8,717 research outputs found
Cosmography: Cosmology without the Einstein equations
How much of modern cosmology is really cosmography? How much of modern
cosmology is independent of the Einstein equations? (Independent of the
Friedmann equations?) These questions are becoming increasingly germane -- as
the models cosmologists use for the stress-energy content of the universe
become increasingly baroque, it behoves us to step back a little and carefully
disentangle cosmological kinematics from cosmological dynamics. The use of
basic symmetry principles (such as the cosmological principle) permits us to do
a considerable amount, without ever having to address the vexatious issues of
just how much "dark energy", "dark matter", "quintessence", and/or "phantom
matter" is needed in order to satisfy the Einstein equations. This is the
sub-sector of cosmology that Weinberg refers to as "cosmography", and in this
article I will explore the extent to which cosmography is sufficient for
analyzing the Hubble law and so describing many of the features of the universe
around us.Comment: 7 pages; uses iopart.cls setstack.sty. Based on a talk presented at
ACRGR4, the 4th Australasian Conference on General Relativity and
Gravitation, Monash University, Melbourne, January 2004. To appear in the
proceedings, in General Relativity and Gravitatio
Modelling Planck-scale Lorentz violation via analogue models
Astrophysical tests of Planck-suppressed Lorentz violations had been
extensively studied in recent years and very stringent constraints have been
obtained within the framework of effective field theory. There are however
still some unresolved theoretical issues, in particular regarding the so called
"naturalness problem" - which arises when postulating that Planck-suppressed
Lorentz violations arise only from operators with mass dimension greater than
four in the Lagrangian. In the work presented here we shall try to address this
problem by looking at a condensed-matter analogue of the Lorentz violations
considered in quantum gravity phenomenology. Specifically, we investigate the
class of two-component BECs subject to laser-induced transitions between the
two components, and we show that this model is an example for Lorentz
invariance violation due to ultraviolet physics. We shall show that such a
model can be considered to be an explicit example high-energy Lorentz
violations where the ``naturalness problem'' does not arise.Comment: Talk given at the Fourth Meeting on Constrained Dynamics and Quantum
Gravity (QG05), Cala Gonone (Sardinia, Italy) September 12-16, 200
Theft and Deterrence
We report results from economic experiments of decisions that are best described as petty larceny, with high school and college students who can anonymously steal real money from each other. Our design allows exogenous variation in the rewards of crime, and the penalty and probability of detection. We find that the probability of stealing is increasing in the amount of money that can be stolen, and that it is decreasing in the probability of getting caught and in the penalty for getting caught. Furthermore, the impact of the certainty of getting caught is larger when the penalty is bigger, and the impact of the penalty is bigger when the probability of getting caught is larger.crime, punishment, incentives, deterrence, juvenile, arrest, risk, larceny
Hawking radiation without black hole entropy
In this Letter I point out that Hawking radiation is a purely kinematic
effect that is generic to Lorentzian geometries. Hawking radiation arises for
any test field on any Lorentzian geometry containing an event horizon
regardless of whether or not the Lorentzian geometry satisfies the dynamical
Einstein equations of general relativity. On the other hand, the classical laws
of black hole mechanics are intrinsically linked to the Einstein equations of
general relativity (or their perturbative extension into either semiclassical
quantum gravity or string-inspired scenarios). In particular, the laws of black
hole thermodynamics, and the identification of the entropy of a black hole with
its area, are inextricably linked with the dynamical equations satisfied by the
Lorentzian geometry: entropy is proportional to area (plus corrections) if and
only if the dynamical equations are the Einstein equations (plus corrections).
It is quite possible to have Hawking radiation occur in physical situations in
which the laws of black hole mechanics do not apply, and in situations in which
the notion of black hole entropy does not even make any sense. This observation
has important implications for any derivation of black hole entropy that seeks
to deduce black hole entropy from the Hawking radiation.Comment: Uses ReV_TeX 3.0; Five pages in two-column forma
An Experimental Test of Criminal Behavior Among Juveniles and Young Adults
We report results from economic experiments that provide a direct test of the hypothesis that criminal behavior responds rationally to changes in the possible rewards and in the probability and severity of punishment. The experiments involve decisions that are best described as petty larceny, and are done using high school and college students who can anonymously take real money from each other. We find that decisions about whether and how much to steal are, in general, rational and responsive to the variations in tradeoffs, and sometimes, though not always, to the overall availability of criminal opportunities.
Bounding the Hubble flow in terms of the w parameter
The last decade has seen increasing efforts to circumscribe and bound the
cosmological Hubble flow in terms of model-independent constraints on the
cosmological fluid - such as, for instance, the classical energy conditions of
general relativity. Quite a bit can certainly be said in this regard, but much
more refined bounds can be obtained by placing more precise constraints (either
theoretical or observational) on the cosmological fluid. In particular, the use
of the w-parameter (w=p/rho) has become increasingly common as a surrogate for
trying to say something about the cosmological equation of state. Herein we
explore the extent to which a constraint on the w-parameter leads to useful and
nontrivial constraints on the Hubble flow, in terms of constraints on density
rho(z), Hubble parameter H(z), density parameter Omega(z), cosmological
distances d(z), and lookback time T(z). In contrast to other partial results in
the literature, we carry out the computations for arbitrary values of the space
curvature k in [-1,0,+1], equivalently for arbitrary Omega_0 <= 1.Comment: 15 page
Tolman wormholes violate the strong energy condition
For an arbitrary Tolman wormhole, unconstrained by symmetry, we shall define
the bounce in terms of a three-dimensional edgeless achronal spacelike
hypersurface of minimal volume. (Zero trace for the extrinsic curvature plus a
"flare-out" condition.) This enables us to severely constrain the geometry of
spacetime at and near the bounce and to derive general theorems regarding
violations of the energy conditions--theorems that do not involve geodesic
averaging but nevertheless apply to situations much more general than the
highly symmetric FRW-based subclass of Tolman wormholes. [For example: even
under the mildest of hypotheses, the strong energy condition (SEC) must be
violated.] Alternatively, one can dispense with the minimal volume condition
and define a generic bounce entirely in terms of the motion of test particles
(future-pointing timelike geodesics), by looking at the expansion of their
timelike geodesic congruences. One re-confirms that the SEC must be violated at
or near the bounce. In contrast, it is easy to arrange for all the other
standard energy conditions to be satisfied.Comment: 8 pages, ReV-TeX 3.
Signature change events: A challenge for quantum gravity?
Within the framework of either Euclidian (functional-integral) quantum
gravity or canonical general relativity the signature of the manifold is a
priori unconstrained. Furthermore, recent developments in the emergent
spacetime programme have led to a physically feasible implementation of
signature change events. This suggests that it is time to revisit the sometimes
controversial topic of signature change in general relativity. Specifically, we
shall focus on the behaviour of a quantum field subjected to a manifold
containing regions of different signature. We emphasise that, regardless of the
underlying classical theory, there are severe problems associated with any
quantum field theory residing on a signature-changing background. (Such as the
production of what is naively an infinite number of particles, with an infinite
energy density.) From the viewpoint of quantum gravity phenomenology, we
discuss possible consequences of an effective Lorentz symmetry breaking scale.
To more fully understand the physics of quantum fields exposed to finite
regions of Euclidean-signature (Riemannian) geometry, we show its similarities
with the quantum barrier penetration problem, and the super-Hubble horizon
modes encountered in cosmology. Finally we raise the question as to whether
signature change transitions could be fully understood and dynamically
generated within (modified) classical general relativity, or whether they
require the knowledge of a full theory of quantum gravity.Comment: 33 pages. 4 figures; V2: 3 references added, no physics changes; V3:
now 24 pages - significantly shortened - argument simplified and more focused
- no physics changes - this version accepted for publication in Classical and
Quantum Gravit
Quantum Dynamics of Lorentzian Spacetime Foam
A simple spacetime wormhole, which evolves classically from zero throat
radius to a maximum value and recontracts, can be regarded as one possible mode
of fluctuation in the microscopic ``spacetime foam'' first suggested by
Wheeler. The dynamics of a particularly simple version of such a wormhole can
be reduced to that of a single quantity, its throat radius; this wormhole thus
provides a ``minisuperspace model'' for a structure in Lorentzian-signature
foam. The classical equation of motion for the wormhole throat is obtained from
the Einstein field equations and a suitable equation of state for the matter at
the throat. Analysis of the quantum behavior of the hole then proceeds from an
action corresponding to that equation of motion. The action obtained simply by
calculating the scalar curvature of the hole spacetime yields a model with
features like those of the relativistic free particle. In particular the
Hamiltonian is nonlocal, and for the wormhole cannot even be given as a
differential operator in closed form. Nonetheless the general solution of the
Schr\"odinger equation for wormhole wave functions, i.e., the wave-function
propagator, can be expressed as a path integral. Too complicated to perform
exactly, this can yet be evaluated via a WKB approximation. The result
indicates that the wormhole, classically stable, is quantum-mechanically
unstable: A Feynman-Kac decomposition of the WKB propagator yields no spectrum
of bound states. Though an initially localized wormhole wave function may
oscillate for many classical expansion/recontraction periods, it must
eventually leak to large radius values. The possibility of such a mode unstable
against growth, combined withComment: 37 pages, 93-
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