Pre- and post-selected ensembles and time-symmetry in quantum mechanics

An expression is proposed for the quantum mechanical state of a pre- and post-selected ensemble, which is an ensemble determined by the final as well as the initial state of the quantum systems involved. It is shown that the probabilities calculated from the proposed state agree with previous expressions, for cases where they both apply. The same probabilities are found when they are calculated in the forward- or reverse-time directions. This work was prompted by several problems raised by Shimony recently in relation to the state, and time symmetry, of pre- and post-selected ensembles.Comment: RevTex4, 17 pages, no fig

On Graphical Modeling of Preference and Importance

In recent years, CP-nets have emerged as a useful tool for supporting preference elicitation, reasoning, and representation. CP-nets capture and support reasoning with qualitative conditional preference statements, statements that are relatively natural for users to express. In this paper, we extend the CP-nets formalism to handle another class of very natural qualitative statements one often uses in expressing preferences in daily life - statements of relative importance of attributes. The resulting formalism, TCP-nets, maintains the spirit of CP-nets, in that it remains focused on using only simple and natural preference statements, uses the ceteris paribus semantics, and utilizes a graphical representation of this information to reason about its consistency and to perform, possibly constrained, optimization using it. The extra expressiveness it provides allows us to better model tradeoffs users would like to make, more faithfully representing their preferences

Maximum Entanglement in Squeezed Boson and Fermion States

A class of squeezed boson and fermion states is studied with particular emphasis on the nature of entanglement. We first investigate the case of bosons, considering two-mode squeezed states. Then we construct the fermion version to show that such states are maximum entangled, for both bosons and fermions. To achieve these results, we demonstrate some relations involving squeezed boson states. The generalization to the case of fermions is made by using Grassmann variables.Comment: 4 page

Bell inequalities for random fields

The assumptions required for the derivation of Bell inequalities are not usually satisfied for random fields in which there are any thermal or quantum fluctuations, in contrast to the general satisfaction of the assumptions for classical two point particle models. Classical random field models that explicitly include the effects of quantum fluctuations on measurement are possible for experiments that violate Bell inequalities.Comment: 18 pages; 1 figure; v4: Essentially the published version; extensive improvements. v3: Better description of the relationship between classical random fields and quantum fields; better description of random field models. More extensive references. v2: Abstract and introduction clarifie

Bell's theorem as a signature of nonlocality: a classical counterexample

For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local probabilistic interaction in the measurement process can lead to a violation of the Bell inequalities. We first introduce two-particle phase-space distributions in classical mechanics constructed to be the analogs of quantum mechanical angular momentum eigenstates. These distributions are then employed in four schemes characterized by different types of detectors measuring the angular momenta. When the model includes an interaction between the detector and the measured particle leading to ensemble dependencies, the relevant Bell inequalities are violated if total angular momentum is required to be conserved. The violation is explained by identifying assumptions made in the derivation of Bell's theorem that are not fulfilled by the model. These assumptions will be argued to be too restrictive to see in the violation of the Bell inequalities a faithful signature of nonlocality.Comment: Extended manuscript. Significant change

Quantum Preferred Frame: Does It Really Exist?

The idea of the preferred frame as a remedy for difficulties of the relativistic quantum mechanics in description of the non-local quantum phenomena was undertaken by such physicists as J. S. Bell and D. Bohm. The possibility of the existence of preferred frame was also seriously treated by P. A. M. Dirac. In this paper, we propose an Einstein-Podolsky-Rosen-type experiment for testing the possible existence of a quantum preferred frame. Our analysis suggests that to verify whether a preferred frame of reference in the quantum world exists it is enough to perform an EPR type experiment with pair of observers staying in the same inertial frame and with use of the massive EPR pair of spin one-half or spin one particles.Comment: 5 pp., 6 fig

On the role of the corpus callosum in interhemispheric functional connectivity in humans

Resting state functional connectivity is defined in terms of temporal correlations between physiologic signals, most commonly studied using functional magnetic resonance imaging. Major features of functional connectivity correspond to structural (axonal) connectivity. However, this relation is not one-to-one. Interhemispheric functional connectivity in relation to the corpus callosum presents a case in point. Specifically, several reports have documented nearly intact interhemispheric functional connectivity in individuals in whom the corpus callosum (the major commissure between the hemispheres) never develops. To investigate this question, we assessed functional connectivity before and after surgical section of the corpus callosum in 22 patients with medically refractory epilepsy. Section of the corpus callosum markedly reduced interhemispheric functional connectivity. This effect was more profound in multimodal associative areas in the frontal and parietal lobe than primary regions of sensorimotor and visual function. Moreover, no evidence of recovery was observed in a limited sample in which multiyear, longitudinal follow-up was obtained. Comparison of partial vs. complete callosotomy revealed several effects implying the existence of polysynaptic functional connectivity between remote brain regions. Thus, our results demonstrate that callosal as well as extracallosal anatomical connections play a role in the maintenance of interhemispheric functional connectivity

MR diffusion changes in the perimeter of the lateral ventricles demonstrate periventricular injury in post-hemorrhagic hydrocephalus of prematurity

OBJECTIVES: Injury to the preterm lateral ventricular perimeter (LVP), which contains the neural stem cells responsible for brain development, may contribute to the neurological sequelae of intraventricular hemorrhage (IVH) and post-hemorrhagic hydrocephalus of prematurity (PHH). This study utilizes diffusion MRI (dMRI) to characterize the microstructural effects of IVH/PHH on the LVP and segmented frontal-occipital horn perimeters (FOHP). STUDY DESIGN: Prospective study of 56 full-term infants, 72 very preterm infants without brain injury (VPT), 17 VPT infants with high-grade IVH without hydrocephalus (HG-IVH), and 13 VPT infants with PHH who underwent dMRI at term equivalent. LVP and FOHP dMRI measures and ventricular size-dMRI correlations were assessed. RESULTS: In the LVP, PHH had consistently lower FA and higher MD and RD than FT and VPT (p\u3c.050). However, while PHH FA was lower, and PHH RD was higher than their respective HG-IVH measures (p\u3c.050), the MD and AD values did not differ. In the FOHP, PHH infants had lower FA and higher RD than FT and VPT (p\u3c.010), and a lower FA than the HG-IVH group (p\u3c.001). While the magnitude of AD in both the LVP and FOHP were consistently less in the PHH group on pairwise comparisons to the other groups, the differences were not significant (p\u3e.050). Ventricular size correlated negatively with FA, and positively with MD and RD (p\u3c.001) in both the LVP and FOHP. In the PHH group, FA was lower in the FOHP than in the LVP, which was contrary to the observed findings in the healthy infants (p\u3c.001). Nevertheless, there were no regional differences in AD, MD, and RD in the PHH group. CONCLUSION: HG-IVH and PHH results in aberrant LVP/FOHP microstructure, with prominent abnormalities among the PHH group, most notably in the FOHP. Larger ventricular size was associated with greater magnitude of abnormality. LVP/FOHP dMRI measures may provide valuable biomarkers for future studies directed at improving the management and neurological outcomes of IVH/PHH

Testing the Dirac equation

The dynamical equations which are basic for the description of the dynamics of quantum felds in arbitrary space--time geometries, can be derived from the requirements of a unique deterministic evolution of the quantum fields, the superposition principle, a finite propagation speed, and probability conservation. We suggest and describe observations and experiments which are able to test the unique deterministic evolution and analyze given experimental data from which restrictions of anomalous terms violating this basic principle can be concluded. One important point is, that such anomalous terms are predicted from loop gravity as well as from string theories. Most accurate data can be obtained from future astrophysical observations. Also, laboratory tests like spectroscopy give constraints on the anomalous terms.Comment: 11 pages. to appear in: C. L\"ammerzahl, C.W.F. Everitt, and F.W. Hehl (eds.): Gyros, Clocks, Interferometers...: Testing Relativistic Gravity in Space, Lecture Notes in Physics 562, Springer 200