Thermal effects of acceleration for a spatially extended electromagnetic system in classical electromagnetic zero-point radiation: Transversely positioned classical oscillators.

Abstract

Thermal properties of acceleration have been investigated in the past for both quantum-mechanical and classical pointlike systems. Here, for the first time, a spatially extended electromagnetic system is examined. This system consists of two spatially separated classical dipole simple harmonic oscillators that are uniformly accelerated through classical electromagnetic zero-point radiation and that interact with each other through emitted electromagnetic radiation. The two oscillators are assumed to be oriented such that their centers lie in a plane perpendicular to the direction of acceleration; no restrictions are placed upon the direction of oscillations. The behavior of this system is analyzed under the conditions of a small-oscillator assumption, the narrow-linewidth approximation, a small-laboratory approximation, and the unretarded van der Waals condition. The statistical properties investigated for this accelerated spatially extended system are found to agree with the corresponding statistical properties of a pair of similarly constructed, but unaccelerated oscillators that are bathed in a classical electromagnetic Planckian radiation spectrum characterized by the Unruh-Davies temperature of T=\ensuremath{\Elzxh}a/2\ensuremath{\pi}ck. The properties examined include the van der Waals force acting between the two oscillators and the correlation functions of the oscillators' positions and their time derivatives. During the course of obtaining these properties, a set of exact relationships are deduced involving the electromagnetic fields of a uniformly accelerated electric dipole and the correlation functions of classical electromagnetic zero-point fields, evaluated along relativistic hyperbolic trajectories.