Whittaker potential

Vectorial fields M = VA ( ) and N = VAVA ( ) are respectively known as toroidal and poloidal fields. The scalar potentials and are called Debye potentials, while the vector potentials F = and G = are known as Whittaker potentials. 

X. Scalar Interferometry and Canonical Quantization from Whittaker s Potentials... 

An important by-product of the development in this chapter (Section X) is the possible existence of scalar interferometry, which is interferometry between structured scalar potentials, first introduced by Whittaker [27,28] and that can be defined in terms of B<3 This is a type of interferometry that depends on physically meaningful potentials that can exist self-consistently, as we have argued, only in a non-singly connected 0(3) vacuum, because potentials in the nonsingly connected U(l) vacuum are assumed to be unphysical. 

X. SCALAR INTERFEROMETRY AND CANONICAL QUANTIZATION FROM WHITTAKER S POTENTIALS... 

Whittaker s early work [27,28] is the precursor [4] to twistor theory and is well developed. Whittaker showed that a scalar potential satisfying the Laplace and d Alembert equations is structured in the vacuum, and can be expanded in terms of plane waves. This means that in the vacuum, there are both propagating and standing waves, and electromagnetic waves are not necessarily transverse. In this section, a straightforward application of Whittaker s work is reviewed, leading to the feasibility of interferometry between scalar potentials in the vacuum, and to a trouble-free method of canonical quantization. 

Potential differences are primary in gauge theory, because they define both the covariant derivative and the field tensor. In Whittaker s theory [27,28], potentials can exist without the presence of fields, but the converse is not true. This conclusion can be demonstrated as follows. Equation (479b) is invariant under... 

This result is consistent with Whittaker s main conclusion [27,28], that the scalar potential is structured and physical in the vacuum, leading to the possibility of interferometry between different scalar potentials, without the presence of fields. To reinforce this conclusion, we can differentiate Eq. (484)... 

Physical potentials are present in Whittaker s theory without fields. This is demonstrated as follows in the special case of a plane wave for the transverse parts of E and B. In this special case... 

The work of Whittaker described in the previous section can be summarized by the potential... 

Any dipole has a scalar potential between its ends, as is well known. Extending earlier work by Stoney [23], in 1903 Whittaker [8] showed that the scalar potential decomposes into—and identically is—a harmonic set of bidirectional longitudinal EM wavepairs. Each wavepair is comprised of a longitudinal EM wave (LEMW) and its phase conjugate LEMW replica. Hence the formation of the dipole actually initiates the ongoing production of a harmonic set of such biwaves in 4-space (see Section III.A.l). 

Further, in 1904 Whittaker [28] showed that any EM held or wave pattern can be decomposed into two scalar potential functions. Each of these two potential functions, of course, decomposes into the same kind of harmonic longitudinal EM wavepairs as shown in Whittaker [8], plus superposed dynamics. In other words, the interference of scalar14... 

Further, each composite dipole has its own scalar potential between its end charges. With the previously stated reservation (see Section III.A.l), this scalar potential decomposes per Whittaker [8] and thus initiates a giant negentropic reordering of the vacuum energy as previously discussed. So any charge is really an entire set of composite dipoles, composite negative resistors, and broken... 

In 1904 Whittaker [28] showed that any EM field or wave consists of two scalar potential functions, initiating what is known as superpotential theory [77]. By Whittaker s [8] 1903 paper, each of the scalar potential functions is derived from internally structured scalar potentials. Hence all EM fields, potentials, and waves may be expressed in terms of sets of more primary interior or infolded longitudinal EM waves and their impressed dynamics.35 This is indeed a far more fundamental electrodynamics than is presently utilized, and one that provides for a vast set of new phenomenology presently unknown to conventional theorists. 

In addition to Whittaker s sum set of waves comprising the scalar potential, Ziolkowski [49] added the product set. See also Refs. 76a and 76b. 

T. Whittaker, Math. Ann. 57, 333-355 (1903) (an excellent paper which decomposes the scalar potential into a harmonic set of bi-directional phase conjugate longitudinal wavepairs). 

We recovered a major fundamental principle from Whittaker s [1] profound but much-ignored work in 1903. Any scalar potential is a priori a set of EM energy flows, hence a set of electromagnetic energy winds, so to speak. As shown by Whittaker, these EM energy winds pour in from the complex plane (the time domain) to any x,y,z point in the potential, and pour out of that point in all directions in real 3-space [1,16,20]. 

Further, in 1904 Whittaker [56] (see also Section V.C.2) showed that any electromagnetic field, wave, etc. can be replaced by two scalar potential functions, thus initiating that branch of electrodynamics called superpotential theory [58]. Whittaker s two scalar potentials were then extended by electrodynamicists such as Bromwich [59], Debye [60], Nisbet [61], and McCrea [62] and shown to be part of vector superpotentials [58], and hence connected with A. 

So let us consider the -potential most simply as being replaced with such a Whittaker [1,56] decomposition. Then each of these scalar potentials—from which the A potential function is made—is decomposable into a set of harmonic phase conjugate wavepairs (of longitudinal EM waves). If one takes all the phase conjugate half-set, those phase conjugate waves are converging on... 

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