424 research outputs found
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 , , , ,
, 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 , the magnetic field , the polarization
, the magnetization 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 ,
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 , , , , 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
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