2,147 research outputs found
Effects of sterilization on the energy-dissipating properties of balsa wood
Technical report on the effects of sterilization on the energy-dissipating properties of balsa wood is given. Sterilization by ethylene oxide plus heat enhances the average specific energy of balsa while plastic impregnation followed by irradiation-induced polymerization does not
The Random Walk in Generalized Quantum Theory
One can view quantum mechanics as a generalization of classical probability
theory that provides for pairwise interference among alternatives. Adopting
this perspective, we ``quantize'' the classical random walk by finding, subject
to a certain condition of ``strong positivity'', the most general Markovian,
translationally invariant ``decoherence functional'' with nearest neighbor
transitions.Comment: 25 pages, no figure
A Spin-Statistics Theorem for Certain Topological Geons
We review the mechanism in quantum gravity whereby topological geons,
particles made from non-trivial spatial topology, are endowed with nontrivial
spin and statistics. In a theory without topology change there is no
obstruction to ``anomalous'' spin-statistics pairings for geons. However, in a
sum-over-histories formulation including topology change, we show that
non-chiral abelian geons do satisfy a spin-statistics correlation if they are
described by a wave function which is given by a functional integral over
metrics on a particular four-manifold. This manifold describes a topology
changing process which creates a pair of geons from .Comment: 21 pages, Plain TeX with harvmac, 3 figures included via eps
Large Fluctuations in the Horizon Area and what they can tell us about Entropy and Quantum Gravity
We evoke situations where large fluctuations in the entropy are induced, our
main example being a spacetime containing a potential black hole whose
formation depends on the outcome of a quantum mechanical event. We argue that
the teleological character of the event horizon implies that the consequent
entropy fluctuations must be taken seriously in any interpretation of the
quantal formalism. We then indicate how the entropy can be well defined despite
the teleological character of the horizon, and we argue that this is possible
only in the context of a spacetime or ``histories'' formulation of quantum
gravity, as opposed to a canonical one, concluding that only a spacetime
formulation has the potential to compute --- from first principles and in the
general case --- the entropy of a black hole. From the entropy fluctuations in
a related example, we also derive a condition governing the form taken by the
entropy, when it is expressed as a function of the quantal density-operator.Comment: 35 pages, plain Tex, needs mathmacros.tex and msmacros.te
Energy extremality in the presence of a black hole
We derive the so-called first law of black hole mechanics for variations
about stationary black hole solutions to the Einstein--Maxwell equations in the
absence of sources. That is, we prove that where the black hole parameters and denote mass, surface gravity, horizon area, angular velocity of the
horizon, angular momentum, electric potential of the horizon and charge
respectively. The unvaried fields are those of a stationary, charged, rotating
black hole and the variation is to an arbitrary `nearby' black hole which is
not necessarily stationary. Our approach is 4-dimensional in spirit and uses
techniques involving Action variations and Noether operators. We show that the
above formula holds on any asymptotically flat spatial 3-slice which extends
from an arbitrary cross-section of the (future) horizon to spatial
infinity.(Thus, the existence of a bifurcation surface is irrelevant to our
demonstration. On the other hand, the derivation assumes without proof that the
horizon possesses at least one of the following two (related)properties: ()
it cannot be destroyed by arbitrarily small perturbations of the metric and
other fields which may be present, () the expansion of the null geodesic
generators of the perturbed horizon goes to zero in the distant future.)Comment: 30 pages, latex fil
Comments on the Entanglement Entropy on Fuzzy Spaces
We locate the relevant degrees of freedom for the entanglement entropy on
some 2+1 fuzzy models. It is found that the entropy is stored in the near
boundary degrees of freedom. We give a simple analytical derivation for the
area law using like expansion when only the near boundary degrees of
freedom are incorporated. Numerical and qualitative evidences for the validity
of near boundary approximation are finally given .Comment: 14 pages, 2 figure
Topology Change and Causal Continuity
The result that, for a scalar quantum field propagating on a ``trousers''
topology in 1+1 dimensions, the crotch singularity is a source for an infinite
burst of energy has been used to argue against the occurrence of topology
change in quantum gravity. We draw attention to a conjecture due to Sorkin that
it may be the particular type of topology change involved in the trousers
transition that is problematic and that other topology changes may not cause
the same difficulties. The conjecture links the singular behaviour to the
existence of ``causal discontinuities'' in the spacetime and relies on a
classification of topology changes using Morse theory. We investigate various
topology changing transitions, including the pair production of black holes and
of topological geons, in the light of these ideas.Comment: Latex, 28 pages, 10 figures, small changes in text (one figure
removed), conclusions remain unchanged. Accepted for publication in Physical
Review
Cosmological Constant and Noncommutative Spacetime
We show that the cosmological constant appears as a Lagrange multiplier if
nature is described by a canonical noncommutative spacetime. It is thus an
arbitrary parameter unrelated to the action and thus to vacuum fluctuations.
The noncommutative algebra restricts general coordinate transformations to
four-volume preserving noncommutative coordinate transformations. The
noncommutative gravitational action is thus an unimodular noncommutative
gravity. We show that spacetime noncommutativity provides a very natural
justification to an unimodular gravity solution to the cosmological problem. We
obtain the right order of magnitude for the critical energy density of the
universe if we assume that the scale for spacetime noncommutativity is the
Planck scale.Comment: 7 page
A Causal Order for Spacetimes with Lorentzian Metrics: Proof of Compactness of the Space of Causal Curves
We recast the tools of ``global causal analysis'' in accord with an approach
to the subject animated by two distinctive features: a thoroughgoing reliance
on order-theoretic concepts, and a utilization of the Vietoris topology for the
space of closed subsets of a compact set. We are led to work with a new causal
relation which we call , and in terms of it we formulate extended
definitions of concepts like causal curve and global hyperbolicity. In
particular we prove that, in a spacetime \M which is free of causal cycles,
one may define a causal curve simply as a compact connected subset of \M
which is linearly ordered by . Our definitions all make sense for
arbitrary metrics (and even for certain metrics which fail to be
invertible in places). Using this feature, we prove for a general metric,
the familiar theorem that the space of causal curves between any two compact
subsets of a globally hyperbolic spacetime is compact. We feel that our
approach, in addition to yielding a more general theorem, simplifies and
clarifies the reasoning involved. Our results have application in a recent
positive energy theorem, and may also prove useful in the study of topology
change. We have tried to make our treatment self-contained by including proofs
of all the facts we use which are not widely available in reference works on
topology and differential geometry.Comment: Two small revisions to accomodate errors brought to our attention by
R.S. Garcia. No change to chief results. 33 page
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