Augusto Espinoza

Helmholtz Theorem and the V-Gauge in the Problem of Superluminal and Instantaneous Signals in Classical Electrodynamics

In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the two-parameter Lorentz-like gauge (so called v-gauge), we show that two kinds of magnetic vector potentials exist: one of them (solenoidal) can act exclusively with the velocity of light c and the other one (irrotational) with an arbitrary finite velocity v (including a velocity more than c). We show also that the irrotational component of the electric field has a physical meaning and can propagate exclusively instantaneously.

Experimental test of the compatibility of the definitions of the electromagnetic energy density and the Poynting vector

Abstract.It is shown that the generally accepted definition of the Poynting vector and the energy flux vector defined by means of the energy density of the electromagnetic field (Umov vector) lead to the prediction of the different results touching electromagnetic energy flux. The experiment shows that within the framework of the mentioned generally accepted definitions the Poynting vector adequately describes the electromagnetic energy flux unlike the Umov vector. Therefore one can conclude that a generally accepted definitions of the electromagnetic energy density and the Poynting vector, in general, are not always compatible.

Unusual formations of the free electromagnetic field in vacuum

It is shown that there are exact solutions of the free Maxwell equations (FME) in vacuum allowing the existence of stable spherical formations of the free magnetic field and ring-like formations of the free electric field. It is detected that the form of these spheres and rings does not change with time in vacuum. It is shown that these convergent solutions are the result of the interference of some divergent solutions of the FME. One can surmise that these electromagnetic formations correspond to Kapitsas hypothesis about interference origin and the structure of a fireball.

Self-dual electromagnetic fields

We demonstrate the utility of self-dual fields in electrodynamics. Stable configurations of free electromagnetic fields can be represented as superpositions of standing waves, each possessing zero Poynting vector and zero orbital angular momentum. The standing waves are themselves superpositions of self-dual and anti-self-dual solutions. The idea of self-duality provides additional insights into the geometrical and spectral properties of stable electromagnetic configurations, such as those responsible for the formation of ball lightning.

Reply to Comment on 'Electromagnetic potentials without gauge transformation'

This is a reply to the criticism from Engelhardt and Onoochin of our work (2011 Phys. Scr. 84 015009): a general argument for the possibility of different solutions in different gauges unrelated to gauge transformation; a result that has been given by Engelhardt and Onoochin using examples. For this reason we are not in any sense trying to refute the statements made by Engelhardt and Onoochin, instead we are offering a possible theoretical explanation of their results.

The inertial property of approximately inertial frames of reference

Is it possible to compare approximately inertial frames in the inertial property? If this is the case, the inertial property becomes a measurable quantity. We give a positive answer to this question, and discuss the general principle of design of devices for making the required measurements. This paper is intended for advanced undergraduate and graduate students in high energy physics and relativity. Our aim is twofold: (i) to provide a deeper insight into the essentials of classical dynamics, and (ii) to give impetus to ingenious young people to devise new clever, useful and highly sensitive tools for measuring the inertial property following the pattern outlined in the present discussion.

On the violation of the invariance of the light speed in theoretical investigations

In this review, we analyze some of the most important theoretical attempts to challenge the invariance of the light speed postulated by the Special Theory of Relativity (STR). Most of those studies, however, show that STR has great stability with respect to various kinds of modifications in its axioms. This stability probably is due to the fact that in these modifications there is no so much a violation of the physical postulate of the invariance of the speed of light, as its mathematical expansion in the form of making resort to a more general affine space. In these modifications, we refer to more general transformation groups, including scale transformation of the speed of light and time c′ = γc, t′ = γ−1t.

ON UNEXPECTED DIFFICULTIES IN THE TEACHING OF THE SPECIAL THEORY OF RELATIVITY.

Andrew Chubykalo. The wide availability of information has led to the fact that students are well aware of the difficulties of existing physical theories. In this article we analyze some logical paradoxes of the special relativity theory (SRT), concerning the time dilation and length contraction. The Lorentz transformations and the relativistic law for velocity addition are considered in detail. The notion of relativity and the transverse Doppler effect are discussed. The whole complex of numerous paradoxes in the special theory of relativity worries us by further complications.

The pedagogical value of the four-dimensional picture: III. Solutions to Maxwell’s equations

We outline a regular way for solving Maxwells equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwells equations is seemingly overdetermined. We demonstrate the existence of two fundamental solutions to Maxwells equations whose linear combinations comprise the whole variety of classical electromagnetic field configurations.

Mathematical Foundation of Kapitsa's Hypothesis About the Origin and Structure of Ball Lightning

This paper is devoted to the mathematical rationale of the Kapitsas hypothesis about interference nature of the phenomenon known as “ball lightning.” It is shown that (i) there are exact solutions of the free Maxwell equations in vacuum describing closed spherical magnetic surfaces (with a tangential time dependent magnetic field, and without an electric field) and (ii) ring-like formations with tangential time-dependent electric field (and with a zero magnetic field everywhere on the ring). It is concluded that the form of these spheres and rings does not suffer changes with time.