This article is a revised and upgraded edition of a previous one published in this journal, hence the label (2), see the General Remarks section below. Relativistic Electrodynamics, for many years a purely academic subject from the point of view of the applied physicist and electromagnetic radiation engineer, is nowadays recognized as pertinent to many practical applications. We therefore need to define a syllabus and explore the best methods for educating future generations of such users. Such an attempt is presented here, and is of course biased by personal preferences. What emerges as general guidelines are the facts that Relativistic Electrodynamics should be presented axiomatically, without trying to "explain the physical meaning" of Special Relativity, that four-vectors and their mathematical properties should be emphasized, and that the field tensors, an elegant formalism, albeit of limited practical use, should be avoided. Use of four-fold Fourier transforms not only greatly simplifies the relevant manipulations, it is also of paramount importance for discussion of dispersive media. This approach yields many concepts as mathematical results, e.g., the Relativistic Doppler effect, which therefore do not require a long phenomenological discussion with many "explanations". Introducing this approach as early as possible opens new vistas for the student and the educator, indeed some of the new results here do not appear in textbooks on Special Relativity. One of the main results shown here is the fact that the generalized Fermat principle states that the ray will propagate in such a manner that the proper time will be minimized (or extremized, in general). It also strips the mystique of this principle, showing that it is in fact equivalent to a modest mathematical condition on the smoothness of the phase function. The presentation is constructed in a way that allows the student to gradually overcome difficulties in assimilating new concepts and applying them. In that too it is different from many conventional presentations.
2. Censor, D., "Electrodynamics, topsy-turvy Special Relativity, and generalized Minkowski constitutive relations for linear and nonlinear systems," Progress in Electromagnetics Research, Editor J. A. Kong, Vol. 18, 261–284, Elsevier, 1998.
3. Einstein, A., "Zur Elektrodynamik bewegter Korper," Ann. Phys. (Lpz.), 17, 891–921, 1905; English translation: “On the electrodynamics of moving bodies,” The Principle of Relativity, Dover.
4. Becker, R., Electromagnetic Fields and Interactions, Dover, 1982.
5. Stratton, J. A., Electromagnetic Theory, McGraw-Hill, 1941.
6. Fano, R. M., L. J. Chu, and R. B. Adler, Electromagnetic Fields, Energy, and Forces, Wiley, 1960.
7. Sommerfeld, A., Electrodynamics, Dover, 1964.
8. Jordan, E. C. and K. G. Balmain, Electromagnetic Waves and Radiating Systems, Prentice-Hall, 1968.
9. Panofsky, W. K. H. and M. Phillips, Classical Electricity and Magnetism, Addison-Wesley, 1971.
10., The Electromagnetic Field, McGraw-Hill, 1975.
11. Jackson, J. D., Classical Electrodynamics, Wiley, 1975.
12. Portis, A. M., Electromagnetic Fields, Sources and Media, Wiley, 1978.
13. Lorrain, P. and D. R. Corson, Electromagnetism, Principles and Applications, W. H. Freeman, 1970.
14. Wangness, R. K., Electromagnetic Fields, Wiley, 1979.
15. Griffiths, D. J., Introduction to Electrodynamics, Prentice-Hall, 1981.
16. Frankl, D. R., Electromagnetic Theory, Prentice-Hall, 1986.
17. Chen, H. C., Theory of Electromagnetic Waves, McGraw-Hill, 1985.
18. Kong, J. A., Electromagnetic Wave Theory, Wiley, 1986.
19. Plonus, M. A., Applied Electromagnetics, McGraw-Hill, 1988.
20. Eringen, A. C. and G. A. Maugin, Electrodynamics of Continua, Vol. 2, Springer, 1990.
21. Schwartz, M., Principles of Electrodynamics, Dover, 1987.
22. Van Bladel, J., Relativity and Engineering, Springer, 1984.
23. Lindell, I. V., Methods for Electromagnetic Field Analysis, Oxford, 1992.
24. Minkowski, H., "Die Grundgleichungen f¨ur die elektromagnetische Vorg¨ange in bewegten Korpern," Gottinger Nachrichten, 53-116, 1908.
25. Zangari, M. and D. Censor, "Spectral representations: An alternative to the spatiotemporal world view," Synthese, Vol. 112, 97-123, 1997.
26. Censor, D., "Simultaneity, causality, and spectral representations,", submitted for publication.
27. Abraham, M., "Zur theorie der strahlung und des strahlungdruckes," Ann. Phys. (Lpz.), Vol. 14, 236-287, 1904.
28. Pauli, W., Theory of Relativity, Pergamon, 1958, also Dover Publications.
29. Censor, D., "Dispersion equations in moving media," Proceedings IEEE, Vol. 68, 528-529, 1980.
30. Bohm, D., The Special Theory of Relativity, Benjamin, 1965.
31. Post, E. J., Formal Structure of Electromagnetics, North-Holand, 1962.
32. Hebenstreit, H., "Constitutive relations for moving plasmas," Z. Naturforsch. A, Vol. 34a, 147-154, 1979.
33. Hebenstreit, H., "Calculation of covariant dispersion equations for moving plasmas," Z. Naturforsch. A, Vol. 34a, 155-162, 1979.
34. Hebenstreit, H. and K. Suchy, "Polarization relations and dispersion equations for anisotropic moving media," Z. Naturforsch. A, Vol. 34a, 1147-1157, 1979.
35. Censor, D., "A quest for systematic constitutive formulations for general field and wave systems based on the Volterra differential operators," Progress In Electromagnetics Research, Editor J. A. Kong, Vol. 25, 261–284, Elsevier, 2000.
36. Chawla, B. R. and H. Unz, Electromagnetic Waves in Moving Magnetoplasmas, Univ. Press, Lawrence, Kansas, 1971.
37. Kelso, J. M., Radio Ray Propagation in the Ionosphere, McGraw- Hill, 1964.
38. Van Bladel, J., Electromagnetic Fields, Hemisphere, 1985.
39. Ghatak, A., Optics, McGraw-Hill, 1977.
40. Sommerfeld, A., Optics, Academic Press, 1964.
41. Censor, D., "Quasi doppler effects associated with spatiotemporal translatory, moving, and active boundaries," Journal of Electromagnetic Waves and Applications, Vol. 13, 145-174, 1999.
42. Censor, D., "Application-oriented ray theory," International. J. Electrical. Eng. Education, Vol. 15, 215-223, 1978.
43. Molcho, J. and D. Censor, "A simple derivation and an example of Hamiltonian ray propagation," Am. J. Phys, Vol. 54, 351-353, 1986.
44. Poeverlein, H., "Sommerfeld-Runge law in three and four dimensions," The Physical Review, Vol. 128, 956-964, 1962.
45. Synge, J. L., Geometrical Mechanics and De Broglie Waves, Cambridge University Press, 1954.
46. Censor, D., "““Waves”, “objects” and special relativity," Journal of Electromagnetic Waves and Applications, Vol. 5, 1365-1391, 1991.
47. Censor, D. and J. J. Gavan, "Wave packets, group velocities and rays in lossy media revisited," IEEE Trans. on Electromagnetic Compatibility, Vol. 31, 262-272, 1989.
48. Sonnenschein, E., I. Rutkevich, and D. Censor, "Wave packets, rays and the role of real group velocity in absorbing media," Physical Review E, Vol. 57, 1005-1016, 1998.
49. Sonnenschein, E., I. Rutkevich, and D. Censor, "Wave packet and group velocity in absorbing media: Solutions of the telegrapher’s equation," Journal of Electromagnetic Waves and Applications, 2000.
50. Felsen, L. B. and N. Marcuvitz, Radiation and Scattering of Waves, Prentice-Hall, 1973.
51. Censor, D. and K. Suchy, "Wave packets and ray tracing in lossy media," Proc. URSI Natl. Comm., Fed. Rep. of Germany, Kleinheubacher, 617–623, 1975.
52. Censor, D., "Fermat’s principle and real space-time rays in absorbing media," J. Phys. A: Math. Gen., Vol. 10, 1781-1790, 1977.
53. Censor, D., "Fermat’s principle, Hamiltonian ray equations, group velocity and wave packets in absorptive media," Advances in Thermodynamics, Vol. 3: Theory and Extremum Principles, Editors, S. Sieniuycz and P. Salamon, 448–481, Taylor and Francis, 1990.
54. Sonnenschein, E., D. Censor, I. Rutkevich, and J. A. Bennett, "Ray trajectories in an absorptive ionosphere," JASTRP— Journal of Atmospheric and Solar-Terrestrial Physics, Vol. 59, 2101-2110, 1997.
55. Sonnenschein, E., N. Blaunstein, and D. Censor, "HF ray propagation in the presence of resonance heated ionospheric plasma," JASTRP — Journal of Atmospheric and Solar-Terrestrial Physics, Vol. 60, 1605-1623, 1998.
56. Sonnenschein, M. and D. Censor, "Simulation of Hamiltonian light beam propagation in nonlinear media," JOSA — Journal of the Optical Society of America, B, Vol. 15, 1335-1345, 1998.
57. Volterra, V., Theory of Functionals and of Integral and Integro- Differential Equations, Dover, 1959.
58. Censor, D., "Ray tracing in weakly nonlinear moving media," Journal of Plasma Physics, Vol. 16, 415-426, 1976.
59. Censor, D., "Scattering in velocity dependent systems," Radio Science, Vol. 7, 331-337, 1972.
60. Ben-Shimol, Y. and D. Censor, "Contribution to the problem of near zone inverse Doppler effect," Radio Science, Vol. 33, 463-474, 1998.