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

Adaptive optics program update at TMT

The TMT first light AO facility consists of the Narrow Field Infra-Red AO System (NFIRAOS), the associated Laser Guide Star Facility (LGSF) and the AO Executive Software (AOESW). Design, fabrication and prototyping activities of the TMT first light AO systems and their components have significantly ramped up in Canada, China, France, and in the US. NFIRAOS is an order 60 x 60 laser guide star (LGS) multi-conjugate AO (MCAO) system, which provides uniform, diffraction-limited performance in the J, H, and K bands over 34 x 34 arc sec fields with 50 per cent sky coverage at the galactic pole, as required to support the TMT science cases. NFIRAOS includes two deformable mirrors, six laser guide star wavefront sensors, one high order Pyramid WFS for natural guide star AO, and up to three low-order, IR, natural guide star on-instrument wavefront sensors (OIWFS) and four on-detector guide windows (ODGW) within each client instrument. The first light LGSF system includes six sodium lasers to generate the NFIRAOS laser guide stars. In this paper, we will provide an update on the progress in designing, prototyping, fabricating and modeling the TMT first light AO systems and their AO components over the last two years. TMT is continuing with detailed AO modeling to support the design and development of the first light AO systems and components. Major modeling topics studied during the last two years include further studies in the area of pyramid wavefront sensing, high precision astrometry, PSF reconstruction for LGS MCAO, LGSF wavefront error budget and sophisticated low order mode temporal filtering

Hydrodynamic reductions of the heavenly equation

We demonstrate that Pleba\'nski's first heavenly equation decouples in infinitely many ways into a triple of commuting (1+1)-dimensional systems of hydrodynamic type which satisfy the Egorov property. Solving these systems by the generalized hodograph method, one can construct exact solutions of the heavenly equation parametrized by arbitrary functions of a single variable. We discuss explicit examples of hydrodynamic reductions associated with the equations of one-dimensional nonlinear elasticity, linearly degenerate systems and the equations of associativity.Comment: 14 page

Darwin-Lagrangian Analysis for the Interaction of a Point Charge and a Magnet: Considerations Related to the Controversy Regarding the Aharonov-Bohm and Aharonov-Casher Phase Shifts

The classical electromagnetic interaction of a point charge and a magnet is discussed by first calculating the interaction of point charge with a simple model magnetic moment and then suggesting a multiparticle limit. The Darwin Lagrangian is used to analyze the electromagnetic behavior of the model magnetic moment (composed of two oppositely charged particles of different mass in an initially circular orbit) interacting with a passing point charge. The changing mangetic moment is found to put a force back on a passing charge; this force is of order 1/c^2 and depends upon the magnitude of the magnetic moment. It is suggested that in the limit of a multiparticle magnetic toroid, the electric fields of the passing charge are screened out of the body of the magnet while the magnetic fields penetrate into the magnet. This is consistent with our understanding of the penetration of electromagnetic velocity fields into ohmic conductors. Conservation laws are discussed. The work corresponds to a classical electromagnetic analysis of the interaction which is basic to understanding the controversy over the Aharonov-Bohm and Aharonov-Casher phase shifts and represents a refutation of the suggestions of Aharonov, Pearle, and Vaidman.Comment: 33 page

Some Heuristic Semiclassical Derivations of the Planck Length, the Hawking Effect and the Unruh Effect

The formulae for Planck length, Hawking temperature and Unruh-Davies temperature are derived by using only laws of classical physics together with the Heisenberg principle. Besides, it is shown how the Hawking relation can be deduced from the Unruh relation by means of the principle of equivalence; the deep link between Hawking effect and Unruh effect is in this way clarified.Comment: LaTex file, 6 pages, no figure

American Legal Education: An Agenda for Research and Reform

Reprinted in American Legal Education: An Agenda for Research and Reform, Barry B. Boyer & Roger C. Cramton (American Bar Foundation 1974)

American Legal Education: an Agenda for Research and Reform

Reprinted in American Legal Education: An Agenda for Research and Reform, Barry B. Boyer & Roger C. Cramton (American Bar Foundation 1974)