3.    The field in near and far zones. The vortexes interaction

     through variable fields

 

The understanding of a structure of separate electromagnetic vortexes opens prospects of studying collective processes. We know from a course of electrical technology as constant charges can interact. Therefore here we shall consider forces, which are caused only by variable fields. We shall begin with pair interaction.

At the top of the chart in Fig. 25 you can see a layout view of one-dimensional distribution of one of the fields, electrical or magnetic, from two vortexes the centers of which are located at the distance d₁.

 

 

Fig. 25

In this case the maximum of the accordingly phased field from the left vortex (a firm line) coincides with the maximal density (it is indicated by intensity of shading of a vertical strip) of the right vortex.

The same is true to the same field of the right vortex (dashed lines) with regard to the maximal density of the left vortex. If the same situation has developed concerning the second field (E or H), then the total energy reaches its minimum. It is obvious that there are at least several such minima of total energy, in view of periodical dependence of the fields on the distance d. Their general energy decreases with distance d, as well as the squared cylindrical function of the half-integer argument, describing the envelope turning around the fields in the linear range (see Appendix 4 and 5). Except for distance d such positions depend on phases of oscillating processes in each vortex. And these phases, in turn, are connected with spatial angles, made with each vortex. The types of waves in a vortex, which depend on the corresponding attached Legander polynomials, define the angles. This phenomenon accounts for possible steady, i.e. stationary states of system. Let's pay attention of the reader that vortexes can be the most different and strongly differ among themselves in coefficients m and n of Legander polynomials.

           Unstable intermediate positions (the forbidden values of general energy) are bindingly located between such states, for example at the distance d₂, as it is shown in the low part of Fig. 25. Thus, we can see a fundamental property of vortexes: they have a multilevel system of interaction with a set of the allowed and forbidden states. Further it can be easily subjected to mathematical generalization, all the more so as the whole ideology of calculations and their concrete technology have already been developed by an outstanding Belgian scientist Ilia Romanovich Prigozhin [24, 25]. Even Schrodinger equations are not necessary, for in this case all the problems lead to Liouville equation.

         Basic properties of vortexes group transients from one steady state to another state are very important. The elementary statistical problem in this case should be formulated so: there is a system of vortexes, which comprises, at least, two subsystems. The first subsystem contains vortexes pairs which are being in the first steady state, the second - in the second. Each of these subsystems is characterized by a fundamental oscillations frequency of corresponding vortical pairs. Change of the state of system means change of proportions between subsystems. All system is parametrical owing to nonlinear character of internal interactions of all vortexes. Transitions of parametrical system from one state in another are well investigated in 60^th years of the last century (see, for example, [26, 27]) within the limits of the properties studying of parametric amplifiers for needs of radio astronomy and of a radiolocation.

Comparison of these researches results to conditions of our problem leads to a unequivocal conclusion: any transitions of vortical systems from one steady state in another should be accompanied by radiation or absorption by an environment of electromagnetic waves on to the difference frequency. And we know, that Max Planck has already established a linear dependence of this frequency from of the system energy on an experimental database. Let's in addition notice that here we discuss the lowest and most powerful harmonic. One this frequency according to the theory of parametrical systems does not limit the general background of radiations and absorptions. And other frequencies but with much smaller amplitudes should exist. It illustrates the fundamental difference of the real nature from "palliative" model in a quantum electrodynamics. The exchange of a energy with external space on high harmonics brings essentially new aspects in a high-energy physics. In particular, it draws attention to a question on existence a neutrino. These particles can simply be absent in the nature. Their energies and impulses can quite be attributes of the higher harmonics.

In general, it is probably the essence of nuclear interactions and covalent connections, which are formed between the blocks (clusters) of vortexes. However, only real experiment is of interest here as only it can confirm such unexpected surprises of the nature.

         Distant interactions can be of interest too, inasmuch as gravitation can be. It can also be easily calculated with the help of Prigozhin's methods. The matter is that at greater distances average energy is not set to zero, since forces of interaction are not rigid. In dynamic electrodynamics, with which we are deal now (see Appendix 2), they are either potential, or quasi-potential. I.e. we can observe elasticity, which causes field extension and field squeeze with the general energy having a tendency to reach its minimum. This leads to gravitation in accordance with Kulon's law. It is this law that follows from the quadratic dependence of interaction forces according to the amplitudes of the radial (Bessel) functions, which describe the dependence of fields on the distance. We operate with these functions in Appendixes 4 and 5.

The area of an existence of Casimir’s forces [28] is located somewhere in between forces of near (zone) interaction and gravitation.

Thus, peripheral electromagnetic fields of a set of vortexes are a source of a gravitational field, and not at all Mileva Marich’s grandfather (see the preface) as the academician Okun thinks.

These conclusions acquire special importance, if you take into consideration that the natural nonlinearity, connected with the structure of the dynamic equations of the field, can generate vortexes in vacuum, forming fundamental particles with the same quantum and gravitational properties. One just needs greater amplitudes of the field. And charges and moments will naturally show up in conditions of nonlinearity as the lowest spatial harmonics.

In view of everything that was told here it should be also noted that there is not any problem of unification of all the forces, the so-called problem of “Great Unification”, and there probably has never been any. All the forces are electromagnetic. The problem was declared artificially in the falsification process of the Maxwell theory and the nulling of its role in a natural science.