766 research outputs found
Physical Logic
In R.D. Sorkin's framework for logic in physics a clear separation is made
between the collection of unasserted propositions about the physical world and
the affirmation or denial of these propositions by the physical world. The
unasserted propositions form a Boolean algebra because they correspond to
subsets of an underlying set of spacetime histories. Physical rules of
inference, apply not to the propositions in themselves but to the affirmation
and denial of these propositions by the actual world. This physical logic may
or may not respect the propositions' underlying Boolean structure. We prove
that this logic is Boolean if and only if the following three axioms hold: (i)
The world is affirmed, (ii) Modus Ponens and (iii) If a proposition is denied
then its negation, or complement, is affirmed. When a physical system is
governed by a dynamical law in the form of a quantum measure with the rule that
events of zero measure are denied, the axioms (i) - (iii) prove to be too rigid
and need to be modified. One promising scheme for quantum mechanics as quantum
measure theory corresponds to replacing axiom (iii) with axiom (iv) Nature is
as fine grained as the dynamics allows.Comment: 14 pages, v2 published version with a change in the title and other
minor change
Gravity and Matter in Causal Set Theory
The goal of this paper is to propose an approach to the formulation of
dynamics for causal sets and coupled matter fields. We start from the continuum
version of the action for a Klein-Gordon field coupled to gravity, and rewrite
it first using quantities that have a direct correspondent in the case of a
causal set, namely volumes, causal relations, and timelike lengths, as
variables to describe the geometry. In this step, the local Lagrangian density
for a set of fields is recast into a quasilocal expression
that depends on pairs of causally related points and
is a function of the values of in the Alexandrov set defined by those
points, and whose limit as and approach a common point is .
We then describe how to discretize , and use it to define a
discrete action.Comment: 13 pages, no figures; In version 2, friendlier results than in
version 1 are obtained following much shorter derivation
Evidence for a continuum limit in causal set dynamics
We find evidence for a continuum limit of a particular causal set dynamics
which depends on only a single ``coupling constant'' and is easy to
simulate on a computer. The model in question is a stochastic process that can
also be interpreted as 1-dimensional directed percolation, or in terms of
random graphs.Comment: 24 pages, 19 figures, LaTeX, adjusted terminolog
Noise kernel for a quantum field in Schwarzschild spacetime under the Gaussian approximation
A method is given to compute an approximation to the noise kernel, defined as
the symmetrized connected 2-point function of the stress tensor, for the
conformally invariant scalar field in any spacetime conformal to an
ultra-static spacetime for the case in which the field is in a thermal state at
an arbitrary temperature. The most useful applications of the method are flat
space where the approximation is exact and Schwarzschild spacetime where the
approximation is better than it is in most other spacetimes. The two points are
assumed to be separated in a timelike or spacelike direction. The method
involves the use of a Gaussian approximation which is of the same type as that
used by Page to compute an approximate form of the stress tensor for this field
in Schwarzschild spacetime. All components of the noise kernel have been
computed exactly for hot flat space and one component is explicitly displayed.
Several components have also been computed for Schwarzschild spacetime and
again one component is explicitly displayed.Comment: 34 pages, no figures. Substantial revisions in Secs. I, IV, and V;
minor revisions elsewhere; new results include computation of the exact noise
kernel for hot flat space and an approximate computation of the noise kernel
for a thermal state at an arbitrary temperature in Schwarzschild spacetime
when the points are split in the time directio
Metric fluctuations of an evaporating black hole from back reaction of stress tensor fluctuations
This paper delineates the first steps in a systematic quantitative study of
the spacetime fluctuations induced by quantum fields in an evaporating black
hole under the stochastic gravity program. The central object of interest is
the noise kernel, which is the symmetrized two-point quantum correlation
function of the stress tensor operator. As a concrete example we apply it to
the study of the spherically-symmetric sector of metric perturbations around an
evaporating black hole background geometry. For macroscopic black holes we find
that those fluctuations grow and eventually become important when considering
sufficiently long periods of time (of the order of the evaporation time), but
well before the Planckian regime is reached. In addition, the assumption of a
simple correlation between the fluctuations of the energy flux crossing the
horizon and far from it, which was made in earlier work on
spherically-symmetric induced fluctuations, is carefully scrutinized and found
to be invalid. Our analysis suggests the existence of an infinite amplitude for
the fluctuations when trying to localize the horizon as a three-dimensional
hypersurface, as in the classical case, and, as a consequence, a more accurate
picture of the horizon as possessing a finite effective width due to quantum
fluctuations. This is supported by a systematic analysis of the noise kernel in
curved spacetime smeared with different functions under different conditions,
the details are collected in the appendices. This case study shows a pathway
for probing quantum metric fluctuations near the horizon and understanding
their physical meaning.Comment: 21 pages, REVTe
Stochastic Gravity: Beyond Semiclassical Gravity
The back-reaction of a classical gravitational field interacting with quantum
matter fields is described by the semiclassical Einstein equation, which has
the expectation value of the quantum matter fields stress tensor as a source.
The semiclassical theory may be obtained from the quantum field theory of
gravity interacting with N matter fields in the large N limit. This theory
breaks down when the fields quantum fluctuations are important. Stochastic
gravity goes beyond the semiclassical limit and allows for a systematic and
self-consistent description of the metric fluctuations induced by these quantum
fluctuations. The correlation functions of the metric fluctuations obtained in
stochastic gravity reproduce the correlation functions in the quantum theory to
leading order in an 1/N expansion. Two main applications of stochastic gravity
are discussed. The first, in cosmology, to obtain the spectrum of primordial
metric perturbations induced by the inflaton fluctuations, even beyond the
linear approximation. The second, in black hole physics, to study the
fluctuations of the horizon of an evaporating black hole.Comment: 12 pages, no figures, proceedings of the XXIX Spanish Relativity
Meetin
Recycling of epidermal growth factor-receptor complexes in A431 cells: identification of dual pathways
The intracellular sorting of EGF-receptor complexes (EGF-RC) has been studied in human epidermoid carcinoma A431 cells. Recycling of EGF was found to occur rapidly after internalization at 37 degrees C. The initial rate of EGF recycling was reduced at 18 degrees C. A significant pool of internalized EGF was incapable of recycling at 18 degrees C but began to recycle when cells were warmed to 37 degrees C. The relative rate of EGF outflow at 37 degrees C from cells exposed to an 18 degrees C temperature block was slower (t1/2 approximately 20 min) than the rate from cells not exposed to a temperature block (t1/2 approximately 5-7 min). These data suggest that there might be both short- and long-time cycles of EGF recycling in A431 cells. Examination of the intracellular EGF-RC dissociation and dynamics of short- and long-time recycling indicated that EGF recycled as EGF-RC. Moreover, EGF receptors that were covalently labeled with a photoactivatable derivative of 125I-EGF recycled via the long-time pathway at a rate similar to that of 125I-EGF. Since EGF-RC degradation was also blocked at 18 degrees C, we propose that sorting to the lysosomal and long-time recycling pathway may occur after a highly temperature-sensitive step, presumably in the late endosomes
The Generalized Second Law implies a Quantum Singularity Theorem
The generalized second law can be used to prove a singularity theorem, by
generalizing the notion of a trapped surface to quantum situations. Like
Penrose's original singularity theorem, it implies that spacetime is null
geodesically incomplete inside black holes, and to the past of spatially
infinite Friedmann--Robertson--Walker cosmologies. If space is finite instead,
the generalized second law requires that there only be a finite amount of
entropy producing processes in the past, unless there is a reversal of the
arrow of time. In asymptotically flat spacetime, the generalized second law
also rules out traversable wormholes, negative masses, and other forms of
faster-than-light travel between asymptotic regions, as well as closed timelike
curves. Furthermore it is impossible to form baby universes which eventually
become independent of the mother universe, or to restart inflation. Since the
semiclassical approximation is used only in regions with low curvature, it is
argued that the results may hold in full quantum gravity. An introductory
section describes the second law and its time-reverse, in ordinary and
generalized thermodynamics, using either the fine-grained or the coarse-grained
entropy. (The fine-grained version is used in all results except those relating
to the arrow of time.) A proof of the coarse-grained ordinary second law is
given.Comment: 46 pages, 8 figures. v2: discussion of global hyperbolicity revised
(4.1, 5.2), more comments on AdS. v3: major revisions including change of
title. v4: similar to published version, but with corrections to plan of
paper (1) and definition of global hyperbolicity (3.2). v5: fixed proof of
Thm. 1, changed wording of Thm. 3 & proof of Thm. 4, revised Sec. 5.2, new
footnote
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
Dynamics & Predictions in the Co-Event Interpretation
Sorkin has introduced a new, observer independent, interpretation of quantum
mechanics that can give a successful realist account of the 'quantum
microworld' as well as explaining how classicality emerges at the level of
observable events for a range of systems including single time 'Copenhagen
measurements'. This 'co-event interpretation' presents us with a new ontology,
in which a single 'co-event' is real. A new ontology necessitates a review of
the dynamical & predictive mechanism of a theory, and in this paper we begin
the process by exploring means of expressing the dynamical and predictive
content of histories theories in terms of co-events.Comment: 35 pages. Revised after refereein
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