Cosmological and Black Hole Horizon Fluctuations

The quantum fluctuations of horizons in Robertson-Walker universes and in the Schwarzschild spacetime are discussed. The source of the metric fluctuations is taken to be quantum linear perturbations of the gravitational field. Lightcone fluctuations arise when the retarded Green's function for a massless field is averaged over these metric fluctuations. This averaging replaces the delta-function on the classical lightcone with a Gaussian function, the width of which is a measure of the scale of the lightcone fluctuations. Horizon fluctuations are taken to be measured in the frame of a geodesic observer falling through the horizon. In the case of an expanding universe, this is a comoving observer either entering or leaving the horizon of another observer. In the black hole case, we take this observer to be one who falls freely from rest at infinity. We find that cosmological horizon fluctuations are typically characterized by the Planck length. However, black hole horizon fluctuations in this model are much smaller than Planck dimensions for black holes whose mass exceeds the Planck mass. Furthermore, we find black hole horizon fluctuations which are sufficiently small as not to invalidate the semiclassical derivation of the Hawking process.Comment: 22 pages, Latex, 4 figures, uses eps

Adaptive Scheduling Algorithms for Planet Searches

High-precision radial velocity planet searches have surveyed over ~2000 nearby stars and detected over ~200 planets. While these same stars likely harbor many additional planets, they will become increasingly challenging to detect, as they tend to have relatively small masses and/or relatively long orbital periods. Therefore, observers are increasing the precision of their observations, continuing to monitor stars over decade timescales, and also preparing to survey thousands more stars. Given the considerable amounts of telescope time required for such observing programs, it is important use the available resources as efficiently as possible. Previous studies have found that a wide range of predetermined scheduling algorithms result in planet searches with similar sensitivities. We have developed adaptive scheduling algorithms which have a solid basis in Bayesian inference and information theory and also are computationally feasible for modern planet searches. We have performed Monte Carlo simulations of plausible planet searches to test the power of adaptive scheduling algorithms. Our simulations demonstrate that planet searches performed with adaptive scheduling algorithms can simultaneously detect more planets, detect less massive planets, and measure orbital parameters more accurately than comparable surveys using a non-adaptive scheduling algorithm. We expect that these techniques will be particularly valuable for the N2K radial velocity planet search for short-period planets as well as future astrometric planet searches with the Space Interferometry Mission which aim to detect terrestrial mass planets.Comment: 20 pages, 6 figures, accepted to A

Spectral Line Broadening and Angular Blurring due to Spacetime Geometry Fluctuations

We treat two possible phenomenological effects of quantum fluctuations of spacetime geometry: spectral line broadening and angular blurring of the image of a distance source. A geometrical construction will be used to express both effects in terms of the Riemann tensor correlation function. We apply the resulting expressions to study some explicit examples in which the fluctuations arise from a bath of gravitons in either a squeezed state or a thermal state. In the case of a squeezed state, one has two limits of interest: a coherent state which exhibits classical time variation but no fluctuations, and a squeezed vacuum state, in which the fluctuations are maximized.Comment: 21 pages, 2 figures. Dedicated to Raphael Sorkin on the occasion of his 60th birthday. (v2: several references added and some minor errors corrected

Energy Density-Flux Correlations in an Unusual Quantum State and in the Vacuum

In this paper we consider the question of the degree to which negative and positive energy are intertwined. We examine in more detail a previously studied quantum state of the massless minimally coupled scalar field, which we call a ``Helfer state''. This is a state in which the energy density can be made arbitrarily negative over an arbitrarily large region of space, but only at one instant in time. In the Helfer state, the negative energy density is accompanied by rapidly time-varying energy fluxes. It is the latter feature which allows the quantum inequalities, bounds which restrict the magnitude and duration of negative energy, to hold for this class of states. An observer who initially passes through the negative energy region will quickly encounter fluxes of positive energy which subsequently enter the region. We examine in detail the correlation between the energy density and flux in the Helfer state in terms of their expectation values. We then study the correlation function between energy density and flux in the Minkowski vacuum state, for a massless minimally coupled scalar field in both two and four dimensions. In this latter analysis we examine correlation functions rather than expectation values. Remarkably, we see qualitatively similar behavior to that in the Helfer state. More specifically, an initial negative energy vacuum fluctuation in some region of space is correlated with a subsequent flux fluctuation of positive energy into the region. We speculate that the mechanism which ensures that the quantum inequalities hold in the Helfer state, as well as in other quantum states associated with negative energy, is, at least in some sense, already ``encoded'' in the fluctuations of the vacuum.Comment: 21 pages, 7 figures; published version with typos corrected and one added referenc

Stochastic Spacetime and Brownian Motion of Test Particles

The operational meaning of spacetime fluctuations is discussed. Classical spacetime geometry can be viewed as encoding the relations between the motions of test particles in the geometry. By analogy, quantum fluctuations of spacetime geometry can be interpreted in terms of the fluctuations of these motions. Thus one can give meaning to spacetime fluctuations in terms of observables which describe the Brownian motion of test particles. We will first discuss some electromagnetic analogies, where quantum fluctuations of the electromagnetic field induce Brownian motion of test particles. We next discuss several explicit examples of Brownian motion caused by a fluctuating gravitational field. These examples include lightcone fluctuations, variations in the flight times of photons through the fluctuating geometry, and fluctuations in the expansion parameter given by a Langevin version of the Raychaudhuri equation. The fluctuations in this parameter lead to variations in the luminosity of sources. Other phenomena which can be linked to spacetime fluctuations are spectral line broadening and angular blurring of distant sources.Comment: 15 pages, 3 figures. Talk given at the 9th Peyresq workshop, June 200

Who is in the transition gap? Transition from CAMHS to AMHS in the Republic of Ireland

Objective: The ITRACK study explored the process and predictors of transition between Child and Adolescent Mental Health Services (CAMHS) and Adult Mental Health Services (AMHS) in the Republic of Ireland. Method: Following ethical approval, clinicians in each of Ireland's four Health Service Executive (HSE) areas were contacted, informed about the study and invited to participate. Clinicians identified all cases who had reached the transition boundary (i.e. upper age limit for that CAMHS team ) between January and December 2010. Data were collected on clinical and socio-demographic details and factors that informed the decision to refer or not refer to AMHS and case notes were scrutinised to ascertain the extent of information exchanged between services during transition

The averaged null energy condition and difference inequalities in quantum field theory

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical space, although the stress-energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (non-achronal) null geodesics, when the ``Casimir-vacuum" contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ``difference inequalities." Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary two-dimensional spacetime, using the same techniques as those we relied on to prove ANEC in an earlier paper with Robert Wald. I begin with an overview of averaged energy conditions in quantum field theory.Comment: 20 page

Relation Between Einstein And Quantum Field Equations

We show that there exists a choice of scalar field modes, such that the evolution of the quantum field in the zero-mass and large-mass limits is consistent with the Einstein equations for the background geometry. This choice of modes is also consistent with zero production of these particles and thus corresponds to a preferred vacuum state preserved by the evolution. In the zero-mass limit, we find that the quantum field equation implies the Einstein equation for the scale factor of a radiation-dominated universe; in the large-mass case, it implies the corresponding Einstein equation for a matter-dominated universe. Conversely, if the classical radiation-dominated or matter-dominated Einstein equations hold, there is no production of scalar particles in the zero and large mass limits, respectively. The suppression of particle production in the large mass limit is over and above the expected suppression at large mass. Our results hold for a certain class of conformally ultrastatic background geometries and therefore generalize previous results by one of us for spatially flat Robertson-Walker background geometries. In these geometries, we find that the temporal part of the graviton equations reduces to the temporal equation for a massless minimally coupled scalar field, and therefore the results for massless particle production hold also for gravitons. Within the class of modes we study, we also find that the requirement of zero production of massless scalar particles is not consistent with a non-zero cosmological constant. Possible implications are discussed.Comment: Latex, 24 pages. Minor changes in text from original versio

Enhanced Geometry Fluctuations in Minkowski and Black Hole Spacetimes

We will discuss selected physical effects of spacetime geometry fluctuations, especially the operational signatures of geometry fluctuations and their effects on black hole horizons. The operational signatures which we discuss involve the effects of the fluctuations on images, and include luminosity variations, spectral line broadening and angular blurring. Our main interest will be in black hole horizon fluctuations, especially horizon fluctuations which have been enhanced above the vacuum level by gravitons or matter in squeezed states. We investigate whether these fluctuations can alter the thermal character of a black hole. We find that this thermal character is remarkably robust, and that Hawking's original derivation using transplanckian modes does not seem to be sensitive even to enhanced horizon fluctuations.Comment: 13 pages, 3 figures, based on a talk presented at the Peyresq 12 worksho