2,767 research outputs found
Spacelike distance from discrete causal order
Any discrete approach to quantum gravity must provide some prescription as to
how to deduce continuum properties from the discrete substructure. In the
causal set approach it is straightforward to deduce timelike distances, but
surprisingly difficult to extract spacelike distances, because of the unique
combination of discreteness with local Lorentz invariance in that approach. We
propose a number of methods to overcome this difficulty, one of which
reproduces the spatial distance between two points in a finite region of
Minkowski space. We provide numerical evidence that this definition can be used
to define a `spatial nearest neighbor' relation on a causal set, and conjecture
that this can be exploited to define the length of `continuous curves' in
causal sets which are approximated by curved spacetime. This provides evidence
in support of the ``Hauptvermutung'' of causal sets.Comment: 32 pages, 16 figures, revtex4; journal versio
Codimension-2 surfaces and their Hilbert spaces: low-energy clues for holography from general covariance
We argue that the holographic principle may be hinted at already from
low-energy considerations, assuming diffeomorphism invariance, quantum
mechanics and Minkowski-like causality. We consider the states of finite
spacelike hypersurfaces in a diffeomorphism-invariant QFT. A low-energy
regularization is assumed. We note a natural dependence of the Hilbert space on
a codimension-2 boundary surface. The Hilbert product is defined dynamically,
in terms of transition amplitudes which are described by a path integral. We
show that a canonical basis is incompatible with these assumptions, which opens
the possibility for a smaller Hilbert-space dimension than canonically
expected. We argue further that this dimension may decrease with surface area
at constant volume, hinting at holographic area-proportionality. We draw
comparisons with other approaches and setups, and propose an interpretation for
the non-holographic space of graviton states at asymptotically-Minkowski null
infinity.Comment: 13 pages, 9 eps figures. Added Section VI, improved presentation.
Expanded and split the Introduction into two sections. Added Section VII.
Added reference
Stable Homology as an Indicator of Manifoldlikeness in Causal Set Theory
We present a computational tool that can be used to obtain the "spatial"
homology groups of a causal set. Localisation in the causal set is seeded by an
inextendible antichain, which is the analog of a spacelike hypersurface, and a
one parameter family of nerve simplicial complexes is constructed by
"thickening" this antichain. The associated homology groups can then be
calculated using existing homology software, and their behaviour studied as a
function of the thickening parameter. Earlier analytical work showed that for
an inextendible antichain in a causal set which can be approximated by a
globally hyperbolic spacetime region, there is a one parameter sub-family of
these simplicial complexes which are homological to the continuum, provided the
antichain satisfies certain conditions. Using causal sets that are approximated
by a set of 2d spacetimes our numerical analysis suggests that these conditions
are generically satisfied by inextendible antichains. In both 2d and 3d
simulations, as the thickening parameter is increased, the continuum homology
groups tend to appear as the first region in which the homology is constant, or
"stable" above the discreteness scale. Below this scale, the homology groups
fluctuate rapidly as a function of the thickening parameter. This provides a
necessary though not sufficient criterion to test for manifoldlikeness of a
causal set.Comment: Latex, 46 pages, 43 .eps figures, v2 numerous changes to content and
presentatio
A Bell Inequality Analog in Quantum Measure Theory
One obtains Bell's inequalities if one posits a hypothetical joint
probability distribution, or {\it measure}, whose marginals yield the
probabilities produced by the spin measurements in question. The existence of a
joint measure is in turn equivalent to a certain causality condition known as
``screening off''. We show that if one assumes, more generally, a joint {\it
quantal measure}, or ``decoherence functional'', one obtains instead an
analogous inequality weaker by a factor of . The proof of this
``Tsirel'son inequality'' is geometrical and rests on the possibility of
associating a Hilbert space to any strongly positive quantal measure. These
results lead both to a {\it question}: ``Does a joint measure follow from some
quantal analog of `screening off'?'', and to the {\it observation} that
non-contextual hidden variables are viable in histories-based quantum
mechanics, even if they are excluded classically.Comment: 38 pages, TeX. Several changes and added comments to bring out the
meaning more clearly. Minor rewording and extra acknowledgements, now closer
to published versio
Simulating causal collapse models
We present simulations of causal dynamical collapse models of field theories
on a 1+1 null lattice. We use our simulations to compare and contrast two
possible interpretations of the models, one in which the field values are real
and the other in which the state vector is real. We suggest that a procedure of
coarse graining and renormalising the fundamental field can overcome its
noisiness and argue that this coarse grained renormalised field will show
interesting structure if the state vector does on the coarse grained scale.Comment: 18 pages, 8 fugures, LaTeX, Reference added, discussion of
probability distribution of labellings correcte
Spatial Hypersurfaces in Causal Set Cosmology
Within the causal set approach to quantum gravity, a discrete analog of a
spacelike region is a set of unrelated elements, or an antichain. In the
continuum approximation of the theory, a moment-of-time hypersurface is well
represented by an inextendible antichain. We construct a richer structure
corresponding to a thickening of this antichain containing non-trivial
geometric and topological information. We find that covariant observables can
be associated with such thickened antichains and transitions between them, in
classical stochastic growth models of causal sets. This construction highlights
the difference between the covariant measure on causal set cosmology and the
standard sum-over-histories approach: the measure is assigned to completed
histories rather than to histories on a restricted spacetime region. The
resulting re-phrasing of the sum-over-histories may be fruitful in other
approaches to quantum gravity.Comment: Revtex, 12 pages, 2 figure
Time-Dependent Behavior of Linear Polarization in Unresolved Photospheres, With Applications for The Hanle Effect
Aims: This paper extends previous studies in modeling time varying linear
polarization due to axisymmetric magnetic fields in rotating stars. We use the
Hanle effect to predict variations in net line polarization, and use geometric
arguments to generalize these results to linear polarization due to other
mechanisms. Methods: Building on the work of Lopez Ariste et al., we use simple
analytic models of rotating stars that are symmetric except for an axisymmetric
magnetic field to predict the polarization lightcurve due to the Hanle effect.
We highlight the effects for the variable line polarization as a function of
viewing inclination and field axis obliquity. Finally, we use geometric
arguments to generalize our results to linear polarization from the weak
transverse Zeeman effect. Results: We derive analytic expressions to
demonstrate that the variable polarization lightcurve for an oblique magnetic
rotator is symmetric. This holds for any axisymmetric field distribution and
arbitrary viewing inclination to the rotation axis. Conclusions: For the
situation under consideration, the amplitude of the polarization variation is
set by the Hanle effect, but the shape of the variation in polarization with
phase depends largely on geometrical projection effects. Our work generalizes
the applicability of results described in Lopez Ariste et al., inasmuch as the
assumptions of a spherical star and an axisymmetric field are true, and
provides a strategy for separating the effects of perspective from the Hanle
effect itself for interpreting polarimetric lightcurves.Comment: 6 pages; 4 figures. Includes an extra figure found only in this
preprint versio
Measurements of Sunyaev-Zel'dovich Effect Scaling Relations for Clusters of Galaxies
We present new measurements of the Sunyaev-Zel'dovich (SZ) effect from
clusters of galaxies using the Sunyaev-Zel'dovich Infrared Experiment (SuZIE
II). We combine these new measurements with previous cluster observations with
the SuZIE instrument to form a sample of 15 clusters of galaxies. For this
sample we calculate the central Comptonization, y, and the integrated SZ flux
decrement, S, for each of our clusters. We find that the integrated SZ flux is
a more robust observable derived from our measurements than the central
Comptonization due to inadequacies in the spatial modelling of the
intra-cluster gas with a standard Beta model. This is highlighted by comparing
our central Comptonization results with values calculated from measurements
using the BIMA and OVRO interferometers. On average, the SuZIE calculated
central Comptonizations are approximately 60% higher in the cooling flow
clusters than the interferometric values, compared to only approximately 12%
higher in the non-cooling flow clusters. We believe this discrepancy to be in
large part due to the spatial modelling of the intra-cluster gas. From our
cluster sample we construct y-T and S-T scaling relations. The y-T scaling
relation is inconsistent with what we would expect for self-similar clusters;
however this result is questionable because of the large systematic uncertainty
in the central Comptonization. The S-T scaling relation has a slope and
redshift evolution consistent with what we expect for self-similar clusters
with a characteristic density that scales with the mean density of the
universe. We rule out zero redshift evolution of the S-T relation at 90%
confidence.Comment: Accepted to Astrophysical Journal. 52 pages, 14 tables, 7 figures
;replaced to match ApJ accepted versio
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