Thermal effects of acceleration for a classical dipole oscillator in classical electromagnetic zero-point radiation

In 1976 Unruh showed that a scalar quantum particle in a box accelerating through the vacuum of scalar quantum field theory responded as though it were in a thermal bath at temperature $T=\frac{\hslash a}{2\pi \mathrm{ck}}$. Here we show an analogous result within classical electromagnetic theory. A classical electric dipole oscillator accelerating through classical electromagnetic zero-point radiation responds just as would a dipole oscillator in an inertial frame in classical thermal radiation with Planck's spectrum at temperature $T=\frac{\hslash a}{2\pi \mathrm{ck}}$. In an earlier work it was shown that the electromagnetic field correlation functions for an observer accelerating through classical electromagnetic zero-point radiation correspond to a spectrum different from Planck's. The same spectrum is found in the quantum analysis of a vector field where the departure from Planckian form is assigned to the change in the number of normal modes associated with the event horizon of the accelerating observer. The present work shows that the relativistic radiation reaction for an accelerating classical charge contains a term which exactly compensates the departure of the electromagnetic spectrum from Planckian form so as to bring the oscillator's behavior into precise agreement with the usual Planckian thermal form.