DERIVATION OF IMPROVED MAXWELL’S EQUATIONS WITHTRANSITION TO WAVE EQUATIONS Текст научной статьи по специальности «Физика»

DERIVATION OF IMPROVED MAXWELL'S EQUATIONS WITHTRANSITION TO WAVE

EQUATIONS

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 dynamics of the interaction of global opposites with obtaining the derivation of improved Maxwell's equations and with transition to wave equations.In the beginning, we will define the main paradoxes in the description of electromagnetic processes using the usual Maxwell equations and show the need to improve them to the form of correspondence to real corpuscular-wave objects. Next, we will also define the paradoxes of the transition from the usual Maxwell's equations to the wave equations. At the same time, we will show a transition without paradoxes to wave equations based on the improved Maxwell equations. We will give a real representation of the Louis de Broglie wave function as reflecting electromagnetic processes in contrast. In fact, we will establish that the conclusion of our equations coincides with the conclusion that existed in electrodynamics, but at the taking into account of corrections for the interaction of global opposites, symmetry and the law of conservation of quantity. 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.

Keywords: Einstein SRT and GRT, improved Maxwell equations, equations of the Dirac, general formula of the universe, Louis de Broglie formula, laws of Faraday and Bio-Savard, law of Umov-Poiting.

Conclusion of Maxwell's equations from the laws of the universe

The result of propagation front of the electromagnetic wave, described in [1] is being written according to the formula:

x2+y2+z2-c2T2=0, x2+y2= c2T2—z2. (1)

It should be noted that the first equation of the electromagnetic wave in (1) refers to purely wave processes without corpuscular properties, but the second equation in (1) can be attributed to the movement of a photon along the z axis. Accordingly, along the x and y axes we have a rotational closed process, otherwise at x = 0 and y = 0 we will not have an object at all, and in the variant of the first equation the photon will have decay. This representation should have a connection with the general formula of the universe [2] in any inertial coordinate system, taking into account the regularities while ensuring equality:

cos2(x)+sin2(x)=ch2(w)-sh2(w); exp(/'x)exp(-/'x)=exp(w)exp(-w)=1=const. ( However, this connection is purely intuitive and does not describe the physics of the process, which follows from Maxwell's equations at describing electromagnetic waves. The conclusion of formula (2)is completely based on the axiom of the absence of miracles, and failure to fulfill this formula means a violation of the law of conservation of energy. To establish the connection of formula (2) with the electromagnetic wave, it is necessary to obtain the Maxwell's equations from the derived laws of the universe, which will be done below. Paradoxes of the description of electromagnetic wave and how they are solved on the base of the logic of connection with the laws of the universe.

Why is there such a need to connect Maxwell's equations with the laws of the universe?

This is due to the fact that Maxwell's equations of an electromagnetic wave in their current form describe only the wave properties for definition of an object, and, as it is known, at the beginning of the twentieth century, corpuscular properties were also discovered in an electromagnetic wave (in fact, this is confirmation that any object of the universe has a corpuscular-wave dualism). This meant that Maxwell's usual equations were true only within certain limits. In addition, the main paradox that physicists could not explain was that in Maxwell's equations, energy was calculated strictly from the amplitude of the electric and magnetic fields and did not depend on the frequency of oscillations. In quantum mechanics, at the transition from a wave to a particle, the radiated energy of photons is determined from the frequency of the oscillatory process, i.e. the intensity of electric field and of magnetic field is not used. Physicists could not solve this paradox (within the framework of existing theories), since they did not know the mechanism of the connection between frequency and intensity.

This condition of connection must is being fulfilled not with the help of a postulate in which energy was defined as multiplying Planck's constant by frequency, but directly. It is clear that it is impossible to measure the intensity of electric and of magnetic fields for waves with a length of microns. Therefore, there is a problem of measuring E and H depending on frequency and it is not possible to solve it without involving opposites. For example, the frequency is included in Maxwell's equations, but does not affect the energy calculations, although the frequency describes the nature of the wave motion. On the other hand, photons have a pronounced corpuscular character in their properties, but their energy depends on frequency, that is, from wave properties. Hence, we have the well-known

Louis de Broglie formula, which reflects the relationship between frequency and mass [3]:

hf = mc2.

In addition, the connection of orthogonal magnitudes of electric and of magnetic strengths, although it followed from Faraday's practical experiments, but any mathematician knows, that orthogonal magnitudes must be independent. And here the connection of orthogonal quantities is accepted as a postulate following from practical data. Such a paradox of physics with mathematics is obvious and also subject to explanation. One can also notice

of the electromagnetic wave in the graphic image, for example, in Fig. 1, we see that there are areas along the edges where the electric and magnetic strengths of the electromagnetic field are directed not orthogonally to the direction of motion, but in parallel to the direction of motion of the wave at the speed of light. In addition, in order to obtain a force effect, for example, for the intensity of the same static electric field, it is necessary to have a potential difference, but with a closed power line it simply cannot be, because there must be a section with the opposite direction of intension for potentials.

Fig. 1. Image of an electromagnetic wave in the dynamics of radiation Similarly, we see a paradox in the representation of electromagnetic wave on flat surface in Fig. 2.

Fig. 2. Electromagnetic wave in the image of the coordinate axes on flat surface

Here it is necessary to assume that the intensity vectors of electric and magnetic fields must have both a beginning and an end. And this means the presence of charges to create a potential difference, both for the electric field and for the magnetic field. But this means

that there are no differences between the electrical and magnetic components, which mean that there are no op-posites. The contradiction with Fig. 1 in the presence of a continuous line of one magnitude of intension is also

seen in Fig. 3.

Fig. 3. Radiation of the electromagnetic field by the antenna

It can be seen here that, depending on the angular direction is being changed the intensity and energy of the electromagnetic field. It is clear that this contradicts the isolation of the force line of one magnitude of intension according to Fig. 1 and requires the transformation of the electromagnetic field into a space-time curvature and, conversely, otherwise there would be a miracle of disappearance into nothing and appearance from nothing. In other words, it is not possible to obtain complete closed magnitude only on the basis of one type of representation of an object in the form of, for example, of field of strength. Thus, we see that a simplified description of the electromagnetic interaction gives paradoxes. We will try to identify these paradoxes in more detail on the basis of known laws of physics and present solutions without paradoxes, taking into account our derived laws and the theory of the universe. From here, let's consider three well-known laws of physics in electrodynamics and try to come from them to the description of the simplest objects, because the laws of physics must also be fulfilled for the simplest objects, otherwise it would mean a break in the scheme from simple to complex.

The first known law of physics, proven in practice - is Faraday's law, according to which a change in the magnetic field causes a closed electric field, and mathematically this is expressed in the form of the formula:

S8 SH

— = un — = - rotE.

St St

(4)

3R

j = ev = e— = rot H. J St

(5)

We are comparing equation (5) with the classical Maxwell equation of the form:

SD SE

— = sn — = rot H. (6)

St 0 St

It is easy to notice that when the right-hand sides of equations (5) and (6) are equal, there remains the only option in which the movement of the so-called charge characterizing one of the two opposites always causes a change in electrical induction in current time:

SD SE

— = sn — = j = ev = rotH . (7)

St 0 St

Equality (7) will mean that the straight motion in one opposite (we have the change of system of coordi-

nates due to the motion) present a closed motion in another opposite, that is, it is a transition from kinetic energy to potential energy. The validity of this equality follows from the fact that the charge, for example, of an electron e (q) can act only through its electric field in space. In fact, we have a reflection of the same law, where a change in one quantity in current time, and characterized as the first opposite, causes the isolation of another quantity in space (closed rotation), which is characterized as the second opposite, and vice versa. In other words, we have symmetry between opposites, and hence the law of conservation of quantity. However, in the writing of this law, it is easy to see the paradox associated with the fact that the change in the magnitude of one opposite in current time does not give transit into the magnitude of another opposite, since the other opposite characterizes an isolation quantity without changing in space. Similarly, this applies to the integral notation of the classical Maxwell equations:

d (fBds) f d (fDds)

j Edl = --

dt

j Hdl = I

+ -

dt

(8)

We have a closed electric field because otherwise when the magnetic field changes, we have the polarization of charge instead a current in a closed conductor. It is clear that now we are not considering the option of the formation of the closure of the force line itself, but simply represent the process that gives the result in the form of a closed current magnitude and display it as a vector of electric field strength (in the future we will understand which process leads to closed rotation).

The second well-known law of physics, also proven in practice, is the Bio-Savard law, according to which the movement of an electric charge (and in fact, this is a change in time of the electric field) causes a closed magnetic field; this law is expressed in the form of the formula:

There are also closed electric and magnetic fields of forces on the left side of the equal sign, and there is no beginning and no end to the field strengths. If we consider the field strength, for example, as a potential difference, then there should be a gap in the form of charges between the beginning and the end in a closed circuit, which is not observed, and this means that we do not have a force as a homogeneous independent quantity. That is, the force should also be expressed as a reflection of the exchange between discrete smallest objects. In other words, in the mathematical representation of the laws of Faraday and Bio-Savard, we have the fulfillment of the laws according to the geometry of Euclid, that is, the connection of length and time in a closed cycle is missing. Therefore, these two laws, proven in practice, contradict the third law, also proven in practice, and this is the Umov-Poiting law, according to which a change in current time of a quantity corresponds to its change in space, and mathematically this is expressed in the form of a formula [4]:

SW/St = - divS.

(9)

In other words, the usual Maxwell equations (4) and (6) do not correspond to equation (9), because a change in the electromagnetic components in current time, and they are uniquely related to energy, does not lead to a change of electromagnetic components in space. That is, the rotor is a closed quantity and does not give a change in space. Thus, it remains to understand what the member of change in space should be, which is necessary in equations (4) and (6) to comply with the law of conservation of quantity, because we have a change in current time, but it is not accompanied by a change in space. Obtaining this necessary member was intuitively proposed in electrodynamics through additional functions - vector potentials. Here, the closed magnitudes of certain auxiliary functions of the A and ® began to represent in the form of quantities through the magnetic and electric field strengths (that is, objects) which were being unchanged in current time and space. Moreover, the vector potential A had to satisfy the condition div B= 0 (this is immutability in

space), which was achieved by means of the following equation [5]:

B = rotA. (10)

In fact, the magnitude of the magnetic field B is represented by a constant from rot А. In this case, we have, when normalized by the value B, the formula rot A/B = 1, and it is possible under the condition of equality only if there are laws according to the formula of the universe (2) to the right of the equal sign in the first equation. Substituting this expression into the equation rot E = -(dB/dt)gives the equation:

ro{E + f] = °. ,11)

To satisfy this equation, the expression in parentheses was equated to the magnitude of the gradient of the potential function, that is, we have the equation:

^ dA ^^ _ ^ dA

E + — = VO; E = -VO--. (12)

dt dt When normalizing (12) to E, taking into account the fact that the magnitude of E reflects the counteraction to the magnitude of B through the minus sign as opposites, we get that in order to fulfill the equality, it is necessary to use the regularities to the left part from the equal sign in the first equation according to the formula of the universe (2). That is, even before us, an intuitive law was introduced into electrodynamics for any objects of the universe corresponding to the formula (2), since otherwise the object would automatically become independent of our universe. In fact, the expression (12) reflects that E as a closed quantity according to the formula (11) also does not change. Further, taking into account the equality H=cE known in electrodynamics (and this is the law of the connection of op-posites through the velocity of exchange, which is equal to the speed of light), when we replace the electromagnetic components with the vector potential equations, which correspond to the change of the observation system through the opposite, we have: ( cdO сдА ]

- rotA =Hio+cr} <l3)

Then we take into account the well-known formula from electrodynamics [6]:

A = v/(c 20). (14)

At the same time, we assume that v = c (due to the fact that we have changed the observation system to the opposite one), and then the vector potentials are also connected as components of the electric and magnetic fields according to the equation H = cE, and characterize the electromagnetic field, but in the system of the opposite. Accordingly, for the members of E and H, here remains no place for other physical analogue except for time and space (when we have observing from the opposite), which are also connected, provided that SRT (and this is the law of conservation of quantity) is being supported by Minkowski transformations in the form of r = ct [7]. Given that the vector mapping does not determine the orthogonality of opposites, which are A and and they are similar to E and H, we must write equation (14) by coordinates, that is, represent it as quantitative values for the four components of two global opposites, for example:

dA dA dO, dOx

—---=^0c— +^0—-

dz dy dx dt (15)

In other words, we have actually obtained a correspondence between the rotor equation and the continuity equation based on vector potentials in accordance with the general formula of the universe (2), to fulfill equation (15). Thus, we have eliminated the paradox of the classical Maxwell equations, since we have isolation (the law of conservation of quantity) through op-posites. At the same time, we take into account that for the derivative of the magnitude x for the vector potential there are no other components to comply with the continuity equation, except for the projection of ® for time, that is, ®t . This is analogous to how it was done by Feynman in [8]. It should be noted here that the electric and magnetic components are uniquely connected in the laws of Faraday and Bio—Savard with real objects, and these objects obey the Lorentz—Min-kowski transformations, with the presence of a projection onto magnitude of time. If the electric and magnetic components did not have a projection onto magnitude of time, then the connection of real objects with electromagnetic processes could be forgotten because of independence, and in this case there is no law oftheir connection. Further, taking into account the use of vector potentials in quantum mechanics [9], the member of the projection onto magnitude of time should be multiplied by an imaginary unit i (actually this is a reflection of the fact that the projections for length and time are opposites). In fact, we turn to the complex-conjugate form, that is, we express any object in the form of op-posites. Such multiplication by an imaginary unit is also connected with obtaining a correspondence with the Dirac's equations, which are derived from the Einstein energy equation, and their essence is to combine wave properties with corpuscular properties according to the law of transformation determined by an imaginary unit with the condition of forming a counteraction to the action (otherwise the independence of the equations). In addition, without the presence of an imaginary unit, it is not possible to obtain the transformation of Maxwell's equations into the Lorenz-Minkowski transformations (and this is a necessary condition for the connection of wave and corpuscular properties), in compliance with the law of conservation of quantity between arguments of functions. As a result, we have: dA- dA . dOt dOx

----- = ^n'C-- + Un--

dz dy ™ dx ™ dt (16)

If we make a change of variables, and this actually means a change of the observation system, and consider H=®t ,H-=®x , Ey=Ay , Ez=Az , then we get a form similar to the improved Maxwell equations [10]:

5H„

^0

^0"

dt

H dt

dH„

dt

- + ^,0ic

- + ic

■ + ^0ic

dH dK dE.

y .

x dy dz

dHt _dEx dEz

dy dz dx

dH t II Si _e dEx

dz

dx dy

E dt

dEy_ dt

E 0 dt

dH dH dH

(17)

y .

-S0ic

dx dy dz

dHt _dHx dH z

dy dz dx

dHt dHy dHx

dz dx dy

Here, i = V-l . There is also a complex conjugate form of writing these equations. Since the obtained equations actually reflect the general formula of the universe (2), and this is a necessary condition for the existence of an object in our universe (otherwise it is zero), then the magnitudes which defined the parameters of the object are the constants of electric and magnetic permeability.

In addition, the members of the electric and magnetic field strengths reflect the regularities of the impact and this is expressed in terms of functions depending on the argument expressed quantitatively. Hence, depending on the electric and magnetic permeability and the magnitudes of the arguments in the functions of the obtained equations (17), the representation of objects in the universe is characterized. It is clear that independent objects described by equations (17) cannot give a real picture of the universe, since they completely exclude hierarchy and, accordingly, the transition of quantity to a new quality (that is, there are only the simplest objects described by equations (17)). Therefore, it is necessary to understand how objects expressed by equations (17) reflect the interaction between themselves with the transition to a new qualitative form. In fact, we must have a representation of the object in a functional form with subordination to the laws of the universe according to the formula (2) on the basis of opposites, otherwise it falls out of our system of the universe and it cannot be detected. It should be noted here that scientists have used the functional relationship in physics long ago, hence, thus, all physical laws arose, and this was done without the connection between the opposites, separately, this result was expressed in a separate perception of wave and corpuscular properties with an attempt to express certain properties through others. However, gradually scientists came to the concept of wave-particle dualism, that is, to the interaction of opposites. Hence, there was an attempt to combine wave and corpuscular properties through the Schrodinger equation. In other words, science has recognized the need for the simultaneous existence of corpuscular and wave properties in any object of the universe, and it is clear that such unity cannot do without interaction.

Louis de Broglie's formulas as a reflection of the representation of an object through the isolation

(closed system with rotation) and the system with rectilinear motion in infinity.

Considering the interaction of opposites in any object in a closed cycle (otherwise the object would have disintegrated), which are expressed through the presence of kinetic and potential energy, Louis de Broglie proposed his formula [11], in which a certain periodic frequency processf0is associated with any particle mass without motion m (for example, the mass of an electron) in the form of a regularity:

hfo = moc2. (18)

Here, to the left of the equal sign is kinetic energy, and to the right is potential energy. In other words, there was an extension of the Einstein energy formula E=mc2 from the point of view of representing an object as two opposites (wave-particle dualism). And this formula was experimentally confirmed in 1927 by Davisson and Germer, when studying the reflection of electrons from a monocrystal of nickel [12]. At the same time, in order to justify the connection of the mass of rest with frequency, Louis de Broglie postulated the existence of a wave field:

%(t, r) = %0 exp(ip) = %0 exp(i®0t). (19)

However, he did not understand that without an opposite observation system with a change of spacetime curvature to an electromagnetic wave process, which is actually reflected in the formula (18), this wave field will correspond to a miracle, since there is no real embodiment and source of its origin (that is, thus scientists invented an electromagnetic vacuum with virtual photons arising from nothing). The same question concerns the Louis de Broglie wave function for a moving particle with velocity v in the form: % (t, r) = % exp(i pd) = exp (ia0td) =

= %oexp

irn

r

t--u

(20)

ra=ray, y = l/^/l-(v2/c2) . The

Where u=

paradox here is also connected with the fact that there is a certain phase velocity u=c2/v, which must exceed the speed of light.

In other words, Louis de Broglie, in order to link wave processes with space-time curvature, had only to recognize the transition from Minkowski transformations to wave functions obtained in [7] in compliance with the law of conservation of quantity in arguments:

% (t, r) = Toexp(zpd) =

T0[cos(Pd ) + i sin(Pd )]: %oexp(-Pdo) = %0[ch(Pd0) - sh(Pd0)].

(21)

Where pd = i pd0. However, he could not do this, due to the fact that electromagnetic functions in accordance with the classical Maxwell equations were considered as real, and not as complex functions (there was no rule for changing functions by changing the attribute of belonging, which is interpreted as a change of the observation system from one contrast to another contrast). In addition, the changes in the current time of the wave

S

-S0ic

0

S

-S0 ic

0

function according to (19) were in no way connected with the statics of the space-time curvature, and we repeat, Minkowski solved this problem in his geometry through equality r = ct, that is, as if he introduced op-posites into the equivalent of one kind. In fact, Min-kowski denoted length and time as opposites connected through the speed of light (the velocity of exchange). Hence, the static condition in one of them will look like the dynamics of movement (change) in the other. The next step on the connection of opposites through an imaginary unit was intuitively made in quantum mechanics [9], and this, in fact, means the fulfillment of the law of action on counteraction with the fulfillment of the difference between opposites, when addition in one opposite looks like subtraction in another. Thus, physicists themselves have actually introduced the connection of corpuscular and wave properties in the form of (21), and we had only to explain it logically and give a physical interpretation. It is clear that since we have found the connection of the rest mass in one opposite with the velocity in the other opposite according to formula [2]

m02 / (1-v2/c2) = m2, (22)

then there must be a relation of velocity with frequency in accordance with the formulas (3, 20).

With the involvement of our theory on the connection of constants, mass of rest, speed of light and Planck's constant in accordance with the formula of Louis de Broglie [3] (which can be derived from the argument of the wave function), we have: Et—pr=0; Et=pr; hft=pr=pct;hf=pc; h/p=c/f; (23)

X = cT = 2vh / p . Next, we take into account that according to our theory h = m0 = 1/c; we get:

h/p=c/f;m(/p=c/f; m0/(m0v)=c/f; (24)

1/v=c/f; f=cv; hf=v. In other words, frequency and speed are related as well as length and time through the speed of light, that is, we have an expression through space-time curvature, but in opposite, which in our observation system are expressed in terms of speed and frequency. It turns out that Louis de Broglie's formula confirms our idea that a closed motion expressed in terms of frequency f in one opposite corresponds to a rectilinear motion with velocity v in the other opposite. In addition, the rectilinear motion of an object with a constant velocity magnitude does not require external exchange, but circular rotation motion is always associated with external exchange and the replacement of some components of kinetic energy during movement by others. It is possible to combine these two contradictory properties in one object only if the representation of the kinetic energy of rectilinear motion in one opposite is represented as a closed exchange of two opposite components, and these magnitudes are electric and magnetic components. In system of the opposite, these components are acting as constants of the type of length and time (the so-called charges and this will be show below), and it was actually proposed above through the representing of the vector potentials with mutual exchange. In other words, the kinetic energy of rectilinear motion, in the form of electric and magnetic components, in one case is acting

in a view of opposite objects of exchange in a closed cycle motion, and in the other case characterizes the op-posites (the magnitude of length and time in a view of charges) between which the exchange is carried out, that is, in fact, determines the potential energy. It is clear that our approach contradicts the dimension of SI or SGS. However, these measurement systems were invented by people, and the Universe operates only with quantity and regularities. Accordingly, taking into account the formula (18) and at h=m0 = 1/c, we get:

hf=m00c2; hcv=c2/c; v=c. (25)

In other words, the rest mass of an electron (positron) is equivalent to the movement of an object in system of opposite with the speed of light. That is, the potential energy of an electron (positron), expressed through the rest mass, in system of opposite, turns into kinetic wave energy with a frequency f = c2 (here it must be remembered that the speed of light is not expressed in SI or SGS units). Next, we will determine the relationship between kinetic and potential energy, from the point of view of subordination to Einstein's SRT, since otherwise it would mean the independence of these energies from the laws of our universe, and then a miracle would be possible! Since, taking into account SRT, the common Louis de Broglie formula has the form (3), and then the rest mass can be painted in accordance with SRT and Einstein's GRT in the form: m=m0 / (1—vnp2/c2)1/2 (26)

Here vnp is the speed of movement, which gives additional mass in system of contrast according to the GRT. Actually, it is impossible to do otherwise, because mass is determined by the space-time curvature, and the space-time curvature depends on speed, but since it is impossible to find an absolute coordinate system in our measurement system due to the principle of relativity in SRT (otherwise it would mean that the laws of physics depend on the coordinate system), then this coordinate system is the opposite associated with our coordinate system through the speed of light. And so, relative to it, it is possible to measure the magnitude of the velocities of the smallest objects of the universe, and the speed in system of opposite gives the necessary spatial-temporal curvature in our system. Hence Louis de Broglie's formula has the form:

hf=mc2=m0c2 / (1— vnp2/c2)1/2 (27)

Taking into account h=m0=1/c, we get:

f=1/T=c2 / (1- vnp2/c2)1/2 (28)

Thus, we get that kinetic and potential energies through variables of frequency and mass are related by the ratio of both length and time, but through the speed of motion in the system of opposite. And accordingly we have an invariant form similar to formula in [2], where the connection of length and time paint in the view:

h = L

tojl - (v / c)2 Vl " (v / c)2

= const.

(29)

For relation of frequency and mass, we have:

hf / (moc2) = c2/(1— Vnp2/c2)1/2 ' 2/„2\1/2l

(30)

vnp '

[c2/(1.- vnp2/c2)1/2] = 1. At the same time, multiplication in an invariant form (29) is replaced through division in (30), and it actually speaks about the representation of the velocity

of Vnp in system of opposite, when addition is replaced by subtraction. Accordingly, kinetic and potential energies, as magnitudes of length and time, also change places depending on the observation system. In this case, the kinetic energy that was reflected through the rectilinear motion will pass into the potential energy of the closed circular motion, and vice versa. It is clear that this cannot happen spontaneously, and this is possible only if the state of the object changes.

Further, we note that the magnitude of frequencies depending on the speed of movement in each opposite according to the formulas of Louis de Broglie differ and in this case, based on (24) and (27) we have:

hfo=v; hfi=mc2=moC2/ (1- Vnp2/c2)1/2=c2/ uo. (31)

This would mean a paradox of ambiguity if we consider these Louis de Broglie frequencies as belonging to one object in one observation system without op-posites. But, since the universe is a closed system of two opposites, therefore, in any case, the law of conservation of quantity must be observed in compliance with the constants of the universe. This means that quantitative changes of one magnitude from one opposite should compensate in the same amount for changes of another magnitude of the same name in another opposite. In fact, it follows that the energy of the frequencies and the associated velocities in systems of opposites has an inversely proportional relationship according to the formula:

E(!Ei=hfohfi=(v/uo)c2=const (32)

After normalized by a constant, we have the same relationship between velocities in opposites as between energy and mass in the view E=hf=c2/uo=v=mc2. That is, again we come to an unambiguous connection between kinetic and potential energy according to the Louis de Broglie formula and the condition (32) is a direct consequence of (27). At the same time, the maximum frequency size in one opposite is the minimum frequency in the other opposite and vice versa. In fact, we see that the multiplication of the frequencies fof is the contrast to the multiplication of the constants of electrical and magnetic permeability, which can also be presented in the form of a connection between energy and mass. In other words, Louis de Broglie intuitively introduced opposites based on the dual representation of frequency according to his formulas (24) and (27), we only gave this a logical justification.

Since kinetic energy and potential energy are uniquely related, now we will determine what must happen for kinetic energy for giving the form of potential energy, as the same form would negate the presence of opposite. If we follow a logical path, then kinetic energy is being transmitted to the object through electromagnetic components of waves with directional motion, and in order to exclude this directional motion, it is necessary to get to closed circular motion. Actually, this is exactly what can be assumed when photons with directional motion are formed during the annihilation of an electron and a positron, and, conversely, when a photon collides with an electron, a new pair is being formed - an electron and a positron. It is clear that such a transformation should be reflected through the known laws of physics with a mathematical quantitative transformation. To this purpose, physics began to consider

the interaction of the usual Maxwell equations through their substitution into each other, with the production of wave equations, which were supposed to characterize the production of photons in accordance with isolation due to the fact that the change in magnitude of time should equal the change in length. It is clear that in the presence of independence, there can be no question of any substitution. At the same time, Maxwell's equations for vacuum in the MKSA system (meter, kilogram, second, ampere) are expressed as:

dD/ dt = rot H ; divD = 0. (33)

SB / dt = - rot E; divB = 0.

(34)

Here: D = s0 E; B = a0H, s0 a0 = 1/c2. Connection of the improved Maxwell's equations with the wave equations When describing the interaction, we will write Maxwell's equations in partial derivatives;

A)

dH dEv SE„

dt

dE„

dz

dH„

dy ' dH, "

(35)

dt dy dz

For finding a solution in the form of wave equation, two mathematical methods were used. The first is a method of applying some mathematical operation to both parts of a linear equation; the second is a method of substituting one equation through another equation to reduce the number of unknown variables. But here the following problems arose, which were not taken into account by mathematicians. The method of solving a system of linear differential equations by substitution by reducing the number of unknown variables does not cause a violation of logic and actually characterizes the interaction of objects itself. No new mathematical operations are introduced here. But the method of using of additional mathematical operation (previously nonexistent) is questionable.

And the first problem is that every mathematical operation applied in mathematics is equivalent in physics to the effect of a real object, which leads to the formation of a new object. There are no miracles in physics, and if there is a need to transform the original form, then it is associated with changes. Otherwise, the original, independent view should remain. In other words, if there was an original differential equation, then in physics it is a real object, and if you apply a mathematical operation to this object, then physically it will mean the impact of another object onto this object with changing a view, and not the presence of the same unchanged object, but which is written in other form. Thus, in mathematics, the application of mathematical operation to both parts of the equation does not affect the result, and in physics - it means the interaction of real objects that form a new object.

Hence there is the second problem. If there was a transformation of the original object as a result of the interaction of two objects, then is question: "Can be applicable the method of the substitution of variables from another differential equation, the equivalence of which was not in doubt at applying of the mathematical operation in the form of an impacting object?"

Why this is a problem can be understood from the following example. If in formula energy of Einstein in the view[12]

E = c(P2 + M02c2)1/2 = c£ AkPk, (36)

instead of extracting the square root in the form of Dirac matrices, we apply the mathematical operation of squaring of both parts of equality, then as a result we violate the condition of the need to move from one system of the opposite into another system of opposite with a change in the attribute of belonging, that is, in fact, we assume the possibility of opposites separately from each other. Mathematically (quantitatively) we have not violated equality, since from the point of view of mathematics, squaring equality does not affect the result, however, a change in quantity in physics should give a change in quality, and this is due to the transition to the opposite. Otherwise, it is impossible to fix the change itself due to uniformity. Physically, this mathematical operation means the transformation of an object, and in order to use the method of substitution of variable now, we must be sure that we have the same variables as in the initial differential equations, and have not received new ones. This doubt is based on the transformation of the coordinate of length into a time magnitude, and, conversely, with any changes in accordance with Einstein's SRT. Here, the deriving of the wave equation for the electric and magnetic field strength is obtained on the basis of the usual Maxwell

equations. However, the substitution of one Maxwell equation into another equation was made only after the mathematical operation of the rotor was performed with first usual Maxwell equation and the procedure of differentiation by variables was changed. Let's take a closer look at the errors that occur in this case.

We present the well-known mathematical method of transforming of the usual Maxwell equations to the wave equations. At the same time, we take into account that the well-known relation is true for the vector H:

rot rot H = grad div H - V 2H.

(37)

Since div H =0, the equation (37) can be represented as:

—- _0 —►

rot rot H = - V2H. (38)

However, the vector notation of the equation does not make it clear the very scheme of transformations of orthogonal electric and magnetic components. Therefore, the operation of using the rotor will be considered sequentially on a specific electromagnetic oscillation. First, we show what give the application of function of the rotor to the last equation of the system of equations (35).In this case here is not needing make operation of the rotor through the component (d/dy - d/dz), because together with the components (d/dz - d/dx) and (d/dx - d/dy) we get zero. Therefore, as a result, for the usual Maxwell equation in partial derivatives we have:

s0d2E /dzdt-s0d2Ex /dxdt + s0d2Ex /dxdt -s0d2Ex /dydt = = d2 Hz / dydz -d2 Hz / dxdy + d2 Hy / dxdz + d2 Hz / dxdy --d2 H / dxdz + d2 H / dzdy - (d2H / dz2 +d2Hz / dy2).

(39)

Considering that in ordinary mathematics, the procedure of differentiation by variables can be changed, it is assumed that dHz /dz = 0 and dHy /dy = 0 due to the isolation of magnetic field lines. Through deletion the same opposite in sign of members we have:

s0d2Ex / dzdt - s0d2Ex / dydt = = -(d2Hy / dz2 + d2Hz / dy2).

(40)

In equation (40), we changed the procedure of differentiation by variables in the left part, although from the point of view of our theory, this could not be done due to the fact that any differentiation is a change, and subsequent differentiation has relationship with a new object, and not with the previous one. Practically, if the permutation of variables did not affect the result, it would actually mean the possibility of creating a perpetual motion machine in one opposite, since in this way it would be possible to restore the original position in the same opposite without costs. It should be noted that the introducing of the second order of differentiation of the type V2HjVy2 is correct from the point of view of Euclidean mathematics, but not physics, because in physics this means that there is a double change of the divisible, while the divisor has squaring. And this indicates the nonequivalence of changing variables, what immediately violates the law of equality of changes, and at the same time, changing of one magnitude does not change another magnitude. In addition,

squaring immediately eliminates the transition to the opposite, which means that the magnitude can change abruptly only in one opposite. It is clear that there is an element of miracle in the form of a singularity (of break or leap) and the need for opposites based on wave-particle dualism should be forgotten here. It is possible to do this when considering processes only on the basis of one opposite, for example, wave properties. In addition, such a substitution is acceptable if the variable is expressed in terms of exponential functions, and it was noticed earlier. It is clear that the significance of the electric field strength Ex does not agree in any way with the magnitudes of Ez and Ey , which really correspond to the components of the rotor for these partial derivatives according to the formula:

dH„

dEy dE„

(41)

dt dz dy

At the same time, if we follow the rule of considering the significances of partial derivatives as vectors

E and H, we get that we must assume Ey=Ez=Ex . However, the following paradoxes follow from such a substitution.

From the point of view of Maxwell's equations, the change Hx in current time in the equation is equal to their change Ex in the z and y coordinates, because Ey=Ez=Ex . In other words, the orthogonality of the

electrical and magnetic components disappears. In addition, it turns out that the electrical component in this case should have three coordinates, and this indicates the existence of a divergence from closed solenoid fields, but it cannot be. Thus, thoughtless vector substitution at considering in concrete partial derivatives meets with alogisms.

If this is not taken into account, then after substitution, you can get the wave equation: sA d2Hx /dt2 = -(d2H /dz2 + d2Hz /dy2);

0 , , , , , , (42) 1/c2 d2 H / dt2 =-(d2H / dz2 + d H / dy )•

In general, the question of substituting of equations (41) into equation (40) to obtain equation (42) is paradoxical from the point of view that the significance of zero (which follows from the presence of a rotor along the vector E) corresponds to a numerical significance when magnitude H is being changed in current time, i.e. there is a substitution of a numerical significance instead of zero. But, in addition, the substituted objects are not only orthogonal, but also have a different physical essence. This is the same as if you were given a melon with the same weight instead of a watermelon.

In other words, the formalism of mathematics does not take into account the physical essence of the process.

Naturally, in this case, in order to fulfill the wave equation, it is necessary to have the magnitudes of three components of the magnetic field strength in coordinates at once, which means that the magnetic closed (solenoid) field must also have divergence.

The conclusion follows from this: it is impossible to obtain a wave equation based on the usual Maxwell equations, because instead of the time-varying component Hx , there must be time-varying components Hy and Hz . In any case, the usual Maxwell equations cannot give two time-varying components.

Therefore, a purely mathematical approach has the following paradoxes:

1. The operation of the rotor, which is used for both parts of the Maxwell equation in the transition to the wave equation, has no physical analogue in the form of a real corpuscular-wave object.

2. The substitution of variables in process of differentiation is also not supported by any physical necessity. In other words, "we want to do it through one way, but we can to do it otherwise." But in the universe, it is impossible to change an action immediately to a reaction, i.e., there is always a cause first, and then a consequence effect. Therefore, the secondary effect occurs already on the modified corpuscular-wave object, which is associated with the change of parameters according to the principle of SRT and GRT of Einstein.

3. The substitution of one equation into another equation is also not connected with any physical operation, i.e., the changing in the very type of object (over which the effect is carried out) occurs "at the behest of the creator, at my will."

Thus, the vector recording of the usual Maxwell equations made it possible to hide all the transition errors associated with the transformation of Maxwell's equations into wave equations. In addition, the question

of the legality of substituting of the usual Maxwell equation into the equation of the transformed under the action of a mathematical operation of rotor to reduce the number of unknown variables, is being remained unresolved, because in equation (42) all variables are orthogonal! It should also be noted that in equation (40) we have three differential members, which clearly do not correspond to symmetry when changing in oppo-sites, i.e. the error in the number of variables in the usual Maxwell equation corresponds to the same error in the wave equation (40).

There is also another way to derive the wave equation of an electromagnetic wave on a flat surface [13]. And it is based on the fact that one differential component of the coordinate in Maxwell's equations is considered equal to zero. In this case, Maxwell's equation turns into a continuity equation, and then it makes no sense to talk about deriving of wave equations from Maxwell's equations at all. Let's consider, for clarity, how Feynman makes these mistakes. Feynman begins the proof from Maxwell's equations for empty space medium, rewritten as:

rotE = -dB / dt; D = s0E; divE = 0. (43)

c2 rot B / dt = dE / dt; B = ju0H; s0Ao= 1/c2; divB = 0.

(44)

Considering an electromagnetic wave on a flat surface, he believes that the magnitude of the fields depends only on axis x, so that, simultaneously, the fields do not change with respect to axes y and z. Next, he writes the third equation (43) component-by-component:

div E = dEx / dx + dEy / dy + dEz / dz = 0. (45)

Since Feynman assumed that the fields along the y and z axes do not change, therefore, the last two members of equation (45) are equal to zero. Then according to equation (45) we have:

dEx / dx = 0. (46)

And then follows the conclusion that when waves have propagation at motion in a flat surface, the electric field should be located across the direction of its propagation. Accordingly, this electric intensity still has the opportunity to change in some complicated way along the x coordinate. Then the transverse field E can be divided into two components along the y and z axes. Here we choose a case with only one transverse component along the y axis, that is, with a zero z-component. It is stipulated that the general solution can always be represented as a superposition of two such fields. The next step concerns to the record in private components from rot E:

(rotE)x = dEz / dy - dEy / dz = 0. (47) (rotE)y = dEx / dz - dEz / dx = 0. (48) (rotE)z = dEy / dx -dEx / dy = dEy / dx. (49)

And here we already have an error in the equation (49). It is connected with the fact that we no longer have the equation of the rotor, characterizing a closed circular electric field, but has a vector with a beginning and an end, that is, we have movement from the source to the absorber. In other words, the rotor does not have a

(54)

return direction of movement with such a recording. The formula (43) can actually be equivalent to writing for the vector potential according to the formula (10), if we assume that a change in one opposite in current time or in space gives a constant in the other opposite ®=(rot E):= ~\EylVx (it is analog of the equation of decay or synthesis). However, it is further assumed that, according to the first equation of the system (43), we have:

ffix / dt = 0; dBy / dt = 0; dB2 / dt = -dEy / dx. (50)

In the last equation of the system (50), the continuity equation is actually obtained, which corresponds to the presence of charges. In other words, Maxwell's equation was replaced by the continuity equation. A similar approach with the same reasoning applies to the magnetic component: c2 (rotB)x = c2 (dBz / dy - dBy / dz) = dEx / dt = 0. (51)

c2 (rotB)^ = c2 (dBx / dz - dBz / dx) = dEy / dt. (52)

c2 (rotB)z = c2(dBy / dx -dBx / dy) = dEz / dt = 0. (53)

Accordingly we receive:

c2(-dBz / dx) = dEy / dt.

Here, too, the Maxwell's equation is being substituted through the continuity equation. Next, we differentiate the last equation in the system (50) by x, and the equation (54) by t, then the left sides of the equations will coincide up to the multiplier c2. In fact, such a method of differentiation by different variables with getting the same result in the left parts, suggests that a change in opposites is being considered with the condition of the law of conservation of quantity between them, which, by the way, we will also use in the future. As a result, we have the equation:

d2Ey / dx2 -1/c2 d2Ey / dt2 = 0. (55)

Further, a very paradoxical conclusion is made, that Maxwell's equations give information that electromagnetic waves have only field components located at right angles to the direction of wave propagation. It is clear that this conclusion is connected with the transformation of the Maxwell equation into a continuity equation, which, to put it mildly, contradicts the logic of the derivation of the Maxwell equations themselves, in which there are necessarily two differential components in the rotor.

However, if we compare equation (42) and equation (55), we will see that in equation (42) there are three components in coordinates at once. So which of these conclusions is considered correct? Here is an obvious ambiguity; both the first and second methods of deriving the wave equation from the usual Maxwell equations are paradoxical.

And it is based on the fact that one differential component of the coordinate in Maxwell's equations is considered equal to zero. In this case, Maxwell's equation has the transit into a continuity equation, and then it makes no sense to talk about deriving wave equations from Maxwell's equations at all. In addition, it can be seen that the wave equations for (42) and (55) generally exclude the need for the connection of electric and magnetic components, since changes, for example, in the electric field strength in current time lead to a change

in the electric field strength along a other coordinate of length. Moreover, the equation of an electromagnetic wave on a flat surface characterizes the associative addition and subtraction of the components of both the electric and magnetic fields. In this case, when we have subtracting the components (overlapping of waves), further propagation of the wave is impossible; significance of zero cannot give a source of new waves. Hence on the base of the need in a source of secondary electromagnetic waves, otherwise it would not be possible to get a wave around an obstacle, it was necessary to show the transition from Maxwell's equations to wave equations with forced radiation. For this purpose, in the so-called vacuum - the empty space medium, Maxwell's equations with the density of fictitious electric

charge pfc and the presence of only a fictitious (third-

party) current j = jfic (ideal dielectric, a = 0) were used[14]:

rot H = dD / dt + j;

rot E = -dB / dt;

D = ss0E;

div D = pfic; j = jfic; B = mH; s0^0= 1/ c2; div B = 0.

(56)

'0t-l0

In other words, even before us, the interaction of space and time with electromagnetic components was intuitively introduced in electrodynamics through the

density of fictitious electric charge pf and with the presence of the density of fictitious (a third-party) current jfic, because, otherwise, there was no connection between the wave equations for the electric and magnetic components and the change in the direction of photon motion in the space-time curvature, it would not be explained. It should be noted that the connection of the fictitious density of current and density of the charge with the real density of charge and density of current is being carried out by recalculation based on the electromagnetic continuum, similar to how the Lo-rentz magnetic force is being calculated into electric force of the Coulomb through SRT of Einstein. Otherwise, we would have an ambiguity in the formation of an electromagnetic field.

Next, the transition to the system of second-order equations is carried out as follows. We multiply all members of the first Maxwell equation by 1/ s, and the second Maxwell equation by 1 / ^ and apply the operation -rot. This method gives: rot(s-1 rotH) = s0 d (rotE)/ dt + rot(s-Vc);

(57)

rot(|J,-1 rotE) = d (rotH)/ dt.

Now we will replace the rot E and rot H, included in the right parts of equations, through expressions arising from the first two Maxwell equations. As a result, we get:

rot(s-1 rotH) + |/c2 d2H/dt2 = rot(s-1jflc); rot(|-1 rotE) + s/c2 d 2E/dt2 = -|0 djfic /dt. (58)

With a homogeneous medium s = 1 and | = 1, we obtain:

V2H-1/c d2H/dt2 =-rot(jfc);

V2 E -1/c2 d 2E /at2 =e0-1 gradpfc + |i0 djfc /dt.

However, with this solution, we get a lack of symmetry in the formation of the electric and magnetic components from the source of forced radiation, and it indicates the inequality of opposites, which are the electric and magnetic components, and this leads to a violation of quantitative exchange. That is why, along with fictitious (third-party) electric currents and charges, fictitious (third-party) magnetic currents and charges on the principle of reciprocity and equivalence were introduced to obtain symmetry between opposites and for observance of equal quantitative exchange [15]. In other words, we have the need for a closed and equal rotrotH = d(rotD) / dt + rot jE; rotD = s0 rotE = s0 (-dB / dt - jH);

cycle of exchange to have a two-way transformation. (59) And in this case, there should be currents and charges in both opposites, and not in one of them. Otherwise we shall get one opposite.

Let's image Maxwell's equations in a vacuum taking into account the so-called fictitious electric and magnetic currents of jE h jH :

rot H = dD / dt + jE;

rot E = -dB / dt - jH ;

(60)

D = ^E;

B = ah.

Next, we will follow the generally accepted path shown above and will apply to the first equation (60) the function of rotor -rot:

grad div H - V2H = -s0^0 d2H / dt2 -e0 d jH / dt - rot jE ;

(61)

V2H -1/c d2H/ dt2 = grad div H + s0 djH / dt - rot jE. Similarly, we apply the function of rotor to the second equation (60): rot rotE = -d(rotB) / dt - rot jH;

rotB = a0 rotH = A0(s0 dE/dt + jE );

grad divE-V2E = -s0A0 d2E / dt2djE / dt - rot j

V2E-1/c2 d2E / dt2 = grad divE + a0 djE / dt + rot jH. Let's write out the last two equations separately in (61) and (62):

V2H -1/c2 d2H/ dt2 = grad divH + s0 d jH / dt - rot jE,

V2E -1/c2 d2E / dt2 = grad divE + a0 djE / dt + rotjH.

(62)

h ■>

(63)

Now we take into account the relationship of the magnitudes of the field strength divergence with fictitious charges according to [15]. In addition, in quantum mechanics [16], the equality j = cp is introduced on the condition that the Maxwell's equations and Dirac's equations must be invariant with respect to Lorentz transformations, because otherwise there would be independence of electromagnetic properties from space and time with the exception of presence of wave behind obstacle. Here, the density of current and density of charge actually play the role of length and time, and in accordance with [9], where x4=ict (time is being expressed in terms of a coordinate, normalized by the speed of light), we have a similar relationship taking into account the attribute of the opposite in the form of

V2H -1/c2 d2H / dt2 = i grad jH /(c^

(64)

an imaginary unit i, j = cp. Hence follows:

divE = Pe /S0 = i jE /(cs0);

div H = Ph / A =i jH /(cA0).

It should be noted that in this case, we associate the change in the space medium of the magnitudes of E and H with the transition to the opposite, when the changes in length in accordance with the SRT of Einstein are being passed into the significance of time, since otherwise the opposites would simply not be needed. And in this case, the variables jE and jH display the magnitudes of projections on axis of time and display scalar values, because there are simply no other significances with respect to orthogonality. As a result, when substituting in (63) we have:

) + S0 djH / dt - rotj

E>

V2E -1/c2 d E/dt2 = i grad jE /(ce0) + ^0 djE /dt + rotjH;

^0(V2H-1/c2 d2H/dt2) = igradjH/c +1/c2 djH/dt-^0rotjE;

e0(V2E-1/c2 d E/dt2) = i grad jE /c +1/c2 djE /dt + e0rotjH; V2H -1/c2 d2H / dt2 = ice0 grad jH +e0 djH / dt - rot jE ;

(65)

V2E -1/c2 d 2E / dt2 = ic^0 grad jE +^0 d jE / dt + rot j

H-

From the system of equations (65) it can be seen that we have a symmetrical form for the electric and magnetic components, which provides the same conditions and mutual influence due to the components of the

js and jH . We see that in the right side of equation from the sign of equality in (65) we have a form similar to the improved Maxwell equations, but through the so-called fictitious currents. And the fictitious currents jE

and jH (they are also opposites connected through the speed of light and with respect to the dimension in the equations jE=cjH) play the role of parts of projections of electromagnetic components in the opposite, and correspond to auxiliary functions, that is, vector potentials, as can be seen from the comparison (16) with (65). At the same time, fictitious currents participate in the formation of both electric and magnetic components symmetrically. This does not work in the case of using the classical Maxwell equations (59).

Taking into account the observance of the same laws of physics in opposite observation systems, relative to each other, as well as the isolation of the Universe into two global opposites in compliance with the

V2H -1/c2 d2H/ 8t2 = ics0 grad jH +s0 d jH / 8t - rot jE =

= ics0 grad A + s0 dA / dt - rotO.

In the lower equation (65) we get the result:

V2E-1/c2 d2E/dt2 = ic|0 gradjE + |0 djE/dt + rotjH =

= ic|0 grad O +10 dO / dt + rot A

law of conservation of quantity, we can, based on the symmetry between the improved Maxwell equations and vector potentials, replace variables, that is, fictitious currents through vector potentials with the condition of equality:

jE =O; jH = A. (66)

In fact, this is a transition from the so-called fictitious magnitudes of currents to another level of the hierarchy in the opposite system of observation due to the speed of light. Hence, when replacing the variables in the fifth equation (65) we have:

(67)

(68)

Thus, the electromagnetic wave properties E and H in our observation system are expressed in system of opposite through the vector potentials A and ® like the improved Maxwell equations and reflect the fulfillment of the physical laws of Faraday and Bio-Savard, taking into account the fulfillment of SRT and GRT of Einstein. Accordingly, in equations (67) and (68) into the right side of equation from sign of equality, we have two opposite observation systems. Moreover, the magnitudes A and ® in these systems of observation reflect the straightforward and rotational movements of the alternately. Here, the variables under the rotor operators represent some absolute system of coordinates. The significances of the constants of electric s0 and magnetic permeability 10, being some coefficients, actually characterize the magnitude of the space-time curvature from motion in the system of opposite in accordance with GRT of Einstein relative to some absolute system of coordinates. And this movement forms the presence of electromagnetic waves in the opposite, that is, a change in one opposite leads to an electromagnetic exchange in the form of waves in the other opposite.

It should be noted that we also used a mathematical technique related to the application of the rotor operation and the substitution of some equations into others. However, we meant that the operation of the rotor and the substitution of some equations into other equations are associated with the influence of one opposite onto another opposite. And, since we have a symmetric form of Maxwell's equations, both for electric and magnetic components and these components have moving into each other and have the form of a rotor, and at the same time have a mutual influence, we have physical confirmation of such mathematical operations. Otherwise, the electric and magnetic components would not

have a symmetrical appearance and propagation in one electromagnetic wave. At the same time, the symmetric view also provides the law of conservation of quantity between opposites, and of course the vector representation hides the order of the change in the direction of motion along the coordinates during the transformation from the interaction associated with the transition to the opposite, but we get the transition from the improved Maxwell equations to the wave equations correctly. We will now show how the sources of radiation and absorption for electromagnetic waves are formed on the basis of vector potential functions, or rather on base of the Louis de Broglie wave function.

Formation of sources of radiation and of absorption of electromagnetic waves The nature of obtaining waves based on Louis de Broglie functions, with the connection of space-time curvature in one opposite and with the electromagnetic process of wave in the other opposite, is visible when obtaining wave equations based on vector potentials. These vector potentials in the opposite observation system express electromagnetic components, and electromagnetic components are represented as space and time in according to SRT of Einstein in the opposite case. Intuitively, scientists tried to express this by using vector potentials through the classical Maxwell equations in the form (56). At the same time, we do not use changes in the components of fictitious currents under the influence of the rotor, as it was in equations (67) and (68), that is, we consider fictitious currents and charges as some constants characterizing the object of the universe, which form changes in the form of wave equations, and it we show below. Next, we made the substitution of equations (10) and (12) into the first equation of the system (56):

rotrotA -в0ц0 d2E/ dt2 = ц0 j;

-V2 A + grad div A +1/с2 d2A / dt2 +1/с2 d2(VO)/dt = ц0 j; V2 A -1/с2 d2 A / dt2 = 1/с2 d2(VO)/dt + grad div A-ц0 j; V2 A -1/с2 d2 A / dt2 = grad (1/ c2 dO / dt + div A)-ц0 j.

(69)

The very principle of substitution gives the interaction. In fact, this means that the equivalent of the length in the form of H by formula (10) has acquired closed circuit significance during substitution. Physically, this means the rotation of the object in medium of space. Since the expressions of H and E are uniquely related to the vector potential of the A and we get the expression (69). Next, a condition is imposed (Lo-rentz calibration):

1/c 2 dO / dt + div A = 0. (70)

It should be noted here that condition (70) is the opposite of condition (12), because in one case, in (12), we get the significance of the electric field strength E, and in variant (70), when the differentiation variables replacement, the sum is zero. In other words, from the point of view of physics, this is the irreversibility of the process when it comes to transformation according to the scheme: A ^O, O^ A. That is, it means that

the objects inside the universe are always in the dynamics of a change in synthesis or decay, which excludes the complete isolation of the object. In addition, this can be perceived as the fact that the replacement of variables of differentiation lead to a change in the observation system, because, in global opposites the time is being changed onto length, and length is being changed onto significance of time due to the connection of systems through the speed of light (the condition of rest in one system is perceived as movement in another system, due to the principle of relativity). In this case, summation in one opposite looks like subtraction in the other opposite. Thus, even before us, physicists intuitively introduced two systems of observation from op-posites.

Hence, on base of the account of formula (70), we obtain the vector equation of Dalembert for forced radiation:

V2 A -1/с2 d2A / dt2 =-ц0 j.

(71)

With respect to based on (12) and (70) and the fourth equation in (68), we obtain:

div(-d A / dt-VO) = p / s0;

- (d (divA)/dt - divVO = p/s0;

(72)

V2O-1/с2 d2O/dt2 =-p/s0.

vacuum at using operators of absorption and emission for virtual photons [18]. In other words, physicists intuitively came to the need to describe the emission and absorption of electromagnetic waves in the space-time continuum. However, the difference with our concept is that instead of some kind of electromagnetic vacuum, opposites in the form of length and time (they have representation of density of current and charge) act as a source and absorber, obeying Lorentz transformations in accordance with SRT and GRT. At the same time, we recall that Louis De Broglie, according to (21) and (27), has already linked the need for wave processes and this cannot be without electromagnetic radiation and absorption at condition of the preserving of the particle) with mass, and we have shown above by (22) that mass is inversely proportional to velocity, and hence has connection with length and time. In other words, space and time have the same properties as particles, otherwise it would be necessary to find some new laws of physics, in addition to the existing ones, on the connection of space and time with particles, but the common electromagnetic and space-time continuum excludes this. That is why in classical electrodynamics, charges and currents in a vacuum mean fictitious

charges and currents, that is j = jfc

p = pfc. Ac-

j = j fc = cpfc,

Now we need to give some explanation regarding the charge density and current, as there are no ordinary currents and charges in a vacuum (hence we have the name in the form of fictitious currents and charges), but the source of the electromagnetic field is necessary. Actually, the need for this is connected with the presence of electromagnetic waves in medium of space with the subordination of their distribution to the Planck formula [17]. And such presence of electromagnetic waves in medium of space has been interpreted in quantum mechanics as the existence of an electromagnetic

cordingly, these magnitudes

p = pfc can characterize the original significances of space and time, as nothing else is observed in the so-called vacuum besides space and time and electromagnetic components. Hence we accept, in accordance with Dirac's theory [19], p = q = ±1, as otherwise the Einstein energy equation would have to depend on the magnitude of the charge. In other words, in contrast to the idea of Murray Gellman, we reject the presence of quarks and gluons due to the fact that the significances of fractional charges of the form 2/3 and 1/3 contradict the law of conservation of quantity according to the Einstein energy formula. Actually, the physical essence of the charge itself is related not to the magnitude, but with case of radiation and absorption of elementary objects of the universe, described by the improved Maxwell equations, and reflecting the change (movement) of one opposite relative to another opposite, and it is being detected through the laws of Faraday and Bio-Savard. As we have already noted above, taking into account the unambiguous relationship of the initial length and time in the Minkowski geometry, in accordance with the SRT in the form of r = ct, and the implementation of the invariant form, we have a fictitious density of current. Further, we take into account that condition of equality in equation (71) and in the last equation (72), in the form of a constant magnitude there cannot be, as we have a wave form, which, under the

law of conservation of quantity, has the change in cur- the right in the form of the same function, which can be

rent time. It is clear that equality will be only if the re- deleted.

sults of differentiation do not affect the function itself, Hence, we obtain a system of wave equations with

and there will be the same member on the left and on respect to vector potentials in the form:

V2 A -1/c2 d2A / dt2 =-|0 j =-|0cp =-|0cO =-|0 c 2A = -A / s0;

9 9 9 9 (73)

V2O-1/c2 d2O/dt2 =-p/s0 = -O/s0.

divB = pMfc; D = S0E; B = 10H; S0I0 = 1/c2.

In fact, in the presence of only fictitious electric noted in electrodynamics as the principle of reciprocity

currents and charges, we have a representation of only and equivalence. And we use for the derivation of

one opposite in wave form. However, any object of the forced radiation in the presence of magnetic fictitious

universe consists of two opposites, so we cannot ne- currents the equations of the form: glect fictitious magnetic charges and currents, and it is

rotH = dD/ dt; rotE = -dB / dt - ^; divD = 0; jH = jMf'c = cpMfic;

(74)

-0E; B = 10H; s0i0 =1/c2.

In this case, magnetic vector potentials [26] are introduced in the form:

D = rot A M. (75)

H = VO M + d A M / dt. (76)

Next, a substitution is made in the second equation of the system (74) through equations (10) and (12): rotrotAM -s0|0 d2H/ dt2 =-s0 jMfic;

-V2 A m + grad div A m +1/c2 d2 A m / dt2 +1/c2 d 2(VO m )/dt = -S0 jj""-

V2 A m -1 / c2 d2 A m / dt2 = grad div A m +1 / c2 d2 (VO m ) / dt + s 0 jMfc;

V2 A m -1/ c2 d2 A m / dt2 = grad(1/ c2 dO m / dt + div A m ) + S0 jMfc. Then the condition (Lorentz calibration) is imposed:

(1/c2 dOM / dt + div A M) = 0. (78) Based on the account of (78), we obtain the Dalembert vector equation for forced radiation:

V2 Am -1 /c2 d2AM /dt2 = S0 jMfic = S0 c2AM = AM /IV (79) With respect to ®m, we get:

(77)

div (dAm / dt + VOm ) = pMfc /10;

d(divA m )/dt + divVOM =pMfc /1>;

V2Om -1/c2 d2OM /dt2 =pMfc/10 = Om /10;

|0(V2Om -1/c2 d2OM /dt2) = OM.

(80)

Thus, we have obtained that the opposites of universe, reflecting the object of the universe in the spacetime curvature (vacuum), are determined by the significances of the constants of electric and magnetic permeability, and at the same time the opposites have an inversely proportional relationship, because cs0c|0 = 1 = const, with AAm=1. In other words, the excitation of electromagnetic waves, where the vector potentials are acting as electric and magnetic components, is determined only by the parameters of the medium in the form of constants of electric and magnetic permeability, which, as will be seen later, are associated with the average kinetic energy in the opposite system (in non-existence). In this case, in (73) and (80), in comparison with the wave equations based on the classical Maxwell equations, where there are no sources of wave occurrence (and this means independent motion without the presence of secondary waves), the paradox of the presence of the wave behind an obstacle is solved. Moreover, in the absence of sources, the wave equations for electric and magnetic components have

no connection, and it is not observed in practice.

Accordingly, radiation in one opposite means absorption in the other opposite, which is determined by the signs of functions ® and , and a closed circular exchange process, means the immutability of space and time with subordination to the Planck radiation formula. An attentive reader will notice that we have also improved the wave equations with forced radiation with respect to ® and . In fact, we have received a representation of the Louis de Broglie formula, if we assume that the magnitudes of the constants of electric and magnetic permeability reflect the space-time curvature in two opposites from space and time in accordance with Einstein's GRT, and the electromagnetic wave process formed by this curvature is considered in system of the opposite. Indeed, for the solution of the equations in (73) and (80) are being used functions of the form:

O(t, r) = exp{i [ct ± (r + r / s01/2)]};

^9 (81)

Om (t, r ) = exp{i [(ct + ct /10 ) ± r]}.

Here the frequency is related to the significances of the constants of electrical and magnetic permeability.

Comparing equations (71), (72) and (73), (80), we see that in the left side from the sign of equality are the wave equations, but in the right side from the sign of equality in equations (71), (72) are the improved Maxwell equations, which, as will be shown later in next articles of this journal, characterize the electronic neutrinos and muonic neutrinos (antineutrinos), and in equations (73), (80) the significances of fictitious electric and magnetic charges (of currents) are being characterized by the condition of the medium through the constants of electric and magnetic permeability taking into account the same representation of wave functions. Since wave processes in a vacuum have only one physical nature associated with electromagnetic phenomena, we can make an equalization of the right parts of the our equations, taking into account the fact that phenomena in opposites are considered on the left and on the right, where static condition in one opposite is formed due to the dynamics of the fulfillment of Faraday's laws and Bio-Savard in the other opposite. At the same time, we will consider electromagnetic processes to exist in equations (73), (80). Given (73), (80), we can replace the wave equations in (71) and (72) by the equivalent of the wave function. Then the form of the equations (71) and (72) can be represented as:

H/s0 = ic grad A + dA/dt -1/s0 rot®;

(8

E/= ic grad® + S®/St +1/roiA.

The principle of equating the parts of equations is also not our invention and was done by Feynman during the transition from the usual Maxwell equations to

wave equations. It is clear that the type of wave functions in the left side and in right side from sign of equality cannot differ in any way (since otherwise there will be no equality), and the difference can only be by the coefficient of normalization. Actually, this is a necessary condition for symmetry between opposites in compliance with the law of conservation of quantity. Also, in the left part from the sign of equality, it is necessary to take into account belonging to the opposite through an imaginary unit, with normalization and presentation in the opposite with multiplication on the speed of light. This multiplication of member of function on an imaginary unit was also not invented by us, it was actually introduced by Dirac in his system of equations derived from the invariant form of Einstein's energy, as will be seen later in [12] in account of multiplying these equations on /'=(-1)1/2. In this case, we have equalities in the form:

is ® / sn = ic grad A + dA/dt -1/sn rot®;

0 0 (83)

igA/= ic grad® + S®/St +1/^0rotA.

He significances of sand g are being determined due to normalization in the system of equation of Dirac. It is clear that all mathematics must have a physical meaning, and it manifests itself in the fact that the space-time continuum has a connection with the electromagnetic continuum at exchange. It should be noted that we do everything in accordance with the equations of classical electrodynamics, and therefore the form (82) is similar to the form obtained in the complex representation using vector potentials in classical electrodynamics [20]:

m .

V2E + k E = -M3; V2H + kH = -M

- M3 = -i©|a0 j3_CT + 1/(i©s0)graddiv j3_CT - rot jM_

- MM = -i©s0jM_CT + 1/(i©|a0)graddiv jM_CT - rot j3

(84)

The difference in the results in (82) and (84) is that at obtaining the members of the form graddiv j , the

Lorentz calibration was used in representation:

3_CT

divj3_CT=-s0a<p _ /st=-cs0a<p3_CT/d(ct)=-cs0a<p3_CT/ Sr.

When differentiating the complex form in current time, we have:

3_CT

1/(i©s 0) div j =-93_CT And this formula was substituted into the equation:

• O' 3_CT 3_CT 3_CT

M =-grad-^05j_ /St = -grad-i©^0j .

(85)

(86) (87)

At the same time, differentiation in current time is removed by multiplication by © , but differentiation by coordinates of lengths is left and thereby the unambiguous relationship between length and time is removed, and it is incorrect and contradicts SRT and GRT. In fact, here the relationship between the significances of

j3_CT and 93_CT is replaced through the equality of changes in length and time, at a new connection, when the change in length of j3_CT is not equal to the change in 93-CT in current time, but is equal to the value of 93_CT, taking into account some normalization coeffi-

cient. In other words, the equation of continuity is replaced by the equation of decay or synthesis, and this is another level of hierarchy in the universe. As a result, it turns out that the magnitudes of and can coincide in the direction of motion, and this contradicts the principle of the formation of electromagnetic components from them that are perpendicular to each other. If we take into account one-to-one transformations with equal increment changes by (85), then integrating both parts of the equation into (85) along the length r = ct will give the ratio:

1/(cs0)j3 CT = 1/(cs0)cp3_CT = -93_CT. (88) That is, we have a correspondence with a fictitious

charge according to the formula (59). In other words, we used the Feynman approach when he introduced the changing through differentiating one equation (54) in current time, and of the other equation (50) in length to obtain the same magnitudes in the left parts from sign of equality of these equations (50) and (54) for the wave equation (55), but we applied integration instead differentiation in account of the law of conservation of quantity. It is clear that here there can be no jumps due to constant magnitude of integration, since equal changes give the same increase in magnitudes, but the initial quantitative difference due to constant integration would correspond to the miracle of the emergence of this difference from nothing. The ratio (88) is similar to the equation for vector potentials in (14) according to the formula:

A 3_CT = (v / c2) 0 = 0 /(csnp). (89)

And here we have the difference, because in (89) the vector potentials are being connected with our observation system, as the magnitude of the velocity v relate to the significance of the moving charge, but we are considering the option without charges in vacuum, and here the fictitious currents refer to charges in the opposite observation system associated with our system through the speed of light. That is, we associate in (88) education s0 due to movement in the opposite system.

Accordingly, we can replace the value 93-CT through vV^ 3

the value j3-CT, then:

M 3 = 1/(cSo)grad j3_CT j3

7 dt. 0)

(9

Recall that for vacuum the significances s0 and 10 take into account the condition of space-time curvature. Now we take into account that the projection of vector potentials for time [8] multiplied by an imaginary unit was introduced in [9] as:

i0 = A4; Ax = Ai; Ay = A2; Az = A3. (9 y 1)

And the magnitudes ^3-CT and j3_CT, as opposites, have exactly the same relationship as the vector potentials. Then, this dependence, in account of an imaginary unit, is being spread to completely equivalent values

93-CT and j3_CT. In this case, in accordance with [20], we have:

M3 = i /(cso)grad j3_CT-|od j3_CT / dt = = i(c|o)grad j3_CT -|od j3_CT / dt;

(92)

M-CT- M3 = M3 + M.

M 3" = - rot j

It is clear that in our case, for the first equation in (92), we have a complete coincidence of the changes in length with the change in current time with the fulfillment of the law of conservation of quantity. For a complete coincidence of records (83) and (92), you need to write:

Similarly:

iM3 = i /(cso ) grad j3 CT - |od j3 CT / dt - rot jM

1/(c|o)div jM_CT = -dqM_cm / d(ct ),1/(c|o) jM_CT = -9M-CT;

MM' = i /(c|o)grad jM_CT-sod jM_CT / dt;

(93)

MM' = rotj3_CT; MM = MMM + MMM"; iMM = i /(c|o)grad jM_CT -sod jM_CT / dt + rot j3

(94)

i / |o M 3 = ic grad j3_CT-d j3_CT / dt -1/|o rot jM_CT; i / so MMM = ic grad jM_CT -d jM_CT / dt +1/ sorot j3_CT; i / |o M3 - ic grad j3_CT = -d j3_CT / dt -1/|o rot jM_CT; i / so MMM - ic grad jM_CT = -d jM_CT / dt +1/ so rot j3_CT; i / |o (V2E -1/ c2 d2E/dt2) - ic grad j3_CT = -d j3_CT / dt -1/ |o rot jM i / s0 (V2 H -1/ c2 d 2H/dt2) - ic grad jM_CT = -d jM_CT / dt +1/ s0 rot j3

(95)

From the third and fourth equations in (95) it can be seen that the usual Maxwell equations reflect the type of changes only in one opposite, but in the other opposite we get the equivalent of these changes in the

form of some fictitious static charges MM3 and MM, as in (56) and (74) with the only difference that the divergence is replaced by a gradient along one coordinate, since all changes in length that give divergence in one opposite are converted into a change in current time represented in the equivalent of length in the other opposite in according to Einstein's SRT. Otherwise, it would exclude the connection of space and time. The

last two equations in (95) say that, since changes in currents in current time coincide with changes in space according to the continuity equation, then in fact a closed change by the rotor in one opposite is equivalent to rectilinear propagation of wave in the other opposite. In other words, we see what a closed circular line of force in our observation system, in system of contrast, is displayed as a wave with direct motion.

The attentive reader sees that all our transformations in mathematics completely coincide with what was previously done before us and the only difference is that we consider processes from the point of view of opposites based on corpuscular-wave properties, where

electromagnetic properties in one opposite describe the space-time curvature in the other opposite. At the same time, the need to invent some fictitious currents disappears. Actually, the vector potentials can be changed to electromagnetic components, and it will mean a transition into the opposite observation system. Further, we take into account that the view of vector record (83) does not allow us to identify the orthogonally of the A and Ф, and respectively, the components E and H. Hence, it is necessary to image the components by significances of coordinates, and at the same time, the need for a projection of the electro-magnetic components onto magnitude of time is revealed, as all orthogonal components of projections to length coordinates are already used in the usual Maxwell equations and only the projection onto significance of time remains, and this is being done in (17).

Thus, we have shown that elementary objects expressed through Faraday's law (this is the Bio-Savard law in contrast system), at interacting, what is reflected through substituting of some equations by other equations with introducing of changes through the rotor, allow us to obtain the electromagnetic properties of wave in one opposite, and to obtain the corpuscular properties in the other opposite through a sources of radiation or absorption.

It is clear that new objects obtained through interaction, in order to exclude independence from our universe, must also obey the general formula of the universe, the equivalent of which is the Einstein energy equation, due to the invariant form. Hence Dirac's intuitive attempt to decompose the Einstein energy equation according to (36) into simple equations of the form (83) on the connection of corpuscular and wave properties has a logical justification.

The conclusions:

1) The improved equations of Maxwell (17) helped to solve the paradox between the ordinary Maxwell equations (4 and 6) and the equation of the Umov-Poiting (9).

2) Formula Louis de Broglie (23) on the relationship of the wavelength and the magnitude of the impulse is a direct consequence of the General formula of the universe (2) on the basis of equality of arguments of opposites in exponential functions. The Louis de Broglie function reflects the electromagnetic components in the opposite observation system with the connection of frequency and speed of movement at closed exchange.

3) On the basis of our theory, the paradoxes of the derivation of wave equations are resolved. This is done through replacing of usual equations of Maxwell by improved equations of Maxwell, which give closed symmetric solutions.

4) It is shown that the existence of an electromagnetic wave behind an obstacle is determined by the parameters of the electric and magnetic permeability, which characterize the sources of secondary excitation and have relationship with kinetic energy in system of opposite.

5) It is determined that all our conclusions are based on solutions already obtained earlier in electrodynamics with the removal of errors in transformations and taking into account the particle-wave dualism. In

other words, it was only necessary to correctly determine the principle of the interaction of opposites on the basis of the formulas already obtained.

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