Green’s Function - Reciprocity Theorem - Mutual Energy Theorem - Huygens’ Principle - Poynting’s Theorem - Mutual Energy Flow Theorem - Law of Conservation of Energy - Photon
Abstract
Shuang-ren Zhao
Maxwell’s electromagnetic theory is a single-source electromagnetic theory. In contrast, the reciprocity theorem involves two sources. The electromagnetic theory with two sources is fundamentally different from that with a single source. This paper elucidates the step-by-step development of the two-source electromagnetic theory. It clarifies the relationships between Green’s function, the reciprocity theorem, Poynting’s theorem, the mutual energy theorem, Huygens’ principle, the mutual energy flow theorem, the mutual energy flow law, and the law of conservation of energy. It also attempts to reconstruct the historical devel- opment sequence of these theorems and laws. Shortly after Maxwell proposed his electromagnetic theory, Poynting’s theorem was introduced in 1884, followed by Lorentz’s reciprocity theorem in 1896. In 1954, Rumsey proposed the principle of action and reaction. Welch proposed the time-domain reciprocity theorem in 1960. In 1987, the author proposed the mutual energy theorem. The mutual energy theorem is the Fourier transform of Welch’s time-domain reciprocity theorem. However, the au- thor emphasizes that it is an energy theorem, not merely a reciprocity theorem. The author’s formulation of the mutual energy theorem was questioned by most scientists in the electromagnetic field at the time. The main point of contention was that the so-called mutual energy theorem was not truly an energy theorem but still a reciprocity theorem. To address this, the author further proposed the mutual energy flow theorem in 2017, considering it the law of conservation of energy in electromagnetic field theory, and introduced the concept of self-energy flow reverse collapse. In 2020, the author made a first revision to the mutual energy flow, adding a normalization factor of 1/2. After 2022, the author replaced the concept of self-energy flow reverse collapse with the concept of self-energy flow as reactive power. The idea that self-energy flow is reactive power contradicts Maxwell’s electromagnetic theory, leading the author to revise Maxwell’s theory, primarily concerning the magnetic field. The author argues that the magnetic field in Maxwell’s electromagnetic theory is not the true magnetic field but rather the average magnetic field along a loop. Maxwell’s theory provides this average magnetic field, and obtaining the true magnetic field re- quires a phase correction to this average magnetic field.