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.
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 60th 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.
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.
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.