12,961 research outputs found
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
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
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
A spacetime characterization of the Kerr metric
We obtain a characterization of the Kerr metric among stationary,
asymptotically flat, vacuum spacetimes, which extends the characterization in
terms of the Simon tensor (defined only in the manifold of trajectories) to the
whole spacetime. More precisely, we define a three index tensor on any
spacetime with a Killing field, which vanishes identically for Kerr and which
coincides in the strictly stationary region with the Simon tensor when
projected down into the manifold of trajectories. We prove that a stationary
asymptotically flat vacuum spacetime with vanishing spacetime Simon tensor is
locally isometric to Kerr. A geometrical interpretation of this
characterization in terms of the Weyl tensor is also given. Namely, a
stationary, asymptotically flat vacuum spacetime such that each principal null
direction of the Killing form is a repeated principal null direction of the
Weyl tensor is locally isometric to Kerr.Comment: 23 pages, No figures, LaTeX, to appear in Classical and Quantum
Gravit
On the distribution of estimators of diffusion constants for Brownian motion
We discuss the distribution of various estimators for extracting the
diffusion constant of single Brownian trajectories obtained by fitting the
squared displacement of the trajectory. The analysis of the problem can be
framed in terms of quadratic functionals of Brownian motion that correspond to
the Euclidean path integral for simple Harmonic oscillators with time dependent
frequencies. Explicit analytical results are given for the distribution of the
diffusion constant estimator in a number of cases and our results are confirmed
by numerical simulations.Comment: 14 pages, 5 figure
Contact spheres and hyperk\"ahler geometry
A taut contact sphere on a 3-manifold is a linear 2-sphere of contact forms,
all defining the same volume form. In the present paper we completely determine
the moduli of taut contact spheres on compact left-quotients of SU(2) (the only
closed manifolds admitting such structures). We also show that the moduli space
of taut contact spheres embeds into the moduli space of taut contact circles.
This moduli problem leads to a new viewpoint on the Gibbons-Hawking ansatz in
hyperkahler geometry. The classification of taut contact spheres on closed
3-manifolds includes the known classification of 3-Sasakian 3-manifolds, but
the local Riemannian geometry of contact spheres is much richer. We construct
two examples of taut contact spheres on open subsets of 3-space with nontrivial
local geometry; one from the Helmholtz equation on the 2-sphere, and one from
the Gibbons-Hawking ansatz. We address the Bernstein problem whether such
examples can give rise to complete metrics.Comment: 29 pages, v2: Large parts have been rewritten; previous Section 6 has
been removed; new Section 5.2 on the Gibbons-Hawking ansatz; new Sections 6
and
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