Thermal effects of acceleration through random classical radiation

The thermal effects of acceleration found by Davies and Unruh within quantum field theory are shown to exist within random classical radiation. The two-field correlation functions for random classical radiation are used as the basis for investigating the spectrum of radiation observed at an accelerating point detector. An observer with proper acceleration $a$ relative to the Lorentz-invariant spectrum of random classical scalar zero-point radiation finds a spectrum identical with that given by Planck's law for scalar thermal radiation where the temperature is related to the acceleration by $T=\frac{\hslash a}{2\pi \mathrm{ck}}$. An observer with proper acceleration $a$ relative to the Lorentz-invariant spectrum of random classical electromagnetic radiation finds a stationary radiation spectrum which is not Planck's spectrum. Rather, the observed spectrum in the electromagnetic case contains a term agreeing with Planck's electromagnetic spectrum plus an additional term. This spectrum for the electromagnetic case appears in the work of Candelas and Deutsch for an accelerating mirror and corresponds to thermal radiation in the non-Minkowskian space-time of the accelerating observer. The calculations reported here involve an entirely classical point of view, but are shown to have immediate connections with quantum field theory.