Reduction and Emergence in Bose-Einstein Condensates

A closer look at some proposed Gedanken-experiments on BECs promises to shed light on several aspects of reduction and emergence in physics. These include the relations between classical descriptions and different quantum treatments of macroscopic systems, and the emergence of new properties and even new objects as a result of spontaneous symmetry breaking

Infinitesimal Idealization, Easy Road Nominalism, and Fractional Quantum Statistics

It has been recently debated whether there exists a so-called “easy road” to nominalism. In this essay, I attempt to fill a lacuna in the debate by making a connection with the literature on infinite and infinitesimal idealization in science through an example from mathematical physics that has been largely ignored by philosophers. Specifically, by appealing to John Norton’s distinction between idealization and approximation, I argue that the phenomena of fractional quantum statistics bears negatively on Mary Leng’s proposed path to easy road nominalism, thereby partially defending Mark Colyvan’s claim that there is no easy road to nominalism

Differences between dual X-ray absorptiometry using pencil beam and fan beam modes and their determinants in vivo and in vitro

The aim of this study was to determine the influence of individual factors on differences in bone mineral density (BMD) using dual X-ray absorptiometry pencil beam (PB) and fan beam (FB) modes in vivo and in vitro. PB.BMD and FB.BMD of 63 normal Caucasian females ages 21-80 yr were measured at the lumbar spine and hip. Residuals of the FB/PB regression were used to assess the impact of height, weight, adiposity index (AI) (= weight/height(3/2)), back tissue thickness, and PB.BMD, respectively, on FB/PB difference. The Hologic Anthropomorphic Spine Phantom (ASP) was measured using the PB and FB modes at two different levels to assess the impact of scanning mode and focus distance. The European Spine Phantom (ESP) prototype, a geometrically well-defined phantom with known vertebral densities, was measured using PB and FB modes and analyzed manually to determine the impact of bone density on FB/PB difference and automatically to determine the impact of edge detection on FB/PB difference. Population BMD results were perfectly correlated, but significantly overestimated by 1.5% at the lumbar spine and underestimated by 0.7% at the neck, 1.8% at the trochanter, and 2.0% at the total hip, respectively, when using the FB compared with PB mode. At the lumbar spine, the FB/PB residual correlated negatively with height (r = 0.34, p < 0.01) and PB.BMD (r = 0.48, p &lt: 0. 0001) and positively with AI (r = 0.26, p < 0.05). At the hip, residual of trochanter correlated positively with weight (r = 0.36, p < 0.01) and AI (r = 0.36, p < 0.01). The FB mode significantly increased ASP BMD by 0.7% compared with PB. Using the FB mode, increasing focus distance significantly (p < 0.001) decreased area and bone mineral content, but not BMD. By contrast, increasing focus distance significantly decreased PB.BMD by 0.7%. With the ESP, the PB mode supplied accurate projected are of the bone (AREA) results but significant underestimation of specified BMD in the manual analysis. The FB mode significantly underestimated PB. AREA by 2.9% but fitted specified BMD quite well. FB/PB overestimation was larger for the low-density (+8.7%) than for the high-density vertebra (+4. 9%). The automated analysis resulted in more than 14% underestimation of PB. AREA (low-density vertebra) and an almost 13% overestimation of PB.BMD (high-density vertebra) using FB. In conclusion, FB and PB measurements are highly correlated at the lumbar spine and hip with small but significant BMD differences related to height, adiposity, and BMD. In clinical practice, it can be erroneous to switch from one method to another, especially in women with low bone density