Conjectured derivation of the Planck radiation spectrum from Casimir energies

Numerical calculation suggests that there is an intimate connection between the Planck radiation spectrum and Casimir energies. The Planck spectrum including zero-point radiation seems to satisfy a natural maximum-uniformity principle for Casimir energies whereas alternative choices of spectra do not. Specifically, we consider a set of identical conducting-walled boxes at the same temperature, but each has a conducting partition placed at a different location in the box, so that across the collection of boxes the partitions are uniformly spaced across the volume; then the Planck spectrum corresponds to that spectrum of random radiation satisfying the Wien displacement theorem (having constant energy kBT per normal mode at low frequencies and zero-point energy (1/2) h-bar ω per normal mode at high frequencies) which gives a monotonic change in Casimir energies with partition position and maximum uniformity for the Casimir energies across the collection of boxes. For simplicity, the analysis is presented for waves in one space dimension