``Faster than Light'' Photons in Gravitational Fields -- Causality, Anomalies and Horizons

A number of general issues relating to superluminal photon propagation in gravitational fields are explored. The possibility of superluminal, yet causal, photon propagation arises because of Equivalence Principle violating interactions induced by vacuum polarisation in QED in curved spacetime. Two general theorems are presented: first, a polarisation sum rule which relates the polarisation averaged velocity shift to the matter energy-momentum tensor and second, a `horizon theorem' which ensures that the geometric event horizon for black hole spacetimes remains a true horizon for real photon propagation in QED. A comparision is made with the equivalent results for electromagnetic birefringence and possible connections between superluminal photon propagation, causality and the conformal anomaly are exposed.Comment: 15 pages, Plain Te

`Faster than light' photons and rotating black holes

The effective action for QED in curved spacetime includes equivalence principle violating interactions between the electromagnetic field and the spacetime curvature. These interactions admit the possibility of superluminal yet causal photon propagation in gravitational fields. In this paper, we extend our analysis of photon propagation in gravitational backgrounds to the Kerr spacetime describing a rotating black hole. The results support two general theorems -- a polarisation sum rule and a `horizon theorem'. The implications for the stationary limit surface bounding the ergosphere are also discussed.Comment: Plain TeX, 12 pages, 1 figur

Light propagation in non-trivial QED vacua

Within the framework of effective action QED, we derive the light cone condition for homogeneous non-trivial QED vacua in the geometric optics approximation. Our result generalizes the ``unified formula'' suggested by Latorre, Pascual and Tarrach and allows for the calculation of velocity shifts and refractive indices for soft photons travelling through these vacua. Furthermore, we clarify the connection between the light velocity shift and the scale anomaly. This study motivates the introduction of a so-called effective action charge that characterizes the velocity modifying properties of the vacuum. Several applications are given concerning vacuum modifications caused by, e.g., strong fields, Casimir systems and high temperature.Comment: 13 pages, REVTeX, 3 figures, to appear in Phys. Rev.

Ecosystem Services and Opportunity Costs Shift Spatial Priorities for Conserving Forest Biodiversity

Inclusion of spatially explicit information on ecosystem services in conservation planning is a fairly new practice. This study analyses how the incorporation of ecosystem services as conservation features can affect conservation of forest biodiversity and how different opportunity cost constraints can change spatial priorities for conservation. We created spatially explicit cost-effective conservation scenarios for 59 forest biodiversity features and five ecosystem services in the county of Telemark (Norway) with the help of the heuristic optimisation planning software, Marxan with Zones. We combined a mix of conservation instruments where forestry is either completely (non-use zone) or partially restricted (partial use zone). Opportunity costs were measured in terms of foregone timber harvest, an important provisioning service in Telemark. Including a number of ecosystem services shifted priority conservation sites compared to a case where only biodiversity was considered, and increased the area of both the partial (+36.2%) and the non-use zone (+3.2%). Furthermore, opportunity costs increased (+6.6%), which suggests that ecosystem services may not be a side-benefit of biodiversity conservation in this area. Opportunity cost levels were systematically changed to analyse their effect on spatial conservation priorities. Conservation of biodiversity and ecosystem services trades off against timber harvest. Currently designated nature reserves and landscape protection areas achieve a very low proportion (9.1%) of the conservation targets we set in our scenario, which illustrates the high importance given to timber production at present. A trade-off curve indicated that large marginal increases in conservation target achievement are possible when the budget for conservation is increased. Forty percent of the maximum hypothetical opportunity costs would yield an average conservation target achievement of 79%

Assessing ecosystem services from multifunctional trees in pastures using Bayesian belief networks

A Bayesian belief network (BBN) was developed to assess preferred combinations of trees in live fences and on pastures in silvopastoral systems. The BBN was created with information from Rivas, Nicaragua, using local farmer knowledge on tree species, trees' costs and benefits, farmers' expressed needs and aspirations, and scientific knowledge regarding tree functional traits and their contribution to ecosystem services and benefits. The model identifies combinations of trees, which provide multiple ecosystem services from pastures, improving their productivity and contribution to farmer livelihoods. We demonstrate how the identification of portfolios of multifunctional trees can satisfy a profile of desired ecosystem services prioritized by the farmer. Diagnostics using Bayesian inference starts with an identification of farmer needs and ‘works backwards’ to identify a silvopastoral system structure. We conclude that Bayesian belief networks are a promising modeling technique for multi-criteria decisions in farm adaptation processes, where interventions must be adapted to specific contexts and farmer preferences

Faster than Light Photons in Gravitational Fields II - Dispersion and Vacuum Polarisation

Vacuum polarisation in QED in a background gravitational field induces interactions which effectively violate the strong equivalence principle and affect the propagation of light. In the low frequency limit, Drummond and Hathrell have shown that this mechanism leads to superluminal photon velocities. To confront this phenomenon with causality, however, it is necessary to extend the calculation of the phase velocity \vp(\w) to high frequencies, since it is \vp(\infty) which determines the characteristics of the effective wave equation and thus the causal structure. In this paper, we use a recently constructed expression, valid to all orders in a derivative expansion, for the effective action of QED in curved spacetime to determine the frequency dependence of the phase velocity and investigate whether superluminal velocities indeed persist in the high frequency limit.Comment: 27 pages, 7 figures, TeX with harvma

Influence of enhanced melt supply on upper crustal structure at a mid-ocean ridge discontinuity: A three-dimensional seismic tomographic study of 9°N East Pacific Rise

We present a three-dimensional upper crustal model of the 9°03′N overlapping spreading center (OSC) on the East Pacific Rise that assists in understanding the relationship between melt sills and upper crustal structure at a ridge discontinuity with enhanced melt supply at crustal levels. Our P wave velocity model obtained from tomographic inversion of ∼70,000 crustal first arrival travel times suggests that the geometry of extrusive emplacement are significantly different beneath the overlapping spreading limbs. Extrusive volcanic rocks above the western melt sill are inferred to be thin (∼250 m). More extensive accumulation of extrusives is inferred to the west than to the east of the western melt sill. The extrusive layer inferred above the eastern melt sill thickens from ∼350 (at the neovolcanic axis) to 550 m (to the west of the melt sill). Volcanic construction is likely to be significant in the formation of ridge crest morphology at the OSC, particularly at the tip of the eastern limb. On the basis of our interpretation of the velocity model, we propose that enhanced magma supply at crustal levels at the OSC may provide an effective mechanism for the migration of ridge discontinuities. This “dynamic magma supply model” may explain the commonly observed nonsteady migration pattern of ridge discontinuities by attributing this to the temporal fluctuations in melt availability to the overlapping spreading limbs

Dynamical Casimir effect without boundary conditions

The moving-mirror problem is microscopically formulated without invoking the external boundary conditions. The moving mirrors are described by the quantized matter field interacting with the photon field, forming dynamical cavity polaritons: photons in the cavity are dressed by electrons in the moving mirrors. The effective Hamiltonian for the polariton is derived, and corrections to the results based on the external boundary conditions are discussed.Comment: 12 pages, 2 figure

Phase fluctuations in the ABC model

We analyze the fluctuations of the steady state profiles in the modulated phase of the ABC model. For a system of $L$ sites, the steady state profiles move on a microscopic time scale of order $L^3$. The variance of their displacement is computed in terms of the macroscopic steady state profiles by using fluctuating hydrodynamics and large deviations. Our analytical prediction for this variance is confirmed by the results of numerical simulations

Systematics of Leading Particle Production

Using a QCD inspired model developed by our group for particle production, the Interacting Gluon Model (IGM), we have made a systematic analysis of all available data on leading particle spectra. These data include diffractive collisions and photoproduction at HERA. With a small number of parameters (essentially only the non-perturbative gluon-gluon cross section and the fraction of diffractive events) good agreement with data is found. We show that the difference between pion and proton leading spectra is due to their different gluon distributions. We predict a universality in the diffractive leading particle spectra in the large momentum region, which turns out to be independent of the incident energy and of the projectile type.Comment: 13 pages, Latex, 4 ps figures. To appear in Phys. Rev.