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

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

A Determination of the Intergalactic Redshift Dependent UV-Optical-NIR Photon Density Using Deep Galaxy Survey Data and the Gamma-ray Opacity of the Universe

We calculate the intensity and photon spectrum of the intergalactic background light (IBL) as a function of redshift using an approach based on observational data obtained in many different wavelength bands from local to deep galaxy surveys. This allows us to obtain an empirical determination of the IBL and to quantify its observationally based uncertainties. Using our results on the IBL, we then place 68% confidence upper and lower limits on the opacity of the universe to gamma-rays, free of the theoretical assumptions that were needed for past calculations. We compare our results with measurements of the extragalactic background light and upper limits obtained from observations made by the Fermi Gamma-ray Space Telescope.Comment: 32 pages, 6 figures, Accepted for publication in the Astrophysical Journa

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

Sorobon (Abacus) to Silicon Chip

This report covers the objectives with which the writer was guided in the planning and implementation of his faculty development leave in Japan for the academic year 1983-84. today, (2) Japanese Initial objectives were to study language, (3) women in (1) Japanese culture leadership roles, (4) characteristics of high-achieving Japanese students in the areas of mathematics and science, and (5) the reasons why Japanese students surpass their American counterparts in these areas