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.

Some Remarks on the Question of Charge Densities in Stationary-Current-Carrying Conductors

Recently, some discussions arose as to the definition of charge and the value of the density of charge in stationary-current-carrying conductors. We stress that the problem of charge definition comes from a misunderstanding of the usual definition. We provide some theoretical elements which suggest that positive and negative charge densities are equal in the frame of the positive ions.Comment: 14 pages, TeX, macro newsym.tex include

Axiomatic geometric formulation of electromagnetism with only one axiom: the field equation for the bivector field F with an explanation of the Trouton-Noble experiment

In this paper we present an axiomatic, geometric, formulation of electromagnetism with only one axiom: the field equation for the Faraday bivector field F. This formulation with F field is a self-contained, complete and consistent formulation that dispenses with either electric and magnetic fields or the electromagnetic potentials. All physical quantities are defined without reference frames, the absolute quantities, i.e., they are geometric four dimensional (4D) quantities or, when some basis is introduced, every quantity is represented as a 4D coordinate-based geometric quantity comprising both components and a basis. The new observer independent expressions for the stress-energy vector T(n)(1-vector), the energy density U (scalar), the Poynting vector S and the momentum density g (1-vectors), the angular momentum density M (bivector) and the Lorentz force K (1-vector) are directly derived from the field equation for F. The local conservation laws are also directly derived from that field equation. The 1-vector Lagrangian with the F field as a 4D absolute quantity is presented; the interaction term is written in terms of F and not, as usual, in terms of A. It is shown that this geometric formulation is in a full agreement with the Trouton-Noble experiment.Comment: 32 pages, LaTex, this changed version will be published in Found. Phys. Let

Trouton-Noble paradox revisited

An apparent paradox is obtained in all previous treatments of the Trouton-Noble experiment; there is a three-dimensional torque in an inertial frame S in which a thin parallel-plate capacitor is moving, but there is no 3D torque in S', the rest frame of the capacitor. In this paper instead of using 3D quantities and their ``apparent'' transformations we deal with 4D geometric quantities their Lorentz transformations and equations with them. We introduce a new decomposition of the torque N (bivector) into 1-vectors N_{s} and N_{t}. It is shown that in the frame of ``fiducial'' observers, in which the observers who measure N_{s} and N_{t} are at rest, and in the standard basis, only the spatial components N_{s}^{i} and N_{t}^{i} remain, which can be associated with components of two 3D torques. In such treatment with 4D geometric quantities the mentioned paradox does not appear. The presented explanation is in a complete agreement with the principle of relativity and with the Trouton-Noble experiment without the introduction of any additional torque

The Lorentz transformations of the vectors E, B, P, M and the external electric fields from a stationary superconducting wire with a steady current and from a stationary permanent magnet

In the first part of this paper we review the fundamental difference between the usual transformations of the three-dimensional (3D) vectors of the electric field $\mathbf{E}$, the magnetic field $\mathbf{B}$, the polarization $\mathbf{P}$, the magnetization $\mathbf{M}$ and the Lorentz transformations of the 4D geometric quantities, vectors E, B, P, M, with many additional explanations and several new results. In the second part, we have discussed the existence of the electric field vector E outside a stationary superconducting wire with a steady current and also different experiments for the detection of such electric fields. Furthermore, a fundamental prediction of the existence of the external electric field vector E from a stationary permanent magnet is considered. These electric fields are used for the resolution of the "charge-magnet paradox" with 4D geometric quantities for a qualitative explanation of the Aharonov-Bohm effect in terms of fields and not, as usual, in terms of the vector potential and for a qualitative explanation that the particle interference is not a test of a Lorentz-violating model of electrodynamics according to which a magnetic solenoid generates not only a static magnetic field but also a static electric field.Comment: 57 pages, minor changes, this version will be published in the Proceedings of the IARD 201

The Constitutive Relations and the Magnetoelectric Effect for Moving Media

In this paper the constitutive relations for moving media with homogeneous and isotropic electric and magnetic properties are presented as the connections between the generalized magnetization-polarization bivector $$ and the electromagnetic field F. Using the decompositions of F and $\mathcal{M}$, it is shown how the polarization vector P(x) and the magnetization vector M(x) depend on E, B and two different velocity vectors, u - the bulk velocity vector of the medium, and v - the velocity vector of the observers who measure E and B fields. These constitutive relations with four-dimensional geometric quantities, which correctly transform under the Lorentz transformations (LT), are compared with Minkowski's constitutive relations with the 3-vectors and several essential differences are pointed out. They are caused by the fact that, contrary to the general opinion, the usual transformations of the 3-vectors $$, $\mathbf{B}$, $\mathbf{P}$, $\mathbf{M}$, etc. are not the LT. The physical explanation is presented for the existence of the magnetoelectric effect in moving media that essentially differs from the traditional one.Comment: 18 pages, In Ref. [10] here, which corresponds to Ref. [18] in the published paper in IJMPB, Z. Oziewicz's published paper is added. arXiv admin note: text overlap with arXiv:1101.329

Mapping low-latitude stellar substructure with SEGUE photometry

Encircling the Milky Way at low latitudes, the Low Latitude Stream is a large stellar structure, the origin of which is as yet unknown. As part of the SEGUE survey, several photometric scans have been obtained that cross the Galactic plane, spread over a longitude range of 50 to 203 degrees. These data allow a systematic study of the structure of the Galaxy at low latitudes, where the Low Latitude Stream resides. We apply colour-magnitude diagram fitting techniques to map the stellar (sub)structure in these regions, enabling the detection of overdensities with respect to smooth models. These detections can be used to distinguish between different models of the Low Latitude Stream, and help to shed light on the nature of the system.Comment: To appear in the proceedings of IAU Symposium 254 "The Galaxy disk in a cosmological context", Copenhagen, June 200