Quantum Field Theory Constrains Traversable Wormhole Geometries

Recently a bound on negative energy densities in four-dimensional Minkowski spacetime was derived for a minimally coupled, quantized, massless, scalar field in an arbitrary quantum state. The bound has the form of an uncertainty principle-type constraint on the magnitude and duration of the negative energy density seen by a timelike geodesic observer. When spacetime is curved and/or has boundaries, we argue that the bound should hold in regions small compared to the minimum local characteristic radius of curvature or the distance to any boundaries, since spacetime can be considered approximately Minkowski on these scales. We apply the bound to the stress-energy of static traversable wormhole spacetimes. Our analysis implies that either the wormhole must be only a little larger than Planck size or that there is a large discrepancy in the length scales which characterize the wormhole. In the latter case, the negative energy must typically be concentrated in a thin band many orders of magnitude smaller than the throat size. These results would seem to make the existence of macroscopic traversable wormholes very improbable.Comment: 26 pages, plain LaTe

Using SPARQL – the practitioners’ viewpoint

A number of studies have analyzed SPARQL log data to draw conclusions about how SPARQL is being used. To complement this work, a survey of SPARQL users has been undertaken. Whilst confirming some of the conclusions of the previous studies, the current work is able to provide additional insight into how users create SPARQL queries, the difficulties they encounter, and the features they would like to see included in the language. Based on this insight, a number of recommendations are presented to the community. These relate to predicting and avoiding computationally expensive queries; extensions to the language; and extending the search paradigm

Statistical analysis of thermospheric gravity waves from Fabry-Perot Interferometer measurements of atomic oxygen

Data from the Fabry-Perot Interferometers at KEOPS (Sweden), Sodankylä (Finland), and Svalbard (Norway), have been analysed for gravity wave activity on all the clear nights from 2000 to 2006. A total of 249 nights were available from KEOPS, 133 from Sodankylä and 185 from the Svalbard FPI. A Lomb-Scargle analysis was performed on each of these nights to identify the periods of any wave activity during the night. Comparisons between many nights of data allow the general characteristics of the waves that are present in the high latitude upper thermosphere to be determined. Comparisons were made between the different parameters: the atomic oxygen intensities, the thermospheric winds and temperatures, and for each parameter the distribution of frequencies of the waves was determined. No dependence on the number of waves on geomagnetic activity levels, or position in the solar cycle, was found. All the FPIs have had different detectors at various times, producing different time resolutions of the data, so comparisons between the different years, and between data from different sites, showed how the time resolution determines which waves are observed. In addition to the cutoff due to the Nyquist frequency, poor resolution observations significantly reduce the number of short-period waves (5 h) detected. Comparisons between the number of gravity waves detected at KEOPS and Sodankylä over all the seasons showed a similar proportion of waves to the number of nights used for both sites, as expected since the two sites are at similar latitudes and therefore locations with respect to the auroral oval, confirming this as a likely source region. Svalbard showed fewer waves with short periods than KEOPS data for a season when both had the same time resolution data. This gives a clear indication of the direction of flow of the gravity waves, and corroborates that the source is the auroral oval. This is because the energy is dissipated through heating in each cycle of a wave, therefore, over a given distance, short period waves lose more energy than long and dissipate before they reach their target

High time resolution measurements of the thermosphere from Fabry-Perot Interferometer measurements of atomic oxygen

Recent advances in the performance of CCD detectors have enabled a high time resolution study of the high latitude upper thermosphere with Fabry-Perot Interferometers(FPIs) to be performed. 10-s integration times were used during a campaign in April 2004 on an FPI located in northern Sweden in the auroral oval. The FPI is used to study the thermosphere by measuring the oxygen red line emission at 630.0 nm, which emits at an altitude of approximately 240 km. Previous time resolutions have been 4 min at best, due to the cycle of look directions normally observed. By using 10 s rather than 40 s integration times, and by limiting the number of full cycles in a night, high resolution measurements down to 15 s were achievable. This has allowed the maximum variability of the thermospheric winds and temperatures, and 630.0 nm emission intensities, at approximately 240 km, to be determined as a few minutes. This is a significantly greater variability than the often assumed value of 1 h or more. A Lomb-Scargle analysis of this data has shown evidence of gravity wave activity with waves with short periods. Gravity waves are an important feature of mesospherelower thermosphere (MLT) dynamics, observed using many techniques and providing an important mechanism for energy transfer between atmospheric regions. At high latitudes gravity waves may be generated in-situ by localised auroral activity. Short period waves were detected in all four clear nights when this experiment was performed, in 630.0 nm intensities and thermospheric winds and temperatures. Waves with many periodicities were observed, from periods of several hours, down to 14 min. These waves were seen in all parameters over several nights, implying that this variability is a typical property of the thermosphere

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

Restrictions on Negative Energy Density in Flat Spacetime

In a previous paper, a bound on the negative energy density seen by an arbitrary inertial observer was derived for the free massless, quantized scalar field in four-dimensional Minkowski spacetime. This constraint has the form of an uncertainty principle-type limitation on the magnitude and duration of the negative energy density. That result was obtained after a somewhat complicated analysis. The goal of the current paper is to present a much simpler method for obtaining such constraints. Similar ``quantum inequality'' bounds on negative energy density are derived for the electromagnetic field, and for the massive scalar field in both two and four-dimensional Minkowski spacetime.Comment: 17 pages, including two figures, uses epsf, minor revisions in the Introduction, conclusions unchange

A Superluminal Subway: The Krasnikov Tube

The ``warp drive'' metric recently presented by Alcubierre has the problem that an observer at the center of the warp bubble is causally separated from the outer edge of the bubble wall. Hence such an observer can neither create a warp bubble on demand nor control one once it has been created. In addition, such a bubble requires negative energy densities. One might hope that elimination of the first problem might ameliorate the second as well. We analyze and generalize a metric, originally proposed by Krasnikov for two spacetime dimensions, which does not suffer from the first difficulty. As a consequence, the Krasnikov metric has the interesting property that although the time for a one-way trip to a distant star cannot be shortened, the time for a round trip, as measured by clocks on Earth, can be made arbitrarily short. In our four dimensional extension of this metric, a ``tube'' is constructed along the path of an outbound spaceship, which connects the Earth and the star. Inside the tube spacetime is flat, but the light cones are opened out so as to allow superluminal travel in one direction. We show that, although a single Krasnikov tube does not involve closed timelike curves, a time machine can be constructed with a system of two non-overlapping tubes. Furthermore, it is demonstrated that Krasnikov tubes, like warp bubbles and traversable wormholes, also involve unphysically thin layers of negative energy density, as well as large total negative energies, and therefore probably cannot be realized in practice.Comment: 20 pages, LATEX, 5 eps figures, uses \eps

Averaged Energy Conditions and Quantum Inequalities

Connections are uncovered between the averaged weak (AWEC) and averaged null (ANEC) energy conditions, and quantum inequality restrictions on negative energy for free massless scalar fields. In a two-dimensional compactified Minkowski universe, we derive a covariant quantum inequality-type bound on the difference of the expectation values of the energy density in an arbitrary quantum state and in the Casimir vacuum state. From this bound, it is shown that the difference of expectation values also obeys AWEC and ANEC-type integral conditions. In contrast, it is well-known that the stress tensor in the Casimir vacuum state alone satisfies neither quantum inequalities nor averaged energy conditions. Such difference inequalities represent limits on the degree of energy condition violation that is allowed over and above any violation due to negative energy densities in a background vacuum state. In our simple two-dimensional model, they provide physically interesting examples of new constraints on negative energy which hold even when the usual AWEC, ANEC, and quantum inequality restrictions fail. In the limit when the size of the space is allowed to go to infinity, we derive quantum inequalities for timelike and null geodesics which, in appropriate limits, reduce to AWEC and ANEC in ordinary two-dimensional Minkowski spacetime. We also derive a quantum inequality bound on the energy density seen by an inertial observer in four-dimensional Minkowski spacetime. The bound implies that any inertial observer in flat spacetime cannot see an arbitrarily large negative energy density which lasts for an arbitrarily long period of time.Comment: 20pp, plain LATEX, TUTP-94-1

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 $d$-dimensional Minkowski space ($d\ge 2$) for the free real scalar field of mass $m\ge 0$. 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