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 Comparison of Actual and Hypothetical Willingness to Pay of Parents and Non-Parents for Protecting Infants' Health: The Case of Nitrates in Drinking Water

The objective of this research was to estimate adults' willingness to pay to reduce health risks to their or other families's infants, the latter to test for altruism. A choice experiment was conducted by having adults pay for bottled water for infants to reduce infants' exposure to nitrates in drinking water. Since nitrates only affect infants' health, we have isolated the adults' willingness to pay just for infants' health by buying bottled water to avoid infants' nitrate intake. Respondents were separated into two treatments, one with hypothetical choices, and the other where respondents were told that one of their four choices would be binding, and they would actually buy bottled water using money given to them at the beginning of the experiment. Results indicate that the marginal willingness to pay for a .001 reduction in risk of shock, brain damage and mortality in the real cash treatment was $2,$3.50 and $10, respectively. In the hypothetical treatment these amounts were$13, $23 and$64, indicating substantial hypothetical bias for the risk reductions. Nonetheless, in both treatments the relative marginal values across the severity of risk reductions are sensible, with willingness to pay to avoid the less severe health effects (e.g., shock) being much less than for the more serious effects such as brain damage and death. While the ratio of hypothetical WTP to actual WTP was rather high at a factor of nearly seven, such degree of hypothetical bias has been found in other experiments (Neil et al., 1994). This high hypothetical bias may be due to the nature of the good being valued, i.e. infant health. Many people express a very strong desire to protect infants, since infants cannot control their own health outcomes. Several statistical tests consistently confirmed that the marginal WTP for the risk reduction was not influenced by whether the individual was buying for his or her own infant or buying for another infant. This suggests there is a high degree of altruism reflected in our WTP results. This altruism continued to hold even when we focused solely on the consequential treatment where real money was involved.altruism, conjoint, drinking water, validity, willingness to pay, Health Economics and Policy,

Fluctuating hydrodynamics of multi-species, non-reactive mixtures

In this paper we discuss the formulation of the fuctuating Navier-Stokes (FNS) equations for multi-species, non-reactive fluids. In particular, we establish a form suitable for numerical solution of the resulting stochastic partial differential equations. An accurate and efficient numerical scheme, based on our previous methods for single species and binary mixtures, is presented and tested at equilibrium as well as for a variety of non-equilibrium problems. These include the study of giant nonequilibrium concentration fluctuations in a ternary mixture in the presence of a diffusion barrier, the triggering of a Rayleigh-Taylor instability by diffusion in a four-species mixture, as well as reverse diffusion in a ternary mixture. Good agreement with theory and experiment demonstrates that the formulation is robust and can serve as a useful tool in the study of thermal fluctuations for multi-species fluids. The extension to include chemical reactions will be treated in a sequel paper

A spectral deferred correction strategy for low Mach number reacting flows subject to electric fields

We propose an algorithm for low Mach number reacting flows subjected to electric field that includes the chemical production and transport of charged species. This work is an extension of a multi-implicit spectral deferred correction (MISDC) algorithm designed to advance the conservation equations in time at scales associated with advective transport. The fast and nontrivial interactions of electrons with the electric field are treated implicitly using a Jacobian-Free Newton Krylov approach for which a preconditioning strategy is developed. Within the MISDC framework, this enables a close and stable coupling of diffusion, reactions and dielectric relaxation terms with advective transport and is shown to exhibit second-order convergence in space and time. The algorithm is then applied to a series of steady and unsteady problems to demonstrate its capability and stability. Although developed in a one-dimensional case, the algorithmic ingredients are carefully designed to be amenable to multidimensional applications

A Comparison of Actual and Hypothetical Willingness to Pay of Parents and Non-Parents for Protecting Infant Health: The Case of Nitrates in Drinking Water

We estimate adults’ willingness to pay (WTP) to reduce health risks to their own or other families’ infants to test for altruism. A conjoint analysis of adults paying for bottled water found marginal WTP for reduction in risk of shock, brain damage, and mortality in the cash treatment of $2,$3.70, and $9.43, respectively. In the hypothetical market these amounts were$14, $26, and$66, indicating substantial hypothetical bias, although not unexpected due to the topic of infant health. Statistical tests confirm a high degree of altruism in our WTP results, and altruism held even when real money was involved.altruism, conjoint, drinking water, nitrates, validity, willingness to pay, Agricultural and Food Policy, Consumer/Household Economics, Food Consumption/Nutrition/Food Safety, Health Economics and Policy, Institutional and Behavioral Economics, I10, Q53,

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