325 research outputs found
Teachers' beliefs about knowledge and learning: A Singapore perspective
The purpose of this study is to explore the complex nature of Singapore teachers' beliefs about knowledge and learning and how these beliefs influence pedagogical practices in their classes. This paper presents findings from a large-scale survey study with 1806 teachers in Singapore. Data revealed that while teachers' beliefs about pedagogies, knowledge and learning were largely consistent, they also believed and practiced both teacher-centered and learner-centered pedagogies and assessment methods
Hawking Spectrum and High Frequency Dispersion
We study the spectrum of created particles in two-dimensional black hole
geometries for a linear, hermitian scalar field satisfying a Lorentz
non-invariant field equation with higher spatial derivative terms that are
suppressed by powers of a fundamental momentum scale . The preferred frame
is the ``free-fall frame" of the black hole. This model is a variation of
Unruh's sonic black hole analogy. We find that there are two qualitatively
different types of particle production in this model: a thermal Hawking flux
generated by ``mode conversion" at the black hole horizon, and a non-thermal
spectrum generated via scattering off the background into negative free-fall
frequency modes. This second process has nothing to do with black holes and
does not occur for the ordinary wave equation because such modes do not
propagate outside the horizon with positive Killing frequency. The horizon
component of the radiation is astonishingly close to a perfect thermal
spectrum: for the smoothest metric studied, with Hawking temperature
, agreement is of order at frequency
, and agreement to order persists out to
where the thermal number flux is ). The flux
from scattering dominates at large and becomes many orders of
magnitude larger than the horizon component for metrics with a ``kink", i.e. a
region of high curvature localized on a static worldline outside the horizon.
This non-thermal flux amounts to roughly 10\% of the total luminosity for the
kinkier metrics considered. The flux exhibits oscillations as a function of
frequency which can be explained by interference between the various
contributions to the flux.Comment: 32 pages, plain latex, 16 figures included using psfi
The thermodynamic evolution of the cosmological event horizon
By manipulating the integral expression for the proper radius of the
cosmological event horizon (CEH) in a Friedmann-Robertson-Walker (FRW)
universe, we obtain an analytical expression for the change \dd R_e in
response to a uniform fluctuation \dd\rho in the average cosmic background
density . We stipulate that the fluctuation arises within a vanishing
interval of proper time, during which the CEH is approximately stationary, and
evolves subsequently such that \dd\rho/\rho is constant. The respective
variations 2\pi R_e \dd R_e and \dd E_e in the horizon entropy and
enclosed energy should be therefore related through the cosmological
Clausius relation. In that manner we find that the temperature of the CEH
at an arbitrary time in a flat FRW universe is , which recovers
asymptotically the usual static de Sitter temperature. Furthermore, it is
proven that during radiation-dominance and in late times the CEH conforms to
the fully dynamical First Law T_e \drv S_e = P\drv V_e - \drv E_e, where
is the enclosed volume and is the average cosmic pressure.Comment: 6 page
Precision neutron interferometric measurements of the n-p, n-d, and n-3He zero-energy coherent neutron scattering amplitudes
We have performed high precision measurements of the zero-energy neutron
scattering amplitudes of gas phase molecular hydrogen, deuterium, and He
using neutron interferometry. We find
fm\cite{Schoen03},
fm\cite{Black03,Schoen03}, and
fm\cite{Huffman04}. When combined with the previous world data, properly
corrected for small multiple scattering, radiative corrections, and local field
effects from the theory of neutron optics and combined by the prescriptions of
the Particle Data Group, the zero-energy scattering amplitudes are:
fm, fm, and fm. The precision of
these measurements is now high enough to severely constrain NN few-body models.
The n-d and n-He coherent neutron scattering amplitudes are both now in
disagreement with the best current theories. The new values can be used as
input for precision calculations of few body processes. This precision data is
sensitive to small effects such as nuclear three-body forces, charge-symmetry
breaking in the strong interaction, and residual electromagnetic effects not
yet fully included in current models.Comment: 6 pages, 4 figures, submitted to Physica B as part of the Festschrift
honouring Samuel A. Werner at the International Conference on Neutron
Scattering 200
Phenomenological description of quantum gravity inspired modified classical electrodynamics
We discuss a large class of phenomenological models incorporating quantum
gravity motivated corrections to electrodynamics. The framework is that of
electrodynamics in a birefringent and dispersive medium with non-local
constitutive relations, which are considered up to second order in the inverse
of the energy characterizing the quantum gravity scale. The energy-momentum
tensor, Green functions and frequency dependent refraction indices are
obtained, leading to departures from standard physics. The effective character
of the theory is also emphasized by introducing a frequency cutoff. The
analysis of its effects upon the standard notion of causality is performed,
showing that in the radiation regime the expected corrections get further
suppressed by highly oscillating terms, thus forbiding causality violations to
show up in the corresponding observational effects.Comment: 14 pages, to be published in Obregon Festschrift 2006, Gen. Rel. and
Gra
Unitarity of Quantum Theory and Closed Time-Like Curves
Interacting quantum fields on spacetimes containing regions of closed
timelike curves (CTCs) are subject to a non-unitary evolution . Recently, a
prescription has been proposed, which restores unitarity of the evolution by
modifying the inner product on the final Hilbert space. We give a rigorous
description of this proposal and note an operational problem which arises when
one considers the composition of two or more non-unitary evolutions. We propose
an alternative method by which unitarity of the evolution may be regained, by
extending to a unitary evolution on a larger (possibly indefinite) inner
product space. The proposal removes the ambiguity noted by Jacobson in
assigning expectation values to observables localised in regions spacelike
separated from the CTC region. We comment on the physical significance of the
possible indefiniteness of the inner product introduced in our proposal.Comment: 13 pages, LaTeX. Final revised paper to be published in Phys Rev D.
Some changes are made to expand our discussion of Anderson's Proposal for
restoring unitarit
On the Origin of the Outgoing Black Hole Modes
The question of how to account for the outgoing black hole modes without
drawing upon a transplanckian reservoir at the horizon is addressed. It is
argued that the outgoing modes must arise via conversion from ingoing modes. It
is further argued that the back-reaction must be included to avoid the
conclusion that particle creation cannot occur in a strictly stationary
background. The process of ``mode conversion" is known in plasma physics by
this name and in condensed matter physics as ``Andreev reflection" or ``branch
conversion". It is illustrated here in a linear Lorentz non-invariant model
introduced by Unruh. The role of interactions and a physical short distance
cutoff is then examined in the sonic black hole formed with Helium-II.Comment: 12 pages, plain latex, 2 figures included using psfig; Analogy to
``Andreev reflection" in superfluid systems noted, references and
acknowledgment added, format changed to shorten tex
Variations on the Seventh Route to Relativity
As motivated in the full abstract, this paper further investigates Barbour,
Foster and O Murchadha (BFO)'s 3-space formulation of GR. This is based on
best-matched lapse-eliminated actions and gives rise to several theories
including GR and a conformal gravity theory. We study the simplicity postulates
assumed in BFO's work and how to weaken them, so as to permit the inclusion of
the full set of matter fields known to occur in nature.
We study the configuration spaces of gravity-matter systems upon which BFO's
formulation leans. In further developments the lapse-eliminated actions used by
BFO become impractical and require generalization. We circumvent many of these
problems by the equivalent use of lapse-uneliminated actions, which furthermore
permit us to interpret BFO's formulation within Kuchar's generally covariant
hypersurface framework. This viewpoint provides alternative reasons to BFO's as
to why the inclusion of bosonic fields in the 3-space approach gives rise to
minimally-coupled scalar fields, electromagnetism and Yang--Mills theory. This
viewpoint also permits us to quickly exhibit further GR-matter theories
admitted by the 3-space formulation. In particular, we show that the spin-1/2
fermions of the theories of Dirac, Maxwell--Dirac and Yang--Mills--Dirac, all
coupled to GR, are admitted by the generalized 3-space formulation we present.
Thus all the known fundamental matter fields can be accommodated. This
corresponds to being able to pick actions for all these theories which have
less kinematics than suggested by the generally covariant hypersurface
framework. For all these theories, Wheeler's thin sandwich conjecture may be
posed, rendering them timeless in Barbour's sense.Comment: Revtex version; Journal-ref adde
Corrections to Hawking-like Radiation for a Friedmann-Robertson-Walker Universe
Recently, a Hamilton-Jacobi method beyond semiclassical approximation in
black hole physics was developed by \emph{Banerjee} and
\emph{Majhi}\cite{beyond0}. In this paper, we generalize their analysis of
black holes to the case of Friedmann-Robertson-Walker (FRW) universe. It is
shown that all the higher order quantum corrections in the single particle
action are proportional to the usual semiclassical contribution. The
corrections to the Hawking-like temperature and entropy of apparent horizon for
FRW universe are also obtained. In the corrected entropy, the area law involves
logarithmic area correction together with the standard inverse power of area
term.Comment: 10 pages, no figures, comments are welcome; v2: references added and
some typoes corrected, to appear in Euro.Phys.J.C; v3:a defect corrected. We
thank Dr.Elias Vagenas for pointing out a defect of our pape
Linking the trans-Planckian and the information loss problems in black hole physics
The trans-Planckian and information loss problems are usually discussed in
the literature as separate issues concerning the nature of Hawking radiation.
Here we instead argue that they are intimately linked, and can be understood as
"two sides of the same coin" once it is accepted that general relativity is an
effective field theory.Comment: 10 pages, 2 figures. Replaced with the version to be published in
General Relativity and Gravitatio
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