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Superpotentials, Scalar interferometry, and Internally Structuring of Fields and Potentials

Tom Bearden

(Many thanks to Dr. Bob Flowers,
who examined the contributions by
the various cited authors.)

Whittaker’s decomposition of potentials and fields
. In 1903 and 1904, E. T. Whittaker published two fundamental papers of interest to (i) the "infolding" of longitudinal wave (LW) electrodynamics inside the scalar potential {[i]}, and also (ii) the expression of any EM field or wave as comprised of two potentials with appropriate differential functions applied {[ii]}.

For any EM field or wave: Suppose the two potentials are taken as scalar potentials (as advanced by Whittaker in 1904), and each of these two “basis potentials” is also first decomposed into longitudinal EM waves as shown by Whittaker in 1903, and then the appropriate differential functions are applied to each of the two decompositions, yielding the necessary EM field or wave pattern. Then all EM potentials, fields, and waves are shown (i) to be sets of ongoing EM energy flows in the form of longitudinal EM waves comprising the basis scalar potential(s), and (ii) to be comprised of internal longitudinal EM waves and strong internal structuring.

Scalar Interferometry: It follows that longitudinal EM wave interferometry (e.g., interfering the inner structures of two scalar potential beams in a distant interference zone in space), can create any known EM field or wave or pattern. Rigorous proof in a higher group symmetry O(3) electrodynamics is given by Evans {[iii]}. Of course, the later superpotential theory using two vector potentials can also be utilized.

Since the specific pattern of EM force fields and waves and potentials produced in distant charged matter in the interference zone is determined by the interacting specific composite structures of the two scalar potentials used in the interferometry, then one can produce (in charged matter targets) specific force fields and forces (and their directions and strengths) in that distant targeted charged matter. Obviously development of such technology will yield a very powerful type of superweapon for inducing “specific force engines” and effects in distant targets.

Superpotential theory: Whittaker’s 1904 paper initiated the entire area called superpotential theory. The Whittaker initial superpotential theory using two scalar potentials was extended in a magnetization potential direction (indicated in 1901 by Ricci) by other scientists such as Nisbet {[iv]}, Bromwich {[v]}, McCrae {[vi]}, Debye {[vii]}, and others.

An overview of superpotential theory is given by Phillips {[viii]}. Paraphrasing: Whittaker (published 1904) was the first to prove that one can derive a general electromagnetic field from two scalar functions, which are really components of the vector superpotentials, with proper choices of the gauge functions. Whittaker's method is well-known in the source distribution (assumed given) by a suitable choice of stream functions. The Debye potentials and the Bromwich potentials are essentially radial components of the vector potentials of which Whittaker potentials are the real parts. So in general the particular integral (i.e., the stream potentials) of the inhomogeneous Maxwell equations may be chosen such that the complementary function can be expressed in terms of only two scalars, which are components of the vector superpotentials. The Whittaker and the Debye-Bromwich potentials are special cases of two vector superpotentials.

Also paraphrasing Phillips: Nisbet has extended the Whittaker and Debye two-potential solutions of Maxwell's equations to points within the source distribution. This is a full generalization of the vector superpotentials (for media of arbitrary properties) together with their relations to such scalar potentials as those of Debye. (See A. Nisbet, Physica, Vol. 21, 1955, p. 799. Also, A. Ricci in 1901 introduced what may be called the magnetization potential, satisfying a certain equation, as an alternate to the Hertz vector. This was a part of early vector superpotentials.

For the general properties of the superpotentials and their gauge transformations in tensor form, particularly see W.H. McCrea {6}. McCrea's treatment is more concise than that of Nisbet, but entirely equivalent when translated into ordinary spacetime coordinates.



[i].          E. T. Whittaker, "On the Partial Differential Equations of Mathematical Physics," Math. Ann., Vol. 57, 1903, p. 333-355.

[ii].          E. T. Whittaker, "On an Expression of the Electromagnetic Field Due to Electrons by Means of Two Scalar Potential Functions," Proc. Lond. Math. Soc., Vol. 1, 1904, p. 367-372.

[iii].         M. W. Evans et al., "On Whittaker's Representation of the Electromagnetic Entity in Vacuo, Part V: The Production of Transverse Fields and Energy by Scalar Interferometry," J. New Energy, 4(3), Special Issue, Winter 1999, p. 76-78.

[iv].         A. Nisbet, “Source representations for Debye’s electromagnetic potentials, Physica, Vol. 21, 1955, p. 799-802.

[v].         Thomas John I’Anson Bromwich, “Electromagnetic waves,” Phil. Mag. J. Sci.; London, Edinburgh Dublin; Vol. 38, 1919, p. 143-164.

[vi].         W. H. McCrea, Proc. Roy. Soc. Lond. A., Vol. 240, 1957, p. 447.

[vii].        P. Debye, “Der lichtdruck auf Kugeln von beliegigem Material,” Ann. Phys., (Leipzig), Vol. 30, 1909, p. 57-136.

[viii].       Melba Phillips, "Classical Electrodynamics," in Principles of Electrodynamics and Relativity, Vol. 4 of Encyclopedia of Physics, edited by S. Flugge, Springer Verlag, 1962.