1,420 research outputs found
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
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
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
Quantum interest in two dimensions
The quantum interest conjecture of Ford and Roman asserts that any
negative-energy pulse must necessarily be followed by an over-compensating
positive-energy one within a certain maximum time delay. Furthermore, the
minimum amount of over-compensation increases with the separation between the
pulses. In this paper, we first study the case of a negative-energy square
pulse followed by a positive-energy one for a minimally coupled, massless
scalar field in two-dimensional Minkowski space. We obtain explicit expressions
for the maximum time delay and the amount of over-compensation needed, using a
previously developed eigenvalue approach. These results are then used to give a
proof of the quantum interest conjecture for massless scalar fields in two
dimensions, valid for general energy distributions.Comment: 17 pages, 4 figures; final version to appear in PR
Quantum inequalities and `quantum interest' as eigenvalue problems
Quantum inequalities (QI's) provide lower bounds on the averaged energy
density of a quantum field. We show how the QI's for massless scalar fields in
even dimensional Minkowski space may be reformulated in terms of the positivity
of a certain self-adjoint operator - a generalised Schroedinger operator with
the energy density as the potential - and hence as an eigenvalue problem. We
use this idea to verify that the energy density produced by a moving mirror in
two dimensions is compatible with the QI's for a large class of mirror
trajectories. In addition, we apply this viewpoint to the `quantum interest
conjecture' of Ford and Roman, which asserts that the positive part of an
energy density always overcompensates for any negative components. For various
simple models in two and four dimensions we obtain the best possible bounds on
the `quantum interest rate' and on the maximum delay between a negative pulse
and a compensating positive pulse. Perhaps surprisingly, we find that - in four
dimensions - it is impossible for a positive delta-function pulse of any
magnitude to compensate for a negative delta-function pulse, no matter how
close together they occur.Comment: 18 pages, RevTeX. One new result added; typos fixed. To appear in
Phys. Rev.
Weak energy condition violation and superluminal travel
Recent solutions to the Einstein Field Equations involving negative energy
densities, i.e., matter violating the weak-energy-condition, have been
obtained, namely traversable wormholes, the Alcubierre warp drive and the
Krasnikov tube. These solutions are related to superluminal travel, although
locally the speed of light is not surpassed. It is difficult to define
faster-than-light travel in generic space-times, and one can construct metrics
which apparently allow superluminal travel, but are in fact flat Minkowski
space-times. Therefore, to avoid these difficulties it is important to provide
an appropriate definition of superluminal travel.Comment: 15 pages, 3 figures, LaTeX2e, Springer style files -included.
Contribution to the Proceedings of the Spanish Relativity Meeting-2001
(Madrid, September 2001
Quantum Weak Energy Inequalities for the Dirac field in Flat Spacetime
Quantum Weak Energy Inequalities (QWEIs) have been established for a variety
of quantum field theories in both flat and curved spacetimes. Dirac fields are
known (by a result of Fewster and Verch) to satisfy QWEIs under very general
circumstances. However this result does not provide an explicit formula for the
QWEI bound, so its magnitude has not previously been determined. In this paper
we present a new and explicit QWEI bound for Dirac fields of arbitrary mass in
four-dimensional Minkowski space. We follow the methods employed by Fewster and
Eveson for the scalar field, modified to take account of anticommutation
relations. A key ingredient is an identity for Fourier transforms established
by Fewster and Verch. We also compare our QWEI with those previously obtained
for scalar and spin-1 fields.Comment: 8 pages, REVTeX4, version to appear in Phys Rev
Quantum inequalities for the free Rarita-Schwinger fields in flat spacetime
Using the methods developed by Fewster and colleagues, we derive a quantum
inequality for the free massive spin- Rarita-Schwinger fields in
the four dimensional Minkowski spacetime. Our quantum inequality bound for the
Rarita-Schwinger fields is weaker, by a factor of 2, than that for the
spin- Dirac fields. This fact along with other quantum inequalities
obtained by various other authors for the fields of integer spin (bosonic
fields) using similar methods lead us to conjecture that, in the flat
spacetime, separately for bosonic and fermionic fields, the quantum inequality
bound gets weaker as the the number of degrees of freedom of the field
increases. A plausible physical reason might be that the more the number of
field degrees of freedom, the more freedom one has to create negative energy,
therefore, the weaker the quantum inequality bound.Comment: Revtex, 11 pages, to appear in PR
Detection of negative energy: 4-dimensional examples
We study the response of switched particle detectors to static negative
energy densities and negative energy fluxes. It is demonstrated how the
switching leads to excitation even in the vacuum and how negative energy can
lead to a suppression of this excitation. We obtain quantum inequalities on the
detection similar to those obtained for the energy density by Ford and
co-workers and in an `operational' context by Helfer. We revisit the question
`Is there a quantum equivalence principle?' in terms of our model. Finally, we
briefly address the issue of negative energy and the second law of
thermodynamics.Comment: 10 pages, 7 figure
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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