The Completeness of Classical Electromagnetic Theory

Abstract

The core of classical electromagnetic field theory is Maxwell electromagnetic field equations. Each of its formulas is supported by experimental facts, and its mathematical logic is rigorous and self-consistent, which has been tested for a long time in application.Therefore, its correctness is beyond doubt. In this paper, on the premise of affirming the great significance and important contribution of Maxwell equations(ME), the possible problems and solutions are discussed. Since ME and its derived wave equation (MWE) are vectorized partial differential equations, it is difficult to solve them strictly. In this paper, the solutions of vectorized ME and vectorized MWE are discussed in depth, and the necessity of Hansen function analysis is illustrated before the concrete calculation of engineering structures. Another method is to use vector partial differential operator theory to derive the standard basic equations expressed by state functions, and change the traditional calculation in Euclid space to the calculation in wave function space. Singularities and singularity are also avoided in the process. This paper argues that the completeness and modernity of traditional electromagnetic theory can only be improved by introducing the concept of particle, because the wave field processed by ME is actually a quantum field of light. The motion equation of electromagnetic field in classical theory is ME. In quantum theory, the field vector is an operator, governed by ME. The photon theory successfully explained the photoelectric effect in a way that ME could not. But in the mainstream theory, the photon rest mass  is equal to zero, which blocks the way to add particle concept to ME. In 1936, Proca equations assumed ≠0, and with the support of quantum electrodynamics(QED), ME was improved. In this paper, the Proca equations are approved and the Proca wave equation (PWE) is further derived. In short, it reflects the adherence to the concept of wave-particle duality. The extended Maxwell equations proposed by Chinese scientist recently should be emphasized and discussed in this paper.