J.S. Bell's Concept of Local Causality

John Stewart Bell's famous 1964 theorem is widely regarded as one of the most important developments in the foundations of physics. It has even been described as "the most profound discovery of science." Yet even as we approach the 50th anniversary of Bell's discovery, its meaning and implications remain controversial. Many textbooks and commentators report that Bell's theorem refutes the possibility (suggested especially by Einstein, Podolsky, and Rosen in 1935) of supplementing ordinary quantum theory with additional ("hidden") variables that might restore determinism and/or some notion of an observer-independent reality. On this view, Bell's theorem supports the orthodox Copenhagen interpretation. Bell's own view of his theorem, however, was quite different. He instead took the theorem as establishing an "essential conflict" between the now well-tested empirical predictions of quantum theory and relativistic \emph{local causality}. The goal of the present paper is, in general, to make Bell's own views more widely known and, in particular, to explain in detail Bell's little-known mathematical formulation of the concept of relativistic local causality on which his theorem rests. We thus collect and organize many of Bell's crucial statements on these topics, which are scattered throughout his writings, into a self-contained, pedagogical discussion including elaborations of the concepts "beable", "completeness", and "causality" which figure in the formulation. We also show how local causality (as formulated by Bell) can be used to derive an empirically testable Bell-type inequality, and how it can be used to recapitulate the EPR argument.Comment: 19 pages, 4 figure

A Numerical Study of Methods for Moist Atmospheric Flows: Compressible Equations

We investigate two common numerical techniques for integrating reversible moist processes in atmospheric flows in the context of solving the fully compressible Euler equations. The first is a one-step, coupled technique based on using appropriate invariant variables such that terms resulting from phase change are eliminated in the governing equations. In the second approach, which is a two-step scheme, separate transport equations for liquid water and vapor water are used, and no conversion between water vapor and liquid water is allowed in the first step, while in the second step a saturation adjustment procedure is performed that correctly allocates the water into its two phases based on the Clausius-Clapeyron formula. The numerical techniques we describe are first validated by comparing to a well-established benchmark problem. Particular attention is then paid to the effect of changing the time scale at which the moist variables are adjusted to the saturation requirements in two different variations of the two-step scheme. This study is motivated by the fact that when acoustic modes are integrated separately in time (neglecting phase change related phenomena), or when sound-proof equations are integrated, the time scale for imposing saturation adjustment is typically much larger than the numerical one related to the acoustics

Trends and Regional Variation in Hip, Knee and Shoulder Replacement

Analyzes patterns in underuse or overuse of joint replacements among Medicare beneficiaries by geographic regions and race/ethnicity. Explores underlying factors and highlights the need for physician and patient education and shared decision making

The GHOSTS survey. II. The diversity of Halo Color and Metallicity Profiles of Massive Disk Galaxies

We study the stellar halo color properties of six nearby massive highly inclined disk galaxies using Hubble Space Telescope Advanced Camera for Surveys and Wide Field Camera 3 observations in both F606W and F814W filters from the GHOSTS survey. The observed fields, placed both along the minor and major axis of each galaxy, probe the stellar outskirts out to projected distances of ~ 50-70 kpc from their galactic centre along the minor axis. The 50% completeness levels of the color magnitude diagrams are typically at two mag below the tip of the red giant branch. We find that all galaxies have extended stellar halos out to ~ 50 kpc and two out to ~ 70 kpc. We determined the halo color distribution and color profile for each galaxy using the median colors of stars in the RGB. Within each galaxy we find variations in the median colors as a function of radius which likely indicates population variations, reflecting that their outskirts were built from several small accreted objects. We find that half of the galaxies (NGC 0891, NGC 4565, and NGC 7814) present a clear negative color gradient, reflecting a declining metallicity in their halos; the other have no significant color or population gradient. In addition, notwithstanding the modest sample size of galaxies, there is no strong correlation between their halo color/metallicity or gradient with galaxy's properties such as rotational velocity or stellar mass. The diversity in halo color profiles observed in the GHOSTS galaxies qualitatively supports the predicted galaxy-to-galaxy scatter in halo stellar properties; a consequence of the stochasticity inherent in the assembling history of galaxies.Comment: Accepted by MNRAS, 31 pages, 18 figures. Appendix added and some editions to match accepted version. Conclusions unchange

Hierarchical relationships in dependency grids : explorations in survivors of childhood sexual abuse

Original article can be found at: http://www.informaworld.com/ Copyright Informa / Taylor & FrancisA methodology for representing the patterns of dependency in a dependency grid using partial order scalogram analysis by coordinates (POSAC) is presented. The technique, devised by Shye (1985), shows these patterns as hierarchical relationships that indicate superordinate and subordinate resources. An index of depth of resource support is calculated in addition to an index of breadth of resource (which is shown to correspond to an index of dispersion of dependency). The procedure was applied to data from 54 survivors of child sexual abuse and a similar number of control subjects who all completed both an adult and child dependency grid. There was significantly less breadth of resource in the abuse group, more so for the child version than the adult, but there was significantly more depth of resource in the dependency grids from the child sexual abuse survivors.Peer reviewe