Derivation of the blackbody radiation spectrum from the equivalence principle in classical physics with classical electromagnetic zero-point radiation

Abstract

A derivation of Planck's spectrum including zero-point radiation is given within classical physics from recent results involving the thermal effects of acceleration through classical electromagnetic zero-point radiation. A harmonic electric-dipole oscillator undergoing a uniform acceleration $\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}$ through classical electromagnetic zero-point radiation responds as would the same oscillator in an inertial frame when not in zero-point radiation but in a different spectrum of random classical radiation. Since the equivalence principle tells us that the oscillator supported in a gravitational field $\stackrel{\ensuremath{\rightarrow}}{\mathrm{g}}=\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{\mathrm{a}}$ will respond in the same way, we see that in a gravitational field we can construct a perpetual-motion machine based on this different spectrum unless the different spectrum corresponds to that of thermal equilibrium at a finite temperature. Therefore, assuming the absence of perpetual-motion machines of the first kind in a gravitational field, we conclude that the response of an oscillator accelerating through classical zero-point radiation must be that of a thermal system. This then determines the blackbody radiation spectrum in an inertial frame which turns out to be exactly Planck's spectrum including zero-point radiation.