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

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

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

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

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