345 research outputs found
Bounds on negative energy densities in flat spacetime
We generalise results of Ford and Roman which place lower bounds -- known as
quantum inequalities -- on the renormalised energy density of a quantum field
averaged against a choice of sampling function. Ford and Roman derived their
results for a specific non-compactly supported sampling function; here we use a
different argument to obtain quantum inequalities for a class of smooth, even
and non-negative sampling functions which are either compactly supported or
decay rapidly at infinity. Our results hold in -dimensional Minkowski space
() for the free real scalar field of mass . We discuss various
features of our bounds in 2 and 4 dimensions. In particular, for massless field
theory in 2-dimensional Minkowski space, we show that our quantum inequality is
weaker than Flanagan's optimal bound by a factor of 3/2.Comment: REVTeX, 13 pages and 2 figures. Minor typos corrected, one reference
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Spatially Averaged Quantum Inequalities Do Not Exist in Four-Dimensional Spacetime
We construct a particular class of quantum states for a massless, minimally
coupled free scalar field which are of the form of a superposition of the
vacuum and multi-mode two-particle states. These states can exhibit local
negative energy densities. Furthermore, they can produce an arbitrarily large
amount of negative energy in a given region of space at a fixed time. This
class of states thus provides an explicit counterexample to the existence of a
spatially averaged quantum inequality in four-dimensional spacetime.Comment: 13 pages, 1 figure, minor corrections and added comment
Dynamic wormholes
A new framework is proposed for general dynamic wormholes, unifying them with
black holes. Both are generically defined locally by outer trapping horizons,
temporal for wormholes and spatial or null for black and white holes. Thus
wormhole horizons are two-way traversible, while black-hole and white-hole
horizons are only one-way traversible. It follows from the Einstein equation
that the null energy condition is violated everywhere on a generic wormhole
horizon. It is suggested that quantum inequalities constraining negative energy
break down at such horizons. Wormhole dynamics can be developed as for
black-hole dynamics, including a reversed second law and a first law involving
a definition of wormhole surface gravity. Since the causal nature of a horizon
can change, being spatial under positive energy and temporal under sufficient
negative energy, black holes and wormholes are interconvertible. In particular,
if a wormhole's negative-energy source fails, it may collapse into a black
hole. Conversely, irradiating a black-hole horizon with negative energy could
convert it into a wormhole horizon. This also suggests a possible final state
of black-hole evaporation: a stationary wormhole. The new framework allows a
fully dynamical description of the operation of a wormhole for practical
transport, including the back-reaction of the transported matter on the
wormhole. As an example of a matter model, a Klein-Gordon field with negative
gravitational coupling is a source for a static wormhole of Morris & Thorne.Comment: 5 revtex pages, 4 eps figures. Minor change which did not reach
publisher
Nominal Logic Programming
Nominal logic is an extension of first-order logic which provides a simple
foundation for formalizing and reasoning about abstract syntax modulo
consistent renaming of bound names (that is, alpha-equivalence). This article
investigates logic programming based on nominal logic. We describe some typical
nominal logic programs, and develop the model-theoretic, proof-theoretic, and
operational semantics of such programs. Besides being of interest for ensuring
the correct behavior of implementations, these results provide a rigorous
foundation for techniques for analysis and reasoning about nominal logic
programs, as we illustrate via examples.Comment: 46 pages; 19 page appendix; 13 figures. Revised journal submission as
of July 23, 200
The Quantum Interest Conjecture
Although quantum field theory allows local negative energy densities and
fluxes, it also places severe restrictions upon the magnitude and extent of the
negative energy. The restrictions take the form of quantum inequalities. These
inequalities imply that a pulse of negative energy must not only be followed by
a compensating pulse of positive energy, but that the temporal separation
between the pulses is inversely proportional to their amplitude. In an earlier
paper we conjectured that there is a further constraint upon a negative and
positive energy delta-function pulse pair. This conjecture (the quantum
interest conjecture) states that a positive energy pulse must overcompensate
the negative energy pulse by an amount which is a monotonically increasing
function of the pulse separation. In the present paper we prove the conjecture
for massless quantized scalar fields in two and four-dimensional flat
spacetime, and show that it is implied by the quantum inequalities.Comment: 17 pages, Latex, 3 figures, uses eps
Scalar Field Quantum Inequalities in Static Spacetimes
We discuss quantum inequalities for minimally coupled scalar fields in static
spacetimes. These are inequalities which place limits on the magnitude and
duration of negative energy densities. We derive a general expression for the
quantum inequality for a static observer in terms of a Euclidean two-point
function. In a short sampling time limit, the quantum inequality can be written
as the flat space form plus subdominant correction terms dependent upon the
geometric properties of the spacetime. This supports the use of flat space
quantum inequalities to constrain negative energy effects in curved spacetime.
Using the exact Euclidean two-point function method, we develop the quantum
inequalities for perfectly reflecting planar mirrors in flat spacetime. We then
look at the quantum inequalities in static de~Sitter spacetime, Rindler
spacetime and two- and four-dimensional black holes. In the case of a
four-dimensional Schwarzschild black hole, explicit forms of the inequality are
found for static observers near the horizon and at large distances. It is show
that there is a quantum averaged weak energy condition (QAWEC), which states
that the energy density averaged over the entire worldline of a static observer
is bounded below by the vacuum energy of the spacetime. In particular, for an
observer at a fixed radial distance away from a black hole, the QAWEC says that
the averaged energy density can never be less than the Boulware vacuum energy
density.Comment: 27 pages, 2 Encapsulated Postscript figures, uses epsf.tex, typeset
in RevTe
Quantum inequalities in two dimensional curved spacetimes
We generalize a result of Vollick constraining the possible behaviors of the
renormalized expected stress-energy tensor of a free massless scalar field in
two dimensional spacetimes that are globally conformal to Minkowski spacetime.
Vollick derived a lower bound for the energy density measured by a static
observer in a static spacetime, averaged with respect to the observers proper
time by integrating against a smearing function. Here we extend the result to
arbitrary curves in non-static spacetimes. The proof, like Vollick's proof, is
based on conformal transformations and the use of our earlier optimal bound in
flat Minkowski spacetime. The existence of such a quantum inequality was
previously established by Fewster.Comment: revtex 4, 5 pages, no figures, submitted to Phys. Rev. D. Minor
correction
Quantum Inequalities and Singular Energy Densities
There has been much recent work on quantum inequalities to constrain negative
energy. These are uncertainty principle-type restrictions on the magnitude and
duration of negative energy densities or fluxes. We consider several examples
of apparent failures of the quantum inequalities, which involve passage of an
observer through regions where the negative energy density becomes singular. We
argue that this type of situation requires one to formulate quantum
inequalities using sampling functions with compact support. We discuss such
inequalities, and argue that they remain valid even in the presence of singular
energy densities.Comment: 18 pages, LaTex, 2 figures, uses eps
Quantum Inequalities for the Electromagnetic Field
A quantum inequality for the quantized electromagnetic field is developed for
observers in static curved spacetimes. The quantum inequality derived is a
generalized expression given by a mode function expansion of the four-vector
potential, and the sampling function used to weight the energy integrals is
left arbitrary up to the constraints that it be a positive, continuous function
of unit area and that it decays at infinity. Examples of the quantum inequality
are developed for Minkowski spacetime, Rindler spacetime and the Einstein
closed universe.Comment: 19 pages, 1 table and 1 figure. RevTex styl
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