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

By numerical calculation, the Planck spectrum with zero-point radiation is shown to satisfy a natural maximum-entropy principle whereas alternative choices of spectra do not. Specifically, if we consider a set of conducting-walled boxes, each with a 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 correspond to that spectrum of random radiation (having constant energy kT per normal mode at low frequencies and zero-point energy (1/2)hw per normal mode at high frequencies) which gives maximum uniformity across the collection of boxes for the radiation energy per box. The analysis involves Casimir energies and zero-point radiation which do not usually appear in thermodynamic analyses. For simplicity, the analysis is presented for waves in one space dimension.Comment: 11 page

Scaling Symmetries of Scatterers of Classical Zero-Point Radiation

Classical radiation equilibrium (the blackbody problem) is investigated by the use of an analogy. Scaling symmetries are noted for systems of classical charged particles moving in circular orbits in central potentials V(r)=-k/r^n when the particles are held in uniform circular motion against radiative collapse by a circularly polarized incident plane wave. Only in the case of a Coulomb potential n=1 with fixed charge e is there a unique scale-invariant spectrum of radiation versus frequency (analogous to zero-point radiation) obtained from the stable scattering arrangement. These results suggest that non-electromagnetic potentials are not appropriate for discussions of classical radiation equilibrium.Comment: 13 page

The Blackbody Radiation Spectrum Follows from Zero-Point Radiation and the Structure of Relativistic Spacetime in Classical Physics

The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell's equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect it to non-zero-temperature; time-dilating conformal transformations carry the Lorentz-invariant zero-point radiation spectrum into zero-point radiation and carry the thermal radiation spectrum at non-zero temperature into thermal radiation at a different non-zero-temperature. However, in a non-inertial frame, a time-dilating conformal transformation carries classical zero-point radiation into thermal radiation at a finite non-zero-temperature. By taking the no-acceleration limit, one can obtain the Planck radiation spectrum for blackbody radiation in an inertial frame from the thermal radiation spectrum in an accelerating frame. Here this connection between zero-point radiation and thermal radiation is illustrated for a scalar radiation field in a Rindler frame undergoing relativistic uniform proper acceleration through flat spacetime in two spacetime dimensions. The analysis indicates that the Planck radiation spectrum for thermal radiation follows from zero-point radiation and the structure of relativistic spacetime in classical physics.Comment: 21 page

Acid catalyzed reactions of alpha and beta styryl azides

Acid degradation of alpha and beta styryl azide

The formation of 3,6-diphenylpyridazine and 2,5-diphenylpyrrole from alpha-styryl azide

Formation of 3,6-diphenylpyridazine and 2,5- diphenylpyrrole from alpha-styryl azid

Damming Grand Canyon: The 1923 USGS Colorado River Expedition

In 1923, America paid close attention, via special radio broadcasts, newspaper headlines, and cover stories in popular magazines, as a government party descended the Colorado to survey Grand Canyon. Fifty years after John Wesley Powell\u27s journey, the canyon still had an aura of mystery and extreme danger. At one point, the party was thought lost in a flood. Something important besides adventure was going on. Led by Claude Birdseye and including colorful characters such as early river-runner Emery Kolb, popular writer Lewis Freeman, and hydraulic engineer Eugene La Rue, the expedition not only made the first accurate survey of the river gorge but sought to decide the canyon\u27s fate. The primary goal was to determine the best places to dam the Grand. With Boulder Dam not yet built, the USGS, especially La Rue, contested with the Bureau of Reclamation over how best to develop the Colorado River. The survey party played a major role in what was known and thought about Grand Canyon. The authors weave a narrative from the party\u27s firsthand accounts and frame it with a thorough history of water politics and development and the Colorado River. The recommended dams were not built, but the survey both provided base data that stood the test of time and helped define Grand Canyon in the popular imagination.https://digitalcommons.usu.edu/usupress_pubs/1160/thumbnail.jp