Heaviside’s approach to deriving electromagnetic waves from the Maxwell equations is detailed by Nahin (P. J. Nahin: OLIVER HEAVISIDE, The Johns Hopkins University Press, 2002). In this session, we will follow Nahin’s approach to show how Heaviside derived electromagnetic waves. Namely, the current I(x) is obtained from H using the inverse of Ampere’s law. Since electromagnetic fields and electromagnetic waves satisfy duality, the voltage −V(x) is obtained from E using the inverse of Faraday’s law of induction. The current and voltage obtained here are complex functions because the operator method is used; they are not real functions (trigonometric functions) used in vector analysis and tensor analysis. Also, these complex functions of the current and voltage are the wave equations, slightly different from telegrapher’s equations, and the mathematics involved differs somewhat from Hilbert’s or Fourier’s mathematics. In this session, we refer to this mathematics as Heaviside’s extension. Since Heaviside’s extension does not involve the behavior of electrons, the behavior of electrons remains a future research topic.
Nagai et al. (Sat,) studied this question.