The Quantum Newton's Law

Using the quantum Hamilton-Jacobi equation within the framework of the equivalence postulate, we construct a Lagrangian of a quantum system in one dimension and derive a third order equation of motion representing a first integral of the quantum Newton's law. We then integrate this equation in the free particle case and compare our results to those of Floydian trajectories. Finally, we propose a quantum version of Jacobi's theorem.Comment: 10 pages, LateX, no figures, minor change

An Empirical Determination of the Intergalactic Background Light Using NIR Deep Galaxy Survey Data out to 5 microns and the Gamma-ray Opacity of the Universe

We extend our previous model-independent determination of the intergalactic background light (IBL), based purely on galaxy survey data, out to a wavelength of 5 microns. Our approach enables us to constrain the range of photon densities, based on the uncertainties from observationally determined luminosity densities and colors. We further determine a 68% confidence upper and lower limit on the opacity of the universe to gamma-rays up to energies of 1.6/(1+z) TeV. A comparison of our lower limit redshift-dependent opacity curves to the opacity limits derived from the results of both ground-based air Cherenkov telescope and Fermi-LAT observations of PKS 1424+240 allows us to place a new upper limit on the redshift of this source, independent of IBL modeling.Comment: version accepted for publication in the Astrophysical Journal, 23 pages, 4 figure

An Empirical Determination of the Intergalactic Background Light from UV to FIR Wavelengths Using FIR Deep Galaxy Surveys and the Gamma-ray Opacity of the Universe

We have previously calculated the intergalactic background light (IBL) as a function of redshift in the far ultraviolet to near infrared range, based purely on data from deep galaxy surveys. Here we utilize similar methods to determine the mid- and far infrared IBL out to a wavelength of 850 microns. Our approach enables us to constrain the range of photon densities, based on the uncertainties from observationally determined luminosity densities and colors. By also including the effect of the 2.7 K cosmic background photons, we determine 68% confidence upper and lower limits on the opacity of the universe to gamma-rays up to PeV energies. Our direct results on the IBL are consistent with those from complimentary gamma-ray analyses using observations from the Fermi $\gamma$-ray space telescope and the H.E.S.S. air Cherenkov telescope. Thus, we find no evidence of previously suggested processes for the modification of gamma-ray spectra other than that of absorption by pair production alone.Comment: 33 pages, 11 figures, replacement matches article published in ApJ 827:6 (2016

Is the Universe More Transparent to Gamma Rays Than Previously Thought?

The MAGIC collaboration has recently reported the detection of the strong gamma-ray blazar 3C279 during a 1-2 day flare. They have used their spectral observations to draw conclusions regarding upper limits on the opacity of the Universe to high energy gamma-rays and, by implication, upper limits on the extragalactic mid-infrared background radiation. In this paper we examine the effect of gamma-ray absorption by the extragalactic infrared radiation on intrinsic spectra for this blazar and compare our results with the observational data on 3C279. We find agreement with our previous results, contrary to the recent assertion of the MAGIC group that the Universe is more transparent to \gray s than our calculations indicate. Our analysis indicates that in the energy range between ~80 and ~500 GeV, 3C279 has a best-fit intrinsic spectrum with a spectral index ~1.78 using our fast evolution model and ~2.19 using our baseline model. However, we also find that spectral indices in the range of 0.0 to 3.0 are almost as equally acceptable as the best fit spectral indices. Assuming the same intrinsic spectral index for this flare as for the 1991 flare from 3C279 observed by EGRET, viz., 2.02, which lies between our best fit indices, we estimate that the MAGIC flare was ~3 times brighter than the EGRET flare observed 15 years earlier.Comment: version accepted for publication in ApJ Letter

The high energy limit of the trajectory representation of quantum mechanics

The trajectory representation in the high energy limit (Bohr correspondence principle) manifests a residual indeterminacy. This indeterminacy is compared to the indeterminacy found in the classical limit (Planck's constant to 0) [Int. J. Mod. Phys. A 15, 1363 (2000)] for particles in the classically allowed region, the classically forbiden region, and near the WKB turning point. The differences between Bohr's and Planck's principles for the trajectory representation are compared with the differences between these correspondence principles for the wave representation. The trajectory representation in the high energy limit is shown to go to neither classical nor statistical mechanics. The residual indeterminacy is contrasted to Heisenberg uncertainty. The relationship between indeterminacy and 't Hooft's information loss and equivalence classes is investigated.Comment: 12 pages of LaTeX. No figures. Incorporated into the "Proceedings of the Seventh International Wigner Symposium" (ed. M. E. Noz), 24-29 August 2001, U. of Maryland. Proceedings available at http://www.physics.umd.edu/robo

The Equivalence Postulate of Quantum Mechanics

The Equivalence Principle (EP), stating that all physical systems are connected by a coordinate transformation to the free one with vanishing energy, univocally leads to the Quantum Stationary HJ Equation (QSHJE). Trajectories depend on the Planck length through hidden variables which arise as initial conditions. The formulation has manifest p-q duality, a consequence of the involutive nature of the Legendre transform and of its recently observed relation with second-order linear differential equations. This reflects in an intrinsic psi^D-psi duality between linearly independent solutions of the Schroedinger equation. Unlike Bohm's theory, there is a non-trivial action even for bound states. No use of any axiomatic interpretation of the wave-function is made. Tunnelling is a direct consequence of the quantum potential which differs from the usual one and plays the role of particle's self-energy. The QSHJE is defined only if the ratio psi^D/psi is a local self-homeomorphism of the extended real line. This is an important feature as the L^2 condition, which in the usual formulation is a consequence of the axiomatic interpretation of the wave-function, directly follows as a basic theorem which only uses the geometrical gluing conditions of psi^D/psi at q=\pm\infty as implied by the EP. As a result, the EP itself implies a dynamical equation that does not require any further assumption and reproduces both tunnelling and energy quantization. Several features of the formulation show how the Copenhagen interpretation hides the underlying nature of QM. Finally, the non-stationary higher dimensional quantum HJ equation and the relativistic extension are derived.Comment: 1+3+140 pages, LaTeX. Invariance of the wave-function under the action of SL(2,R) subgroups acting on the reduced action explicitly reveals that the wave-function describes only equivalence classes of Planck length deterministic physics. New derivation of the Schwarzian derivative from the cocycle condition. "Legendre brackets" introduced to further make "Legendre duality" manifest. Introduction now contains examples and provides a short pedagogical review. Clarifications, conclusions, ackn. and references adde

Trajectories in the Context of the Quantum Newton's Law

In this paper, we apply the one dimensional quantum law of motion, that we recently formulated in the context of the trajectory representation of quantum mechanics, to the constant potential, the linear potential and the harmonic oscillator. In the classically allowed regions, we show that to each classical trajectory there is a family of quantum trajectories which all pass through some points constituting nodes and belonging to the classical trajectory. We also discuss the generalization to any potential and give a new definition for de Broglie's wavelength in such a way as to link it with the length separating adjacent nodes. In particular, we show how quantum trajectories have as a limit when $\hbar \to 0$ the classical ones. In the classically forbidden regions, the nodal structure of the trajectories is lost and the particle velocity rapidly diverges.Comment: 17 pages, LateX, 6 eps figures, minor modifications, Title changed, to appear in Physica Script

Unresolved Blazar Component of the Extragalactic Gamma-Ray Background

We present new theoretical estimates of the relative contribution of unresolved blazars and star forming galaxies to the extragalactic gamma-ray background and discuss constraints on the contributions from other possible components. We find that the Fermi data do not rule out a scenario in which the extragalactic gamma-ray background is dominated by emission from unresolved blazars. The spectrum of unresolved FSRQs, when accounting for the energy dependent effects of source confusion, could be consistent with the combined spectrum of the low energy EGRET extragalactic gamma-ray background measurements and the Fermi-LAT measurements above 200 MeV

Age grading \u3cem\u3eAn. gambiae\u3c/em\u3e and \u3cem\u3eAn. arabiensis\u3c/em\u3e using near infrared spectra and artificial neural networks

Background Near infrared spectroscopy (NIRS) is currently complementing techniques to age-grade mosquitoes. NIRS classifies lab-reared and semi-field raised mosquitoes into \u3c or ≥ 7 days old with an average accuracy of 80%, achieved by training a regression model using partial least squares (PLS) and interpreted as a binary classifier. Methods and findings We explore whether using an artificial neural network (ANN) analysis instead of PLS regression improves the current accuracy of NIRS models for age-grading malaria transmitting mosquitoes. We also explore if directly training a binary classifier instead of training a regression model and interpreting it as a binary classifier improves the accuracy. A total of 786 and 870 NIR spectra collected from laboratory reared An. gambiae and An. arabiensis, respectively, were used and pre-processed according to previously published protocols. The ANN regression model scored root mean squared error (RMSE) of 1.6 ± 0.2 for An. gambiae and 2.8 ± 0.2 for An. arabiensis; whereas the PLS regression model scored RMSE of 3.7 ± 0.2 for An. gambiae, and 4.5 ± 0.1 for An. arabiensis. When we interpreted regression models as binary classifiers, the accuracy of the ANN regression model was 93.7 ± 1.0% for An. gambiae, and 90.2 ± 1.7% for An. arabiensis; while PLS regression model scored the accuracy of 83.9 ± 2.3% for An. gambiae, and 80.3 ± 2.1% for An. arabiensis. We also find that a directly trained binary classifier yields higher age estimation accuracy than a regression model interpreted as a binary classifier. A directly trained ANN binary classifier scored an accuracy of 99.4 ± 1.0 for An. gambiae and 99.0 ± 0.6% for An. arabiensis; while a directly trained PLS binary classifier scored 93.6 ± 1.2% for An. gambiae and 88.7 ± 1.1% for An. arabiensis. We further tested the reproducibility of these results on different independent mosquito datasets. ANNs scored higher estimation accuracies than when the same age models are trained using PLS. Regardless of the model architecture, directly trained binary classifiers scored higher accuracies on classifying age of mosquitoes than regression models translated as binary classifiers. Conclusion We recommend training models to estimate age of An. arabiensis and An. gambiae using ANN model architectures (especially for datasets with at least 70 mosquitoes per age group) and direct training of binary classifier instead of training a regression model and interpreting it as a binary classifier