de Broglie matter-wave equation from the Hamilton-Jacobi equation

The emergence of the Evans-Vigier fieldB ⁽³⁾ of vacuum electromagnetism has been accompanied by a novel charge quantization condition inferred from 0(3) gauge theory. This finding is used to derive the de Broglie matter-wave equation from the classical Hamilton-Jacobi (HJ) equation of one electron in the electromagnetic field. The HJ equation is used with the charge quantization condition to show that, in a perfectly elastic photon-electron interaction, complete transfer of angular momentum occurs self-consistently, and the electron acquires the angular momentum of the photon. In this limit the electron travels infinitesimally near the speed of light, and its concomitant electromagnetic fields become indistinguishable from those of the uncharged photon. This result independently proves the validity of the charge quantization condition and demonstrates unequivocally the existence of the vacuum fieldB ⁽³⁾.     

Forms of the evans-vigier fieldB (3)

The newly inferred longitudinal magnetic field of vacuum electromagnetism is given in a number of equivalent forms derived in several different ways. It is therefore overwhelmingly likely that the Evans-Vigier fieldB ⁽³⁾ will be isolated experimentally through its characteristic square root power density dependence. It is the first classical field of vacuum electromagnetism to be inferred since Maxwell and as such fundamentally extends our understanding of the nature of electromagnetism and field-particle theory.     

Photon mass and the fieldB (3)

The connection between finite photon mass and the fieldB ⁽³⁾ is developed with reference to special relativity in the vacuum. The existence of the physical and longitudinal fieldB ⁽³⁾ implies that there are three degrees of polarization associated with the photon, which cannot therefore be a massless boson. The fieldB ⁽³⁾ can be observed experimentally through the magnetization of a plasma with microwave pulses, and this experiment serves to demonstrate unequivocally the existence of photon mass.     

Magnetization of an electron plasma by microwave pulses: Experiment to detect the longitudinal vacuum fieldB (3)

By solving the relativistic Hamilton-Jacobi equation of one electron in classical, circularly polarized, electromagnetic radiation, it is shown that the orbital electronic angular momentum is induced and governed entirely by the novel longitudinal vacuum fieldB ⁽³⁾. The presence of this field in the vacuum is detectible easily in principle by measuring its characteristicsquare root power density dependence using megawatt microwave pulses to magnetize an electron plasma set up in an inert gas such as helium.     

Non-abelian electrodynamics and the vacuumB (3)

By using an 0(3) gauge group, a non-Abelian theory of vacuum electrodynamics is developed in which the newly discovered longitudinal vacuum fieldsB ⁽³⁾ andi E ⁽³⁾ appear self-consistently with the usual plane wavesB ⁽¹⁾,B ⁽²⁾,E ⁽¹⁾, andE ⁽²⁾ in the circular basis (1), (2), (3), a complex representation of space. Using the charge quantization condition the vacuum Maxwell equations are given in the non-Abelian representation.     

The connection between photon mass andB (3) : The poincaré group

The longitudinal vacuum fieldB ⁽³⁾ is an experimental observable which produces by magnetization a well-defined square-root beam power density dependence. Its longitudinal polarization implies that the helicities of the photon are +1, 0, and –1, and that the little group of the Poincaré group is the rotation group 0(3) of a massive boson. The mass of the photon (m) is therefore related directly toB ⁽³⁾ through the Proca equation, and it is concluded that experimental evidence forB ⁽³⁾ is also evidence for finitem.     

Derivation of the B (3) Field and Concomitant Vacuum Energy Density from the Sachs Theory of Electrodynamics

The archetypical and phaseless vacuum magnetic flux density of O(3) electrodynamics, the B ⁽³⁾ field, is derived from the irreducible representation of the Einstein group and is shown to be accompanied by a vacuum energy density which depends directly on the square of the scalar curvature R of curved spacetime. The B ⁽³⁾ field and the vacuum energy density are obtained respectively from the non-Abelian part of the field tensor F and the non-Abelian part of the metrical field equation. Both of these terms are given by Sachs [5].     

One photon and macroscopic B cyclic equations: Reply to van Enk

The B cyclics of electrodynamics, which relate transverse and longitudinal fields in vacuo, are one photon relations which are also valid on a macroscopic scale. In the same way, the Maxwell equations in the received view were originally phenomenological relations between electric and magnetic fields, but, in the received view are also written down for one photon. Point by point replies to van Enk are given.     

Group theoretical aspects ofU B(6) ⊗U F(20) symmetry limits of IBFM related to theU B(5) andO B(6) limits of IBM

TheU ^B(6)⊗U ^F(20) Bose-Fermi dynamical symmetry of interacting boson-fermion model arises when the odd nucleon occupies single particle orbits withj=1/2, 3/2, 5/2, and 7/2. The subgroup structures ofU ^B(6)⊗U ^F(20) related to theU ^B(5) andO ^B(6) limits of sdIBM (U ^B(6)) are analysed. Broadly speaking,U ^B(6)⊗U ^F(20) admitsU ^BF(5)⊗U _s ^F (4), Spin^BF(5)⊗U _k ^F (5) andU ^BF(5)⊗U _s ^F (2) limits withU ^B(5) core and Spin^BF(6),O ^BF(5)⊗U _s ^F (4), Spin^BF(6)⊗U _k ^F (5) andO ^BF(6)⊗U _s ^F (2) limits withO ^B(6) core respectively. For each of these seven symmetry limits, group chains, quantum numbers labelling the basis states, generators and Casimir operators for the various subgroups and energy formulas are given. Recoupling coefficients (reduced Wigner coefficients) for constructing wavefunctions of low-lying states are tabulated and these will allow (together with sdIBMU ^B(5) andO ^B(6) limit results) one to calculateB(E2)’s,B(M1)’s, one and two nucleon transfer strengths etc. in the seven symmetry limits. Experimental examples for theU ^B(6)⊗U ^F(20) symmetry limits are briefly discussed.     

Derivation of O(3) Electrodynamics from the Irreducible Representations of the Einstein Group

By considering the irreducible representations of the Einstein group (the Lie group of general relativity), Sachs [1] has shown that the electromagnetic field tensor can be developed in terms of a metric q , which is a set of four quaternion-valued components of four-vector. Using this method, it is shown that the electromagnetic field vanishes [1] in flat spacetime, and that electromagnetism in general is a non-Abelian field theory. In this paper the non-Abelian component of the field tensor is developed to show the presence of the B ⁽³⁾ field of the O(3) electrodynamics, and the basic structure of O(3) electrodynamics is shown to be a sub-structure of general relativity as developed by Sachs. The extensive empirical evidence for both theories is summarized.     

Noether's theorem and the fieldB (3)

It is shown that the longitudinal, magnetic flux density,B ⁽³⁾ , of vacuum electromagnetic radiation can be accommodated rigorously within Noether's theorem, which relates fundamental spacetime symmetries to fundamental conservation laws. This demonstration linksB ⁽³⁾ to the canonical energy-momentum tensorT _µv that appears in Einstein's field equations of general relativity. Thus,B ⁽³⁾ provides a link between electromagnetism and gravitation which might eventually lead to an unified understanding of field theory.     

Brief comment on W. S. Warren et al II: Optical NMR and the B(3) field

It is pointed out that the only possible artifact, free opticalNMR (ONMR) shift of up to 0.1Hz reported by Warrenet al. [1] is the same precisely, 0.1Hz, as that predicted byB ³ theory. However, the great majority of the data by Warrenet al. are almost completely artifactual and cannot be used to discriminate between differentONMR mechanisms with any objectivity. Some references toB ³ theory andrecent ONMR data uncited by Warrenet al. are pointed out, data which show that the Warren group–s failure to see very well known [2,3] polarization-dependent effects of irradiation inNMR is a major design failure, not one of theory.