Derivation of the Blackbody Radiation Spectrum from a Natural Maximum-Entropy Principle Involving Casimir Energies and Zero-Point Radiation

摘要

By numerical calculation, the Planck spectrum with zero-point radiation isshown to satisfy a natural maximum-entropy principle whereas alternativechoices of spectra do not. Specifically, if we consider a set ofconducting-walled boxes, each with a partition placed at a different locationin the box, so that across the collection of boxes the partitions are uniformlyspaced across the volume, then the Planck spectrum correspond to that spectrumof random radiation (having constant energy kT per normal mode at lowfrequencies and zero-point energy (1/2)hw per normal mode at high frequencies)which gives maximum uniformity across the collection of boxes for the radiationenergy per box. The analysis involves Casimir energies and zero-point radiationwhich do not usually appear in thermodynamic analyses. For simplicity, theanalysis is presented for waves in one space dimension.