Correlation functions for homogeneous, isotropic random classical electromagnetic radiation and the electromagnetic fields of a fluctuating classical electric dipole.

Abstract

The two-point field correlation functions for homogeneous and isotropic random (Gaussian) classical electromagnetic radiation are shown to be related to the electromagnetic fields of a fluctuating electric dipole. The relationships derived between these two quantities are useful in calculations involving classical electric dipole oscillators bathed in classical electromagnetic radiation. Using these relationships, the van der Waals force is evaluated for a harmonic dipole oscillator that is a member of an arbitrary configuration of N oscillators, all of which are bathed in thermal plus zero-point classical electromagnetic radiation. Also, the expectation value of the Poynting vector is shown to be unchanged from its null value when a classical harmonic dipole oscillator is included within a classical electromagnetic isotropic and homogeneous random radiation field. A sketch is given as to how these calculations may be carried over to the case of a system of harmonic dipole oscillators uniformly accelerating through classical electromagnetic zero-point radiation. What enables these calculations to be extended to the situation of acceleration through zero-point radiation is a recent finding that the two-point field correlation functions, evaluated along trajectories described by uniform acceleration through classical electromagnetic zero-point radiation, are related to the electromagnetic fields of a uniformly accelerating electric dipole.