TRANSFORMATION OF IMPROVED MAXWELL’S EQUATIONS (ELECTRONIC AND MUONIC NEUTRINOS AND ANTINEUTRINOS) IN EQUATION OF PARTICLE (ELECTRON AND POSITRON) Текст научной статьи по специальности «Физика»

Как известно, основная часть излучающего наблюдаемого барионного вещества во Вселенной заключена в звездах. С Земли даже в самые сильные телескопы все звезды (за исключением Солнца) видны как светящиеся точки на фоне черного ночного неба. Вместе с тем, согласно данным астрономических исследований на известной диаграмме Герцшпрунга - Рессела главная последовательность звезд проходит по диагонали: из верхнего левого угла (высокие светимости, синий цвет) в правый нижний угол (низкие светимости, красный цвет). Если следовать приведенным в таблице результатам вычисления, то для фрагмента звезд главной последовательности по мере повышения их светимости от 0,001 до 1,8 • 106 Вт температура ядра звезды (то есть области, где происходит термоядерный синтез гелия из водорода) понижается от 8,27-107 до 2,18 • 107 К, а радиус ядра звезды повышается от 0,11 до 66570 м.

Полагаем, что предлагаемое нами простое решение сложной астрофизической задачи не относится к области научной фантастики. Эпиграф принят согласно работе [9, а 9].

Литература

1. Главная последовательность [Электронный ресурс]. URL: file:///C:/Users/user/Desk-top/Главная последовательность-Википедия.htm (дата обращения 20 ноября 2021).

2. Эволюция звезд и диаграмма Герцшпрунга - Рассела [Электронный ресурс]. URL: https://easy-physic.ru/evolyuciya-zvezd-i-diagramma-gercshprunga-rassela (дата обращения 20 ноября 2021).

3. Звезды // Физическая энциклопедия. Т. 2. М. Советск. энциклопедия. 1990. С. 68 - 69.

4. Санкт - Петербургский государственный. Физика звезд [Электронный ресурс]. URL: chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/viewe .html?pdfurl=http (дата обращения 2 октября 2021).

5. Соболев В.В. Курс теоретической астрофизики: учебник. М.: Наука. 1985. - 504 с.

6. Самойлович А.Г. Термодинамика и статистическая физика: учебное пособие. М.: ГИТТЛ. 1955. - 368 с.

7. Цвибах Б. Начальный курс теории струн / пер. с англ. М.: Едиториал УРСС, 2011. - 784 с.

8. Сажин М.В. Современная космология в популярном изложении. М.: Едиториал УРСС, 2002.240 с.

9. Трефил Дж. 200 законов мироздания. М.: Гелиос. 2007. - 528 с.

TRANSFORMATION OF IMPROVED MAXWELL'S EQUATIONS (ELECTRONIC AND MUONIC NEUTRINOS AND ANTINEUTRINOS) IN EQUATION OF PARTICLE (ELECTRON AND

POSITRON)

Rysin A.,

ANO "STRC" Technical Committee "Moscow, radio engineer

Nikiforov I.,

Chuvash State University, Cheboksary, candidate of technical sciences, associate professor

Boykachev V.

ANO "STRC" Technical Committee "Moscow, director, candidate of technical sciences

ABSTRACT

In this article we will show the derivation of the equation of motion of particles with rest mass from the interaction of improved Maxwell equations, which correspond to real physical objects in the form of electronic and muonic neutrinos and antineutrinos. In the previous article [1], we showed how photons are formed from electronic and muonic neutrinos (antineutrinos). This approach explains why the annihilation of an electron and a positron leads to the formation of photons. The decay of corpuscular particles with the participation of electronic and muonic neutrinos (antineutrinos) confirms the need for the logic of such a representation in accordance with practice. To this purpose, we will show the transition from probabilistic wave functions to real electromagnetic functions. Actually, we give a real representation of the Louis de Broglie wave function as reflecting electromagnetic processes in system of opposite. The improvement of the Dirac system, taking into account external electromagnetic fields, made it possible to explain all the interaction of particles on base of the Coulomb's force and the Lorentz's force. Here the counteraction is being formed from motion with space-time curvature in SRT and GRT of Einstein. Next, we will calculate the ratio of the mass of a proton to the mass of an electron based on the parameters of the environment, because otherwise the object would either disintegrate or increase indefinitely, due to the fact that without an exchange with the environment at presence of complete closed object, this object would impossibly to detect in the universe. At the same time, we show the need to take into account the common electromagnetic and space-time continuum in the formation of the electromagnetic process. This makes it possible to explain all processes in the universe on base of the exchange between two global opposites, and this is expressed in the form of the movement of objects in both opposites with the emission and absorption of elementary objects in the form of electronic and muonic neutrinos (antineutrinos), which actually reflect the Coulomb's force and Lorentz's force. In other words, we do not have the miracles of previous theories.

Keywords: Einstein SRT and GRT, improved Maxwell equations, equations of the Dirac, general formula of the universe, Louis de Broglie formula, Planck 's formula for the equilibrium state.

Formation of system of Dirac's equations for the description of particles with a mass of rest by wave function of Louis de Broglie

The first attempt to link corpuscular properties with wave properties was made by Schrodinger [2]. At the same time, he used the well-known Hamilton-Ja-cobi equation, but in order to get the satisfaction of this

- ih t)/ dt = h2 /(2m )[V2^(r, t)] + V¥(r, t).

corpuscular equation with wave properties, he used multiplication of the time derivative onto an imaginary unit. Otherwise, when differentiating in length and time, the orthogonal wave functions of sine and cosine would be obtained, and it exclude equality. At the same time, Schrodinger must use exponential functions with an imaginary argument. In result we have: 2m,.. .M . tatv..* (1)

Here ¥(r, t) - the wave function in exponential

form. However, this form of record did not correspond to the invariant form that was used in the Einstein energy equation, due to the presence of a potential external field - V and the formation of the Hamilton-Jacobi equation under the action of external forces. Therefore,

E = c(P2 + m 2c 2f2 =

Dirac decided to extend the combination of wave properties with corpuscular properties to the Einstein energy equation. The Einstein energy equation originally taken by Dirac has the view, according to (2), in the form of a quantitative dependence of kinetic and potential energy to each other in statics [3].

3

cX«kPk • (2)

k

Here k varies from 0 to 3; P0=M0c; Pi =PX ; P2=Py; P3=Pz .

To move to the dynamics of changes through quantitative transformations, it is necessary to present the Einstein energy equation through functional dependencies between the objects of the universe. With this purpose, Dirac used the wave functions of Louis de Broglie - ¥ as functions characterizing the objects of the universe, and he designated quantitative transformations in the form of changes through the influence of operators on functions of Louis de Broglie. At the same time, he obtained a system of equations from these objects of the universe, which, when interacting through

E2 = c 2(P 2 + m 2c 2) = c2

substituting some equations by other equations, were supposed to give the original Einstein energy equation, which ensured the stability of the resulting particle-object in compliance with the law of conservation of quantity. In this case, he carried out the so-called "linearization" of the Einstein energy equation in the form (2). In order to establish the conditions for significances of ak which must be satisfied, taking into account the disintegration of the Einstein energy equation into a system of initial equations in dynamics through functions, we will use the squaring of both parts of the relation (2):

X PP.

k=0

(3)

Thus we have:

72 2/n2

3 3

E2 = c2(P2 + mo2c 2) = c 2 X X PP* k *

kP k a k ak' k=0k '=0

To execute conformity of the given form to the initial for decomposition:

"0 0 0 1 " "0 0 0 - i ' "0 0 1 0 " "1 0 0 0 "

0 0 1 0 0 0 i 0 0 0 0 -1 0 1 0 0

0 1 0 0 ; a2 = 0 - i 0 0 ; a3 = 1 0 0 0 ; a4 =p3 0 0 -1 0

1 0 0 0 i 0 0 0 0 -1 0 0 0 0 0 -1

33

= c2/2 XX PkPk'(a k a W + a k* k > (4)

k=0k '=0

equation of energy of Einstein, the Dirac used matrixes

(5)

a =

As a result, he obtained an equation for a free par- Dirac in the presence of an electromagnetic field can be ticle in the form: written as:

sion:

(E - Н)Ъ = 0. (6)

Here the Hamiltonian H is defined by the expres-

(7)

H = c(ap) + p3m0c2. Where operators E and p are equal:

E = ihd/ dt, p = -iKW. (8)

When a particle moves along an electromagnetic field, generalized significances were used for operators of energy and impulses, taking into account vector and scalar potentials (A, ®):

F = ihd/dt -eO, p = -ihV-e/cA. (9) Here e (q) - charge. Hence, the wave equation of

[F - c(ap) -p3 mc 2]W = 0. (10)

In accordance with the number of rows and columns of the matrices a and p3, the wave function ¥ must have four components, which we will combine in the form of a matrix consisting of one column:

(wA

Ъ =

Ъ Ъ

ЧЪ4 J

(11)

Thus, the Dirac matrix of wave equations is equivalent to a system of four equations:

(F -moc2)Ъ -c(Px -iPy)^4 -cPz^3 = 0; (F - moc 2)Ъ - c(Px + iPy)^3 + cPz^4 = 0; (F + moc2 )Ъ - c(Px - iPy )Ъ - cPzЪ = 0; (F + m0c2 )Ъ4 - c(Px + iPy )Ъ + cPzЪ2 = 0.

(12)

It is clear that Dirac acted intuitively, and he had not of the bases for an explanation of the physics of processes between particles. In this variant of "linearization" Dirac expressed the values of F and p in the form of differential operators, and it is done without proof, but at the same time he did not present the significance of m0 in the form of a differential operator, that is, he left mo unchanged, but we haven't base of logical essence of this approach. If significance m0 is a constant, then the differential from the constant magnitude is zero, and then this quantity cannot be in the equation. In addition, a constant magnitude is a completely self-contained system, and from here it is impossible to identify this significance in the universe. Another arbitrarily chosen step is also unclear - this is the multiplication of mac2 by the function W. In other words, I can multiply function by significance moc2, but I can this step don't. Dirac's wave function W is considered probabilistic, and probability already initially contradicts the presence of wave regularity, that is,

(ih d/dt - m0c2)W + c(ih d/dx +h

probability excludes any law, including wave law. That is, we already have three paradoxes initially. In addition, Dirac decided that each function Ъ in the system of equations (12) is being calculated not on the basis of three other functions Ъ, but on the basis of two functions Ъ, and this representation allowed Dirac to provide a transition to the Einstein energy equation. The justification for this step can be obtained only on the basis of our theory, according to which opposites have the same quantitative transformation into each other, if object is constant magnitude. Therefore the fourth function is always quantitatively equal to the third function (otherwise, we shall not have the closed process of exchange), and hence here the law of transformation of the first two functions into the third or the fourth function is important. These functions reflect the opposites, and it is being seen in the difference of the signs in the equations. Accordingly, the equations (12) without an external electromagnetic field can be written in differential form:

д / ду)ЪА+ cih д / dz%= 0;

(ih д/dt - m0c2)Ъ + c(ih д/dx -h д/ду)Ъъ- cih д/д^Ъ = 0; (ih д / дг + m0c2)%+ c(ih д / дхх +h д / ду)Ъ2+ cih д / = 0; (ih д/дг + m0c2)Ъ + c(ih д/дх-h д/ду)Ъх-cih д/дхЪ2 = 0.

(13)

In fact, we can say that, for example, in the last two equations (13), the changes according to the rules of the equation of two opposites of one object (wave-particle dualism, in which subtraction in one opposite is considered as addition in the other opposite) in the form of functions Ъ and Ъ , gives the formation of an object in the other of system of supervision from opposite in the form of functions Ъ3 and Ъ . And this

object, based on the functions W3 and W4 , also characterizes the previous object from the functions W and W2 in a closed interaction cycle through the first two equations (13). Accordingly, the form of wave functions here is presented monotonously in the form of functions similar to the wave function for the Schrodinger's equation without external interference:

Ъ(г,r) = exp[-i/h(Et - Pr)] = exp[-i/h(Et - Pxx -P y - Pzz)].

(14)

The same type of functions is determined by the into account the differentiation operation by ¥, we absence of external influence, and the difference in in- have: teraction is determined by the type of equations. Taking

(E - moc2)¥x - cPx¥4 + icPy¥4 - cPz¥3 = 0;

(E - moc2)¥2 - cPx¥3 - icPy¥3 + cPz¥4 = 0;

(15)

(E + m0c2 )¥3 - cPx¥2 + icPy¥2 - cPz¥x = 0;

(E + m0c2 )¥ - cPx¥ - icPy¥ + cPz¥2 = 0.

When expressing some functions through other functions for a free particle without an external electromagnetic field, we get:

¥ = (cPx¥4 - icPy¥4 + cPz¥3)/(E - m0c2);

¥2 = (cPx¥3 + icPy¥3 - cPz¥t)/(E - m0c2);

(16)

¥3 = (cPx¥2 - icPy¥2 + cPz¥X)/(E + m0c2);

¥4 = (cPx¥ + icPy¥x -cPz¥2)/(E + m0c2).

Next, we substitute the some functions by the other functions and do the shortening the similar members with contrast signs:

¥ = c2[Px(Px¥ + iPy¥ -Pz¥2) -iPy (Px¥ + iPy¥x -Pz¥2) +

+ Pz (Px¥2 - iPy¥2 + Pz¥x)]/[(E - m0c2)(E + m0c2)];

7 2 2 (17)

¥ = c 2(Px ¥j + iPxPy ¥ - PxPz¥2 - iPyPx¥ + Py2¥x + iPyPz¥2 +

+ PzPx¥2 -iPzPy¥2 + Pz2¥j)/[(E-m0c2)(E + m0c2)].

Through deletion of the probability wave function, we obtain the Einstein energy equation for a free particle:

E2 = m02c4 + c 2(Px2 + Py2 + Pz 2). (18)

We have a similar result for other wave functions, for example, for ¥2 :

¥2 = c2[Px (Px¥2 - iPy¥2 + Pz¥x) + iPy (Px¥2 - iPy¥2 + Pz¥x) -

- Pz (Px ¥ + iPy ¥ - Pz ¥2)]/[(E - m0c 2)(E + m0c 2)];

¥2 = c 2(Px 2¥2 - iPxPy ¥2 + PxPz ¥ + iPyPx ¥2 + Py 2¥2 + iPyPz ¥ - (19)

- PzPx ¥ - iPzPy ¥ + Pz 2 ¥2)/[(E - m0c 2)(E + m0c 2)];

(E2 -m02c4)¥2 = c2(Px2 + Py2 + Pz2)¥2.

Thus, it turns out that for a free particle, all the el- this approach, we get another paradox associated with

ementary objects, which make up this particle during the fact that the probabilistic wave functions ¥ and interaction and have the expressing in significances of 1

wave functions, obey the Einstein energy equation. We ¥2 , as well as ¥3 and ¥4 , are not tied to any real

can also say that in all four observation systems with physical processes, so no further conclusions can be

respect to the initial interacting objects in the view of drawn over the connection between objects. Dirac also

functions ¥ , we have the fulfillment of the energy used the approach of representing some functions

equation for a free moving particle. The difference in through other functions, but at the same time, in the sys-

the observation systems is not determined by the view tem of equations (15), intuitively without justification,

of interacting objects themselves by the type of func- he applied such a change of signs that eventually gave

tions, but is determined by the type of impact by sum- equation (18). Why the some functions need the substi-

mation and subtraction, when subtraction in one obser- tute by other functions, if they are all probabilistic in

vation system is represented by addition in another op- nature and it means that there is not dependencies in

posite observation system. However, there are four the form of regularities between them? Therefore, we

wave functions ¥, and if we had the difference of ob- win ^ to express probabilistic wave functions in terms servation systems only in summation and subtraction, of real electromagnetic functions, taking into account then we would have decomposition into only two wave the previously °btained equations for the electromag-functions instead of four functions. In addition, with netic field based on Faraday's law [1]. In [1] we get improved equation of Maxwell in the view:

SHx . SH, ^ —x + z^0c St

SHy . + ^

et

sh .

se se.

y .

Sx Sy Sz

SHt _SEx SEz

Sy Sz Sx

SHt SEy SEx

et

Sz Sx Sy

SEx

St

SEy St

SE,

sh sh sh

(20)

■- /s0c

-- /s0c

in /Sf! C

0 St 0 Sz

y .

Sx Sy Sz '

SHt _SHx SH z

Sy Sz Sx

SHt SHy SHx

In addition, analyzing the connection of the improved Maxwell equations with wave equations, we obtained a form of equations similar to the form of Dirac

isO/s0 = icgradA + dA/ dt -1/s0 rot O;

igA/= icgradO + dO/dt +1/rot A.

SX Sy

equations through vector potentials [1]:

(21)

We have installed in [1], that the vector potentials reflect the electromagnetic components in the opposite observation system, then we can replace the vector potentials with electromagnetic components. Hence, on the basis of the equivalent form of Dirac equations (13) with equations (21), and considering that probability contradicts the existence of regularities, we can assume the need to move from probabilistic wave functions to real electromagnetic functions.

Connection of wave functions of the Dirac's equation system with electromagnetic functions. The conclusion of ratio of the mass of a proton to the mass of an electron

To this purpose, we note that the system of Dirac equations (15) with mass of rest equal to zero mo=0 turns into wave equations of neutrino and antineutrino [4] (Fig. 1).

right a

orcineutrino v

right matter

W S ^

V light

neutrino

S

0

S

0

left v

antineutrino

left

neutrino

1' P.C

left matter

Fig. 1. Neutrino and antineutrino

It is clear that the concept of matter has no physical justification in our theory, since it does not have a mathematical description with the presence of quantity, and it is associated with lack of understanding of the

processes taking place in the universe. To describe neutrino and antineutrino, an equation with two-row Pauli matrices (the Weyl's equation) or the Dirac's equation (m0=0) is used, and they splits into two independent equations [4].

îh ô% / ôt + c(îh ôW4 / ôx +h ôW4 / ôy) + cîh ô% / ôz = 0; îh ôW2 /ôt + c(îh ïï¥3 /ôx -h ôW^ /ôy) - cîh / ôz = 0; îh ôW3 /ôt + c(îh ôW2 /ôxx +h ôW2 /ôy) + cîh ôW1 /ôz = 0; îh ôW4 / ôt + c(îh ôW1 / ôx -h ôW1 / ôy) - cîh ôW2 / ôz = 0.

(22)

We see that the differences between the first and second pair in the system (22) are only in the designation of functions. At the same time, we cannot leave the previous designations of functions reflecting composite objects, since neutrino and antineutrino reflect objects moving at the speed of light, and it of course implies a different interaction of composite objects, otherwise there would be no changes. If we shall consider the accordance of the second and fourth equation in the form

of the improved Maxwell equations (20), which we derived from Faraday's practical law taking into account the law of conservation of quantity, we can represent the second and fourth equations in the system (22) (at replacing the electric and magnetic field strengths on Louis de Broglie wave functions W) similarly in the form:

îh / ôt - ch / ôy + cî h ôW2 / ôx - cîh ôW2 / ôz = 0; îh d¥3 / ôt - ch d¥3 / ôy + cîh / ôx - cîh / ôz = 0.

(23)

At the excluding on Planck's constant h, and at the multiplying by -i, we obtain:

dWx / dt + ic dWx / dy + c dW2 / dx - c dW2 / dz = 0;

dW3 / dt + ic dW3 / dy + cdW4 / dx - c dW4 / dz = 0.

(24)

In other words, we have two identical equations proceed from the improved Maxwell equations, then that can only differ through functions. However, if we we can express:

W1 =s0E; c W2 = H = cE;

W3 =1^0 H = E /(cs0); W2 = cW4 = E. (25)

In other words, we obtain physical analogues of the realizations of the functions W and W , as well as W and W4 , expressed in terms of real electromagnetic components according to (20), taking into account the constants of electric and magnetic permeability, that is, of the parameters of the medium of vacuum. It is clear that it is necessary to take into account the parameters of the medium at interacting, because otherwise there is no environment at all, and it is miracle. This means that the improved Maxwell equations reflect real

,2 a2i

objects in the form of electronic and muonic neutrino and anti-neutrino at substitute of the probabilistic wave functions by real electromagnetic functions. Actually, this explains the effect of annihilation of electron and positron, which are being described by the Dirac equation system with the appearance of photons, because the interaction of the improved equations of Maxwell (20) gives an electromagnetic wave and this we shown in [1] according to equations:

V2H-1/c ôH/ôt = îcs0 gradjH + s0ôjH /ôt -rot jE = îcz0 grad A + z0ô A / ôt -rot O.

V2E-1/c ô2E/ôt = îc^0 gradjE +^0ôjE/ôt +rot jH = = îc^0 grad O + ^0ôO / ôt + rot A.

(26) (27)

In addition, we have a physical meaning of the differences between electronic neutrino (antineutrino) and muonic neutrino (antineutrino) due to the constants of electric and magnetic permeability without inventing the left and right matter (Fig. 1). Considering that the Dirac equations are derived from the Einstein energy

equation, and we have established the connection between Dirac functions and electromagnetic components, it is natural to assume that the use of electromagnetic functions in the system of Dirac equations should also lead to compliance with the Einstein energy equation, hence, taking into account the formulas (21) we have:

M*0 [ôHy0 / ôt + îcô Ht 0 / ôy] -ôEz 0 / ôx -ôEx0 / ôz = îG; M*0 [ôHy0 /ôt - îcôHt0 / ôy] -ôEz0 /ôx +ôEx0 / ôz = îG; s0 [ôEy0 / ôt + îcôEt0 / ôy] -ôHz0 / ôx -ôHx0 / ôz = -îS; s0 [ôE 0 / ôt - îcôEt0 / ôy] -ôHz0 / ôx +ôHx0 / ôz = -îS.

Here, changes in the observation system, on basis formation, because if the appearance of the similar ob-

of sign of subtraction or summation, effect the first and ject - an electronic or muonic neutrino (antineutrino) in

third equations relative to the initial equations for elec- opposites would be the same, then there would be noth-

tromagnetic components (20), as rotor is absent. This ing to transform into new view. Actually, if we write

can be interpreted by the fact that the first and third down a system of equations in the same form, then we

equations of electronic or muonic neutrinos (antineutri- will never get from this system the equation of energy

nos) are included in the system of equations as objects of Einstein through substitution of some equations in

displaying the contrast to the electronic and muonic other equations. The method of substituting some equa-

neutrinos (antineutrinos) in the opposite observation tions into other equations is possible only at interaction,

system in the view of spatial-temporary curvature, and this excludes the uniformity of representation and

where subtraction is replaced by summation. Other- is expressed through opposites. Thus, we have a system

wise, we would simply have an associative addition of of equations similar to the system of Dirac equations

identical objects instead of interacting with the trans- (13) and it can be led to the form: dHy0 / dt - iG-dEz0 /dx + i^0 cdHt0 /dy -dEx0 /dz = 0;

dHy0 / dt - iG-dEz0 / dx - i^0 cdHt0 / dy +dEx0 / dz = 0;

y (29)

s0 dEy0 / dt + iS -dHz0 / dx + is0 cdEM / dy -dHx0 / dz = 0;

s0 dEy0 / dt + iS -dHz0 / dx - is0cdEt0 / dy +dHx0 / dz = 0.

Functions G, S too according to necessity of the electromagnetic functions that are similar (21). There-decision of the equations should be expressed through fore we consider, that G = gHy , and S = sEy. From

here we write these equations in the form:

dHy0 / dt - igHy0 / -1/ dEz0 / dx + i cdHt0 / dy -1/ dEx0 / dz = 0;

dH 0 / dt - igHy0 / -1/ dEz0 / dx - i cdHt0 / dy +1/ dEx0 / dz = 0;

y0 y0 0 0 z0 t0 0 x0 (30)

dEy0 /dt + isEy0 /s0 -1/s0dHz0 /dx + icdEt0 /dy -1 /s0dHx0 / dz = 0;

dEy0 / dt + isEy0 / S0 - 1/ S0 dHz0 /dx - icdEt0 /dy +1/s0dHx0 /dz = 0.

It should be noted that the Louis de Broglie wave change the significances Et on Ht, and vice versa. This

functions and the electromagnetic functions in (30) wi^ can be done if we take into account the difference in the

coincide °nly if each equation in system (30) is being constants of the electric and magnetic permeability in

considered in its own observation system. In other the medium in terms of length coordinates, based on the words, electromagnetic components should be reflected 2

in the system of Dirac equations as derivatives of dif- equality Ht = s0cEt a™ Et = ^0(c ' c)Ht, that is, it

ferent variables in terms of length coordinates and time is a connection that should be in contrast between a

magnitude similarly to functions of Louis de Broglie. moving object and stationary object in SRT of Einstein.

We will show this transition below. It can be seen that Hence we have the correct equations:

in order to lead it to a single form, it is necessary to

dHy0 / dt - igHy0 / ^0 -1 / ^0 dEz0 / dx + ic Et0 / dy -1/ ^ dEx0 / dz = 0; d Hy 0 / dt - igHy0 / ^0 -1 / ^0 d Ez 0 / dx - ic2 S0d Et 0 / dy +1/ ^ d Ex0 / dz = 0; dEy0 / dt + isEy0 /s0 -1 /s0dHz0 / dx + ic2^0 dHt0 / dy -1/s0dHx0 / dz = 0; dEy0 / dt + isEy0 / s0 -1/ s0 dHz0 / dx - ic2^0 dHt0 / dy +1 / s0dHx0 / dz = 0.

(31)

If we take into account that according to theory ^^ = 1/c2 , we get the following type of equations:

dHy0 / dt - igHy0 / ^0 -1/ ^0 dEz0 / dx +i / ^0dEt0 / dy -1 / ^0 dEx0 / dz = 0;

dHy0 / dt - igHy0 / ^0 -1/ ^0 dEz0 / dx - i / ^0dEt0 / dy +1 / ^ dEx0 / dz = 0; dEy0 / dt + isEy0 /s0 -1/s0dHz0 /dx + i/s0 dHt0 / dy -1/s0dHx0 / dz = 0; dEy0 /dt + isEy0 /s0 -1/s0 dHz0 /dx - i/s0 dHt0 /dy +1/s0dHx0 /dz = 0.

We see that the first two equations differ in electro-magnetic functions from the last two, but in order to represent these equations as a system of Dirac equations with subordination to the Einstein energy equation, these equations must be shown in the similar form.

With this purpose, we take into account that the constants of electrical and magnetic permeability can be represented as some general variable U0 in the form:

s0 = tt0 / c, ju0= 1/(cw0). (33)

Then the system of equations (32) will take the

form:

dHy0 /dt - iu0cgHy0 - u0c SEz0 /dx + i u0cdEt0 / dy - u0c dEx0 /Sz = 0;

SH 0 /St - iu0cgH0 - ^c SEz0 / Sx -1 u0cSEi0 / Sy + ^c SEx0 /Sz = 0;

y0 0 y0 0 z0 0 t0 0 x0 (34)

SE 0 / St + icsEy0 / u0 -c / u0SHz0 / Sx + i c / u0 SHi0 / Sy -c / u0SHx0 / Sz = 0; SEy0 / St + icsEy0 /u0 - c/u0 SHz0 / Sx - ic/u0 SHt0 / Sy +c/u0SHx0 / Sz = 0.

Considering the connection between the electric speed of light without taking into account SRT), we can and magnetic components in the form of H = cE (this write: is the initial connection between opposites through the

SEyl /St - iu^cgE^ - u0 SEzl / Sx + iu0 SEtX /Sy - u0 SExl /Sz = 0;

SEyl /St - iu0cgEyl - u0 SEzl /Sx - i u0SEtl / Sy + u0 SExl / Sz = 0;

SE j / St + zcsEyl / u0 -c2 / u0SEzl / Sx + i' c2 / u0 SEn / Sy -c2 / u0SExl / Sz = 0; ( )

SEyl / St + icsEyl / u0 - c2 / u0 SEzl / Sx - ic2 / u0 SEn / Sy +c2 / u0SExl / Sz = 0.

At the same time, we have: and these electromagnetic functions are being reflected

g = s / u02 = c / u02; s = c. (36) by the different functions of the form ¥j and ¥2

as

In this case, by analogy with the system of equa- well as ¥3 and ¥4, as is customary in the system of

tions of Dirac, at presence of the initial functions of the Dirac equations. In this case, the significances of the

£x1 , £y1 , Ez1 , Et1 , we must satisfy solution of system of functions Ex1 , Ey1 , , Ea have a representation in all

four equations to correspond to the Einstein energy four coordinates, that is, they are completely defined in

equation. However, this is possible only if, in each of space and time and have no independence from space

the equations (observation systems), the significances and time. As a result, we have decomposition in coor-

of the functions (objects) Ex1 , Ey1 , Ez1 , Et1 have the ac- dinates of length and time, where the wave functions

tion in quality of changing magnitudes belonging to dif- have the form: ferent systems of representation of coordinate systems,

¥1 = Rl, Eyl' Ezl' Etl)'; ¥2 = {Ex2' Ey 2' Ez 2' Et 2};

y y (37)

¥3 = {Ex3' Ey3' Ez3' Et3}; ¥4 = {Ex4' Ey 4' Ez 4' Et4}.

In fact, we have a closed interaction of four objects represent these functions similarly to the Schrodinger (similarly to a closed interaction in length coordinates wave functions, but here the Planck constant is absent: and time magnitude in invariant form), with the reflection of these objects in the space-time environment. We

¥(t,r) = exp[-i(Et - Pr)] = exp[-i(Ett -Pxx - Pyy - Pzz)]. (38)

In this case, the equations (35) will be written by functions in accordance with the Dirac' s system in the form:

S¥ /St - - u0 SY4 /Sx + i u0 SY4 /Sy - u0 S¥3 /Sz = 0;

S Y2 / St - zu0cg¥2 - u0 S¥ / Sx - i u0S¥ / Sy + u0 S¥4 / Sz = 0;

S¥3 /St + ics¥3 /u0 -c2 /u0S¥2 /Sx + i'c2 /u0S¥2 /Sy-c2 /u0S¥l /Sz = 0;

S¥ / St + zcs¥4 /u0 - c2 / u S¥1 / Sx - i'c2/ u0 S¥x / Sy +c2 /u0S¥2 / Sz = 0.

Taking into account the differentiation operation by ¥ we have:

(E - u0cg)¥l - ^Px¥4 + iu0Py¥4 - "0Pz¥3 = 0;

(E - u,cg)¥ - u0Px¥3 - uPy¥3 + u0Pz¥4 = 0;

(39)

(E + cs/u0)¥3 -c2/u0Px¥2 + ic2/u0Py¥2 -cz/u0Pz¥l = 0; (E + cs/u0)¥4 -c2/u0Px¥l -ic2/u0Py¥l + c2/u0Pz¥2 = 0.

(40)

Taking into account the expression of some functions through the other functions for a free particle without an external electromagnetic field, we obtain:

^ = (u0P^4 - iu,Py^ + u0Pz^)/(E - u0cg);

= (uoPx^3 + iuoPy^3 -uPz^)/(E-uoCg); ^3 = (c2/u0Px^2 -ic2/uoPy^2 + c2/uoPz%)/(E + cs/uo);

(41)

T4 = (c2/u0PxT + ic2/u0PyT - c2/u0PzT2)/(E + cs/u0). Next, we substitute the some functions by other functions and exclude similar members, but with contrast

signs:

T = c 2[PX (Px T + iPy T - Pz T2)- iPy (Px T + iPy T - Pz T2) +

+ Pz (PxT2 - iPyT2 + PzTX)]/[(E - ^cg)(E + cs/^)];

T = c2(Px2T + iPxPyT -PxPzT2)-iPyPxT + Py2T + iPyPzT2 +

+ PzPxT2 -iPzPyT2 + Pz2Tx)/[(E-«0cg)(E + cs/^)];

(E2 -c V)T = c2(Px2T + Py2T + Pz2TX). Excluding the wave function, we obtain the Einstein energy equation for a particle:

E2 = c X2 + c 2(Px2 + Py2 + Pz2);

E2 = c V + c 2(Px2 + Py2 + Pz2);

E2 =^o2c6 + c 2(PX 2 + Py2 + Pz2).

2(t>2

(42)

(43)

Here we have: m2=1/u02. Thus, we see that the mass of rest of the particles is determined by the parameters of the constants of the electric and magnetic permeability of the medium. Actually, this conclusion was expected, since any object interacts with other objects through its surrounding environment, and it is clear that without changes in this environment, there can be no changes in the object itself. We will get similarly the

0(t,r) = exp{i [ct ± (r + r^)]};

result for other wave functions. At the magnitude uo = c, that is, when the observation system is changing to the opposite system, connected to the initial system through the speed of light, we get the Einstein energy equation squaring.

Earlier in [1] we were convinced on base of formulas:

Om (t,r) = exp{i[(ct + ct/^) ± r ]}

(44)

that the frequency of wave processes is directly re- hf = mc2 (45) lated to the constants of electric and magnetic permeability. Next, we take into account the Louis de Broglie In next step, we take into account that according formula in the form: to our theor^ h=m0=1/c; hence we get:

h / p = c / f; m0 / p = c / f; m0/(m0v) = c / f; 1/v = c / f; f = cv; hf = v.

In result, we have a direct relationship of frequency, mass of rest and velocity. It is clear that in the presence of only the mass of rest, the velocity can has relation to the opposite observation system relative to the absolute system of coordinates in accordance with GRT of Einstein, because the potential energy in one opposite looks like kinetic energy in the other opposite. Louis de Broglie's formula (45) also says that the frequency of a certain wave process is also associated with the mass of rest. However, according to physics, wave processes are associated with radiation or absorption, and this would mean that the object would have to decay or, conversely, increase indefinitely due to absorption. And here we have to pay attention to the fact that

in the system of equations (39) is being included members of view: { - iu0 cgT + iu0 dT4 /dy },{

- i«0cgT2 - i«0 dT,/ dy },{

icsT3/ u0 + ic2/u0 dT2/ dy}, and {

icsT4/ u0 - ic 2/u0 dTj/ dy }. Considering the formula (36) at presence y=ct, we take into account that the imaginary unit i reflects the opposite, and the transition to the opposite observation system is associated with an exchange of the length on significance of time. Further, with a reduction by the similar multipliers, we have:

-c/u0 + u0/cd¥4 /dt = 0, -c2/u0 -u0/cd¥3 /dt = 0; c2¥3 /u0 + c2 /(u0 c)d¥2 / & = 0, c2¥4 /u0 - c 2/(u0 c)d¥x / dt = 0;

= -u07c / dt, -¥2 = u / c / dt; ¥3 = -1/cd¥2 / dt, ¥4 = 1/cd^ / dt.

(47)

In fact, it turns out that in the system of equations (39) in the opposite observation system, the condition is being fulfilled at which the object expressed in terms of ¥l has a negative significance and is being increased. At the same time, an object having a negative significance and expressed in magnitude of ¥2 is being decreased to zero. Accordingly, an object having a positive significance and expressed in terms of ¥ also is being decreased to zero, at the same time the object, having a positive significance and having the expressing in magnitude of ¥4 , is being increased. Considering that the system of equations (39) characterizes the

Einstein energy equation, that is, a closed cycle of exchange over objects which are being expressed as functions ¥j and ¥2, as well as ¥ and ¥4, it follows that in order to ensure the existence of an object, in any invariant form, the remaining differential members in the system of equations (39) must give an inverse equivalent transformation. And of course this should be expressed through the well-known law of electrodynamics, which is Faraday's law in opposites, and it we have discussed in [1]. We will show it on the basis of electromagnetic components. In this case, for example, the second equation in the system (34) can be represented as separate equalities in the form:

dHy0 / dt - iu0cgHy0 - u0c dEz0 / dx - i u0cdEt0 / dy + u0c dEx0 / dz = 0;

*y0

- iUocgHyo = -i / Uqc 2 H y o = i Uocd Et q / dy;

y 0"

- Eyo = Uq /c3dEtq/dt;

(48)

dHy0 / dt = u0c dEz0 / dx - u^c dEx0 / dz; dEy0 / dt = u0dEz0 / dx - u0dEx0 / dz.

Similarly, we will present the fourth equation in the system (34):

SEy0 / St + icsEy0 / u0 - c / u0 SHzo / dx - ic/u0 SHi() / dy +c / u0SHx0 / Sz = 0;

icsEy0 / u0 = ic/ u0 SHt0 / Sy, c2Ey0 / u0 = c2/u0 SEt0 / Sy; Ey0 = l/ cS Et 0/ St;

SEy 0 / St = c2 / u0 SEz0 / Sx -c2 / u0SEx0 / Sz.

We see that there are differences between the significances of Er0 in (48) and (49) at determining the dependence on Effl . This is due to the fact that the second and fourth equations in (34) reflect opposites, because time and length have exchange of displaying in system of representation. From here, if in the system (48) instead of the significance of SEt0 / St in the third equation to do the substitute through the significance of SEy0 / St from the fourth equation (49), then we get an

Ey0 = u0/ c[SEz0/ Sx -S

equation similar to the representation of the vector potential:

B = rotA. (50)

From here we have an equation by analogy:

- Ey0 = u0/c[SEz0/Sx SEx0 / Sz]. (51)

Similarly, we will do this step for the significance of SEt0 / St in the third equation (49) with the substitution through the significance of SEy0 /St from the fifth equation (48), and we will get: :x0/ Sz]. (52)

As a result, we see that the exchange is equal, and the action is equal to the reaction. At the same time, subtraction over formulas (51) and (52) in system of one opposite from sign of equality in left part of formulas (51) and (52) will mean summation in the other opposite in right part from sign of equality. This corresponds to the case of the formation of standing electromagnetic waves in a waveguide. From this, it follows, that the decay or absorption in system of one opposite means the manifestation of Faraday's law in the other opposite. Decay and absorption, which is expressed in

terms of an exponential function in the form of exp(±g), are possible only on the basis of the most elementary objects, and these objects can only be electronic and muonic neutrino (antineutrino), the transmission process of which is expressed through Faraday's law. This means that the electromagnetic energy of electronic and muonic neutrino (antineutrino) in system of one opposite gives the sources of radiation and absorption in another opposite observation system, connected to the first through the speed of light. It is this electromagnetic field formed around the inductor that provides current

after switching off the potential difference in conductor. Otherwise, if there was no reaction of medium to the effect of the current in the coil, it is clear that then we would not have observed any effect, since zero does not give changes. In other words, there is absorption of energy by the medium, and there is its return, and this cannot be without radiation and absorption. The characteristics of the absorption and radiation sources are expressed in terms of the constants of electrical and

V0c = 1/ u0 = l/[cj 1 - vnp2/ c 2 ]

magnetic permeability and determine the spatial-temporal change under external influence. It is clear that the constants of electric and magnetic permeability can be expressed in terms of a certain average generalized velocity Vnp , which determines the average kinetic energy in contrast system over the formula:

S0 = u0 / C = V1 - Vnp2/C2- (53)

In this case at 2c6 = m2c4 , we have: = «0^1 - vnp2/ c2 = m. (54)

In other words, we get a mass of rest at motion in contrast system to the fulfillment of SRT and GRT of Einstein.

Hence, on the basis of the formulas of Louis de Broglie, taking into account our theory, it is being assumed that the additional rest mass of the proton in our observation system is associated with the movement of the positron in the system of opposite on orbit around the antiproton. Accordingly, the motion along the orbit gives electromagnetic radiation, but since there is symmetry between opposites, the radiation in one opposite

is perceived as absorption in the other opposite, and it corresponds to a closed system of exchange between opposites. In other words, due to the formulas of Louis de Broglie, taking into account our theory, the paradox associated with the fall of an electron on the nucleus is solved, and the parameters of orbits and energies should follow from the equilibrium of thermodynamic exchange between the opposites. However, according to the general equations of the universe in [5]:

cos2( x) + sin2( x) = ch2( g ) - sh2( g) = 1 = const; exp(ix)exp(-ix) = exp(g )exp(- g ) = 1,

(55)

we see that if the equality of oppositely directed electromagnetic components is observed in the left part of the equations from the sign of equality, then in the right part, due to the inversely proportional relationship of opposites, there will be inequality, that is, heterogeneity. For equality on the right it is necessary to have argument significance equal to zero, that is, the object must be absent. Hence the conclusion - it is impossible to obtain uniformity in opposites at the same time.

Then, accordingly, we have the question: "With what uneven electromagnetic distribution over frequency and spatial-temporal heterogeneity, equilibrium between global opposites at closed circular exchange can occur?"

On the basis of the general formula of the universe (55), we see that the process of decay from some initial quantity can be represented as: exp(-g) or 1/exp(g). In this form, we have a quantity normalized to one in accordance with the presence of constants. In contrast system, decay is presented as a synthesis with the law of conservation of quantity: l-exp(-g), 1-1/exp(g). Actually, this is equivalent to the principle of radioactive decay in [6], and the reverse process gives synthesis. Accordingly, we have a distribution over magnitude (frequency) similar to Planck's formula [7]:

Vs0^0 =V [1/(UoC)]/[Uo/ c] = 1/u

<g> = g exp(-g)/[1 - exp(-g)] = g/[exp(g) -1].

56)

This formula (56) excludes the "ultraviolet catastrophe" and corresponds to a closed system. That is, on the basis of the formula (56), taking into account the number of frequencies per unit of volume of the medium of vacuum, the well-known Planck formula was obtained, from which the energy distribution over frequencies is calculated and the maximum of the radiation spectrum œmax is determined. Next, we will recall that the space-time curvature in the universe is determined by the ratio of the constants of electrical and magnetic permeability according to the formula:

80^0 = 1/c2. (57)

Taking into account (33) and (53) = 1/(u0c),

Sq — UQ / c,

where uQ =

i

c2 - V,

np

and Vnp is the

significance of the integral average velocity of objects in the contrast system (that is, it is a representation of kinetic energy), the ratio of the constants of magnetic and electrical permeability in this case will give the significance of:

1/[^ 1 - Vnp2/ c2 ] = 12071.

(58)

2

We see here a discrepancy with the SI system, which gives a dimensionless coefficient, but we get the measurement significance in units of speed, if consider the using magnitude uo in our theory. However, the magnitude of velocity - Vnp refers to the system of opposite, and the opposites themselves are connected

through the speed of light, like length and time, so at switching to the opposite observation system, we must take this connection into account by multiplying the value 1/uo by the speed of light, and as a result we will have a dimensionless coefficient. In addition, the universe does not "know" anything about measurement

systems and operates only with quantity, and it is di-mensionless. As a result, the resulting ratio is equivalent to the fulfillment of Einstein's SRT and the difference is determined in the speed of light, that is, in the magnitude of the interaction of opposites. Further, this parameter turned out to be in full accordance with the

, / m0 = 4,965/ ^0/ so = 4,965/ u0 =

ratio of the mass of the proton to the mass of the electron, taking into account the transition from the average integral magnitude to the maximum of the radiation spectrum in contrast system due to the coefficient of 4,965, which was calculated in [7]:

m

np

= 4,'

,965/[c^ 1 - vnp 2 / c2 ] = 4,965-120ti = 1871,76.

(59)

Here mnp is the mass of a proton; mo is the mass of

an electron. The significance obtained in (59) differs from the magnitude calculated in physics mnp/m0=1836 by less than 2 %. And this difference is due to a different space-time curvature in the universe, that is, heterogeneity. Actually, according to (59), the energy parameters of corpuscular-wave objects should also be determined, since mass has an unambiguous relationship with energy due to multiplication by c2. It is clear that the interaction varies the parameters of electrical and magnetic permeability in the medium, and this changes the mass ratio, otherwise the current in the inductor after removing the potential difference in conductor would not be observed. Thus, the object varies the environment with the formation of counteraction to the action of the object. When the influence of the object ceases, the environment already affects the object, since medium cannot instantly change its parameters at presence of velocity of light. In other words, the medium has an exchange with the object (and it cannot be without the initial simplest objects, which are electronic and muonic neutrinos and antineutrinos) and this, by the way, determines, in addition to the radiation field, the presence of a quasi-static electromagnetic field. It is

F = ma = md 2s / dt2 = mdv / dt;

this interaction of the object and the environment that gives the Louis de Broglie function a certain frequency. In other words, we have a kind of closed resonant system of interaction through the exchange between the object and the environment. However, the obtained result concerns the free particles and determines the total energy of the particle, that is, both potential and kinetic energy. There is no division into positive and negatively charged particles, since the square of energy is being considered. In order to solve equations in the interaction of particles, it is necessary to take into account the interaction with the presence of forces, and for this it is necessary to go to the Hamilton-Jacobi equation, that is, to consider not completely closed solutions.

Transition from the Dirac's system of equations to the Hamilton-Jacobi equation. Connection

of equation of the wave, of the Hamilton-Jacobi equations, and the conclusions about the existence of interaction of the equations

As it is known, the Hamilton-Jacobi equation in the presence of the influence of force F can be considered as a direct consequence of the well-known Newton's law:

E = JFds = JFvdt = Jmvdv = mv2 /2 = p2 /(2m).

(60)

Further, according to classical physics, a certain action function S(r,t) is taken taking into account the

equalities VS = p and dS/ dt = -E. As a result, we

have the Hamilton-Jacobi equation:

- SS(r, t )/ dt = 1 /(2m)[VS(r, t )]2

(61)

That is, in the Hamilton-Jacobi equation (as well as in the Schrodinger and Pauli equation) there is a proportionality coefficient equal to 2 - between energy and impulse. In the Einstein energy equation, from which the system of equations of Dirac is obtained, this coefficient is not present. Therefore, it is not possible to go directly from the Einstein energy equation to the Ham-ilton-Jacobi equation, and all attempts will have paradoxes. This is being connected with the fact that in the Einstein energy equation, all quantitative relations are given as if to one general system of observation, at presence a of closed system in the form of a circle equation

[F

(T O'A 0' r

ff(

- c

vv

a'

A A P

J J

and at the existence of an invariant form in all systems of coordinates. It is clear that in this case, the Hamil-ton-Jacobi equation must correspond to its own system of interaction equations different from the Dirac system of equations for a free particle. However, let's see how Dirac managed to move to the system of equations of Pauli, which replaces the Hamilton-Jacobi equation in a wave form, in the view of system of Schrodinger equations. For this purpose, the Dirac equation (10) was presented in the form of a matrix equation:

- moc

(I' 0' A

v o' - r 'j

V¥2 J (¥3 A

¥

Vv¥ JJ

= o.

(62)

]

In this case, the matrices have the form:

' 1 0A r 0 0 A r 0 1A ' 0 - i A r 1 0 a

I'= ; 0'= ; ^1'= ; ^2'= ; ^3'=

V0 1 y V 0 0 y V 0 0 y j 0 y V 0 - 1y

(63)

Then, splitting (62) into two matrix equations with two-row matrices, we get two equations with two-row matrices instead of one equation with four-row matrices:

(F - m0c2) 1 = c(a' P

(F + m0c2)

V¥2 y

'¥3 A

¥

VT4 y

= c(a' P)

¥4 y

A

v¥2 y

(64)

In the transition to the case of stationary process and the independence of the electric and magnetic fields from time, the wave function for the case of stationary process is used in the form:

¥(t, r) = exp[-i / Ä(E + m0c 2)t ]¥r (r).

(65)

Actually, when using the function (65), we turn to In this case, the magnitude of E is calculated from com-the case when the relativistic energy in the approximate pliance with Newton's formula (60). Substituting (65) case at v2/c2<< 1 can be represented as Erel=E+m0C2 [8]. into (64) and deleting from the equation the function of

the time factor exp[-i/h(E+m0C2)t], we get:

(E - eO) 1 = c(a' P

¥

A

V¥2 y

¥

4 y

f¥,A

(E - eO + 2m0c 2) 3 = c(a' P

¥

V¥ y

¥1A

¥

2 y

From the last equation follows:

'¥3 A

V¥4 y

= 1 /(2m0c)[1 + (E - eO) /(2m0c2)]-1 (a' P

'¥1A

¥

2 y

Further, it is taken into account that:

E - eO = mnv2/2.

Hence, at low speeds v/c<<1 we have;

(E - e$)/(2m0c2) = (m0v 2/2)/(2m0c2) << l. Then from the formula (68) we find:

¥3 = l/(2moc)(.'P) ¥1

V ¥ 4 y V ¥ 2 y

Substituting (71) into (66) we get:

f¥A / v /¥A

(E - eO) 1 = 1/(2m0 )(a' P)(ff' P 1

V¥2 y

¥

2 y

Accordingly, the following transformations are taken into account:

(aP \a'P ) = (a, Px + a 2 'Py + <3 'P2)(al Px + a 2 'Py + <73 PJ;

_ ^2 *2 *2 rt t r — i— i i— 1 — 1—1 —1—1 i— 1.

<1 = a2 = <3 = I , <1 a2 = -<2 <1 = 173, a2 <3 = -73 a2 = i<1.

2

(aP Xa P) = Px2 + Py2 + Pz2 + ia3'(PxPy - PyPx) +

3 ' x y y x

+ ia2'(PzPx - PxPz) + iOX'(PyPz - PzPy). As a result, we have equality:

(a' PXo- ' P) = P2 + i(a '[PP]).

Next, we substitute the significance:

P = p - e/cA.

From here we find:

e

[PP]¥ = --(|pA]+[Ap])¥.

(66) (67)

(68)

(69)

(70)

(71)

(72)

(73)

(74)

(75)

Considering that the operator p acts on all functions to the right of itself, we can write:

|pA] W = -Ap]W+W |pA] = -[Ap]W + (h / i)HW. (77)

Where: H=rot A - intensity of a magnetic field. Hence:

[PP]W = [-eh /(ic)]HW. (78)

Therefore, we have:

(a' P)(a' P) = P2 - [eh / c](a' H). (79)

Thus, the Dirac equation, taking into account the members which have proportionality only to v/c, is being reformed into the Pauli equation:

[E - eO - P2 /(2m0) - eh /(2m0c)(a' H)]W. (80)

On the basis of the results obtained, here is being asserted that an additional expression appears for the energy of an electron in a magnetic field:

Vmagn =-^spH = -eh /(2m0c)(a' H). (81)

It automatically leads to the existence of the mag- we will analyze in more detail the extension of differ-

netic moment of the electron, the magnitude of which ential operators in the form (9). Physically, the intro-

in Pauli's theory was postulated on the basis of the anal- duction of additional dependence on vector potentials

ysis of experimental data: means that the energy and significances of impulses are

^ = -eh /(2mc)a. (82) determined by the distribution of vector potential fields

sp in space of medium in addition to the magnitudes of the

However, we rnU Anther show that this approach schrodinger wave function of the form is the purest adjustment to the result. For this purpose,

W(t, r) = exp[-i / h(Et - Pr)] = exp[-i / h(Et - Pxx - Pyy - Pzz)].

In this case, the system of Dirac equations can be written as [9]:

(ihd/ St - eO - m0c2)WX + c(ihd/ 8x - hd/ dy + e/cAx + ie/cAy )W4 -

- c(ihd / dz + e / cAz )W = 0;

(ihd / dt - eO - m0c2) W2 + c(ihd / dx + hd / cy + e / cAx - ie / cAy )W3 +

+ c(ihd / dz + e / cAz )W4 = 0;

(ihd / dt - eO + m0c2 )W3 + c(ihd / dx - hd / dy + e / cAx + ie / cAy)W -

- c(ihd / dz + e / cAz )W = 0;

(ihd / dt - eO - m0c2) W + c(ihd / dx + hd / dy + e / cAx - ie / cAy )W +

+ c(ihd / dz + e / cAz) W2 = 0.

If we use the wave function (65), taking into account the differentiation operation by W we have: (E - eO)W = cPxW4 + eAxW4 + icPyW4 + ieAyW4 - cPzW3 - W3;

(E - eO) W2 = cPx W3 + eA W3 - icPy W3 - ieAy W3 + cPz W4 + ^Az W4;

9 (84)

(E - eO + 2moc2)W3 = cPxW2 + eA,W2 + icPyW2 + ieAy W2 - cPzWx - eAzWx; ( )

(E - eO + 2m0c2)W = cPx W + eA W - icPy W - ieA W + cPz W2 + eA W.

But then the assumption is being made, that the insignificant (mov2/2)/(2moc2)<<1 in accordance with velocity of particle is determined by the amount of en- (70), and has only a radial component to the centrally ergy according to the formula (69) in the form of E- symmetric electric field. Hence the system is being ob-e®=mov2/2. In this case, the magnitude of impulse is tained:

(E - eO)W = cPxW4 + eAxW4 + icPyW4 + ieAyW4 - cPzW3 - W3;

(E - eO)W2 = cPx W3 + ^4 W3 - icPy W3 - ieAy W3 + cPz W4 + ^Az W4;

9 (85)

(2moc2)W3 = cPxW2 + eAxW2 + icPyW2 + ieAyW2 -cPzW -eAWt; ( )

(2moc2)W4 = cPx W + eAx W1 - icPy - ieAy + cPzW2 + eAWV

But, in this case, we have ambiguity in determin- eAx , icPy , eAy , cPz ,eAz , and on the other hand, the en-ing the energy of impulse of a particle, on the one hand, ergy of impulse (and it is related to the speed of motion, it is determined by the magnitudes standing to the right that is, with kinetic energy), has the basis on the as-of the sign of equality in (85) by the significances cPx, sumptions made on the left from the sign of equality,

and this magnitude has already be equal to E-

(83)

(86)

46 Sciences of Europe # 88, (2022)

e®=mov2/2, in the first two equations (85). In the two cance of the internal potential energy. Now, accord-

last equations (85), the energy to the right of the sign of ingly, we will express some functions %, % through equality in (85) is equal to the constant (2moc2), that is, 1T1 1T1 , , . _ „ .

here impulse is absent at all, and we have the signifi- others %, %, as we did above in the system of Dirac

equations with the transition to the Einstein energy equation (17), (19) and (42). From here we have:

%3 = (cPx%2 + eAx%2 + icPy%2 + ieAy% -cP%i -eAz%i)/(2rn0c2);

% = (cPx%i + eAx% -icPy% -ieAy% + cP%1 + eAz%2)/(2m>c2). Next, we need to perform substitution actions in the form: (E - eO)%1 =

= [cPx (cPx% + eAx% - icPy% - ieAy% + cPz% + eAz+ + (cPx % + eAx % - icPy % - ieAy % + cPz % + eAz %2) +

+ icPy (cPx% + eAx% - icPy % - i^Ay% + cPz%2 + eAz+ (87)

+ ieAy (cPx % + eAx % - icPy % - ieAy % + cPz % + eAz -

- cPz (cPx %2 + eAx %2 + icPy %2 + ieAy % - cPz % - %i) -

- eAz (cPx % + % + icPy % + ieAy % - cPz % - eAz %i)]/(2m>c2).

After the exclusion of similar members with oppo- by the significances of the vector of potentials in the site signs, the significances of the impulses in the coor- same coordinates x, y, z only remain. From here, we dinates in the square, the magnitudes of the vector po- have: tential in the coordinates in the square, and the members of multiplication of the magnitudes of the impulses

(E - efc)^ = (c2Px + c2 Py + c2 Pz + e2Ax + e2 Ay +

7 2 7 (88)

+ e Az2^ + 2ecPxAx^ + 2ecPyAy^ + 2ecPzAzT1)/(2moc2).

It is clear that the magnitude of the multiplication of the impulse P by the vector potential A at the same coordinate cannot give the Lorentz's force, and accordingly these significances must be zero. That is, we have obtained a result contrary to practice, in which there is no counter force for the Coulomb's force. This means that in the system of Dirac equations, the matrices for

the significances of the vector potential A in coordinates should have a different form from matrices of Di-rac, which would lead to the formation of the real Lo-rentz force associated with the motion of the particle. However, we will continue to determine the errors made in quantum mechanics, and when removing the multiplication of the impulse P by the vector potential A at the same coordinates, we have the formula:

(E-eO)T1 = (c2Px2^1 + c2P ^ + c2Pz/^1)/(2m0c2) +

2n2x

Jn2i

+ (e2Ax ^e2 Ay ^ + e2 Az ^1)/(2m>c2).

,2 A 2

2 a 2,

(89)

It can be seen that equation (89) characterizes the of expressions is made in result of the operations, and

Hamilton-Jacobi equation, and clearly does not corre- instead of a magnitudes equal to zero in (17), (19) and

spond to equation (80). This is due to the following al- (42), we have for the same members in (73) a signifi-ogisms made by Dirac. The first is that the substitution cance not equal to zero:

W2PxPy % - W2PyPx% - c2PxPz% + c2PzPx%

+ ic2PP %2 - ic2PP %2 = 0,

y z 2 z y 2 (90)

(a' P)(a' P) - P2 = ia\ (PxPy - PyPx) + ia\ (PZPX - PxPz) +

+ ia\(PyPz -PzPy) = i(a'[PP]).

That is, in fact, the numerical magnitudes of the impulses were replaced by operators, and instead of significances of subtraction equal to zero, we received magnitudes not equal to zero. In addition, the matrix a' 2 has an imaginary form with numerical coefficients

from the imaginary unit, and this is also due to the retreat from the original representation of Dirac matrices, since a' is a complex quantity. This contradicts the monotonous representation of the operation of subtracting at the multiplication of impulses at different coor-

dinates with their permutation according to the last formula in (90), as there is difference of the view for a\ not in the imaginary number at subtraction, but in real domain, and it excludes the possibility of obtaining of formula (76) for a rotor in (78). It is clear that in this case, at (73), we cannot in any way come to the Einstein energy equation in the private case with the invariant form. However, then another assumption was made on the basis of the operators in the form of equations (76) and (75). Moreover, it turned out that the impulse operator p had to act in some way on the magnitude of the vector potential A, which is an external quantitative parameter in coordinates, with its transformation into a rotor: W[pA] = W rot A = h / iHW. In other words, the operator of impulse p no longer refers to a particle with an influence on the wave function W, but refers and acts on the external field A with its change and turning it into a rotor. Thus, we have an obvious adjustment to the result! Next, we note that the Hamilton-Jacobi equation (89) is an energy relation for describing the condition of a particle in space medium on the basis of its initial parameters in energy and impulse, taking into account the influence of external fields. However, it does not define the laws of physics that give these changes, since here we considered addition and subtraction by energy on the basis of probabilistic wave functions. Thus, we see that if we follow the approach proposed in quantum mechanics for the vector potential A, according to the equations (83), then we get the independence of the vector potential A from the momentum of motion with the summation of magnitudes which have squaring, and it obviously does not correspond to the expression of the effect of the magnetic field through the action of the Lorentz force.

It follows that before correctly characterizing the influence of external forces on a wave-particle object, we first need to determine the interaction and type of Dirac functions with a transition to the Hamilton-Ja-cobi equation for a freely moving particle. At the same time, it is necessary to understand the reasons for the

formation of signs which characterize radiation and absorption by opposite charged particles, because we get the same kind of Einstein energy equations for opposite functions W and W2 according to the system (83). Earlier we showed that without radiation and absorption, interactions cannot be obtained, and it excludes the formation of a common object.

It is clear, in cause without taking into account the influence of external fields and at the reduction by the wave function W, equation (89), will connect energy and impulse in the form of:

E = (Px2 + Py2 + Pz 2)/(2m0) = my1/2. (91)

But this type of removal of the influence of external fields for the transition to the Hamilton-Jacobi equation for a free particle is impossible, since Dirac could not get transition to equations of Pauli without external fields (at least without the electric Coulomb field), since he used a probabilistic wave function of the form (65) for both W and W2, and for W3 and W4 . That is, without taking into account the external field, we will not get the form of equations (66) and (67). In other words, to describe the impulse of motion of a particle on the basis of obtaining energy from a force action, it is necessary to represent the functions Wj and W2, as well as W3 and W4, depending on the observation system. In one case, in the form of a wave function, it is similar to the wave function for the Schrodinger equation according to (38), and it defines objects as reflecting kinetic energy with motion at the speed of light (electronic and muonic neutrinos and antineutrinos), but in the other case as a source of radiation or absorption according to (44) and (65), which corresponds to objects reflecting radiation and absorption sources. Then for the system of equations (39), taking into account the private solution from some observation system, we have the following form of W - the functions in the view:

% = exp[i(c2 / u0t + Pxx + Pyy + Pzz)]; % = exp[i(c2/ u0t + PxX + Pyy + Pzz)l %3 = exp[i( Et + c2 / u0t + PXx + Pyy + Pzz)]; %4 = exp[i(Et + c2 / u0t + Pxx + P y + Pzz)].

(92)

We see that the form of the first two functions % and % corresponds to the wave form similarly (38) and at the same time the wave energy is determined by the magnitude c2/uo . The lower two % - functions,

%3 and %4 actually determine the condition for the

formation of radiation from the magnitude c2/uoo similarly to (44) and (65). That is, the radiation energy of the source is equal to the propagation energy. From the system of the differential equations (39), when we use the normalization on i, we have:

id% / dt -c2/ u0 % - iu0 / dx - u0 d% / dy - iu0 d% / dz = 0; id% /dt -c2 /u0 % - iu0 d*¥3 / dx + u0d% /dy + iu0 <9% /dz = 0;

id% / dt + c2 / u0% -ic2 / u0/ dx -c2 / u0 / dy -ic2 / u0/ dz = 0; id% / dt + c2 / u0% - ic2 /u0 d% / dx +c2 / u0 d% / dy +ic2 / u0d% / dz = 0.

(93)

With the substitution of functions (92), taking into account the differentiation operation by W, we obtain:

(-2c2/w,,)^ + u0PxY4 -iu0PyY4 + u0Pz% = 0; (-2c2/u0)Y2 + UoPx^3 + iu,PyY3 -u,Pz% = 0;

- EY3 + c2 / u0PxY2 - ic2 / u0PyY2 + c2 / u0PzYx = 0;

- EY4 + c2 / u0Px Yx + ic2 / u0Py Yx - c2 / u0Pz Y2 = 0.

Taking into account the expression of some functions through other functions, for a free particle without the influence of an external electromagnetic field, the equations follow:

Y = ^Y4 -iuP Y4 + u,PzY3)/(2c2/u0);

^ xx 4 yx 4' zx '"0^

);

(95)

= (UoPx^3 + Vy^3 -UoPz2/Uo);

Y3 = (c2/u0Px Y2 - ic1/u,Py Y2 + c2/u0 Pz Yj)/ E; Y4 = (c2 /u0PxYj + ic2 /u0PyYj -c2 /u0PzY2)/E.

Next, we substitute some functions instead of other functions and exclude the similar members with contrast signs:

EYj = c2[Px (Px Y + iPy Y - Pz Y2) -

- iPy (Px Y + iPy Yj - Pz Y2) +

+ Pz (PxY2 - IPy Y2 + Pz Yj)]/(2c 2/u0) =

9 2 2 (96)

= c 2[PX 2 Yx + iPxPy W - PxPz Y2 - PP W + Py 2 Yx + iPyPz Y2 +

z\p x p 2 "y A 2' pz MyJ'V^ '"0y

P W - P P W - IP P , , , , , P , ,

y T1 P xP z T2 iP yP x W 1 Py W 1 lPyPz W

+ PzPx W2 - iPzPy W2 + Pz 2 WJ/(2c 2/Uo); EWi = Uo/2(Px2 Wi + Py 2Wi + Pz2 Wi).

Here: m=l/uo . Excluding a wave probability func- this case we do not have the so-called division into postion, we obtain the Hamilton-Jacobi equation for a itive and negative charged particles with their annihila-freely moving particle: tion. That is, there simply cannot be such a physical E = l/(2m)(P 2 + P 2 + P 2) (97) process as annihilation with transformation into pho-x y z tons in the presence of only positive energy signifi-However, in this case we do not have closed en- cances because there is no "zeroing" of the previous

ergy solutions with compensation as for the invariant representation. Therefore, instead of the system (92) for

energy equation of Einstein, since the energy of a par- . ^ . . .. .. ^ iTr , ,

, . . , , , , particles on the basis of functions-obiects w , depend-

ticle is determined only by half of the kinetic energy. r J r

At the same time, according to the functions (92), the ing on a certain observation system, it is necessary to energy is determined by a positive magnitude, and in consider options with compensation at presence of motion, then:

Wi = exp[i(c2/ Uot + Pxx + Pyy + Pzz)]; Y2 = exp[i(c2 / Uot - Pxx - Pyy - Pzz)];

(98)

W3 = exp[i( Et + c2 / Uot + Pxx + Pyy + Pzz)]; W4 = exp[i(Et + c2 / Uot + Pxx + Pyy + Pzz)].

Here impulses for W2 have contrast representa- particle has no interaction. With the substitution of the tion of signs regarding (92). This can be allowed in the function W from (98X taking into account tte opera-absence of external electromagnetic fields, since the tion of differentiation by W , we have:

(-2c2 /Uo)Wi + UoPxW4 -iUoPyW4 + UoPzW3 = o;

(-2c2/Uo)W2 -UoPxW3 -iUoPyW3 + UoPzWA = o;

- EW3 + c2 / Uo Px W2 - ic2 / Uo Py W2 + c2 / Uo Pz Wi = o;

- EW4 + c2 / UoPx Wi + ic2 / UoPy Wi - c2 / UoPz W2 = o.

Taking into account the expression of some functions through other functions for a free particle without the influence of an external electromagnetic field, we obtain:

% = (UoPx% - iUoPy%4 + UoPz%3)/(2c2/«o)

%2 = (-«oPx%3 - iUoPy %3 + «oPz%4)/(2c2/«o)

(100)

% = (c2/UoPx%2 -ic2/«oPy%2 + c2/UoPz%l)/E;

%4 = (c2 / «oPx% + ic2 / «oPy% - c2 / «oPz%2)/E.

We see that the functions % and % differ in would be the decay or an increase to infinity. Next, for

signs relative to the coordinates of x and z, similar to the object %2, we substitute some functions instead of the magnitude of the rotors (51) and (52), which give other functions and exclude the similar members with opposite sign significances. And this actually charac- contrast sign: terizes a closed exchange, since the objects remain unchanged, otherwise according to (48) and (49) there

E%2 = c'[(-Px(Px%2 -iPy%2 + Pz%l) -

- iPy (Px % - iPy %2 + Pz %l) + Pz (Px % + iPy % - Pz %2)]/(2c2/«o); 2 - c [-Px !%2 + iPxPy %2

PyPx%2 - Py %2 - iPyPz%1 1 PzP x % 1 zPy % P z A2]/(2c / «o);

E%2 - «o/2(-Px 2%2 - Py 2 %2 - Pz 2%2).

E%2 - c2[-Px2%2 + iPxPy%2 -PxPz%1 - (101)

- iPyPx %2 - Py 2%2 - iPyPz %1 + PzPx %1 + iPzPy %1 - Pz2 %2]/(2c 2 / «o);

Excluding a wave probability function, we obtain the Hamilton-Jacobi equation for a freely moving particle with negative energy, and this in our theory means the belonging to type of charge:

- E%2 - «o /2(Px2%2 + Py2%2 + PZ2%2) :

x y z ^-2)

- 1/(2m)(Px 2%2 + Py 2%2 + Pz 2%2).

(102)

In fact, on the basis of (97) and (102), we justified the presence of an electron and a positron. It should be noted here that the representation of objects in the form of functions also changes from the observation system (and there are four of them), otherwise there would be no opposites. The same type of functions according to (38) exists only for the variant describing the entire universe, since in this case the total energy is being reflected taking into account all interactions and therefore we have the accordance of the Einstein energy equation to the circle equation. Thus, we get that there is no movement of a positively charged particle without the movement of a negatively charged particle, but in opposite systems. At the same time, it turns out that, as there is annihilation between the contrast charged particles with transformation into photons, they are interconnected through exchange, where in one observation system one of them is the emitter of the simplest objects, but the other is the absorber of the simplest objects in representation of electronic and muonic neutrino (antineutrino). In another observation system, everything is conversely, because otherwise there is no mutual the exchange cycle with the preservation of particles, hence the Coulomb forces of attraction give a closed exchange. The division of objects on so-called the positively charged particles and negatively charged particles, which characterize radiation or absorption in a given observation system, means that there are no objects outside of interaction and exchange, and the presence of a neutral rest mass is justified only from the

standpoint of the entire universe. In this case, it becomes clear why, when electromagnetic waves interact with the opposite phase (interference of waves), their compensation does not occur with the transformation into zero, and the electromagnetic wave has propagation the further. That is, instead of compensation, there is an increase in the closed exchange process through radiation and absorption between objects reflecting space and time, with a change in the constants of electrical and magnetic permeability.

How these changes occur in opposites can be seen on the example of standing electromagnetic waves. Here compensation of contrast forces, for example, over the electric field strength is being associated with closed rotation motion of simple initial objects between so-called positively charged particles and negatively charged particles in the view of magnitudes of time and length of medium of propagation. At the same time it gives a doubling of the magnetic field strength. In other words, no object of the universe can disappear together with another object of the universe, the only thing that can happen between them is the strengthening of interaction through the exchange of initial objects with transforming in object from opposite, and it is displayed in the form of a rotor. It should be noted here that the minimum object in one opposite is the maximum in the other opposite due to the inversely proportional relationship, and therefore can be represented as other objects in the hierarchy. On the basis of practice,

when subtraction ("disappearing" of object) in one system of opposite means the doubling the size of the object in the other opposite, we should assume that this law should also be displayed mathematically. At the same time, we note that a closed physical process is invariant in any observation system and must correspond to the circle equation, as well as the Einstein energy equation.

Now, after justifying the necessity of opposite charged particles, we can proceed to solving the paradoxes allowed in solving the Dirac's system of equations due to the frivolous handling of impulses and vector potentials.

The only force that is known in practice and can be opposed to the force of attraction of the Coulomb is the Lorentz force. This force excludes attraction due to the rotation of one particle relative to another opposite particle and it can actually be considered as a way to preserve oppositely charged objects. Otherwise, we had annihilation with the exclusion of any corpuscular particles. Therefore, if we want to correctly reflect the interaction based on a system of Dirac equations in the motion of a particle, then along with the Coulomb force known from practice, there must be a Lorentz's force, and not something unknown in terms of force formation, such as magnetic spin of electron.

It is clear that in order to reflect the influence of the vector potential A in view of an effect associated with the Lorentz force, we must have the members which have the multiplication of impulses by vector potentials with different coordinates. However, the solution to this problem requires the fulfillment of the condition under which, in order to determine the direction of the Lorentz's force for achievement of the counteracting to Coulomb's force, it is necessary to have a strict

orthogonal arrangement of electric and magnetic lines of force along coordinates with an unambiguous orthogonal arrangement of the direction of motion of the particle to them. In this case, we should leave only those members of the vector potential A in the system of Dirac equations that would eventually give the Lo-rentz force counteracting the Coulomb force.

In other words, we must have our own special matrix for the vector potential A due to the fact that the Lorentz's force depends on the vector of velocity of the particle, unlike the Coulomb force.

At the same time, we take into account the presence of a common electromagnetic continuum, in which, depending on the observation system, electric forces turn into magnetic forces, and vice versa, and it was noted by Feynman:

F = F

Lorentz Coulomb

■2/ c 2.

Earlier we noted that

the system of Dirac equations perform, depending on the functions, existence of opposites, and it should also be reflected here, when electric forces, depending on the observation system, are being turned into magnetic forces, and vice versa.

Therefore, we will write the vector potential A according to the Dirac system equations, taking into account the physics of the occurrence of the Lorentz's force with standpoint of the presence of consideration of an instantaneous stationary coordinate system at the location of a moving particle. In this case, the radius of the orbit will lie along the x axis, the velocity of the particle will be directed along the z axis, and the magnetic field will be directed along the y axis. Since the motion along the orbit has a stationary form, then, accordingly, we get a system of equations:

(E - eO)% = cPx%4 + icPy%4 - cPz%;

(E-eO)% = cPx% -icPy% + cPz^4;

(2m0c2)% = cPx% + icPy% + eAy%2 -cPz% (2m0c 2)% = cPx % - icPy % - eAy% + cPz %2.

(103)

The difference in the signs for the functions

and for the member eAy is explained by the fact that these functions already have opposite directional movement, since they are represented in the system of Dirac by opposite members in the equations. The electric force (e®) has the same form relative to the energy

E, since it takes into account the interaction of opposite particles for the functions % and %, through the forces of attraction. Hence in equations we have the view of functions % and % from the common observation system in which the electric force is expressed:

(E - eO)% = [cPx (cPx % - icPy % - eAy% + cPz %2) +

+ icPy (cPx % - icPy % - eAy% + cPz %2) -

- cPz (cPx%2 + icPy%2 + eAy%2 - cPz%)]/(2moc2) = {c2PX2% + c2Py2% + c2PZ2% -ec[PxAy]% -iecPyAy%l -ed[PzAyTO^c2);

(E-eO)%2 = [cPx(cPx%2 + icPy%2 + eAy%2 -cPz%) -

- icPy (cPx%2 + icPy%2 + eAy%2 - cPz%) +

+ cPz (cPx% - icPy % - eAy% + cPz %2)]/(2moc2) = {c 2P2 % + c2Py2%2 + c2PZ2%2 + ec[PxAy]%2 -iecPyAy%2 -ec[PzAy]%t}/(2moc2).

With the same observation system for functions Y3 and Y4, we have: (2^c2)Y3 = [cPx(cPxY3 -icPyY3 + cPzY4) +

+ icPy (cPx Y3 - icPy Y3 + cPz Y4) + eAy (cPx Y3 - icPy Y3 + cPz Y4)

- cPz (cPx Y4 + icPy Y4 - cPz Y3ME - eO) = {c2Px2 Y3 + c2Py2 Y3 + c2Pz2Y3 + ec[AyPx]Y3 - iecAyPyY3 + ec[AyPz^/(E - eO);

(2m0c2)Y4 = [cPx(cPxY4 + icPyY4 -cPzY3) - (105)

- icPy (cPx Y4 + icPy Y4 - cPz Y3) -

- eAy (cPx Y4 + icPy Y4 - cPz Y3) +

+ cPz (cPx Y3 - icPy Y3 + cPz Y4ME - eO) = {c2Px2 Y4 + c2Py2 Y4

+ c2PZ2Y4 - ec[AyPx]Y4 - iecAyPy Y4 + ed[AyPz^/(E - eO).

In fact, we see that, in contrast to the variant with functions Y1 and Y2, characterize one common parti-

the free movement of the particle, here, in the presence cle-wave object, hence in result, the system of Dirac's

of external forces, it is necessary to take into account equations itself was formed through opposites. Here, by

the interaction in two opposites with external forces. At analogy with the system of Pauli equations [10], we

the same time, we also take into account that, in fact, must represent the object in the form of equations from the electric forces in one opposite reflect the magnetic

forces in the other opposite on the basis of a common electromagnetic continuum. Opposites, in the form of

Y and Y2:

(E - eO)Y = (c2Px2 Y + c2Py 2Yx + c2Pz2 Yx --ec[PxAy]YX -iecPyAyYx -ed[PzAy]Y2)/(2m0c2);

7 2 7 2 7 2 (106)

(E - eO) Y2 = (c2Px2 Y2 + c2Py2 Y2 + c2Pz2 Y2 + + ec[PxAy ]Y2 - iecPAY - ec[PzAy ]Yt)/(2m0c2).

However, the external magnetic force has relation to the entire particle in the form of Ay, and effect of this member is manifested in both opposites, at representing of particle in view of one common object in the form of functions Y j and Y2. In other words, a particle-wave object acts as a closed system based on the fact that in one case this object is considered as a source of radiation, which allows object to be characterized as, for example, a negative charged particle, but if there were no interaction through absorption, in the form of, for example, a positive charged particle, then the this object would disintegrate. The significances of the squared impulses over the functions Yj and Y2 , as well as the energy of the particle, are being considered in opposites in the same corpuscular form in the view the Hamilton-Jacobi equation with one common directional motion (otherwise we would have different objects). The external magnetic force manifests itself depending on the motion and acts on the object at presentation both as a positive charged particle and as a negative charged particle in accordance to functions. Hence, the Lorentz force is determined on base of its representation in both opposites in accordance with the functions Yj and Y2 . At the same time, the external influence of electric and

magnetic forces is associated with the interaction through summation and subtraction on base of Coulomb's force and Lorentz's force. And since we have to take into account the interaction of external forces both in one and in another representation of one common corpuscular-wave object, we see that on base of the condition of interaction of opposites of one object in the form of functions Y and Y , we have a subtraction in the effect of the Lorentz force along the z axis in the form of { + ed[PxAy ]Y2 - ec{PxAy ]Y }, which in

the unchangeable case of orbital motion is zero, since the action is equal to the reaction. In the case of inequality of impact, the sign is determined depending on the magnitudes of the functions Yj and Y2, and there would be acceleration with a change of orbits. Next, we see that there is a reflection of the Lorentz's force, which counteracts the force of Coulomb along the x axis in the form of the members { - ec[AyPz ] Y } and

{ - ed[AyPz]Y2 }. As a result, we can express the interaction of a particle with external electric and magnetic forces in the form of a function Y = Yj = Y2, taking into account the influence of forces in both oppo-sites:

(E - eO)W = [c2 p2W + c2 Py 2 W + c2 Pz 2W - iecP^ (Wx + W2 ) + ec[PxAy ](W2 -Wx) -ec[PzAy](W + W2)]/(2rn0c2).

(107)

At magnitude Pz=moVz , iPy=imoVy , we will consider vector potentials, with the condition A=®/c, at v=c, and it corresponds to the connection of opposites through the speed of light. Then, with a radius along the

(E - eO)W = [c2 p2 W + c2 Py 2 W + c2 Pz 2W - iecPyAy (W + W ) + + ec[PA ](W2 - Wx) - ec[PA ](W + '^/(2^2);

x axis O = SoOx , Ay=Oy/c, sx = Vx / c, sy = Vy / c, sz = Vz /c, we have:

(E - es0 Ox )W = [c ZPX 2 W + c2 Py ZW + c2 Pz 2 W]/(2m0c2) + {-iecPy Oy / c(W + W ) + + ec[PxO y ]/c(W2-Wx) - ec[Pz O y ]/c(W + Y2»/(2moc) = = [Px2 W + Py2 W + Pz 2 W]/(2mo) + {-iemVy O y (W + + + em,[VxO y ]( W2-Wx) - emoV O y ]( W +¥2)}/^) = = [Px2 W + Py2 W + Pz2 W]/(2mo) + {-ieVy / cO y (W + + + e[Vx / cO y ]( W2 - Wx) - e[Vz / cO y ]( W + Y2»/2 = = [Px2 W + Py2 W + Pz2 W]/(2mo) + {-/es y O y (W + +

+ e[s xO y ]( W2 - Wx) - e[s z O y ]( W + ^»/2.

(108)

Hence it can be seen that the Lorentz force associated with the magnitude e[sz® ](Yj + Y2) / 2, due to

the magnetic orbital moments from the functions Yj and Y2, compensates the Coulomb force at motion on orbit in the planar surface z, and here Coulomb's force is associated with the magnitude es0®x from the function Y = Yj . At the same time, as in the experiments of Einstein-de Haase (1915), we get a Lande multiplier equal to two for Yj and Y2. This means that an error was made in calculating the Lorentz force at estimating the orbital magnetic moment due to the lack of consideration of opposites, that is, the corpuscular - wave dualism. And this corresponds to the stationary case when the electron rotates in orbit.

At the same time, when the particle moves towards the nucleus, that is, when we have moving in the non-stationary case, we get movement along the z axis due to the member e[sx®y](Y2-Yj)/2. This actually

excludes the falling of electron on the nucleus, since the presence of the magnetic field of the nucleus will necessarily lead to the appearance of a velocity directed perpendicular to the center of the nucleus and then the question of the orbital condition in equilibrium is determined only by the parameters of the medium for the formation of an electromagnetic field based on the constants of electric and magnetic permeability. Accordingly, it remains to understand the role of the member iesy® (Yj + Y2)/2 . It is clear that from the point of

view of multiplying the magnetic field by the velocity in the same direction, we do not get the Lorentz force.

In general, the magnitude of the velocity iVy along the y axis when orbiting in the planar surface z has no

real embodiment Vy=0, and in accordance with our theory, in principle, this is a projection of velocity onto significance of time. This is the speed in contrast system, which ensures the fulfillment of Einstein's GRT by the space-time curvature, because in contrast system, the length is being transformed in significance of time, and vice versa. In this case, the projections of velocities along the coordinates in the planar surface z form the projection of velocity onto significance of time with the condition that the law of conservation of quantity is fulfilled.

However, if we assume that in contrast system, the magnitude of { - iesy ®y (Yj + Y2 ) / 2 } has a real embodiment in coordinates, then in this case, we will have an force without compensation that gives either radiation (braking force) or absorption (acceleration force), because for the opposite system of observation through the functions Y3 and Y4 we have the similar sign { -iesy®y(Y3 +Y4)/2 }.

At the same time, the Lorentz's force in the form of members { - ec[PzAy № } and { - ec[PzAy ] Y2 } counteracts the Coulomb force along the x axis in the observation system Yj and Y2 according to the formulas (104), but Lorentz's force has compensation in the form of the members {ec[PzAy ]Y3} and {

ec[PzAy ]Y4 } in accordance with formulas (105) at

observing from a system of functions Y3 and Y4. That is, a closed form that is characteristic of a particle in the form of a constant magnitude over all four interacting functions will give a zeroing of the Lorentz force of the form { ec[PzAy ]Y }, which must counteracts the

Coulomb force {e®}.

In other words, the external forces of electromag- ec[PzAy ] Y }, due to the interaction of the four func-netic fields should compensate for their impact on the

object only in relation to each other due to the movement of the object in the form of a particle, and not have

tions, and to receive compensation according to the magnitudes { - ies $ (Y + Y ) / 2 } and {

compensation inside the object. Indeed, if the Lorentz _ jeevOv(" + ")/2 }, it is necessary to consider force is being compensated inside the particle, then its

not only magnitude of the positive energies (+£), but to consider magnitude of negative energies (-£)• In other words, we must have for the third and fourth equations

from functions " and "4 the form that we obtained

effect is zero and only the Coulomb force remains without compensation, and this is not observed in practice. That is, we must have the equation

_eO(" + Y) = _ec{PzAy ](" + " + " + Y) •

In this case, the in homogeneity in the environ- for the function " in (99) In this case, instead of the

ment between opposites connected through the speed of system of equations that was used to calculate functions

light (®=cA), has compensation by the motion of ob- " and ", for functions " and " we use a sys-

jects with radiation and the impulse of the object Pz in tem of equations giving a negative sign for the mass of

the view of object as constant magnitude closed by four rest. Then, in this new system of equations for calculat-

functions " • For ^ condition of excluding of com- ing the functions Y3 and Y4, we have a system of pensation of the Lorentz force of the form {

equations:

(E _ eO)"Y = cPx Y4 + icPy Y4 _ cPzY3; (E _ eO)" = cPx Y3 _ icPy Y3 + cPz ";

(109)

(2m0c2)Y =_cPx"2 _icPy"2 + eAy" + cP"; ( )

(2m0c2)"4 =_cPxYj + icPy" _eAy" _cPz"2-Hence for the opposite charge in the observation system with a negative mass for Y3 we have: (2moc 2)Y = [ cPx (cPx Y3 _ icPy Y3 + cPz Y4) _ _ icPy (cPx Y3 _ icPy Y3 + cPz Y4) +

+ eAy (cPxY3 _icPyY3 + cPzY4) + + cPz (cPx"4 + icPy "4 _ cPz Y)]/(E _ eO) = = {_c2Px 2"3 _ c2Py 2"3 _ c2Pz 'Y + + ec[AyPx]"3 _ iecAyPyY3 + e<[AyPz]"4>/(E _ eO). Accordingly, for Y4 we get the form:

(2moc 2)"4 = [ cPx (cPx "4 + icPy "4 _ cPz Y3) +

+ icPy (cPx"4 + icPy"4 _ cPz"3) _ _ eAy (cPx"4 + icPy"4 _ cPz"3) _ _ cPz (cPx"3 _ icPy"3 + cPz Y)]/(E _ eO) = = {_c2Px2Y _ c2Py2"4 _ c2Pz2"4 _ _ec[AyPx]"4 _iecAyPy"4 + ed[AyPz]Y}/(E_eO).

Hence, when passing to the negative mass of the particle, in the observation system from the opposite, we have:

(_2moc 2)"3 = {c2 Px2 "3 + c2 Py 2Y + c2 Pz 2Y

_ ec[AyPx]"3 + iecAyPy"3 _ e<[AyPz]"4}/(E _ eO) (_2moc2)Y = {c 2PX 2"4 + c 2Py 2Y + c 2PZ 2"4 + + ec[AyPx]"4 + iecAyPy"4 _ ec[AyPz]"3}/(E _ eO).

(110)

(111)

In this case, at using of formulas (106) and (112), there is no compensation of the Lorentz force of the form { _ ec[AyPz]" } as in cause it was on base of the

formulas (104) and (105) when all processes have observation from functions Y and "2 with positive

mass. Now we take into account the fact that from the functions "3 and "4 it is necessary to have an opposite charge (mass of rest), and it actually means a change of direction to the opposite movement, which ensures the law of conservation of quantity between the

interacting opposites in closed loop, and it gives a single common object. At the same time, we also receive compensation from the member { _ iecAyPy" } in

(104) at the expense of the member { iecAyPy" } in (112). Thus, in the unchangeable representation, we have " = " = "2, and the force of Lorentz compensates the force of attraction in the view e[^zOy](" +"2)/2 = e£z®xn", at rotating in

£0Ox (xorb) = U0 /cOxE(xorb) = (1

= £zOxH (xorb) = Vz /cOxH (xorb)-

an orbit in the planar surface z, with a radius r=x, and here the Coulomb's force is associated with the magnitude es0O" . Next, we take into account that the significance of the electric permeability in the view of the constant is related to the magnitude of the average integral kinetic velocity in the opposite observation system according to the formula (53) and from here we have the formula:

- v,

np

2/ c2)1/2 $ ( xor& ) =

(113)

Consequently, we see that the interaction, with obtaining a unchangeable mode of rotation of one particle (electron) relative to another opposite particle (proton) with magnitude of velocity (Vz), is being determined only by the forces of the electric ®xE(xorb) and the magnetic field OxH(xorb) at the points of the orbit, taking into account the average velocity in contrast system (vnp), which is associated with the average kinetic energy in opposite system. According to our theory, the forces are actually determined by the space-time curvature, otherwise these forces impossibly to determine in space and time due to independence. Here we have the conclusion that all the interaction of objects in the universe is described on the basis of the velocities of objects in both opposite observation systems, taking into account the space-time curvature formed by them due to movement along the SRT and GRT of Einstein. Next, we take into account that according to our theory m0=1/c and the Louis de Broglie formula can be reduced to the form hf=v. In other words, the electromagnetic distribution of frequency is determined by the speed of objects. This means that in order to observe the equality of opposites in a closed universe, with the Planck formula being fulfilled at equilibrium of thermodynamic distribution, we have a stable rotation mode of the object at the maximum of the spectrum from the Planck formula with a coefficient of 4,965. Taking into account the transition of kinetic energy to potential energy in contrast system, we have a difference in the space-time curvature between a proton and an electron according to the formula (59). That is, we see that in our case there are no fantasies associated with certain quantum numbers and orbitals.

In fact, our approach shows that the system of Di-rac equations for objects, taking into account the re-

placement of probabilistic wave functions by real electromagnetic functions, allows us to describe the interaction of two opposite systems connected through the speed of light, through the exchange associated with the emission and absorption of elementary electronic and muonic neutrinos and antineutrinos represented by the equations. These objects are expressed in terms of magnitudes of velocity, by obtaining a space-time curvature in accordance with SRT and GRT Einstein. In this case, the forces of electric field and the magnetic field are formed in the representation of opposites, and they are connected through the speed of light by analogy with length and time. Accordingly, the magnitudes of elementary charged particles correspond to the Dirac's theory at e=q=± 1, and it is method of radiation and absorption. It is clear that all force action is described by the Lorentz and Coulomb forces and there are no nuclear or gravitational forces. Indeed, nuclear and gravitational forces should give the forces of attraction to infinity of compression and there are no repulsive forces. In addition, there are no objects for exchange and interaction for gravitational and nuclear forces.

Let's try to get the full Hamilton-Jacobi equation based on a closed exchange process. Here, a closed exchange process is performed in the case when the action is equal to the reaction at changing with the condition of preserving the object in the view of a function. Accordingly, in this case, the function of the object will be such that the changes associated with integration (differentiation) do not affect the function itself. Next, we will follow the path proposed by Schrodinger [11], but we will use an exponential function from the opposite observation system in the form:

Y(t, r) = exp[W (t, r)] = exp[iS(t, r)].

(114)

Here W(t,r)=iS(t,r). In other words, the difference between the functions in the arguments is not in quantity, but in belonging, which is characterized by an imaginary unit. Proceeding from the equality of changes

VY = (VW)Y; V2Y = (VW)2Y + VWY; cY/dt = dW/ctY.

between length and time, with a closed cycle of exchange, and the fact that one opposite turns into another opposite, due to differentiation, well-known equalities were used:

(115)

Accordingly, changes in magnitude of time are inevitably associated with changes in space, but in this case the object is being moved. Hence so that the object remained in the same position, it is required that the

varying from changes in space (that is, reverse reaction, double differentiation) would lead to the restoration of the object in the same place. From here we get:

dW / dt = 1/(2m)V2W + 1/(2m)(VW)2. (116)

In the universe, symmetry is observed in a closed W(t, r) = exp(±Et + pr). (117)

exchange and the function W can also be expressed ex- Here we have from two significances to the right

ponentially as: of the equal sign in (116) at m0=1lc:

± E = p2 / m = m0v 2/Vl - v2 / c2 = v 2/V1 - v2/c2;

Vc2 - v2 = ±v2 /E = ±1/m = ±vnp;

P P (118) (c2 -v2) = (±v2/E)2 = (±1/mnp)2 = vnp2

2 2 , 2 c =v + vnp .

That is, in this case we come to the equation of the any observation system. It is clear that physicists intui-circle. And this means that the form of the equation tively came to the form (116) through the equation of (116) provides a complete description of the object in the total energy of the harmonic oscillator [12]:

E = p0 2/ m = p2 /(2m) + mWr2/(2m) = hf. (119)

At the same time, the equation of electron motion is known in the form [12]:

p2/(mr) = q2/r2; p2/m = q2/r. (120)

Such equality apparently implies the removal of the same coefficient equal to two. Taking into account SRT of Einstein:

l = lj1 - (v/c)2. (121)

at h=1lc and q=±1 in accordance with Dirac theory [13] we obtain:

p2 /m = q2 /r; p2 /m = q2 /[^1 - vnp2/c2];

p 2/ m = q 2/[ct - vnp2/ c 2]; (122)

p2 / m = hfo/^1 - vnp2/c2] = hf = mc2.

In other words, equations (119) and (122) are identical and correspond to our equation (116). Moreover, if we assume that /0 = c2, then taking into account m0 = 1lc, we obtain the Louis de Broglie equation:

hf = mc2 = m0c2 /^1 - (vnp / c)2. (123)

Let's rewrite (116) as:

SW / dt -1/(2m)(VW )2 = 1/(2m)V2W. (124)

In this case, the member standing to the right of the sign of equality practically characterizes the potential field according to the Poisson equation [14], and it can be represented as an equivalent equality:

1/(2m)V2W = V 1 -v2 /c2 /(2m0)V2W = 4npW. (125)

From here we get:

1 /(2m)V2W = (a/c2 - v2 / 2)V2W = 4npW = w0W /2 = = cs0 W /2 = W /(2c^0 ). As a result, we have:

dW / dt -1/(2m)(VW )2 = c^W/2. (127)

Compare (127) with formula of wave equation [1]:

(126)

V2®M -1/c2d2®M/dt2 =Pmc/^o = ®M/^o;

1 /a,>2\

(128)

^0 (V2®M-1/c2d2®M /dt2) = ®M.

Next, we take in to account (21):

dW/ dt - 1/(2m)(VW)2 = cs0W/2;

V2®m -1/c2d2®m / dt2 = ®m / ^0 = c2s0®m ; (129)

icgrad Am + dA^ / dt -1/^0 rot ®„ = is®M / ^0 = ic3s0® m .

Consequently, we see that these equations are re- corpuscular motion in the other opposite, and taking

lated through the constants of electrical and magnetic into account the normalization and connection between

permeability, that is, the parameters of the medium. opposites through the speed of light and observing the

Moreover, wave processes in one opposite characterize law of conservation of quantity, we can write:

dW/dt _ 1/(2m)(VW)2 = 1/(2c)V2OM _1/c2d2OM /dt2 = cs0W/2 = = (icgradAм +dAм /dt _ 1/|0 rotOм)/(2c2) = W/(2m) = u0W/2. (130)

As a result, we have four representations of the object of the universe, depending on the observation system:

a) in the form of a charged particle moving in accordance with the Hamilton-Jacobi equation;

b) in the form of a wave displaying one of the strengths of the electromagnetic field;

c) in the form of an electronic or muonic neutrino (antineutrino);

d) in the form of a potential field reflecting an additional mass of rest u0=(c2-v2)1/2 (this magnitude is related to the velocity of motion in the system of opposite in accordance with GRT of Einstein), for example, this field gives a proton.

At the same time, we see that the formation of the universe proceeds from the simple to the complex representation, starting from Faraday's law, displayed in the opposite system through the Bio-Savard law [1]. This law is implemented on the basis of the use of the simplest initial objects in the form of electronic and

V2 E + k 2E = _M3; V2 H + k 2H =

muonic neutrinos (antineutrinos), and they have also been practically described through improved Maxwell's equations by using of fictitious positively charged particles (of fictitious negatively charged particles) and of the fictitious currents. We have only just presented these fictitious charges and currents in the differential form of changes, taking into account the projection of the intensity of the electric and magnetic components on significance of time, which actually brought Maxwell's equations to the form according to the Lorentz-Minkowski transformations, and this gave an unambiguous connection with space and time. In this case, the improved Maxwell equations (20) describe elementary objects such as electronic and muonic neutrinos (antineutrinos). The interaction of two such simplest objects gives an electromagnetic wave, and this transformation through the substitution of some equations into other equations was also done for the first time not by us, but done in electrodynamics, as can be seen from [15]:

_MM;

_ M 3 =-i'®|a 0 j3-CT + 1/(i'®s 0)graddiv j3-CT _ rot jM_CT; (131)

_ MM = _i'©s 0 jM_CT + 1/(i'®| 0)graddiv jM_CT _ rot j3-CT

The interaction of the three simplest objects with the substitution of some equations into other equations was proposed by Dirac on the basis of the Einstein energy equation through the system (13), and gave the formation of so-called charged particles. At the same time, in accordance with the Hamilton-Jacobi equation obtained from the Dirac system of equations, it is possible to describe the motion of the simplest particles, such as an electron and a positron. However, as we noted above, no elementary particle can be described unilaterally in corpuscular form or in wave form without interaction through exchange. Hence, even before us in physics, the equations for the motion of a particle of the form (111) and (112) were obtained, which correspond to the total energy of a particle belonging to a closed system, that is, for the invariant case, and thus the Louis de Broglie formula (45) is obtained. We just got the similar view based on the consideration of the object not only through kinetic energy, but also through potential energy. Our merit is only that, taking into account the fact that, since the transformation of objects can only go with the transition to the opposite in a closed system of universe in compliance with the law of conservation of quantity, (otherwise we would have a miracle of the arising from the zero and disappearing into nothing), we made an equalization of the formulas on the basis of (130).

Actually, such equalization solves the problem of paradoxes at the formation of an electromagnetic wave

[1], since the disappearance of an electromagnetic wave as a result of overlapping contrast forces and the heterogeneities of the electric and magnetic field strength in angular directions during radiation is associated with the transformation of the kinetic energy of directional motion to a closed circular form of potential energy as a result of the interaction of the simplest initial objects of the universe (electronic and muonic neutrinos and antineutrinos). We see this in practice through the curvature of the electric fields between the opposite charging particles and by the magnetic field of the inductor. On the basis of formula (130), it follows that there are four observation systems, and each of them is connected to the previous one through the speed of light. In other words, we have a hierarchical structure. And according to the hierarchy, depending on the surveillance system, the similar objects are being looked differently. A monotonous representation would contradict the presence of opposites themselves. At the same time, the minimum object in one opposite is the maximum in the other opposite, and such representation actually makes it possible for the object to do the changing of other objects and this object is being changed itself under influence of other objects. Otherwise, we would have minimal objects in accordance with Planck's constant, which could no longer change, and therefore interact, and such objects could not be detected in our universe. That is, an inversely proportional relationship is a necessary condition for the connection

of opposites. Given the different representation of the objects of the universe depending on the observation system, we can consider an electronic or muonic antineutrino (neutrino) in one observation system as a moving particle of the electron (of positron). In the next observation system, this particle can be represented by a proton (by antiproton), and the system of interaction of an electron with a proton in the fourth observation system can be considered as an electromagnetic wave, where the components E and H, in contrast system display particles such as proton and moving electron on orbit, and they cannot annihilate the each other, and it determines the presence of the wave itself. Hence, accordingly, depending on the place of observation in the hierarchy of the universe, a moving electron (an electronic antineutrino in contrast) can be considered as a neutron, which, with the loss of electromagnetic energy (and this is in contrast a proton and an electron) is being decayed onto the proton, electron and antineutrino. At the same time, we have a dependence in which the frequency of an electronic or muonic neutrino is a multiple of Planck's constant, that is, to the magnitude of the simplest object in a given observation system, and determines the quantitative hierarchy over the interaction of objects in contrast system. In our observation system, electronic and muonic neutrinos (antineutrinos), on the contrary, are the simplest objects, the interaction of which form all complex objects of the universe.

It is clear that further participation in the formation of objects of even more electronic and muonic neutrinos (anti-neutrinos) leads to the formation of such particles as muons, pions, protons, neutrons and of all other elements from the periodic table. Naturally, every theory must solve and explain practical results. Actually, some of them have already been solved and shown by us:

1. We have defined the laws of interaction between opposites and given an explanation of the constants of the universe, such as the speed of light, of the Planck's constant, the electric and magnetic permeability. At the same time, the number of objects of the universe is limited by the ratio of the speed of light to magnitude of the Planck constant, according to the formula [5]: ch=1 in the form of clh. However, taking into account the SI measurement system, and on the basis of the constant thin structure, here we have the addition of magnitude of a charged particle (in the theory of Dirac

q=±1 [13]) in the view 137c /(2rcq 2h) [16], because the universe knows nothing about the SI system and operates only with the number of objects and their regularities. This amount is the fact that otherwise there will be objects outside of interaction (of exchange), and they will be completely closed on themselves in both oppo-sites, and this means that they are zero for the universe.

2. The limitation of the number of objects in the universe (this is the exception of the ultraviolet catastrophe) determines the quantization in the transmission

Yd (t, r) = Y0 exp(ipd) = Y0 [cos(cpd)

= Y0[ch(9d0) - sh(Pd0)].

of energy by the magnitude of the constant Planck, and each object of the universe is represented both in wave and corpuscular form, which implies its representation in the form of numerical significances in the coordinates of length and time, as well as in the form of magnitudes through electromagnetic components.

3. On the basis of two-fold representation of magnitude of the frequency of Louis de Broglie's by formulas (45) and (123), an inversely proportional relationship between opposites was determined, and they is consistent with the relationship between opposites in the form of electric and magnetic permeability constants.

4. Since no object can be outside of interaction, and this implies its disintegration or synthesis from simpler initial objects, the smallest object of the universe in one observation system will be the largest in another opposite observation system, and this implies a hierarchical structure of the objects of the universe, which is expressed in a different representation of the same object depending on the observation system, which was shown by us through equation (130).

5. The law of interaction between opposites explains the existence of Faraday's physical law, and Maxwell's equations, taking into account fictitious currents and charges, and it are interpreted as real objects of the universe in the form of electronic and muonic neutrinos (antineutrinos).

6. The interaction of an electronic neutrino (antineutrino) with a muonic neutrino (antineutrino) through the substitution of equations gives the formation of an electromagnetic wave (photons), and it was not even considered before in physics.

7. The combination of more interaction objects in the form of electronic and muonic neutrinos (anti-neutrinos) by substituting some equations into other equations, already gives particles in the form of an electron, positron, proton, etc. And this actually explains the annihilation of the electron and positron with the formation of photons and confirms the electromagnetic nature of particle formation.

8. On the basis of the mutual transformation of space and time into electromagnetic components, and vice versa, we calculated the ratio of the mass of a proton to the mass of an electron on base of the constants of electric and magnetic permeability and the maximum of the radiation spectrum under the condition of thermodynamic equilibrium (59).

9. The physical meaning of formulas and function of Louis de Broglie is being shown in account of common space-time and electromagnetic continuum based on closed exchange, and it explains the practical results in diffraction imaging. At the same time, the Louis de Broglie function reflecting the object is expressed to describe space and time in the form of Minkowski geometry laws, and in contrast system, it describes the electromagnetic representation by the formula [1]:

+ i sin(Pd )] = Y0 exp(-pd0) =

Where фд = i фд0. At describing the corpuscular-wave type of an object, the magnitude of can represent both a reflection of the corpuscular type and the wave type of the systems from the opposites. In this case, the object is completely described in the system of the universe on the basis of the Louis de Broglie function both in the form of a wave part and in the corpuscular part, and this fits into the general formula of the universe (55).

10. We have also shown that the propagation of an object at the speed of light in one opposite is interpreted as a mass of rest with a magnitude inversely proportional to this speed of light, and it characterizes the transition of kinetic energy into potential energy depending on the observation system.

11. The principle of the formation of the Lorentz force in the system of Dirac equations as a counter force to the influence of the Coulomb force is determined.

12. It is shown that neither gravitational forces nor nuclear forces are required for interaction.

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