321 research outputs found
Remarks on the Reeh-Schlieder property for higher spin free fields on curved spacetimes
The existence of states enjoying a weak form of the Reeh-Schlieder property
has been recently established on curved backgrounds and in the framework of
locally covariant quantum field theory. Since only the example of a real scalar
field has been discussed, we extend the analysis to the case of massive and
massless free fields either of spin 1/2 or of spin 1. In the process, it is
also shown that both the vector potential and the Proca field can be described
as a locally covariant quantum field theory.Comment: 28 pages, references and remarks added, typos correcte
Quantum effects in the Alcubierre warp drive spacetime
The expectation value of the stress-energy tensor of a free conformally
invariant scalar field is computed in a two-dimensional reduction of the
Alcubierre ``warp drive'' spacetime. The stress-energy is found to diverge if
the apparent velocity of the spaceship exceeds the speed of light. If such
behavior occurs in four dimensions, then it appears implausible that ``warp
drive'' behavior in a spacetime could be engineered, even by an arbitrarily
advanced civilization.Comment: 9 pages, ReVTe
The unphysical nature of "Warp Drive"
We will apply the quantum inequality type restrictions to Alcubierre's warp
drive metric on a scale in which a local region of spacetime can be considered
``flat''. These are inequalities that restrict the magnitude and extent of the
negative energy which is needed to form the warp drive metric. From this we are
able to place limits on the parameters of the ``Warp Bubble''. It will be shown
that the bubble wall thickness is on the order of only a few hundred Planck
lengths. Then we will show that the total integrated energy density needed to
maintain the warp metric with such thin walls is physically unattainable.Comment: 11 pages, 3 figures, latex. This revision corrects a typographical
sign error in Eq. (3
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
adde
Speed Limits in General Relativity
Some standard results on the initial value problem of general relativity in
matter are reviewed. These results are applied first to show that in a well
defined sense, finite perturbations in the gravitational field travel no faster
than light, and second to show that it is impossible to construct a warp drive
as considered by Alcubierre (1994) in the absence of exotic matter.Comment: 7 pages; AMS-LaTeX; accepted for publication by Classical and Quantum
Gravit
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
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
Superluminal travel requires negative energies
I investigate the relationship between faster-than-light travel and
weak-energy-condition violation, i.e., negative energy densities. In a general
spacetime it is difficult to define faster-than-light travel, and I give an
example of a metric which appears to allow superluminal travel, but in fact is
just flat space. To avoid such difficulties, I propose a definition of
superluminal travel which requires that the path to be traveled reach a
destination surface at an earlier time than any neighboring path. With this
definition (and assuming the generic condition) I prove that superluminal
travel requires weak-energy-condition violation.Comment: 5 pages, RevTeX, 2 figures with epsf. This paper now contains all the
material of gr-qc/6805003 and gr-qc/9806091 since these became a single
article in Phys. Rev. Let
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