Multidimensional systems: Flow in electromagnetic fields and some fundamental implications

摘要

For an electromagnetic (EM) field, local properties such as field velocity, rest field, and rest energy density are introduced. These are physically justified and mathematically defined by starting from what are the only assumptions on which this paper rests: the strict validity of Maxwell's equations and their inherent relativistic transformation rules. A variety of additional properties are presented that confirm the judiciousness of the chosen definitions. Based on these, flow equations of an EM field are derived, which offer remarkable analogies with equations of fluid dynamics and thus suggest attempting some mechanistic interpretation. Doing this by strictly adhering to the details of classical theories, however, is found to lead to incompatibilities, but a consistent interpretation is feasible in the context of some alternative relativistic results that have been presented in recent years and have originally been suggested by basic issues concerning passivity and losslessness in one- and multidimensional nonlinear Kirchhoff circuits and related areas of digital signal processing. In the light of these findings, available experimental evidence and original theoretical deductions are reassessed and shown not to contradict the present results. Potential models for electrons (rotating EM field) and photons (localized planar field that offers a natural solution to the wave-particle duality) are obtained as rigorous solutions of Maxwell's equations, and possible consequences are discussed.