The Planck radiation law for the blackbody radiation spectrum is derived without the formalism of quantum theory. The hypotheses assume (a) the existence, at the absolute zero of temperature, of classical homogeneous fluctuating electromagnetic radiation with a Lorentz-invariant spectrum; (b) that classical electrodynamics holds for a dipole oscillator; (c) that a free particle in equilibrium with blackbody radiation has the classical mean kinetic energy $\frac{1}{2}\mathrm{kT}$ per degree of freedom. The Lorentz invariance of the spectrum of zero-temperature radiation is used to derive the zero-point electromagnetic energy-density spectrum, found to be linear in frequency, $\frac{1}{2}\hslash \omega$ per normal mode. The procedures based on classical theory employed by Einstein and Hopf, which were formerly regarded as giving a rigorous derivation of the Rayleigh-Jeans radiation law, are modified and corrected for electromagnetic zero-point energy to allow a rigorous derivation of the full blackbody spectrum from classical theory without any assumptions of discrete or discontinuous processes.

• Received 14 February 1969

DOI:https://doi.org/10.1103/PhysRev.182.1374