The Relational Blockworld Interpretation of Non-relativistic Quantum Mechanics

We introduce a new interpretation of non-relativistic quantum mechanics (QM) called Relational Blockworld (RBW). We motivate the interpretation by outlining two results due to Kaiser, Bohr, Ulfeck, Mottelson, and Anandan, independently. First, the canonical commutation relations for position and momentum can be obtained from boost and translation operators,respectively, in a spacetime where the relativity of simultaneity holds. Second, the QM density operator can be obtained from the spacetime symmetry group of the experimental configuration exclusively. We show how QM, obtained from relativistic quantum field theory per RBW, explains the twin-slit experiment and conclude by resolving the standard conceptual problems of QM, i.e., the measurement problem, entanglement and non-locality

NECROMASS PRODUCTION: STUDIES IN UNDISTURBED AND LOGGED AMAZON FORESTS

Necromass stocks account for up to 20% of carbon stored in tropical forests and have been estimated to be 14–19% of the annual aboveground carbon flux. Both stocks and fluxes of necromass are infrequently measured. In this study, we directly measured the production of fallen coarse necromass (≥2 cm diameter) during 4.5 years using repeated surveys in undisturbed forest areas and in forests subjected to reduced‐impact logging at the Tapajos National Forest, Belterra, Brazil (3.08° S, 54.94° W). We also measured fallen coarse necromass and standing dead stocks at two times during our study. The mean (SE) annual flux into the fallen coarse necromass pool in undisturbed forest of 6.7 (0.8) Mg·ha−1·yr−1 was not significantly different from the flux under a reduced‐impact logging of 8.5 (1.3) Mg·ha−1·yr−1. With the assumption of steady state, the instantaneous decomposition constants for fallen necromass in undisturbed forests were 0.12 yr−1 for large, 0.33 yr−1 for medium, and 0.47 yr−1 for small size classes. The mass weighted decomposition constant was 0.15 yr−1 for all fallen coarse necromass. Standing dead wood had a residence time of 4.2 years, and ∼0.9 Mg·ha−1·yr−1 of this pool was respired annually to the atmosphere through decomposition. Coarse necromass decomposition at our study site accounted for 12% of total carbon re‐mineralization, and total aboveground coarse necromass was 14% of the aboveground biomass. Use of mortality rates to calculate production of coarse necromass leads to an underestimation of coarse necromass production by 45%, suggesting that nonlethal disturbance such as branch fall contributes significantly to this flux. Coarse necromass production is an important component of the tropical forest carbon cycle that has been neglected in most previous studies or erroneously estimated

An error accounting algorithm for electron counting experiments

Electron counting experiments attempt to provide a current of a known number of electrons per unit time. We propose architectures utilizing a few readily available electron-pumps or turnstiles with modest error rates of 1 part per $10^4$ with common sensitive electrometers to achieve the desirable accuracy of 1 part in $10^8$. This is achieved not by counting all transferred electrons but by counting only the errors of individual devices; these are less frequent and therefore readily recognized and accounted for. Our proposal thereby eases the route towards quantum based standards for current and capacitance.Comment: 5 pages, 3 figures. Builds on and extends white paper arXiv:0811.392

An L^2-Index Theorem for Dirac Operators on S^1 * R^3

An expression is found for the $L^2$-index of a Dirac operator coupled to a connection on a $U_n$ vector bundle over $S^1\times{\mathbb R}^3$. Boundary conditions for the connection are given which ensure the coupled Dirac operator is Fredholm. Callias' index theorem is used to calculate the index when the connection is independent of the coordinate on $S^1$. An excision theorem due to Gromov, Lawson, and Anghel reduces the index theorem to this special case. The index formula can be expressed using the adiabatic limit of the $\eta$-invariant of a Dirac operator canonically associated to the boundary. An application of the theorem is to count the zero modes of the Dirac operator in the background of a caloron (periodic instanton).Comment: 14 pages, Latex, to appear in the Journal of Functional Analysi

Hilbert's projective metric in quantum information theory

We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical distinguishability of quantum states and on the decrease of entanglement under LOCC protocols or other cone-preserving operations. The results are formulated in terms of general cones and base norms and lead to contractivity bounds for quantum channels, for instance improving Ruskai's trace-norm contraction inequality. A new duality between distinguishability measures and base norms is provided. For two given pairs of quantum states we show that the contraction of Hilbert's projective metric is necessary and sufficient for the existence of a probabilistic quantum operation that maps one pair onto the other. Inequalities between Hilbert's projective metric and the Chernoff bound, the fidelity and various norms are proven.Comment: 32 pages including 3 appendices and 3 figures; v2: minor changes, published versio