The 4D geometric quantities versus the usual 3D quantities. The resolution of Jackson's paradox

In this paper we present definitions of different four-dimensional (4D) geometric quantities (Clifford multivectors). New decompositions of the torque N and the angular momentum M (bivectors) into 1-vectors N_{s}, N_{t} and M_{s}, M_{t} respectively are given. The torques N_{s}, N_{t} (the angular momentums M_{s}, M_{t}), taken together, contain the same physical information as the bivector N (the bivector M). The usual approaches that deal with the 3D quantities $\mathbf{E}$, $\mathbf{B}$, $\mathbf{F}$, $\mathbf{L}$, $\mathbf{N}$, etc. and their transformations are objected from the viewpoint of the invariant special relativity (ISR). In the ISR it is considered that 4D geometric quantities are well-defined both theoretically and \emph{experimentally} in the 4D spacetime. This is not the case with the usual 3D quantities. It is shown that there is no apparent electrodynamic paradox with the torque, and that the principle of relativity is naturally satisfied, when the 4D geometric quantities are used instead of the 3D quantities.Comment: 13 pages, revte

About the Simultaneous Co-Existence of Instantaneous and Retarded Interactions in Classical Electrodynamics

In this paper it is proved that, contrary to the results found by A.E. Chubykalo and S.J. Vlaev (Int. J. Mod. Phys. A 14, 3789 (1999)), the retarded electric and magnetic fields for an uniformly accelerated charge exactly satisfy Maxwell equations (ME). Furthermore it is shown that ME are correctly written in the usual form with the partial derivatives and thus not, as proposed by Chubykalo and Vlaev, with the total derivatives.Comment: 7 pages, to be published in Int. J. Mod. Phys.

The Two-Component Radio Luminosity Function of QSOs: Star Formation and AGN

Despite decades of study, it remains unclear whether there are distinct radio-loud and radio-quiet populations of quasi-stellar objects (QSOs). Early studies were limited by inhomogeneous QSO samples, inadequate sensitivity to probe the radio-quiet population, and degeneracy between redshift and luminosity for flux-density-limited samples. Our new 6 GHz EVLA observations allow us for the first time to obtain nearly complete (97%) radio detections in a volume-limited color-selected sample of 179 QSOs more luminous than M_i = -23 from the Sloan Digital Sky Survey (SDSS) Data Release Seven in the narrow redshift range 0.2 < z < 0.3. The dramatic improvement in radio continuum sensitivity made possible with the new EVLA allows us, in 35 minutes of integration, to detect sources as faint as 20 microJy, or log[L_6 (W/Hz)] ~ 21.5 at z = 0.25, well below the radio luminosity, log[L_6 (W/Hz)] ~ 22.5, that separates star-forming galaxies from radio-loud active galactic nuclei (AGNs) driven by accretion onto a super-massive black hole. We calculate the radio luminosity function (RLF) for these QSOs using three constraints: (a) EVLA 6 GHz observations for log[L_6 (W/Hz)] < 23.5, (b) NRAO-VLA Sky Survey (NVSS) observations for log[L_6 (W/Hz)] > 23.5, and (c) the total number of SDSS QSOs in our volume-limited sample. We show that the RLF can be explained as a superposition of two populations, dominated by AGNs at the bright end and star formation in the QSO host galaxies at the faint end.Comment: 11 pages, 2 figures. Accepted for publication. This Letter will appear in the ApJL EVLA special issu

Comment on "Classical and Quantum Interaction of the Dipole"

In this paper I have presented Comment on Anandan's paper (J. Anandan, Phys. Rev. Lett. 85, 1354 (2000)) [hep-th/9910018].Comment: 1 page, revtex; small changes, mainly typos, according to the published version in Phys. Rev. Let

Comment on "R\"{o}ntgen Quantum Phase Shift: A Semiclassical Local Electrodynamical Effect?''

This paper is Comment on the paper: S.A.R. Horsley and M. Babiker, Phys. Rev. Lett. 95, 010405 (2005).Comment: minor changes in the text, some references are changed, according to the version which is accepted for publication in Phys. Rev. Let

The Shape and Profile of the Milky Way Halo as Seen by the Canada-France-Hawaii Telescope Legacy Survey

We use Canada-France-Hawaii Telescope Legacy Survey data for 170 deg^2, recalibrated and transformed to the Sloan Digital Sky Survey ugri photometric system, to study the distribution of near-turnoff main-sequence stars in the Galactic halo along four lines of sight to heliocentric distances of ~35 kpc. We find that the halo stellar number density profile becomes steeper at Galactocentric distances greater than R_(gal) ~ 28 kpc, with the power-law index changing from n_(inner) = –2.62 ± 0.04 to n_(outer) = –3.8 ± 0.1. In particular, we test a series of single power-law models and find them to be strongly disfavored by the data. The parameters for the best-fit Einasto profile are n = 2.2 ± 0.2 and R_e = 22.2 ± 0.4 kpc. We measure the oblateness of the halo to be q ≡ c/a = 0.70 ± 0.01 and detect no evidence of it changing across the range of probed distances. The Sagittarius stream is detected in the l = 173° and b = –62° direction as an overdensity of [Fe/H] ~ -1.5 dex stars at R_(gal) ~ 32 kpc, providing a new constraint for the Sagittarius stream and dark matter halo models. We also detect the Monoceros stream as an overdensity of [Fe/H] > -1.5 dex stars in the l = 232° and b = 26° direction at R_(gal) ≲ 25 kpc. In the two sight lines where we do not detect significant substructure, the median metallicity is found to be independent of distance within systematic uncertainties ([Fe/H] ~ -1.5 ± 0.1 dex)