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Regardless of the unspecific notions of photons as light complexes, radiationbundles or wave packets, the radiation from a single state transition is atmost a single continuous wave train that starts and ends with the transition.The radiation equilibrium spectrum must be the superposition sum of the spectraof such wave trains. A classical equipartition of wave trains cannot divergesince they would be finite in number, whereas standing wave modes are bydefinition infinite, which had doomed Rayleigh's theory, and concern only thetotal radiation. Wave trains are the microscopic entities of radiationinteracting with matter, that correspond to molecules in kinetic theory. Theirquantization came from matter transitions in Einstein's 1917 derivation ofPlanck's law. The spectral scatter of wave trains by Doppler shifts, whichcause the wavelength displacements in Wien's law used for the frequencydependence in Einstein's derivation, is shown to yield the shape of the Planckspectrum. A Lorentz transform property of Doppler shifts discovered by Einsteinis further shown equivalently necessary and sufficient to have correctedRayleigh's theory.

The equilibrium classical scatter spectrum of waves