Abstract
The most general form of the vector potential is deduced in curved spacetime using general relativity. It is shown that the longitudinal and timelike components of the vector potential exist in general and are richly structured. Electromagnetic energy from the vacuum is given by the quaternion valued canonical energy-momentum. It is argued that a dipole intercepts such energy and uses it for the generation of electromotive force. Whittaker’sU(l) decomposition of the scalar potential applied to the potential between the poles of a dipole, shows that the dipole continuously receives electromagnetic energy from the complex plane and emits it in real space. The known broken 3-symmetry of the dipole results in a relaxation from 3-flow symmetry to 4-flow symmetry. Considered with its clustering virtual charges of opposite sign, an isolated charge becomes a set of composite dipoles, each having a potential between its poles that, inU(1) electrodynamics, is composed of the Whittaker structure and dynamics. Thus the source charge continuously emits energy in all directions in 3-space while obeying 4-space energy conservation. This resolves the long-vexing problem of the association of the “source” charge and its fields and potentials. In initiating 4-flow symmetry while breaking 3-flow symmetry, the charge, as a set of dipoles, initiates a reordering of a fraction of the surrounding vacuum energy, with the reordering spreading in all directions at the speed of light and involving canonical determinism between time currents and spacial energy currents. This constitutes a giant, spreading negentropy which continues as long as the dipole (or charge) is intact. Some implications of this previously unsuspected giant negentropy are pointed out for the Poynting energy flow theory, and as to how electrical circuits and loads are powered.
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M. Sachs in M. W. Evans, ed. and the Royal Swedish Academy,Modern Nonlinear Optics, a special topical issue in three parts of I. Prigogine and S. A. Rice, series eds.,Advances in Chemical Physics (Wiley, New York, 2001), Vol. 119; 2nd edn. of M. W. Evans and S. Kielich, eds.,Modern Non-Linear Optics, a special topical issue in three parts of I. Prigogine and S. A. Rice, eds,Advances in Chemical Physics (Wiley, New York, 1992, 1993, 1997 (softback)), Vol. 85.
M. W. Evanset al., AIAS group paper,Optik, submitted.
M. W. Evans,O(3) Electrodynamics (Kluwer Academic, Dordrecht, 1999).
M. W. Evans and L. B. Crowell,Classical and Quantum Electrodynamics and the B 3 Field (World Scientific, Singapore, 2000).
M. W. Evans in Ref. (1), Vol. 114(2).
E. T. Whittaker,Math Ann. 57, 333 (1903).
In the latter 1880s, Lorentz apparently introduced this method of discarding the huge non-intercepted, non-diverged component of the electromagnetic energy flow which he stated has “no physical significance.” His use of the method is shown in H. A. Lorentz,Vorlesungen über theoretische Physik an der UniversitÄt Leiden, Vol. V,Die Maxwellsche Theorie (1900-1902) (Akademische Verlagsgesellschaft, Leipzig, 1931),Die Energie im elektromagnetischen Feld, pp. 179–186. Figure 25 on p. 185 shows Lorentz’s concept of integrating the Poynting vector around a closed cylindrical surface surrounding a volumetric element.
G. Johnstone Stoney,Phil. Mag. 42, 332 (1896); 43, 139, 273, 368 (1897).
T. D. Lee,Particle Physics and Introduction to Field Theory (Harwood, New York, 1981), p. 184.
For a discussion of the problem see P. V. Elyutin,Sov. Phys. Usp. 31, 597 (1988).
D. K. Sen,Fields and/or Particles (Academic, London, 1968), p. viii.
Ibrahim Semiz,Am. J. Phys. 63, 151 (1995).
J. H. Poynting,Phil. Trans. Roy. Soc. Lond. 175A, 343 (1884).
Oliver Heaviside,Electromagnetic Induction and Its Propagation, a series of 47 sections, published section by section in numerous issues ofThe Electrician during 1885, 1886, and 1887.
Oliver Heaviside,Electromagnetic Theory, 3 Vols. (Been, London, 1893-1912; 2nd reprint, 1925).
Oliver Heaviside,Phil. Trans. Roy. Soc. Lond.,183A, 423 (1893). Heaviside discusses the Faraday-Maxwell ether medium, outlines his vector algebra for analysis of vectors without quaternions, discusses magnetism, gives the electrodynamic equations in a moving medium, and gives the electrodynamic flux of energy in a stationary medium. On P. 443, he credits Poynting with being the first to discover the formula for energy flow, with Heaviside himself independently discovering and interpreting this flow a little later in an extended form.
J. H. Poynting,Proc. Roy. Soc. Lond. 38, 168 (1984-85).
We have previously nominated this Heaviside dark energy flow, associated with and surrounding every field/charge interaction but presently unaccounted, as a candidate for the case of the excess gravity known to be holding together the spiral arms of distant galaxies. See T. E. Bearden,J. New Energy,4, 4 (2000).
Oliver Heaviside,Electrical Papers, Vol. 2, 1887, p. 94.
E.g., see W. K. H. Panofsky and M. Phillips,Classical Electricity and Magnetism (Addison-Wesley, Reading, MA, 1962), 2nd edn., p. 181. W. Gough, J. P. G. Richards,Eur. J. Phys. 7, 195 (1986).
Panofsky and Phillips,ibid., p. 180.
D. S. Jones,The Theory of Electromagnetism (Pergamon, Oxford, 1964), p. 52.
J. D. Jackson,Classical Electrodynamics, 2nd edn. (Wiley, New York, 1975), p. 237.
However, in conventional (older) classical electrodynamics E and H are not actually “the fields” per se, but are denned and utilized as the local reaction cross section of the field with a unit point static charge. Or, as Feynman put it, in mass free space, the entities represent only thepotentials for the fields to be produced,if a unit point static charge should be made available to interact with them. At best, in space, the fieldsE andH in common electrical power system usage reflect the local intensity of the field insofar as its interaction with astatic charge will be involved. They represent the intensity of the local field interactionshould it occur with astatic charge, not the entities themselves. Resonating the reacting charge, e.g., will result in a larger reaction crosssection for the charge, an increase in the apparent “magnitude of the incident field,” and consequently an increase in the magnitude of the energy that is absorbed. See Craig F. Bohren,Am. J. Phys. 51, 323 (1983); H. Paul and R. Fischer, ibid., p. 327. The prevailing “definition” of the field as only what is diverted from it, is also a part of the unresolved difficulties with the modern view of EM energy flow.
Richard P. Feynman, Robert B. Leighton and Matthew Sands,The Feynman Lectures on Physics, Vol. 1 (Addison-Wesley, New York, 1963), pp. 2–4.
T. E. Bearden,J. New Energy 1, 60 (1996);Proceedings, 4th International Energy Conference, Denver, CO, May 23–27, 1997, p. 16.
M. W. Evans, P. K. Anastasovski, T. E. Bearden,et al., Physica Scripta 61, 513 (2000).
W. M. Schwarz,Intermediate Electromagnetic Theory (Wiley, New York, 1964), pp. 280–281.
D. S. Jones,ibid., p. 53.
For typical points of view, see J. Slepian,Am. J. Phys. 19, 87 (1951). Mario Iona,ibid. 31, 398 (1963). Udo Backhaus and Klaus Schafer,ibid. 54, 279 (1986). C. J. Carpenter,IEE Proc. A (UK) 136A, 55 (1989). J. A. Ferreira,IEEE Trans. Edu. 31, 257 (1988). Mark A. Heald,Am J. Phys. 56, 540 (1988). The debate has also appeared in many other leading journals, e.g., T. H. Boyer,Phys. Rev. D 25, 3246 (1982). Interestingly, M. Abraham and R. Becker,The Classical Theory of Electricity and Magnetism (Blackie, London, 1932), p. 146 and p. 194, give two examples of the controversy over the Poynting vector. Finally, see D. F. Nelson,Phys. Rev. Lett. 76, 47131 (1996), for advanced work requiring a greater generalization of the Poynting vector.
A good illustration is shown by John D. Kraus,Electromagnetics, 4th edn. (McGraw-Hill, New York, 1992) in Fig. 12–60, a andb, p. 578.
Here, we assume a unitary current loop; i.e., one where the current carriers in all segments of the closed current loop have the samem/q ratio. That is not true, e.g., in a battery-powered system, where the ion current is confined internally between the plates (between the dipole ends) and has a much greaterm/q ratio than does the electron current segment of the loop between the outside of the plates through the external circuit. In that case, the two currents have appreciably different response times, and they can be de-phased and decoupled. Bedini has a patent-pending process for such open dissipative battery-powered systems far from thermodynamic equilibrium. For an explanation of the Bedini system, see T. E. Bearden,Bedini’s Method For Forming Negative Resistors in Batteries, Proc. IC-2000, St. Petersburg, Russia, 2000 (in press; also onhttp://www.cheniere.org).
Note that the excitation energy of the circuit is dissipated in a Lorentz symmetrical regauging fashion in the closed unitary current loop. We have previously dealt with the consequences of removing this arbitrarily self-enforced Lorentz excitation regauging; see [34] above.
V. S. Letokhov,Zh. Eksp. Teor. Fiz. 53, 1442 (1967);Contemp. Phys. 36, 235 (1995).
T. D. Lee,Phys. Rev. 104, 254–259 (1956). T. D. Lee, Reinhard Oehme, and C. N. Yang,Phys. Rev. 106, 340–346 (1957). C. S. Wuet ai, Phys. Rev. 105, 1413 (1957). So revolutionary a change was the proof of broken symmetry in early 1957 that Lee and Yang were awarded the Nobel Prize in December of the same year.
F. Mandl and G. Shaw,Quantum Field Theory, revised edn. (Wiley, New York, 1993), Chap. 5.
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Evans, M.W., Bearden, T.E. & Labounsky, A. The most general form of the vector potential in electrodynamics. Found Phys Lett 15, 245–261 (2002). https://doi.org/10.1023/A:1021031520389
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DOI: https://doi.org/10.1023/A:1021031520389