Hidden assumptions in the derivation of the Theorem of Bell

John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT and are the elements of an algebra. Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell's inequality by Einstein-Podolsky-Rosen type of experiments can be explained by Boole's ideas. Violations of Bell's inequality also call for a revision of the mathematical abstractions and corresponding algebra. It will be shown that this particular view of Bell's inequalities points toward an incompleteness of quantum mechanics, rather than to any superluminal propagation or influences at a distance

Early CRT monitoring using time-domain optical coherence tomography does not add to visual acuity for predicting visual loss in patients with central retinal vein occlusion treated with intravitreal ranibizumab:A secondary analysis of trial data

Our primary purpose was to assess the clinical (predictive) validity of central retinal thickness (CRT) and best corrected visual acuity (BCVA) at 1 week and 1 month after starting treatment with ranibizumab for central retinal vein occlusion. The authors also assessed detectability of response to treatment

Two-setting Bell Inequalities for Graph States

We present Bell inequalities for graph states with high violation of local realism. In particular, we show that there is a two-setting Bell inequality for every nontrivial graph state which is violated by the state at least by a factor of two. These inequalities are facets of the convex polytope containing the many-body correlations consistent with local hidden variable models. We first present a method which assigns a Bell inequality for each graph vertex. Then for some families of graph states composite Bell inequalities can be constructed with a violation of local realism increasing exponentially with the number of qubits. We also suggest a systematic way for obtaining Bell inequalities with a high violation of local realism for arbitrary graphs.Comment: 8 pages including 2 figures, revtex4; minor change

Non-local Correlations are Generic in Infinite-Dimensional Bipartite Systems

It was recently shown that the nonseparable density operators for a bipartite system are trace norm dense if either factor space has infinite dimension. We show here that non-local states -- i.e., states whose correlations cannot be reproduced by any local hidden variable model -- are also dense. Our constructions distinguish between the cases where both factor spaces are infinite-dimensional, where we show that states violating the CHSH inequality are dense, and the case where only one factor space is infinite-dimensional, where we identify open neighborhoods of nonseparable states that do not violate the CHSH inequality but show that states with a subtler form of non-locality (often called "hidden" non-locality) remain dense.Comment: 8 pages, RevTe

Dark Matter and Stellar Mass in the Luminous Regions of Disk Galaxies

We investigate the correlations among stellar mass (M_*), disk scale length (R_d), and rotation velocity at 2.2 disk scale lengths (V_2.2) for a sample of 81 disk-dominated galaxies (disk/total >= 0.9) selected from the SDSS. We measure V_2.2 from long-slit H-alpha rotation curves and infer M_* from galaxy i-band luminosities (L_i) and g-r colors. We find logarithmic slopes of 2.60+/-0.13 and 3.05+/-0.12 for the L_i-V_2.2 and M_*-V_2.2 relations, somewhat shallower than most previous studies, with intrinsic scatter of 0.13 dex and 0.16 dex. Our direct estimates of the total-to-stellar mass ratio within 2.2R_d, assuming a Kroupa IMF, yield a median ratio of 2.4 for M_*>10^10 Msun and 4.4 for M_*=10^9-10^10 Msun, with large scatter at a given M_* and R_d. The typical ratio of the rotation speed predicted for the stellar disk alone to the observed rotation speed at 2.2R_d is ~0.65. The distribution of R_d at fixed M_* is broad, but we find no correlation between disk size and the residual from the M_*-V_2.2 relation, implying that this relation is an approximately edge-on view of the disk galaxy fundamental plane. Independent of the assumed IMF, this result implies that stellar disks do not, on average, dominate the mass within 2.2R_d. We discuss our results in the context of infall models of disk formation in cold dark matter halos. A model with a disk-to-halo mass ratio m_d=0.05 provides a reasonable match to the R_d-M_* distribution for spin parameters \lambda ranging from ~0.04-0.08, and it yields a reasonable match to the mean M_*-V_2.2 relation. A model with m_d=0.1 predicts overly strong correlations between disk size and M_*-V_2.2 residual. Explaining the wide range of halo-to-disk mass ratios within 2.2R_d requires significant scatter in m_d values, with systematically lower m_d for galaxies with lower $M_*$.Comment: 18 pages, 2 tables, 7 figures, Accepted to ApJ, Table 1 updated, otherwise minor change

Less than 10 percent of star formation in z=0.6 massive galaxies is triggered by major interactions

Both observations and simulations show that major tidal interactions or mergers between gas-rich galaxies can lead to intense bursts of starformation. Yet, the average enhancement in star formation rate (SFR) in major mergers and the contribution of such events to the cosmic SFR are not well estimated. Here we use photometric redshifts, stellar masses and UV SFRs from COMBO-17, 24 micron SFRs from Spitzer and morphologies from two deep HST cosmological survey fields (ECDFS/GEMS and A901/STAGES) to study the enhancement in SFR as a function of projected galaxy separation. We apply two-point projected correlation function techniques, which we augment with morphologically-selected very close pairs (separation <2 arcsec) and merger remnants from the HST imaging. Our analysis confirms that the most intensely star-forming systems are indeed interacting or merging. Yet, for massive (M* > 10^10 Msun) star-forming galaxies at 0.4<z<0.8, we find that the SFRs of galaxies undergoing a major interaction (mass ratios <1:4 and separations < 40 kpc) are only 1.80 +/- 0.30 times higher than the SFRs of non-interacting galaxies when averaged over all interactions and all stages of the interaction, in good agreement with other observational works. We demonstrate that these results imply that <10% of star formation at 0.4 < z < 0.8 is triggered directly by major mergers and interactions; these events are not important factors in the build-up of stellar mass since z=1.Comment: Submitted to ApJ. 41 pages, 11 figure

GEMS Survey Data and Catalog

We describe the data reduction and object cataloging for the GEMS survey, a large-area (800 arcmin(2)) two-band (F606W and F850LP) imaging survey with the Advanced Camera for Surveys on the Hubble Space Telescope, centered on the Chandra Deep Field-South.STScI HST-GO-9500.01NASA GO-9500, NAS5-26555, NAG5-13063, NAG5-13102European Community’s Human Potential Programunder contractHPRN-CT-2002-00316, HPRN-CT-2002-00305McDonald Observator

An Explanation for the Observed Weak Size Evolution of Disk Galaxies

Surveys of distant galaxies with the Hubble Space Telescope and from the ground have shown that there is only mild evolution in the relationship between radial size and stellar mass for galactic disks from z~1 to the present day. Using a sample of nearby disk-dominated galaxies from the Sloan Digital Sky Survey (SDSS), and high redshift data from the GEMS (Galaxy Evolution from Morphology and SEDs) survey, we investigate whether this result is consistent with theoretical expectations within the hierarchical paradigm of structure formation. The relationship between virial radius and mass for dark matter halos in the LCDM model evolves by about a factor of two over this interval. However, N-body simulations have shown that halos of a given mass have less centrally concentrated mass profiles at high redshift. When we compute the expected disk size-stellar mass distribution, accounting for this evolution in the internal structure of dark matter halos and the adiabatic contraction of the dark matter by the self-gravity of the collapsing baryons, we find that the predicted evolution in the mean size at fixed stellar mass since z~1 is about 15-20 percent, in good agreement with the observational constraints from GEMS. At redshift z~2, the model predicts that disks at fixed stellar mass were on average only 60% as large as they are today. Similarly, we predict that the rotation velocity at a given stellar mass (essentially the zero-point of the Tully-Fisher relation) is only about 10 percent larger at z~1 (20 percent at z~2) than at the present day.Comment: 13 pages, 6 figures, accepted for publication in ApJ. Revised in response to referee's comments to improve clariry. Results are unchange