Measurement uncertainty relations

Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by Heisenberg. Here we prove such relations for the case of two canonically conjugate observables like position and momentum, and establish a close connection with the more familiar preparation uncertainty relations constraining the sharpness of the distributions of the two observables in the same state. Both sets of relations are generalized to means of order $\alpha$ rather than the usual quadratic means, and we show that the optimal constants are the same for preparation and for measurement uncertainty. The constants are determined numerically and compared with some bounds in the literature. In both cases the near-saturation of the inequalities entails that the state (resp. observable) is uniformly close to a minimizing one.Comment: This version 2 contains minor corrections and reformulation

The Standard Model of Quantum Measurement Theory: History and Applications

The standard model of the quantum theory of measurement is based on an interaction Hamiltonian in which the observable-to-be-measured is multiplied with some observable of a probe system. This simple Ansatz has proved extremely fruitful in the development of the foundations of quantum mechanics. While the ensuing type of models has often been argued to be rather artificial, recent advances in quantum optics have demonstrated their prinicpal and practical feasibility. A brief historical review of the standard model together with an outline of its virtues and limitations are presented as an illustration of the mutual inspiration that has always taken place between foundational and experimental research in quantum physics.Comment: 22 pages, to appear in Found. Phys. 199

Fat free mass and obesity in relation to educational level

© 2009 Seppänen-Nuijten et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licens

Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics

We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox "absolute" quantities are good representatives of observable relative quantities if the reference state is suitably localised. We use this relational formalism to critique the literature on the relationship between reference frames and superselection rules, settling a long-standing debate on the subject

Genome-wide association meta-analysis of fish and EPA plus DHA consumption in 17 US and European cohorts

Background Regular fish and omega-3 consumption may have several health benefits and are recommended by major dietary guidelines. Yet, their intakes remain remarkably variable both within and across populations, which could partly owe to genetic influences. Objective To identify common genetic variants that influence fish and dietary eicosapentaenoic acid plus docosahexaenoic acid (EPA+DHA) consumption. Design We conducted genome-wide association (GWA) meta-analysis of fish (n = 86,467) and EPA+DHA (n = 62,265) consumption in 17 cohorts of European descent from the CHARGE (Cohorts for Heart and Aging Research in Genomic Epidemiology) Consortium Nutrition Working Group. Results from cohort-specific GWA analyses (additive model) for fish and EPA+DHA consumption were adjusted for age, sex, energy intake, and population stratification, and meta-analyzed separately using fixed-effect meta-analysis with inverse variance weights (METAL software). Additionally, heritability was estimated in 2 cohorts. Results Heritability estimates for fish and EPA+DHA consumption ranged from 0.13-0.24 and 0.12-0.22, respectively. A significant GWA for fish intake was observed for rs9502823 on chromosome 6: each copy of the minor allele (Freq(A) = 0.015) was associated with 0.029 servings/day (similar to 1 serving/month) lower fish consumption (P = 1.96x10(-8)). No significant association was observed for EPA+DHA, although rs7206790 in the obesity-associated FTO gene was among top hits (P = 8.18x10(-7)). Post-hoc calculations demonstrated 95% statistical power to detect a genetic variant associated with effect size of 0.05% for fish and 0.08% for EPA+DHA. Conclusions These novel findings suggest that non-genetic personal and environmental factors are principal determinants of the remarkable variation in fish consumption, representing modifiable targets for increasing intakes among all individuals. Genes underlying the signal at rs72838923 and mechanisms for the association warrant further investigation.Peer reviewe

Genome-wide association meta-analysis of fish and EPA+DHA consumption in 17 US and European cohorts

Background: Regular fish and omega-3 consumption may have several health benefits and are recommended by major dietary guidelines. Yet, their intakes remain remarkably variable both within and across populations, which could partly owe to genetic influences. Objective: To identify common genetic variants that influence fish and dietary eicosapentaenoic acid plus docosahexaenoic acid (EPA+DHA) consumption. Design: We conducted genome-wide association (GWA) meta-analysis of fish (n = 86, 467) and EPA +DHA (n = 62, 265) consumption in 17 cohorts of European descent from the CHARGE (Cohorts for Heart and Aging Research in Genomic Epidemiology) Consortium Nutrition Working Group. Results from cohort-specific GWA analyses (additive model) for fish and EPA+DHA consumption were adjusted for age, sex, energy intake, and population stratification, and meta-analyzed separately using fixed-effect meta-analysis with inverse variance weights (METAL software). Additionally, heritability was estimated in 2 cohorts. Results: Heritability estimates for fish and EPA+DHA consumption ranged from 0.13