Random electrodynamics: The theory of classical electrodynamics with classical electromagnetic zero-point radiation

The theory of classical electrodynamics with classical electromagnetic zero-point radiation is outlined here under the title random electrodynamics. The work represents a reanalysis of the bounds of validity of classical electron theory which should sharpen the understanding of the connections and dinstinctions between classical and quantum theories. The new theory of random electrodynamics is a classical electron theory involving Newton's equations for particle motion due to the Lorentz force, and Maxwell's equations for the electromagnetic fields with point particles as sources. However, the theory departs from the classical electron theory of Lorentz in that it adopts a new boundary condition on Maxwell's equations. It is assumed that the homogeneous boundary condition involves random classical electromagnetic radiation with a Lorentz-invariant spectrum, classical electromagnetic zero-point radiation. The scale of the spectrum of random radiation is set by Planck's constant $\hslash$. In the limit $\hslash \to 0$, the theory of random electrodynamics becomes Lorentz's theory of electrons. Thus, random electrodynamics stands between two well-known theories—traditional classical electron theory with $\hslash =0\mathrm{}$ on the one hand and quantum electrodynamics with its noncommuting operators on the other. The paper discusses the role of boundary conditions in classical electrodynamics, the motivation for choosing a new boundary condition involving classical zero-point radiation, and the assumed random character of the radiation. Also, the implications of the theory of random electrodynamics are summarized, including the detection of zero-point radiation, the calculation of van der Waals forces, and the change of ideas in statistical thermodynamics. In these cases the summary accounts refer to published calculations which yield results in agreement with experiment. The implications of random electrodynamics for atomic structure, atomic spectra, and particle-interference effects are discussed on an order-of-magnitude or heuristic level. Some detailed mathematical connections and some merely heuristic connections are noted between random electrodynamics and quantum theory.