The Quantum Mechanical Arrows of Time

The familiar textbook quantum mechanics of laboratory measurements incorporates a quantum mechanical arrow of time --- the direction in time in which state vector reduction operates. This arrow is usually assumed to coincide with the direction of the thermodynamic arrow of the quasiclassical realm of everyday experience. But in the more general context of cosmology we seek an explanation of all observed arrows, and the relations between them, in terms of the conditions that specify our particular universe. This paper investigates quantum mechanical and thermodynamic arrows in a time-neutral formulation of quantum mechanics for a number of model cosmologies in fixed background spacetimes. We find that a general universe may not have well defined arrows of either kind. When arrows are emergent they need not point in the same direction over the whole of spacetime. Rather they may be local, pointing in different directions in different spacetime regions. Local arrows can therefore be consistent with global time symmetry.Comment: 9 pages, 4 figures, revtex4, typos correcte

Cross-sectional DXA and MR measures of tibial periarticular bone associate with radiographic knee osteoarthritis severity

SummaryObjectiveWe evaluated the relationship of medial proximal tibial periarticular areal bone mineral density (paBMD) and trabecular morphometry and determined whether these bone measures differed across radiographic medial joint space narrowing (JSN) scores.Methods482 participants of the Osteoarthritis Initiative (OAI) Bone Ancillary Study had knee dual X-ray absorptiometry (DXA) and trabecular bone 3T magnetic resonance imaging (MRI) exams assessed at the same visit. Medial proximal tibial paBMD was measured on DXA and apparent trabecular bone volume fraction (aBV/TV), thickness (aTb.Th), number (aTb.N), and spacing (aTb.Sp) were determined from MR images. Radiographs were assessed for medial JSN scores (0–3). We evaluated associations between medial paBMD and trabecular morphometry. Whisker plots with notches of these measures versus medial JSN scores were generated and presented.ResultsMean age was 63.9 (9.2) years, BMI 29.6 (4.8) kg/m2, and 53% were male. The Spearman correlation coefficients between DXA-measured medial paBMD and aBV/TV was 0.61 [95% confidence interval (CI) 0.55–0.66]; between paBMD and aTb.Th was 0.38 (95%CI 0.30–0.46); paBMD and aTb.N was 0.65 (95%CI 0.60–0.70); paBMD and aTb.Sp was −0.65 (95%CI −0.70 to −0.59). paBMD and the trabecular metrics were associated with medial JSN scores.ConclusionThe moderate associations between periarticular trabecular bone density and morphometry and their relationship with greater severity of knee OA support hypotheses of remodeling and/or microscopic compression fractures in the natural history of OA. Longitudinal studies are needed to assess whether knee DXA will be a predictor of OA progression. Further characterization of the periarticular bone in OA utilizing complementary imaging modalities will help clarify OA pathophysiology

The proximal drivers of large fires: A Pyrogeographic study

Variations in global patterns of burning and fire regimes are relatively well measured, however, the degree of influence of the complex suite of biophysical and human drivers of fire remains controversial and incompletely understood. Such an understanding is required in order to support current fire management and to predict the future trajectory of global fire patterns in response to changes in these determinants. In this study we explore and compare the effects of four fundamental controls on fire, namely the production of biomass, its drying, the influence of weather on the spread of fire and sources of ignition. Our study area is southern Australia, where fire is currently limited by either fuel production or fuel dryness. As in most fire-prone environments, the majority of annual burned area is due to a relatively small number of large fires. We train and test an Artificial Neural Network’s ability to predict spatial patterns in the probability of large fires (>1,250 ha) in forests and grasslands as a function of proxies of the four major controls on fire activity. Fuel load is represented by predicted forested biomass and remotely sensed grass biomass, drying is represented by fraction of the time monthly potential evapotranspiration exceeds precipitation, weather is represented by the frequency of severe fire weather conditions and ignitions are represented by the average annual density of reported ignitions. The response of fire to these drivers is often non-linear. Our results suggest that fuel management will have limited capacity to alter future fire occurrence unless it yields landscape-scale changes in fuel amount, and that shifts between, rather than within, vegetation community types may be more important. We also find that increased frequency of severe fire weather could increase the likelihood of large fires in forests but decrease it in grasslands. These results have the potential to support long-term strategic planning and risk assessment by fire management agencies

Finite-Dimensional Bicomplex Hilbert Spaces

This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including the spectral decomposition theorem. Applications to concepts relevant to quantum mechanics, like the evolution operator, are pointed out.Comment: 21 page

Arrow of time in a recollapsing quantum universe

We show that the Wheeler-DeWitt equation with a consistent boundary condition is only compatible with an arrow of time that formally reverses in a recollapsing universe. Consistency of these opposite arrows is facilitated by quantum effects in the region of the classical turning point. Since gravitational time dilation diverges at horizons, collapsing matter must then start re-expanding ``anticausally" (controlled by the reversed arrow) before horizons or singularities can form. We also discuss the meaning of the time-asymmetric expression used in the definition of ``consistent histories". We finally emphasize that there is no mass inflation nor any information loss paradox in this scenario.Comment: Many conceptual clarifications include

Layer dynamics of a freely standing smectic-A film

We study the hydrodynamics of a freely-standing smectic-A film in the isothermal, incompressible limit theoretically by analyzing the linearized hydrodynamic equations of motion with proper boundary conditions. The dynamic properties for the system can be obtained from the response functions for the free surfaces. Permeation is included and its importance near the free surfaces is discussed. The hydrodynamic mode structure for the dynamics of the system is compared with that of bulk systems. We show that to describe the dynamic correlation functions for the system, in general, it is necessary to consider the smectic layer displacement $u$ and the velocity normal to the layers, $v_z$, together. Finally, our analysis also provides a basis for the theoretical study of the off-equilibrium dynamics of freely-standing smectic-A films.Comment: 22 pages, 4 figure

T violation and the unidirectionality of time

An increasing number of experiments at the Belle, BNL, CERN, DA{\Phi}NE and SLAC accelerators are confirming the violation of time reversal invariance (T). The violation signifies a fundamental asymmetry between the past and future and calls for a major shift in the way we think about time. Here we show that processes which violate T symmetry induce destructive interference between different paths that the universe can take through time. The interference eliminates all paths except for two that represent continuously forwards and continuously backwards time evolution. Evidence from the accelerator experiments indicates which path the universe is effectively following. This work may provide fresh insight into the long-standing problem of modeling the dynamics of T violation processes. It suggests that T violation has previously unknown, large-scale physical effects and that these effects underlie the origin of the unidirectionality of time. It may have implications for the Wheeler-DeWitt equation of canonical quantum gravity. Finally it provides a view of the quantum nature of time itself.Comment: 24 pages, 5 figures. Final version accepted for publishing in Foundations of Physics. The final publication is available at http://www.springerlink.com/content/y3h4174jw2w78322

Comparison of K+K^+ and e−e^- Quasielastic Scattering

We formulate $K^+$-nucleus quasielastic scattering in a manner which closely parallels standard treatments of $e^-$-nucleus quasielastic scattering. For $K^+$ scattering, new responses involving scalar contributions appear in addition to the Coulomb (or longitudinal) and transverse $(e,e')$ responses which are of vector character. We compute these responses using both nuclear matter and finite nucleus versions of the Relativistic Hartree Approximation to Quantum Hadrodynamics including RPA correlations. Overall agreement with measured $(e,e')$ responses and new $K^+$ quasielastic scattering data for $^{40}$Ca at |\qs|=500 MeV/c is good. Strong RPA quenching is essential for agreement with the Coulomb response. This quenching is notably less for the $K^+$ cross section even though the new scalar contributions are even more strongly quenched than the vector contributions. We show that this ``differential quenching'' alters sensitive cancellations in the expression for the $K^+$ cross section so that it is reduced much less than the individual responses. We emphasize the role of the purely relativistic distinction between vector and scalar contributions in obtaining an accurate and consistent description of the $(e,e')$ and $K^+$ data within the framework of our nuclear structure model.Comment: 26 pages, 5 uuencoded figures appended to end of this fil