Conclusion

Here we are compelled to write about the work, which is basically not finished yet, for the scope of work is continuously creeping beyond the boundaries of the initial problem. Therefore, our results are the most initial. They are strongly connected with positioning electrodynamics researches in general physics as the basis of natural science. The matter is that the situation around this problem contains too many contradictions.

Maxwell has opened a new form of a matter approximately 150 years ago [3]. Within the rights of the author, he named it an electromagnetic field. By now, this field has been studied so well and is used in techniques so widely, that we cannot imagine our civilization without the devices, which exploit its properties. It is basically owing to mathematical strictness of formulations in Maxwell theory that we know about an electromagnetic field so much. But the whole theory is fairly complex. To let the scientists of that time understand it better, Maxwell illustrated the general theory with a private example. This example contains the solution of the problem of an ideal flat transversal wave in free space.

It may seem that the concrete situation promoted the direct introduction of Maxwell theory directly into the theoretical physics. Actually, the thing did not happen that way. The field theory, every powerful device of it, was used in practice, while theoretical physics used only a private example from the theory, which concerned flat waves, i.e. the phenomenon, which does not exist in nature. In addition to it, physicists have rejected for some reasons from Maxwell theory its basis – the doctrine about induction. Such a paradox could not exist infinitely long. And it has shown itself in its entirety in our researches of vortical or simply circular motion of electromagnetic waves in inhomogeneous and nonlinear media. Now the problem has gone so far that we should discuss not only the fact of possible existence of vortexes, but also their fundamental properties. And all of this has to be done without a support of theoretical physics, which is so necessary, and sometimes even contrary to its traditions.

In Appendixes we have stated the theoretical basis for the execution of experiments described here. The main requirement is absolute registration of all the four velocities of electrical and magnetic fields, which form each vortex. And in the long term – it is the transformation of electromagnetic-field equations to dynamic form.

1. Individual properties of electromagnetic vortexes

Let us begin with spin and mass. Both these properties of an electromagnetic vortex are connected unequivocally only with the problem of existence of the phenomenon. If it exists, then it is sure to have spin and mass. Calculations have shown that such vortexes are possible, and the behavior of Poiting vector testifies to a circular stream of energy. And it is spin. However, the final answer to all the questions can be given only with the help of a direct experiment with a macroscopic electromagnetic vortex, for which we have defined some initial requirements. First, such a nonlinear medium is necessary, in which self-focusing of laser radiation has been gained. Secondly, there must be a strong rotating electromagnetic field. Both the components are rather accessible to experimenters, and their properties can vary over wide range.

The presence of a charge and a magnetic moment is defined by unequivocally internal nonlinear properties of a vortex. I.e. they inevitably follow from this nonlinearity in a variable electromagnetic field, as display of a zero harmonic in spectroscopic decomposition of these fields.

2. Collective properties of electromagnetic vortexes

Each vortex does not form a completely closed rotational-oscillating system. Waves are spread around it. They decrease along the amplitude in inverse proportion to the distance from the center. In usual linear space, waves from different particles do not interact with one another. However, there are areas of space in which this interaction takes place. Such areas are nonlinear zones of other vortexes. If vortexes are close (within the units of the lengths of waves) to each other, the mutual phasing of these waves has the main role, and the phasing depends on the distance between the vortexes and on their mutual orientation. Moreover, they strictly correspond to spherical harmonics of each local wave process, which is called a particle. In some positions the general energy will be minimal, in others - maximal. Therefore, at small distances the zonal character of interaction becomes apparent. Greater distances and a plenty of interacting vortexes should lead to averaging of interactions, but it should be approximately round the minimum of the general energy. It is already gravitation (we consider the interaction of constant charges separately).

The process of a transition, for example of a pair of vortexes from one steady state into another with the change of total energy, generates great interest. It can be certainly investigated by direct calculations by means of computers that are more powerful, than our PC. But there are also other available analytical methods of studying the fluctuations in nonlinear systems. They at once present the result testifying to an exchange of energy with the surrounding field through radiation or absorption. At that, the frequency of the radiated or absorbed waves should be proportional to the difference between initial and final energy. Ingenious Max Planck has already calculated, as you know, the coefficient of proportionality according to the experimental data.

Thus, collective properties of electromagnetic vortexes include the full number of all the known quantum properties of fundamental particles, and also gravitation.

3. The Phenomenological parallel: an electromagnetic vortex - a fundamental particle

For the sake of convenience the comparison of the basic properties of electromagnetic vortexes with the properties of steady fundamental particles is summarized in tables.

The first table shows, that there is a common area of comparison (Table 1) for electromagnetic vortexes and known fundamental particles. It involves mass, spin, a charge and the magnetic moment. These known properties can be used to compare the results, as well as for the possible introduction of corrections into electrodynamics of greater energies.

Property Phenomena	Mass	Spin	Charge	The magnetic moment
Electro-magnetic vortex	+	+	+	+
Fundamental particles	+	+	+	+

Table 1. Conterminous properties.

Property  Phenomena	Structure	Mutual interference	The nature of gravitation	Trajectory
Electro-magnetic vortex	+	+	+	+
Fundamental particles	-	-	-	-

Table 2. Various properties.

The properties of fundamental particles, which cannot be studied by means of the usual quantum mechanics, limited by a set of postulates, are listed in Table 2. They can be understood and investigated only at the level of electrodynamics, by analyzing the corresponding electromagnetic vortexes and, naturally, their interactions.

4. The Mathematical apparatus of quantum mechanics and real properties of fundamental particles

Mutual relations between a traditional quantum mechanics (as a subdiscipline) and its mathematical apparatus have a character, which is similar to the character of relationship between a dog and its tail. The majority of theorists believe that the tail operates a dog. This interesting point of view was strongly discredited by Dirac. He declared that before solving quantum problems it is necessary to think and choose the mathematical apparatus, meeting the subjective criterion of "beauty". We must admit that he himself did it rather well. Any other scientist in this area could not even come near to Dirac’s achievements, if you take into consideration the immensity of his results. But subjectivity in the choice of a mathematical apparatus does not give the ground for the construction of an objective physical theory on its base.

So Dirac interferes with the magnificent theory of a dog’s tail. We shall reject Dirac. Let the tail dominate. From this, it follows that:

- dualism – a wave-particle,

- the absence of trajectories for fundamental particles,

- indeterminacy principle of Heisenberg,

- Bohr model of an atom,

- a huge family of flying notes: photons, rotons, gravitons, etc.

All the components of this antiworld cannot be listed here. The common sense has a rest here. Money and academic ranks flow as if out of a horn of plenty.

Everything is worse, if Dirac is right. Then we shall have to be reconciled to his opinion [5]: «Thus, the generally-accepted quantum theory of the field should be considered as a palliative without any future». And the worst thing about it is that acceptance of Dirac’s point of view entails the necessity to study other subdisciplines of physics, in particular of the Maxwell and Hertz electrodynamics. It will inevitably lead to vortexes, which will strongly damage the image of the antiworld. Then the findings will be quite different:

- no dualism,

- fundamental particles have their own trajectories,

- the indeterminacy principle of Heisenberg has nothing to do with this,

- Bohr model of an atom is primitive and incorrect,

- a huge family of flying notes: photons, rotons, gravitons, etc. are just a figment of imagination, which is much behind in comparison with the imagination of a chicken. A bird identifies the sources and interprets combinations of notes by implication, i.e. it carelessly carries out arithmetic and integrated operations on streams of two types of information – aprioristic (here you will find imagination) and posteriori.

5. Two quantum mechanics

So, research of electromagnetic vortexes compels us to distinguish two quantum mechanics. The first, it is the traditional with set of conventions and fantastic icons. Its "palliative" character is not absolute since apparent successes of this discipline cannot be denied. But the second quantum mechanics exists. It is based on the Newton mechanic and a Maxwell electrodynamics, and only it can open structure of fundamental particles and the nature of their interaction, exclusively without hypotheses and mystical revelations.

We do not impose our point of view to the reader in any way, but we acquaint him with another approach to problems of the world of fundamental particles, which is probably not new for him (the same could be offered 100 years ago). And it is for him to decide what is more realistic.