The Refractive Index of Curved Spacetime II: QED, Penrose Limits and Black Holes

This work considers the way that quantum loop effects modify the propagation of light in curved space. The calculation of the refractive index for scalar QED is reviewed and then extended for the first time to QED with spinor particles in the loop. It is shown how, in both cases, the low frequency phase velocity can be greater than c, as found originally by Drummond and Hathrell, but causality is respected in the sense that retarded Green functions vanish outside the lightcone. A "phenomenology" of the refractive index is then presented for black holes, FRW universes and gravitational waves. In some cases, some of the polarization states propagate with a refractive index having a negative imaginary part indicating a potential breakdown of the optical theorem in curved space and possible instabilities.Comment: 62 pages, 14 figures, some signs corrected in formulae and graph

Data‐driven basis functions for SuperDARN ionospheric plasma flow characterisation and prediction

The archive of plasma velocity measurements from the Super Dual Auroral Radar Network (SuperDARN) provides a rich dataset for investigation of magnetosphere-ionosphere-thermosphere coupling. However, systematic gaps in this archive exist in space, time, and radar look-direction. These gaps are generally infilled using climatological averages, spatially smoothed models, or a priori relationships determined from solar wind drivers. We describe a new technique for infilling the data gaps in the SuperDARN archive which requires no external information and is based solely on the SuperDARN measurements. We also avoid the use of climatological averaging or spatial smoothing when computing the infill. In this regard, our approach captures the true variability in the SuperDARN measurements. Our technique is based on data-interpolating Empirical Orthogonal Function (EOF) analysis. This method discovers from the SuperDARN data a series of dynamical modes of plasma velocity variation. We compute the modes of a sample month of northern hemisphere winter data, and investigate these in terms of solar wind driving. We find that the By component of the Interplanetary Magnetic Field (IMF) dominates the variability of the plasma velocity. The IMF Bz component is the dominant driver for the background mean field, and a series of non-leading modes which describe the two-cell convection variability, and the substorm. We recommend our new technique for reanalysis investigations of polar-scale plasma drift phenomena, particularly those with rapid temporal fluctuations and an indirect relationship to the solar wind

An empirical orthogonal function reanalysis of the northern polar external and induced magnetic field during solar cycle 23

We apply the method of data-interpolating Empirical Orthogonal Functions (EOFs) to ground-based magnetic vector data from the SuperMAG archive to produce a series of month-length reanalyses of the surface external and induced magnetic field (SEIMF) in 110,000 km2 equal-area bins over the entire northern polar region at 5-minute cadence over solar cycle 23, from 1997.0 to 2009.0. Each EOF re-analysis also decomposes the measured SEIMF variation into a hierarchy of spatio-temporal patterns which are ordered by their contribution to the monthly magnetic field variance. We find that the leading EOF patterns can each be (subjectively) interpreted as well-known SEIMF systems or their equivalent current systems. The relationship of the equivalent currents to the true current flow is not investigated. We track the leading SEIMF or equivalent current systems of similar type by inter-monthly spatial correlation, and apply graph theory to (objectively) group their appearance and relative importance throughout a solar cycle, revealing seasonal and solar cycle variation. In this way, we identify the spatiotemporal patterns which maximally contribute to SEIMF variability over a solar cycle. We propose this combination of EOF and graph theory as a powerful method for objectively defining and investigating the structure and variability of the SEIMF or their equivalent ionospheric currents for use in both geomagnetism and space weather applications. It is demonstrated here on solar cycle 23, but is extendable to any epoch with sufficient data coverage

Spatial variation in the responses of the surface external and induced magnetic field to the solar wind

We analyse the spatial variation in the response of the surface geomagnetic field (or the equivalent ionospheric current) to variations in the solar wind. Specifically, we regress a reanalysis of surface external and induced magnetic field (SEIMF) variations onto measurements of the solar wind. The regression is performed in monthly sets, independently for 559 regularly‐spaced locations covering the entire northern polar region above 50° magnetic latitude. At each location, we find the lag applied to the solar wind data that maximises the correlation with the SEIMF. The resulting spatial maps of these independent lags and regression coefficients provide a model of the localised SEIMF response to variations in the solar wind, which we call ‘Spatial Information from Distributed Exogenous Regression’ (SPIDER). We find that the lag and regression coefficients vary systematically with ionospheric region, season, and solar wind driver. In the polar cap region the SEIMF is best described by the By component of the interplanetary magnetic field (50–75% of total variance explained) at a lag ∼20–25 min. Conversely, in the auroral zone the SEIMF is best described by the solar wind ϵ function (60–80% of total variance explained), with a lag that varies with season and magnetic local time (MLT), from ∼15–20 min for dayside and afternoon MLT (except in Oct‐Dec) to typically 30–40 min for nightside and morning MLT, and even longer (60–65 min) around midnight MLT

Dark energy, non-minimal couplings and the origin of cosmic magnetic fields

In this work we consider the most general electromagnetic theory in curved space-time leading to linear second order differential equations, including non-minimal couplings to the space-time curvature. We assume the presence of a temporal electromagnetic background whose energy density plays the role of dark energy, as has been recently suggested. Imposing the consistency of the theory in the weak-field limit, we show that it reduces to standard electromagnetism in the presence of an effective electromagnetic current which is generated by the momentum density of the matter/energy distribution, even for neutral sources. This implies that in the presence of dark energy, the motion of large-scale structures generates magnetic fields. Estimates of the present amplitude of the generated seed fields for typical spiral galaxies could reach $10^{-9}$ G without any amplification. In the case of compact rotating objects, the theory predicts their magnetic moments to be related to their angular momenta in the way suggested by the so called Schuster-Blackett conjecture.Comment: 5 pages, no figure

The Causal Structure of QED in Curved Spacetime: Analyticity and the Refractive Index

The effect of vacuum polarization on the propagation of photons in curved spacetime is studied in scalar QED. A compact formula is given for the full frequency dependence of the refractive index for any background in terms of the Van Vleck-Morette matrix for its Penrose limit and it is shown how the superluminal propagation found in the low-energy effective action is reconciled with causality. The geometry of null geodesic congruences is found to imply a novel analytic structure for the refractive index and Green functions of QED in curved spacetime, which preserves their causal nature but violates familiar axioms of S-matrix theory and dispersion relations. The general formalism is illustrated in a number of examples, in some of which it is found that the refractive index develops a negative imaginary part, implying an amplification of photons as an electromagnetic wave propagates through curved spacetime.Comment: 54 pages, 19 figures, corrected some signs in formulae and graph

Implications of Space-Time foam for Entanglement Correlations of Neutral Kaons

The role of $CPT$ invariance and consequences for bipartite entanglement of neutral (K) mesons are discussed. A relaxation of $CPT$ leads to a modification of the entanglement which is known as the $\omega$ effect. The relaxation of assumptions required to prove the $CPT$ theorem are examined within the context of models of space-time foam. It is shown that the evasion of the EPR type entanglement implied by $CPT$ (which is connected with spin statistics) is rather elusive. Relaxation of locality (through non-commutative geometry) or the introduction of decoherence by themselves do not lead to a destruction of the entanglement. So far we find only one model which is based on non-critical strings and D-particle capture and recoil that leads to a stochastic contribution to the space-time metric and consequent change in the neutral meson bipartite entanglement. The lack of an omega effect is demonstrated for a class of models based on thermal like baths which are generally considered as generic models of decoherence

Decoherence and CPT Violation in a Stringy Model of Space-Time Foam

I discuss a model inspired from the string/brane framework, in which our Universe is represented as a three brane, propagating in a bulk space time punctured by D0-brane (D-particle) defects. As the D3-brane world moves in the bulk, the D-particles cross it, and from an effective observer on D3 the situation looks like a ``space-time foam'' with the defects ``flashing'' on and off (``D-particle foam''). The open strings, with their ends attached on the brane, which represent matter in this scenario, can interact with the D-particles on the D3-brane universe in a topologically non-trivial manner, involving splitting and capture of the strings by the D0-brane defects. Such processes are described by logarithmic conformal field theories on the world-sheet. Physically, they result in effective decoherence of the string matter on the D3 brane, and as a result, of CPT Violation, but of a type that implies an ill-defined nature of the effective CPT operator. Due to electric charge conservation, only electrically neutral (string) matter can exhibit such interactions with the D-particle foam. This may have unique, experimentally detectable, consequences for electrically-neutral entangled quantum matter states on the brane world, in particular the modification of the pertinent EPR Correlation of neutral mesons in a meson factory.Comment: 41 pages Latex, five eps figures incorporated. Uses special macro

Unfolding of differential energy spectra in the MAGIC experiment

The paper describes the different methods, used in the MAGIC experiment, to unfold experimental energy distributions of cosmic ray particles (gamma-rays). Questions and problems related to the unfolding are discussed. Various procedures are proposed which can help to make the unfolding robust and reliable. The different methods and procedures are implemented in the MAGIC software and are used in most of the analyses.Comment: Submitted to NIM

Implementation of the Random Forest Method for the Imaging Atmospheric Cherenkov Telescope MAGIC

The paper describes an application of the tree classification method Random Forest (RF), as used in the analysis of data from the ground-based gamma telescope MAGIC. In such telescopes, cosmic gamma-rays are observed and have to be discriminated against a dominating background of hadronic cosmic-ray particles. We describe the application of RF for this gamma/hadron separation. The RF method often shows superior performance in comparison with traditional semi-empirical techniques. Critical issues of the method and its implementation are discussed. An application of the RF method for estimation of a continuous parameter from related variables, rather than discrete classes, is also discussed.Comment: 16 pages, 8 figure