144 research outputs found
On the Physical Origin of the Oppenheimer-Ahluwalia Zero-Energy Solutions
In virtue of the Chubykalo - Smirnov-Rueda generalized form of the
Maxwell-Lorentz equation a new form of the energy density of the
electromagnetic field was obtained. This result allows us to explain a physical
origin of the Oppenheimer-Ahluwalia zero-energy solutions of the Maxwell
equations.Comment: Mod. Phys. Lett. style, 8pp., no figure
Reply to `Comment on ``Helmholtz Theorem and the V-Gauge in the Problem of Superluminal and Instantaneous Signals in Classical Electrodynamics" by A. Chubykalo Et Al' by J. A. Heras [FOUND. Phys. Lett. vol. 19(6) p. 579 (2006)]
This is the reply to `COMMENT ON ``HELMHOLTZ THEOREM AND THE V-GAUGE IN THE
PROBLEM OF SUPERLUMINAL AND INSTANTANEOUS SIGNALS IN CLASSICAL ELECTRODYNAMICS"
BY A. CHUBYKALO ET AL' BY J. A. HERAS [FOUND. PHYS. LETT. vol. 19(6) p. 579
(2006)]Comment: 5 pages, submitted to Foundations of Physic
Theorem on the proportionality of inertial and gravitational masses in classical mechanics
We considered the problem of the proportionality of inertial and
gravitational masses in classical mechanics. We found that the kinetic energy
of a material mass point m in a circular motion with a constant angular
velocity around another material point M depends only on its gravitational
mass. This fact, together with the known result that the straight line is a
circumference with an infinite radius, allowed us to prove the proportionality
between the inertial and gravitational masses.Comment: ReVTeX file, 10p
On Two Complementary Types of Total Time Derivative in Classical Field Theories and Maxwell's Equations
Close insight into mathematical and conceptual structure of classical field
theories shows serious inconsistencies in their common basis. In other words,
we claim in this work to have come across two severe mathematical blunders in
the very foundations of theoretical hydrodynamics. One of the defects concerns
the traditional treatment of time derivatives in Eulerian hydrodynamic
description. The other one resides in the conventional demonstration of the
so-called Convection Theorem. Both approaches are thought to be necessary for
cross-verification of the standard differential form of continuity equation.
Any revision of these fundamental results might have important implications for
all classical field theories. Rigorous reconsideration of time derivatives in
Eulerian description shows that it evokes Minkowski metric for any flow field
domain without any previous postulation. Mathematical approach is developed
within the framework of congruences for general 4-dimensional differentiable
manifold and the final result is formulated in form of a theorem. A modified
version of the Convection Theorem provides a necessary cross-verification for a
reconsidered differential form of continuity equation. Although the approach is
developed for one-component (scalar) flow field, it can be easily generalized
to any tensor field. Some possible implications for classical electrodynamics
are also explored.Comment: no figure
Double (implicit and explicit) dependence of the electromagnetic field of an accelerated charge on time: Mathematical and physical analysis of the problem
We considered the electromagnetic field of a charge moving with a constant
acceleration along an axis. We found that this field obtained from the
Li\'enard-Wiechert potentials does not satisfy Maxwell equations if one
considers exclusively a retarded interaction (i.e. pure implicit dependence
this field on time). We show that if and only if one takes into account both
retarded interaction and direct interaction (so called "action-at-a-distance")
the field produced by an accelerated charge satisfies Maxwell equations.Comment: ReVTeX file, no figures, 12p
Criticism of "Necessity of simultaneous co-existence of instantaneous and retarded interactions in classical electrodynamics" by Andrew E. Chubykalo and Stoyan J. Vlaev
The demonstration that the electromagnetic fields derived from the
Lienard-Wiechert potentials do not satisfy the Maxwell equations is proved to
be false. Errors were made in the computation of the derivatives of retarded
quantities. The subsequent inference of the necessity of both instantaneous and
retarded electromagnetic interactions cannot be made. Different choices of
gauge can lead to a variety of forms for the scalar and vector potentials,
always with the same retarded fields. Classical electromagnetic theory is
complete as usually expressed. One may choose to work in the Lorenz gauge in
which all quantities are retarded.Comment: pdf file, 5 pages, submitted to Int. J. Mod. Phy
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