NOTES AND REFERENCES

1. For a good discussion of the modern quantum mechanical view of the vacuum, see I. J. R.
Aitchison, "Nothing's plenty: the vacuum in modern field theory," Contemporary Physics, 26(4),
1985, p. 333-391. See also T. D. Lee, Particle Physics and Introduction to Field Theory,
Harwood Academic Publishers, New York, 1981 -- particularly Chapter 16, "Vacuum as the
source of asymmetry." See Timothy Boyer, "The classical vacuum," Scientific American, Aug.
1985, p. 70; Walter Greiner and Joseph Hamilton, "Is the Vacuum really Empty?", American
Scientist, Mar.-Apr. 1980, p. 154; Jack S. Greenberg and Walter Greiner, "Search for the
sparking of the vacuum," Physics Today, Aug. 1982, p. 24-32; Richard E. Prange and Peter
Strance, "The superconducting vacuum," American Journal of Physics, 52(1), Jan. 1984, p. 19-
21; R. Jackiw and J.R. Schrieffer, "The decay of the vacuum," Nuclear Physics B, Vol. 190,
1981, p. 944. See Paul Davies, Superforce, Simon and Schuster, 1984 for a layman's overview
of modern physics, including the modern view of the vacuum.
2. E. T. Whittaker, "On the partial differential equations of mathematical physics,"
Mathematische Annalen, Vol. 57, 1903, p. 333-355. Since the scalar potential actually consists
totally of a set of hidden bidirectional EM waves, then scalar interferometry is possible, and not
just an oxymoron as it would seem without considering the inner wave structure of the scalar
potential. Two scalar potentials (each of which is a multi-biwave set) can interfere; it is just a
special kind of multiple wave interferometry between their internal wave compositions. This is a
major point of profound impact on physics. Whittaker in fact showed that all classical EM could
be replaced by such scalar EM potential interferometry. See E. T. Whittaker, "On an expression
of the electromagnetic field due to electrons by means of two scalar potential functions,"
Proceedings of the London Mathematical Society, Series 2, Vol. 1, 1904, p. 367-372. Further,
scalar interferometry has been proven; today it is called the Aharonov-Bohm Effect. See Y.
Aharonov and D. Bohm, "Significance of Electromagnetic Potentials in the Quantum Theory,"
Physical Review, Second Series, 115(3), Aug. 1, 1959, p. 458-491. For confirmation and
discussion, see Bertram Schwarzschild, "Currents in normal-metal rings exhibit Aharonov-Bohm
Effect," Physics Today, 39(1), Jan. 1986, p. 17-20. For an extensive discussion of the
Aharonov-bohm effect and an extensive list of references, see S. Olariu and I. Iovitzu Popescu,
"The quantum effects of electromagnetic fluxes," Reviews of Modern Physics, 57(2), April 1985.
Modern scientists have generally been unaware of the inner wave structure of the interfering
potentials and have utilized only quantum mechanical theory for the interference. Consequently,
they have been able to experimentally establish the AB effect for only a few thousand
Angstroms distance. With the Whittaker formulation, the AB effect becomes distantindependent,
because the necessary potentials can be fabricated as laser-like beams, simply by
assembling the proper Whittaker multibeam set. Also, Ignatovich pointed out that the
Schroedinger potential can also be decomposed into just such an internal bidirectional EM wave
set. See V.K. Ignatovich, "The remarkable capabilities of recursive relations," American Journal
of Physics, 57(10), Oct. 1989, p. 873-878.
3. See Richard W. Ziolkowski, "Exact Solutions of the Wave Equation With Complex Source
Locations," Journal of Mathematical Physics, Vol. 26, 1985, p. 861; "Localized Transmission of
Wave Energy," Proc. SPIE, Vol. 1061, Microwave and Particle Beam Sources and Directed
Energy Concepts, 1989, p. 396-397; "Localized Transmission of Electromagnetic Energy,"
Physical Review A, Vol. 39, p. 2005; "Localized Wave Transmission Physics and Engineering,"
Physical Review A, 1992, (in Press); "Localized wave transmission physics and engineering,"
Proc. SPIE Conference on Intense Microwave and Particle Beams II, Los Angeles, CA, vol.
1407, Jan. 1991, p. 375-386. See Richard W.Ziolkowski, Amr M. Shaarawi, and Ioannis M.
Besieris, Nuclear Physics B (Proc. Suppl.), Vol. 6, 1989, p. 255-258; R.W. Ziolkowski, and D.K.
Lewis, D.K., "Verification of the Localized Wave Transmission Effect," Journal of Applied
Physics, Vol. 68, 1990, p.6083; Richard W. Ziolkowski, Ioannis M. Besieris, and Amr M.
Shaarawi, "Localized Wave Representations of Acoustics and Electromagnetic Radiation,"
Proceedings of the IEEE, 79(10), Oct. 1991, p. 1371-1378; I.M. Besieris, A.M. Shaarawi, and
R.W. Ziolkowski, "A bidirectional travelling plane wave representation of exact solutions of the
scalar wave equation," Journal of Mathematical Physics, 30(6), 1989, p. 806; A.M. Shaarawi,
I.M. Besieris, and R.W. Ziolkowski, "A novel approach to the synthesis of nondispersive wave
packet solutions to the Klein-Gordon and the Dirac equations," Journal of Mathematical Physics,
31(10), 1990, p. 2511; "A nondispersive wave packet representation of photons and the waveparticle
duality of light," UCRL-101694, Lawrence Livermore National Laboratory, Livermore,
CA, 1989; "Diffraction of a classical wave packet in a two slit interference experiment," UCRL-
100756, Lawrence Livermore National Laboratory, Livermore, CA 1989; "Localized energy
pulse trains launched from an open, semi-infinite, circular waveguide," Journal of Applied
Physics, 65(2), 1989, p. 805; R.W. Ziolkowski, D.K.Lewis and B.D.Cook, "Experimental
verification of the localized wave transmission effect," Physical Review Letters, 62(2), 1989, p.
147; R.W. Ziolkowski and D.K. Lewis, "Verification of the localized wave transmission effect,"
Journal of Applied Physics, 68(12), 1990, p. 6083; M.K. Tippett and R.W. Ziolkowski, "A
bidirectional wave transformation of the cold plasma equations," Journal of Mathematical
Physics, 32(2) 1991, p. 488; A.M. Vengsarkar, I.M. Besieris, A.M. Shaarawi, and R.W.
Ziolkowski, "Localized energy pulses in optical fiber waveguides: Closed-form approximate
solutions," Journal of the Optical Society of America A, 1991.
4. For a precise statement of the distortion correction theorem, see Amnon Yariv, Optical
Electronics, 3rd Ed., Holt, Rihehart and Winston, New York, 1985, p. 500-501.
5. Both wave and antiwave co-exist in the vacuum simultaneously, forming a stress wave. The
entity that is stressed is the rate of flow of time. In the common interaction with matter, the timeforward
half of the stress wave normally interacts with the electron shells of the atom, giving
electron translations forces. The time-reversed or anti-wave half interacts with the nucleus,
giving the Newtonian 3rd law reaction (recoil) forces. The so-called "EM wave" in vacuum is a
gravitational wave. It is a wave of oscillation of the rate of flow of time. It is rather like a sound
wave in air, as Tesla pointed out, and it is a longitudinal wave, not a transverse "string" wave.
6. As pointed out by Nikola Tesla. Tesla was correct, and all the textbooks with their transverse
"string" waves are in error. There are no strings in the vacuum!
7. E.g., see Clayton R. Paul and Syed A. Nasar, Introduction to Electromagnetic Fields, 2nd
Ed., McGraw-Hill, New York, 1982, p. 113.
8. E.g., see Clayton R. Paul and Syed A. Nasar, ibid., p. 100-101. See also Raymond A.
Serway, Physics For Scientists And Engineers, With Modern Physics, Saunders College
Publishing, Philadelphia, PA, 3rd Ed., Updated Version, 1992, p. 752-755.
9. Sommerfield's theory of metallic conduction was based on Drude's concept that the outer
valence electrons of a conductor, which do not form crystal bonds, are free to migrate through
the crystalline lattice structure, and so to form an electron gas. At room temperature, by
quantum mechanical considerations, these free electrons are moving randomly, but at an
average velocity on the order of 106 meters per sec. E.g., see Martin A. Plonus, Applied
Electromagnetics, McGraw Hill, New York, 1978, p. 54-58, 62-3, 376-7. If you wish to know just
how much power exchange is driving the collisions of the electron gas in a copper wire, here is
an illustration. In one cubic centimeter of copper wire, the power exchange in and out of the
electron gas is some 4 billion billion watts. That's the equivalent of 4 billion large electric power
plants, each of 1,000 megawatt capacity. And one cubic centimeter of copper is a lump about
the size of the end of our little finger.
10. E. g., see Raymond A. Serway, ibid., p. 743-744 for a discussion and calculation of the
electron drift velocity in copper.
11. Richard P. Feynman, Robert B. Leighton, and Matthew Sands, The Feynman Lectures on
Physics, Addison-Wesley, New York, Vol. 1, 1963, p. 2-4. In the classical EM theory launched
by Maxwell and later modified by Heaviside et al, this problem did not exist for the original
theoretical formulation. In that formulation by Maxwell, and continued by Heaviside, a material
ether is assumed for the model. The Michelson-Morley experiments of 1887 destroyed the
notion of the material ether, but the classical electromagnetics model has never been corrected
to rectify its very serious foundations flaw in this respect.
12. Robert Bruce Lindsay and Henry Margenau, Foundations of Physics, Dover Publications,
New York, 1963, p. 283-287. Note on p. 283 that a "field of force" at any point is actually defined
only for the case when a unit mass is present at that point. In spite of this, most classical
electrodynamicists continue to adhere to the notion that the EM field exists as such in the
vacuum, but do admit that physically measurable quantities such as force somehow involve the
product of charge and field. E.g., see J.D. Jackson, Classical Electrodynamics, 2nd Ed., John
Wiley & Sons, New York, 1975, p. 249. Note that holding such a concept is tantamount to
holding on to the material ether, and assuming that the vacuum itself is "measurable" or
"observable."