Understanding zero-point energy in the context of classical electromagnetism

Abstract

Today’s textbooks of electromagnetism give the particular solution to Maxwell’s equations involving the integral over the charge and current sources at retarded times. However, the texts fail to emphasise that the choice of the incoming-wave boundary conditions corresponding to solutions of the homogeneous Maxwell equations must be made based upon experiment. Here we discuss the role of these incoming-wave boundary conditions for an experimenter with a hypothetical charged harmonic oscillator as his equipment. We describe the observations of the experimenter when located near a radio station or immersed in thermal radiation at temperature T. The classical physicists at the end of the 19th century chose the incoming-wave boundary conditions for the homogeneous Maxwell equations based upon the experimental observations of Lummer and Pringsheim which measured only the thermal radiation which exceeded the random radiation surrounding their measuring equipment; the physicists concluded that they could take the homogeneous solutions to vanish at zero temperature. Today at the beginning of the 21st century, classical physicists must choose the incoming-wave boundary conditions for the homogeneous Maxell equations to correspond to the full radiation spectrum revealed by the recent Casimir force measurements which detect all the radiation surrounding conducting parallel plates, including the radiation absorbed and emitted by the plates themselves. The random classical radiation spectrum revealed by the Casimir force measurements includes electromagnetic zero-point radiation, which is missing from the spectrum measured by Lummer and Pringsheim, and which cannot be eliminated by going to zero temperature. This zero-point radiation will lead to zero-point energy for all systems which have electromagnetic interactions. Thus the choice of the incoming-wave boundary conditions on the homogeneous Maxwell equations is intimately related to the ideas of zero-point energy and non-radiating ground states which are introduced in classes of modern physics.