  Regardless of the unspecific notions of photons as light complexes, radiation
bundles or wave packets, the radiation from a single state transition is at
most a single continuous wave train that starts and ends with the transition.
The radiation equilibrium spectrum must be the superposition sum of the spectra
of such wave trains. A classical equipartition of wave trains cannot diverge
since they would be finite in number, whereas standing wave modes are by
definition infinite, which had doomed Rayleigh's theory, and concern only the
total radiation. Wave trains are the microscopic entities of radiation
interacting with matter, that correspond to molecules in kinetic theory. Their
quantization came from matter transitions in Einstein's 1917 derivation of
Planck's law. The spectral scatter of wave trains by Doppler shifts, which
cause the wavelength displacements in Wien's law used for the frequency
dependence in Einstein's derivation, is shown to yield the shape of the Planck
spectrum. A Lorentz transform property of Doppler shifts discovered by Einstein
is further shown equivalently necessary and sufficient to have corrected
Rayleigh's theory.
