12,571 research outputs found
Blackbody Radiation and the Scaling Symmetry of Relativistic Classical Electron Theory with Classical Electromagnetic Zero-Point Radiation
It is pointed out that relativistic classical electron theory with classical
electromagnetic zero-point radiation has a scaling symmetry which is suitable
for understanding the equilibrium behavior of classical thermal radiation at a
spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical
electron theory, the masses of the particles are the only scale-giving
parameters associated with mechanics while the action-angle variables are scale
invariant. The theory thus separates the interaction of the action variables of
matter and radiation from the scale-giving parameters. Classical zero-point
radiation is invariant under scattering by the charged particles of
relativistic classical electron theory. The basic ideas of the matter
-radiation interaction are illustrated in a simple relativistic classical
electromagnetic example.Comment: 18 page
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
The Paradoxical Forces for the Classical Electromagnetic Lag Associated with the Aharonov-Bohm Phase Shift
The classical electromagnetic lag assocated with the Aharonov-Bohm phase
shift is obtained by using a Darwin-Lagrangian analysis similar to that given
by Coleman and Van Vleck to identify the puzzling forces of the Shockley-James
paradox. The classical forces cause changes in particle velocities and so
produce a relative lag leading to the same phase shift as predicted by Aharonov
and Bohm and observed in experiments. An experiment is proposed to test for
this lag aspect implied by the classical analysis but not present in the
currently-accepted quantum topological description of the phase shift.Comment: 8 pages, 3 figure
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
Study of basic bio-electrochemistry Sixth monthly progress report, 1-31 Aug. 1963
Contribution of hydrogen peroxide to electrode reaction in electrochemical cell by considering effect of catalyst on cell curren
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
Unitary Representations of Unitary Groups
In this paper we review and streamline some results of Kirillov, Olshanski
and Pickrell on unitary representations of the unitary group \U(\cH) of a
real, complex or quaternionic separable Hilbert space and the subgroup
\U_\infty(\cH), consisting of those unitary operators for which g - \1
is compact. The Kirillov--Olshanski theorem on the continuous unitary
representations of the identity component \U_\infty(\cH)_0 asserts that they
are direct sums of irreducible ones which can be realized in finite tensor
products of a suitable complex Hilbert space. This is proved and generalized to
inseparable spaces. These results are carried over to the full unitary group by
Pickrell's Theorem, asserting that the separable unitary representations of
\U(\cH), for a separable Hilbert space \cH, are uniquely determined by
their restriction to \U_\infty(\cH)_0. For the classical infinite rank
symmetric pairs of non-unitary type, such as (\GL(\cH),\U(\cH)), we
also show that all separable unitary representations are trivial.Comment: 42 page
L\'evy-like behavior in deterministic models of intelligent agents exploring heterogeneous environments
Many studies on animal and human movement patterns report the existence of
scaling laws and power-law distributions. Whereas a number of random walk
models have been proposed to explain observations, in many situations
individuals actually rely on mental maps to explore strongly heterogeneous
environments. In this work we study a model of a deterministic walker, visiting
sites randomly distributed on the plane and with varying weight or
attractiveness. At each step, the walker minimizes a function that depends on
the distance to the next unvisited target (cost) and on the weight of that
target (gain). If the target weight distribution is a power-law, , in some range of the exponent , the foraging medium induces
movements that are similar to L\'evy flights and are characterized by
non-trivial exponents. We explore variations of the choice rule in order to
test the robustness of the model and argue that the addition of noise has a
limited impact on the dynamics in strongly disordered media.Comment: 15 pages, 7 figures. One section adde
Derivation of the Planck Spectrum for Relativistic Classical Scalar Radiation from Thermal Equilibrium in an Accelerating Frame
The Planck spectrum of thermal scalar radiation is derived suggestively
within classical physics by the use of an accelerating coordinate frame. The
derivation has an analogue in Boltzmann's derivation of the Maxwell velocity
distribution for thermal particle velocities by considering the thermal
equilibrium of noninteracting particles in a uniform gravitational field. For
the case of radiation, the gravitational field is provided by the acceleration
of a Rindler frame through Minkowski spacetime. Classical zero-point radiation
and relativistic physics enter in an essential way in the derivation which is
based upon the behavior of free radiation fields and the assumption that the
field correlation functions contain but a single correlation time in thermal
equilibrium. The work has connections with the thermal effects of acceleration
found in relativistic quantum field theory.Comment: 23 page
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