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

Quantum measurement and decoherence

Distribution functions defined in accord with the quantum theory of measurement are combined with results obtained from the quantum Langevin equation to discuss decoherence in quantum Brownian motion. Closed form expressions for wave packet spreading and the attenuation of coherence of a pair of wave packets are obtained. The results are exact within the context of linear passive dissipation. It is shown that, contrary to widely accepted current belief, decoherence can occur at high temperature in the absence of dissipation. Expressions for the decoherence time with and without dissipation are obtained that differ from those appearing in earlier discussions

A Causal Algebra for Liouville Exponentials

A causal Poisson bracket algebra for Liouville exponentials on a cylinder is derived using an exchange algebra for free fields describing the in and out asymptotics. The causal algebra involves an even number of space-time points with a minimum of four. A quantum realisation of the algebra is obtained which preserves causality and the local form of non-equal time brackets.Comment: 10 page

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

Barriers and predictors of medication use for childhood ADHD: findings from a UK population-representative cohort

This is the final version. Available from Springer Verlag via the DOI in this record.Purpose Little is known about sociodemographic and clinical factors that predict and act as barriers to ADHD medication independently of symptom severity. We examined the proportion of children using medication for ADHD, age of initiation of medication, and predictors of medication use in a population-representative cohort. Methods Data from the Millennium Cohort Study on child ADHD, medication use for ADHD at age 14 (in 2014–2015) and child, parent and sociodemographic variables were collated. Logistic regression models were used to identify factors that predict medication use for ADHD (the main outcome measure), adjusting for symptom severity at age seven. Results The weighted prevalence of ADHD was 3.97% (N = 11,708). 45.57% of children with ADHD (N = 305) were taking medication. The median age at initiation was 9 years (range 3–14). Male gender (AOR 3.66, 95% CI 1.75, 7.66) and conduct problems at age seven (AOR 1.24 95% CI 1.04, 1.47) and 14 predicted medication use at age 14 after adjusting for symptom severity. Conclusions Our study is the first to assess predictors of medication whist adjusting for ADHD symptom severity. Girls with ADHD were less likely to be prescribed medication, even when they displayed similar ADHD symptom levels to boys. Conduct problems also predicted medication independently of ADHD symptoms. ADHD may be more often medicated in boys because clinicians may think a prototypical ADHD child is male, and perhaps conduct problems make boys more disruptive in the classroom, leading to boys being more often treated.Wellcome Trus

The history of mass assembly of faint red galaxies in 28 galaxy clusters since z=1.3

We measure the relative evolution of the number of bright and faint (as faint as 0.05 L*) red galaxies in a sample of 28 clusters, of which 16 are at 0.50<= z<=1.27, all observed through a pair of filters bracketing the 4000 Angstrom break rest-frame. The abundance of red galaxies, relative to bright ones, is constant over all the studied redshift range, 0<z<1.3, and rules out a differential evolution between bright and faint red galaxies as large as claimed in some past works. Faint red galaxies are largely assembled and in place at z=1.3 and their deficit does not depend on cluster mass, parametrized by velocity dispersion or X-ray luminosity. Our analysis, with respect to previous one, samples a wider redshift range, minimizes systematics and put a more attention to statistical issues, keeping at the same time a large number of clusters.Comment: MNRAS, 386, 1045. Half a single sentence (in sec 4.4) change

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

Limits on Lorentz Violation from the Highest Energy Cosmic Rays

We place several new limits on Lorentz violating effects, which can modify particles' dispersion relations, by considering the highest energy cosmic rays observed. Since these are hadrons, this involves considering the partonic content of such cosmic rays. We get a number of bounds on differences in maximum propagation speeds, which are typically bounded at the 10^{-21} level, and on momentum dependent dispersion corrections of the form v = 1 +- p^2/Lambda^2, which typically bound Lambda > 10^{21} GeV, well above the Planck scale. For (CPT violating) dispersion correction of the form v = 1 + p/Lambda, the bounds are up to 15 orders of magnitude beyond the Planck scale.Comment: 24 pages, no figures. Added references, very slight changes. Version published in Physical Review

A Third Planet Orbiting HIP 14810

We present new precision radial velocities and a three-planet Keplerian orbit fit for the V = 8.5, G5 V star HIP 14810. We began observing this star at Keck Observatory as part of the N2K Planet Search Project. Wright et al. (2007) announced the inner two planets to this system, and subsequent observations have revealed the outer planet planet and the proper orbital solution for the middle planet. The planets have minimum masses of 3.9, 1.3, and 0.6 M_Jup and orbital periods of 6.67, 147.7, and 952 d, respectively. We have numerically integrated the family of orbital solutions consistent with the data and find that they are stable for at least 10^6 yr. Our photometric search shows that the inner planet does not transit.Comment: ApJL, accepte