Microscopic Electromagnetics

  • Kurt E. Oughstun
Part of the Springer Series in Optical Sciences book series (SSOS, volume 224)


A mathematically rigorous, physically based development of the classical theory of electromagnetism is introduced here through a consideration of the microscopic Maxwell–Lorentz theory. Although the Lorentz theory of electrons is a purely classical, heuristic model that is incapable of analyzing many fundamental problems associated with the atomic constituency of matter, it is nevertheless an expedient model in providing the proper source terms for the microscopic Maxwell equations. Indeed, the classical Lorentz theory does yield many results connected with the electromagnetic properties of matter that agree in functional form with that given by quantum theory. In particular, the Lorentz theory assumes additional forces of just the right nature such that qualitatively correct expressions are obtained and, by empirical adjustment of the parameters appearing in these ad hoc force relations, quantitatively correct predictions may also be obtained. Even though quantum theory justifies the assumption of these additional forces and shows them to be of electrical origin, the Lorentz theory is incapable of arriving at this fundamental level of understanding.


  1. 1.
    J. C. Maxwell, “A dynamical theory of the electromagnetic field,” Phil. Trans. Roy. Soc. (London), vol. 155, pp. 450–521, 1865.Google Scholar
  2. 2.
    J. C. Maxwell, A Treatise on Electricity and Magnetism. Oxford: Oxford University Press, 1873.zbMATHGoogle Scholar
  3. 3.
    H. A. Lorentz, The Theory of Electrons. Leipzig: Teubner, 1906. Ch. IV.Google Scholar
  4. 4.
    J. M. Stone, Radiation and Optics, An Introduction to the Classical Theory. New York: McGraw-Hill, 1963.Google Scholar
  5. 5.
    A. Einstein, Out of My Later Years. New York: Philosophical Library, 1950. pp. 76–77.zbMATHGoogle Scholar
  6. 6.
    L. Rosenfeld, Theory of Electrons. Amsterdam: North-Holland, 1951.zbMATHGoogle Scholar
  7. 7.
    H. A. Kramers, Quantum Mechanics. Amsterdam: North-Holland, 1957.zbMATHGoogle Scholar
  8. 8.
    A. D. Yaghjian, Relativistic Dynamics of a Charged Sphere. Berlin-Heidelberg: Springer-Verlag, 1992.CrossRefGoogle Scholar
  9. 9.
    K. I. Golden and G. Kalman, “Phenomenological electrodynamics of two-dimensional Coulomb systems,” Phys. Rev. B, vol. 45, no. 11, pp. 5834–5837, 1992.ADSCrossRefGoogle Scholar
  10. 10.
    K. I. Golden and G. Kalman, “Phenomenological electrodynamics of electronic superlattices,” Phys. Rev. B, vol. 52, no. 20, pp. 14719–14727, 1995.ADSCrossRefGoogle Scholar
  11. 11.
    K. I. Golden and G. J. Kalman, “Quasilocalized charge approximation in strongly coupled plasma physics,” Physics of Plasmas, vol. 7, no. 1, pp. 14–32, 2000.ADSCrossRefGoogle Scholar
  12. 12.
    N. Bohr and L. Rosenfeld, “Field and charge measurements in quantum electrodynamics,” Phys. Rev., vol. 78, no. 6, pp. 794–798, 1950.ADSCrossRefGoogle Scholar
  13. 13.
    M. Faraday, Experimental Researches in Electricity. London: Bernard Quaritch, 1855.Google Scholar
  14. 14.
    P. Penfield and H. A. Haus, Electrodynamics of Moving Media. Cambridge, MA: M.I.T. Press, 1967.Google Scholar
  15. 15.
    A. M. Ampère, “Memoir on the mutual action of two electric currents,” Annales de Chimie et Physique, vol. 15, pp. 59–76, 1820.Google Scholar
  16. 16.
    H. Poincaré, Electricité et Optique. Paris: Carré Nadaud, 1901.zbMATHGoogle Scholar
  17. 17.
    H. Poincaré, La Science et l’hypothése. Paris: Flammarion, 1902.zbMATHGoogle Scholar
  18. 18.
    H. Poincaré, “Sur la dynamique de l’électron,” Comptes rendus Acad. Sci. Paris, vol. 140, pp. 1504–1508, 1905.ADSzbMATHGoogle Scholar
  19. 19.
    H. A. Lorentz, “Electromagnetic phenomena in a system moving with any velocity less than that of light,” Proc. Acad. Sci. Amsterdam, vol. 6, pp. 809–832, 1904.Google Scholar
  20. 20.
    K. F. Gauss, “Theoria Attractionis Corporum Sphaeroidicorum Ellipticorum Homogeneorum,” in Werke, vol. 5, pp. 1–22, Göttingen: Royal Society of Science, 1870.Google Scholar
  21. 21.
    T. Young, “Experiments and calculations relative to physical optics,” in Miscellaneous Works (G. Peacock, ed.), vol. 1, pp. 179–191, London: John Murray Publishers, 1855. p.188.Google Scholar
  22. 22.
    J. Bradley, “An account of a new discovered motion of the fix’d stars,” Phil. Trans. Roy. Soc. (London), vol. 35, pp. 637–660, 1728.CrossRefGoogle Scholar
  23. 23.
    A. A. Michelson and E. W. Morley, “On the relative motion of the Earth and the luminiferous ether,” Am. J. Sci., no. 203, pp. 333–345, 1887.ADSCrossRefGoogle Scholar
  24. 24.
    F. T. Trouton and H. R. Noble, “Forces acting on a charged condenser moving through space,” Proc. Roy. Soc. (London), vol. 72, pp. 132–133, 1903.Google Scholar
  25. 25.
    J. H. Poincaré, “L’etat actuel et l’avenir de la physique mathématique,” Bull. Sci. Math., vol. 28, pp. 302–324, 1904. English translation in Monist, vol. 15, 1 (1905).Google Scholar
  26. 26.
    A. Einstein, “Zur elektrodynamik bewegter körper,” Ann. Phys., vol. 17, pp. 891–921, 1905.CrossRefGoogle Scholar
  27. 27.
    R. Resnick, Introduction to Special Relativity. New York: John Wiley & Sons, 1968.Google Scholar
  28. 28.
    J. V. Bladel, Relativity and Engineering. Berlin-Heidelberg: Springer-Verlag, 1984.CrossRefGoogle Scholar
  29. 29.
    A. S. Eddington, The Mathematical Theory of Relativity. New York: Chelsea, third ed., 1975. Section 5.Google Scholar
  30. 30.
    P. M. Morse and H. Feshbach, Methods of Theoretical Physics. New York: McGraw-Hill, 1953. Vol. I.Google Scholar
  31. 31.
    H. A. Lorentz, Versuch einer Theorie der elektrischen und optischen Erscheinungen in bewegten Körpern. Leiden: E. J. Brill, 1895. Sections 89–92. English translation: “Michelson’s Interference Experiment,” in The Principle of Relativity. A Collection of Original Memoirs on the Special and General Theory of Relativity by A. Einstein, H. A. Lorentz, H. Minkowski, and H. Weyl, New York: Dover, 1958.Google Scholar
  32. 32.
    L. D. Broglie, Matière et Lumière. Paris: Albin Michel, 1937.Google Scholar
  33. 33.
    E. Fischbach, H. Kloor, R. A. Langel, A. T. Y. Lui, and M. Peredo, “New geomagnetic limits on the photon mass and on long-range forces coexisting with electromagnetism,” Phys. Rev. Lett., vol. 73, no. 4, pp. 514–517, 1994.ADSCrossRefGoogle Scholar
  34. 34.
    G. Feinberg, “Possibility of faster-than-light particles,” Phys. Rev., vol. 159, no. 5, pp. 1089–1105, 1967.ADSCrossRefGoogle Scholar
  35. 35.
    O.-M. Bilaniuk and E. C. G. Sudarshan, “Particles beyond the light barrier,” Physics Today, vol. 22, no. 5, pp. 43–51, 1969.CrossRefGoogle Scholar
  36. 36.
    A. Stewart, “The discovery of stellar aberration,” Scientific American, vol. 210, no. 3, p. 100, 1964.CrossRefGoogle Scholar
  37. 37.
    M. Born, Einstein’s Theory of Relativity. New York: Dover, 1962.Google Scholar
  38. 38.
    J. H. Poynting, “Transfer of energy in the electromagnetic field,” Phil. Trans., vol. 175, pp. 343–361, 1884.CrossRefGoogle Scholar
  39. 39.
    G. Nicolis, Introduction to Nonlinear Science. Cambridge: Cambridge University Press, 1995. Section 2.2.Google Scholar
  40. 40.
    W. S. Franklin, “Poynting’s theorem and the distribution of electric field inside and outside of a conductor carrying electric current,” Phys. Rev., vol. 13, no. 3, pp. 165–181, 1901.ADSGoogle Scholar
  41. 41.
    MacDonald, Electric Waves. Cambridge: Cambridge University Press, 1902.Google Scholar
  42. 42.
    Livens, The Theory of Electricity. Cambridge: Cambridge University Press, 1926. pp. 238 ff.Google Scholar
  43. 43.
    Mason and Weaver, The Electromagnetic Field. Chicago: University of Chicago Press, 1929. pp. 264 ff.Google Scholar
  44. 44.
    J. A. Stratton, Electromagnetic Theory. New York: McGraw-Hill, 1941.zbMATHGoogle Scholar
  45. 45.
    M. Abraham, “Prinzipien der Dynamik der Elektrons,” Ann. Physik, vol. 10, pp. 105–179, 1903.zbMATHGoogle Scholar
  46. 46.
    H. B. Phillips, Vector Analysis. New York: John Wiley & Sons, 1933.zbMATHGoogle Scholar
  47. 47.
    L. Silberstein, “Electromagnetische Grundgleichungen in bivectorielle Behandlung,” Ann. Phys., vol. 22, pp. 579–586, 1907.CrossRefGoogle Scholar
  48. 48.
    L. Silberstein, “Electromagnetische Grundgleichungen in bivectorielle Behandlung,” Ann. Phys., vol. 24, pp. 783–784, 1907.CrossRefGoogle Scholar
  49. 49.
    H. Bateman, The Mathematical Analysis of Electrical & Optical Wave-Motion. Cambridge: Cambridge University Press, 1905.Google Scholar
  50. 50.
    D. B. Malament, “On the time reversal invariance of classical electromagnetic theory,” Studies in History and Philosophy of Modern Physics, vol. 35, pp. 295–315, 2004.ADSMathSciNetCrossRefGoogle Scholar
  51. 51.
    A. Rubinowicz, “Uniqueness of solution of Maxwell’s equations,” Phys. Zeits., vol. 27, pp. 707–710, 1926.Google Scholar
  52. 52.
    B. Greene, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. New York: W. W. Norton & Company, 1999.zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kurt E. Oughstun
    • 1
  1. 1.College of Engineering and Mathematical Sciences, University of VermontBurlingtonUSA

Personalised recommendations