THE PARADOXES OF MATHEMATICS IN THE LAWS PHYSICS AND SOLUTION OF CONTRADICTIONS BETWEEN SRT AND GRT OF EINSTEIN Текст научной статьи по специальности «Математика»

THE PARADOXES OF MATHEMATICS IN THE LAWS PHYSICS AND SOLUTION OF CONTRADICTIONS BETWEEN SRT AND GRT OF EINSTEIN

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 basic laws that ensure the equality of global opposites. We will show the predominant role of the laws of physics in comparison with mathematical laws. We will reveal the essence of the contradictions between Einstein's special and general theories of relativity as contrast systems, and indicate the way to solve the paradoxes between them. We will determine the rest mass of the particles through the curvature of space-time in accordance with Einstein's special and general theory of relativity. At the same time, for Einstein's GRT, we take the speed of movement from the opposite observation system, and not from the system where the curvature is considered and will proof this fact. This leads to the conclusion, that the mass of rest has not a representation from the point of view of matter, and hence Einstein's equationfor gravitational field is not a reliable reflection of phenomena in the universe.

Keywords: Einstein SRT and GRT, equations of the Dirac and Schrodinger, Klein-Gordon's equation, Einstein's equation for gravitational field.

Definition of the basic laws of the universe in dynamic interaction

Here we continue to develop the laws of the universe, which we considered in [1], that is, in the previous number of this journal in the section of physics and mathematics. Considering that the number of objects, both in system of existence and in system of non-existence - is a constant magnitude (although this number has a sufficiently large value), then, representing being as a single object, we can give it a mathematical value of unity {1} due to normalization. The representation of non-existence as a single object should also be represented as a mathematical value of unit, however, in order to distinguish it from being, it must be attributed an attribute that would not allow it to be confused with being.

Using well-known mathematical analogs, we will attribute to it the attribute of the imaginary unit {i=(-1)1/2} (we will give an explanation a little later based on the interaction of opposites). Given the equality of the opposites of systems of existence and non-existence, this means that:

1 = i. (1)

0 0 0 1 0 0 0 -i

A ! = 0 0 1 0 0 1 0 0 A 2 = 0 0 0 - i i 0 0 0 A 3

1 0 0 0 i 0 0 0

From here, we get the well-known equations, which are obtained from the system of Dirac's equations:

(E -M0c2) -c(Px -iPy) -cPz = 0; (E - M 0c2 ) - c(Px + iPy ) + cPz = 0; (4) (E + Moc2) - c(Px - iPy ) - cPz = 0;

Thanks to this notation, zeroing of variables in article [1] (formula (4): ZXj = Z^,=const) is impossible and the only operations between opposites are multiplication and division.

Such a record seems incompetent to most mathematicians who are accustomed to squaring equalities, but the fact is that the squaring operation does not exist in the universe, due to the fact that then the object would have to change its parameters trough the jump with the break without the interaction of opposites. This means a complete separation of corpuscular and wave properties. At the same time, in physics, such equality (1) has been used since the time of deriving the equations of the Dirac and Schrodinger. Thus, the decomposition of the invariant form of energy in the form of matrices is used to obtain accounting for magnetic spins (according to physicists) and the connection of corpuscular and wave motion according to the formula [2]:

E = c( P2 + Mo2)1'2 = c(Z A Pk ). (2)

k

Here, k varies from 0 to 3; Po=Moc; Pi =PX; P2=Py, P3 =Pz. Hence, from this record when using matrices for decomposition (2) we have: 0 0 1 0 1 0 0 0

0 0 0-1 0 1 0 0

A = . (3)

1 0 0 0 4 0 0 -1 0 ( )

0 -1 0 0 0 0 0 -1

(E+M 0c 2) - c( Px + iPy ) + cPz = 0.

It can be seen that if we move the imaginary component of the equation to the right side of the equation, and are left all the real components in the left part, then, in accordance with the equation, the real part will equal the imaginary, i.e. a=ib, while a=b, and i = V-T . It is

also clear that there can be no zero variant of magnitudes here, because the variants of zero energies and impulses are not considered in physics, since zero energy is nothing.

Naturally, the using of differential operators instead of energy and an impulse does not affect equality, and static magnitudes of equality are being replaced by the corresponding magnitudes of regularities through the dynamics interconnection that give this equality not at a specific time and at the point of space, but in a certain area of this space and in a certain period of time at the change (at motion). The highlight of Dirac's mathematics is that he actually introduced the interaction of opposites using their initial equality, and then introduced the differentiation of this equality to get the dynamics of interaction, and it allowed him to determine, as he thought, the magnetic spin of the electron.

It should be noted that attempts to obtain the magnetic spin in the Klein-Gordon's equation by squaring of the formula (2) gave not the desired result. And the only difference in the methods of obtaining the KleinGordon and Dirac equations from formula (2) is that in the Dirac "linearization" method, an imaginary member of the equation is being obtained, but when we have squaring of the formula (2), an imaginary member simply cannot be. Realizing this difference and in order to avoid the obvious equality of 1 =i, scientists got out of the situation by presenting the magnitudes of impulses and energy without proofs in the form of differential operators acting on probabilistic wave functions. And it is obvious miracles, because the real numbers in the formula (2) are replaced by operators that do not have certain numerical magnitudes at probabilistic wave functions. The laws of the physics are absent.

In addition, in order for the probability to be wavelike, a real force of regularity is needed, and this force gives a wave view, i.e., law (we see, contradictions with probability already arise), but of the force at presence of probability does not exist. At the same time, we note that a member with a rest mass was not replaced by a differential operator, Dirac left unchanged rest mass. Such a difference from the point of view of mathematics is generally unacceptable, because a member with a rest mass as a constant magnitude in this case must be zero at differentiating, or it must also be a differential operator.

In other words, avoiding the equality of imaginary and real numbers gave three paradoxes in one equation at once! It should also be noted that if changes at differentiation did not require equality of real and imaginary magnitude, in account of their mutual transition in view of the opposites, then multiplication of the differential operator of impulse onto an imaginary unit has not the need, since equality from changes in real numbers suffice. Actually, it was impossible the excluding of the equality of imaginary and real numbers, and it was introduced into quantum mechanics in the form of equality [3]:

x4 = ict. (5)

And this equality also turns into equality of formula (1) when is being normalized to the unit. It is clear that the obtained equality of imaginary and real magni-

tudes reflecting opposites with the replacement of summation by subtraction forces us to take a fresh look at the rules of mathematics and consider them in order to exclude paradoxes that do not correspond to physics.

Abstraction of mathematics, which gives paradoxes in physics

The paradox of modern arithmetic is that arithmetic considers processes from the point of view of one opposite. In this case, the magnitudes of real and imaginary numbers are not being intersected. And this justifies itself if, for example, there is some summation of identical objects without the transition of quantity to quality and with the simplification of interaction processes. Indeed, if we had one apple, and this apple is eaten, then we say that we haven't of apples, at subtraction one minus one, we have zero. Hence, people say, there was an apple - and there is no apple, and this fact naturally cannot be refuted. Here the fact is that with this approach, the apple, as a real object, turned into zero, and with it, the energy corresponding to this apple became zero, but it is this energy of eaten apple that gives us the opportunity to have moving. Here, the law of conservation of energy is not observed in mathematics, since we omit the process of converting an apple into something else. We simply consider the very fact of presence or absence, and we are not interested in methods of transformations which were at the time of occurrence or disappearance. Therefore, there is no zero in our universe, because there is no way to interact with zero. In the universe, nothing disappears from a closed system, and the transformation of an apple is considered as a transition from a corpuscular magnitude (potential energy) to a wave magnitude (kinetic energy). At the same time, how many units of regularities were in the apple in accordance with the presence of the Planck constant, in representation of discrete magnitude, such quantity had remained - only they come into another opposite due to the isolation of the universe. The presence of an imaginary component in the Dirac's equations is not accidental, because if we had only real parts, then we would have to admit the idea that there are no opposites, i.e. there is no particle-wave dualism. In other words, equality without an imaginary component means the possibility of full compensation, i.e. complete disappearance, as in the example with the apple, and naturally without the law of conservation of energy. Note that if we assume the possibility of energy compensation, for example, during process of subtraction and overlapping, due to the fact that there are only real components or only imaginary components in equality, and that such similar components can always give zero at subtraction, then we must consider the complete disappearance of our universe possible due to compliance with the laws of arithmetic (in accordance with the formula (4) in [1]). And this, in principle, means miracles, because if it is possible to have the disappearing into zero, then this, accordingly, means the possibility of something appearing out of nothing spontaneously, and without observing laws. Our theory, with its equality of the real and imaginary parts, excludes such a possibility of compensation.

In general, the dispute between physicists and

mathematicians, which science is more rigorous, is going on for a long time. Should mathematics reflect the logic of physics or, conversely, should physics strictly follow the logic of mathematics? It would seem that mathematics is a strict science, which is building on obvious axioms or postulation, and therefore physics should obey the logic of mathematics. But this variant is not here. It turned out that mathematics used abstract things as axioms or postulation that are obvious only at first glance. For example, space and time were considered as absolute and independent magnitudes (Euclidean geometry). Therefore, in the function of a complex variable, the imaginary and real parts were independent as orthogonal components. But what did real physics show? And physics showed that the presence of an absolute concept of space and time means that none of the coordinates of length and magnitude of time can be connected to each other because of orthogonally, i.e. an open system that gives infinity excludes the concept of unity and struggle of opposites in general and the existence of opposites also, because independent quantities do not exist for each other, and any object must disintegrate.

From here the conclusion: if objects in our world are somehow connected by coordinates through the length and time and form a single whole, then our system of the universe cannot be open. And then one option - it is closed (isolation) system.

Our previous arguments have shown this conclusion. This was confirmed by SRT and Einstein's GRT with their transformations of coordinates lengths into magnitude of time and vice versa. But since our system of the universe is closed due to the paradox of an open system, it means that universe cannot interact with anything external, and has the magnitude of a constant size, but it is not zero. But the presence of a uniformity of constant magnitude, displayed as, for example, only real numbers or only imaginary numbers reflecting the quantity, will mean that no changes and transformations within this constant magnitude simply cannot exist. For real or imaginary numbers can only pass into themselves, and according to the axiom of closed system, their number is invariable. In this case, the constants of imaginary and real numbers are completely independent and do not exist for each other. Here we have a paradox, according to which the condition of uniting is not fulfilled when all quantitative changes are being defined only by their transformations in itself. Indeed, if the number five has being changed back to the number five, then what is this change expressed in? Hence, the transition in the opposite is absent! The presence of only real magnitude or only of imaginary magnitude in a closed system will indicate the presence of only one opposite in the world, and it does not correspond to the concept of a corpuscular-wave dualism. It is impossible to define anything! Hence, there is only one single solution - a closed universe consists of two equal oppo-sites, it is real and imaginary numbers in mathematics, since mathematics does not know other opposite numbers. And imaginary magnitude counteracts at transformation previous real member in account of subtraction. The isolation of universe requires their equality, because the transformation of one opposite into another

opposite without an equivalent inverse transformation means getting one opposite with the paradoxes in the result. Therefore, time and coordinate (length) are converted into each other in equal amounts into Einstein's SRT. The representation of the law of opposites is embedded in an invariant energy form, which follows from SRT. And the invariant form of energy reflects the law of conservation, i.e. the equal transformation of opposites, and Dirac noticed this fact, using the decomposition of the invariant energy form into components in the form of his equations. Of these equations, the equality of the real and imaginary parts, as well as the need for their mutual transformation, are being obtained automatically and appear explicitly.

Decomposition of invariant energy relation of Einstein into a system of equations is actually connected with the principle of accordance of each object of the universe to corpuscular-wave properties. At the same time, Dirac used an approach similar to that used by Schrodinger, he equated imaginary and real components for the combining of corpuscular and wave properties. So, he presented impulses along three coordinates and energy as differential operators from some 4-probability wave functions, instead of one probability wave function of Schrodinger. Dirac's differential operators in magnitude of time and length have the same order of changing, and it actually means that changes in magnitude of time are equal to changes in length in accordance with Einstein's SRT. However, Dirac left the mass of rest unchanged and simply multiplied mass of rest on probabilistic wave functions, because the differential from constant of the mass of rest will give zero, and then it will be impossible to return to the Einstein energy equation from the Dirac's system of equations. In other words, Dirac showed through wave representation the Einstein's energy equation with the using of a system of equations (actually of objects), and here at introducing of one equation instead of functions of variables of another equation, which means the interaction of objects, we have the Einstein energy equation multiplied by one of the 4 probabilistic wave functions, which is being deleted. It is clear that he chose the signs of the differential operators, as well as the presence of an imaginary unit in one of them, for the transition to the Einstein energy equation purely intuitively. But this also has a logical explanation, if we accept the results of the conclusions of our theory, when the same equation, which is actually a reflection of an object, is viewed from the position of an observer who is in two opposites alternately with the replacement of summation by subtraction, and vice versa.

In other words, we have established, the mathematics, according to the logic of Euclid's geometry, takes into account quantitative changes, but does not consider qualitative changes. Indeed, in mathematics, a linear change can occur until infinity, but in physics this means a violation of the invariant form and closed system. This is precisely what mathematicians cannot understand, although this logic of the necessity of a closed system is mathematically confirmed. The solution to the paradox of the transition of quantity to a new quality is again connected with the assignment of an imaginary unit attribute to quantity (what characterizes the change

in quantity in account of transition into opposite, since otherwise quantity would remain unchanged), and we will show this variant in more detail below. The next contradiction in mathematics was connected with the appearance of constants during integration, and their zeroing during differentiation, that is, in fact, it meant the emergence of objects from zero and also their disappearance into zero. That is, the quantity arises from zero and also disappears in zero. However, the transition to the opposite of quantity in the form of a constant magnitude multiplied by an imaginary unit solves this problem in result. In addition, it is necessary to take into account the fact that if in mathematics the permutation of the variables of differentiation and integration does not affect the result, then in physics such a permutation means a change in the hierarchy system and, accordingly, in the observation system, which affects the type of laws, and hence the result. This follows from the inversely proportional relationship of opposites, and because of the need of the presence for constants in the speed of light and a minimum discrete value in the form of Planck's constant. That is, we have, as it were, the presence of a «cake with much layers ", and the permutation of variables leads to a change in the hierarchy level. The real fact of changes due to the permutation of differentiation variables is fixed in physics for vector potentials taking into account the Lorentz calibration. So mathematicians' failure to take into account elementary logic that the world is based on the need for the interaction of opposites that are orthogonal only in abstraction led to incorrect conclusions. Our merit lies only in the fact that we were able to show the logic of the proof of the equality of the imaginary and real parts according to the Dirac' s equations and the need for their mutual transformation, without which the opposites would be completely independent. Thus, the formula (1) is a representation in mathematics of the law of op-posites, and equality reflects their equal interaction by exchange, simultaneously the law of conservation of quantity is observed. It is clear that the inequality of the real and imaginary parts would mean that one opposite dominates up the other opposite in the exchange, and as a result, the imaginary or real part would have to disappear. In addition, the initial quantitative inequality means the possibility of the existence of only one opposite and its complete independence. This would mean the negation of the law of opposites and the possibility of miracles with arising anything from zero! The presence of one opposite without an inversely proportional relationship with the other opposite would mean that it would be completely impossible to provide function of amplification of force ( of amplifier) due to the representation of the object only in the form of one quantity. And one quantity would mean only one kind of energy and force. This means that the maximum result that can be obtained in this case is compensation of the same forces. It is clear that a world without opposites contradicts the actually observed practice. Note that in mathematics, the transfer of members from the right side of the equation to the left, and vice versa, with multiplication and division by the same members of equation does not lead to a change in the original laws in the equation.

In physics, such operations, taking into account the existence of the hierarchy of the universe, the transition of quantity into quality and the inversely proportional relationship of opposites, lead to a change in the initial interaction and the place of observation of the process. At the same time, the initial laws of members of the equation may also change. Thus, physics, taking into account the laws of the universe, occupies a dominant position in relation to mathematics.

The formulas for the relationship of opposites

Now we will describe the relationship of opposites from simple operations by quantitative magnitudes. As we know, any changes are expressed either by summation or subtraction. Since systems of existence and nonexistence in presentation of regularities (of objects) exist in the universe eternally, the processes of change which are being carried out by them are mathematically expressed through integration (infinite summation) or differentiation (infinite subtraction). Considering that the systems of existence and non-existence is a closed system of universe, in this case integration and differentiation appear as a direction of movement, and it is obvious that a decrease of quantity in system of existence unambiguously means an increase (addition) of quantity in non-existence, and vice versa. It is clear that such a perception of integration and differentiation should be practically confirmed, and we have this confirmation certainly. The assumption that differentiation and integration of magnitudes, in the conditions of the closed universe, can be considered as directions of movement follows, again, from the using of SRT and GRT Einstein. The Einstein, by virtue of postulation about the constancy of the speed of light, actually legitimized the existence of two opposites in presentation of systems of existence and non-existence, in view of systems with their own space-time relations, where, as a result of movement, quantitative changes occur between these systems. At the same time, any object is being expressed as a vector on a four-dimensional sphere and describes movement along the sphere in accordance with the invariant shape and parameters of quantitative changes. As you know, all operations of integral and differential are associated with quantitative changes, so there are no other space-time systems ex-ceptthan systems of existence and non-existence (this was proved above).

Thus we haveconclusion: the changes of any object can be characterized in the form of a direction of movement.

Indeed, no matter what changes are carried out, it is impossible to go beyond the closed system of the universe, i.e. integration and differentiation cannot be considered as a direction of movement only in case of open system. But, since integration and differentiation reflect changes, they connect two opposite systems closed into each other, and this indicates obvious direction of movement, for example, from system of existence to non-existence, and vice versa. Considering that the existence of opposites is mathematically expressed through the existence of real and imaginary numbers, and based on the proofs given above, we can say that integration and differentiation should reflect this tran-

sition by virtue of the necessary attribute indicating belonging. Such an attribute is an imaginary unit. The absence of this attribute would indicate that the changes do not cause a transition to the opposite, and this would mean that a corpuscle by the magnitude of the size two has the transition through the jump into a corpuscle by the magnitude of the size three separately from the wave representation. A leap is always the presence of a gap (of break) and miracles, which, by the way, are stated in modern mathematics, which does not take into account the transition of quantity into quality. In other words, in this case, interaction with wave properties is not required, and this fundamentally contradicts the wave-particle dualism - this approach generally excludes the very need for interaction through the exchange between opposites. Conventional integration also does not support a system of transition to the opposite, but we have this in real physics. This means that the variant of ordinary integration refers to the case of considering processes in one opposite, here are not interested in what is transformed in quality at changing, since summation gives objects of the same opposite. For example, the usual process of integration from a constant magnitude gives x, i.e. we have a normal calculation of the number of corpuscular objects without an interaction of corpuscular magnitude and wave. But it is impossible to explain how initial objects gave a new quality, since the process of physical change itself is omitted here. Yes, in this way we will calculate the sum of objects (associative addition), but these are all separate objects without interconnection, and in this case it would be impossible to get, for example, a new chemical element, since quantity would not give a new quality. In physics, certain energy of wave quantity for this must pass into a corpuscular view, and here we have a change in quality, and this is characterized by an attribute of belonging in the form of an imaginary unit, which gives a change of laws. Otherwise, as already mentioned, there will be jumps in magnitudes without interconnection! Therefore, in the usual version, at operation of integration, the process is considered only on the basis of the absence of the relationship of opposites. This can be done, since the quantity in opposites is preserved, but it is impossible to obtain a wave-particle dualism. Summation and subtraction in mathematics turned out to be devoid of the physical meaning of changes occurring during the accumulation or reduction of objects and at the same time did not reflect the actual physical process taking place. Note that the infinity of changes or movements is already embedded in the fact that only the changes support the existence of the universe. Therefore, we will choose integration as a pointer of motion the result of which must comply with the laws established above. At the same time, we remember that integration in one opposite means differentiation in another opposite. As already noted, due to the laws of the universe, for systems of existence and non-existence, all laws from the one contrast has influence on objects of other contrast in representation of the objects through quantitative characteristics. The transition of objects (of regularities), for example, from existence to non-existence is accompanied by their accu-

mulation inside of opposite, i.e. their summation (integration). Mathematically, the influence of non-existence onto the objects of existence can be represented as:

J dx = ix. (6)

Thus, the unification leads to the emergence of a new regularity in non-existence ix. As it was emphasized above, the change of objects of system of non-existence generates the appearance of objects of system of existence, which counteracts the former existence, otherwise the objects (regularities) become completely independent magnitude and eternal existence in one opposite is possible, which means a paradox. Therefore, according to these rules we get that:

J (ixdx) = - x2/2!. (7)

Further, for a changing new existence, we must get a new non-existence that counteracts the previous non-existence, i.e. the zeroing (death) of the previous regularity:

J (-x2 / 2! )dx = - ix3 /3!. (8)

The change of this new non-existence also leads to a new existence that counteracts the previous one:

J (-ix3 / 3! )dx =x4/4!. (9)

The result of fourfold integration corresponds to a change in the four components of existence and non-existence, each of which has its own laws. Note at once that there is some violation of the rule of the indefinite integral, in which the constant magnitude of integration must be taken into account, but the presence of a constant magnitude would mean the emergence of something out of nothing. At the same time, we assume a sequential transition from one level of the hierarchy to another, and therefore the magnitude of the constant during integration is zero.

We see that the integration function here has a direction attribute, which can be expressed as:

i = (-1)1/2. (10)

This, as noted above, is quite natural, and otherwise there is no interaction between opposites. By the way, many paradoxes related to singularities (discontinuities) in physics are based on this. One of such paradoxes is associated with distortions of space and time according to Einstein's GRT, when the space-time field is described in the form of discrete smallest homogeneous, space-time elements. The problem is that no matter how the division of elements occurs, there will always be the smallest gap between two adjacent elements, since otherwise we have a common homogeneous element. And this means that there is no connection between elements, and it is contrary to practice, since the space-time field and the object are connected, but there is no connection when we have breaks. According to our theory, the problem of discontinuities is removed as a result of mutual exchange between opposites. Therefore, the option when integration is carried out without multiplication through an imaginary unit indicates that the processes are considered only in one opposite, and this is accordingly permissible when either a purely wave or purely corpuscular process is considered. This confirms the correctness of the approach itself to the

concepts of differentiation and integration, in representation of processes by which the transition between op-posites is carried out. Thus, from the infinite change in system of existence we get the following numerical series:

In system of existence:

1 - x2/2! + x4/4! - x6/6! +...= cos(x); (11a) In system of non-existence:

ix- ix3/3! + ix5/5! -...= isin(x). (116)

Further integration by the obtained functions leads to the complete zeroing of these patterns in systems of existence and non-existence, and means the transition of these laws from non-existence to existence and vice versa. Considering that the movement between system of existence and non-existence occurs simultaneously, synchronously and bilaterally due to isolation of universe, and we have two the paths of movement which are not coincide, then we are obliged also to consider the change of system of non-existence in the direction of decrease. As already noted, opposites have the same number of objects based on the presence of the Planck constant and each object of existence has analog in an object of non-existence, otherwise there would be no opposites. The presence of synchronous motion is also explained by the fact that each object, in addition to an independent part, has a dependent part, which is considered otherwise from systems of existence and non-existence according to the principle of relativity. Therefore, similarly, from the infinite change of non-existence we get the following numerical series: In system of existence:

—x+ r73! - x5/5! +...= -sin(x); (12a)

In system of non-existence: i- ix2/2! + ix4/4! - ix6/6! +...= icos(x). (126) Here, too, further integration leads to the transition of functions from non-existence to existence and vice versa. Independence of formulas (11) and (12) from each other cannot be considered complete, due to the fact that there is only simultaneous two-way movement between systems of existence and non-existence. No regularity in the system (11) can manifest itself without the manifestation of regularity in the system (12), and vice versa. It follows from isolation of a universe. The resulting magnitudes in equations (11) and (12) correspond to the full possible set of basic functions not only in laws, but also in direction, which provide a continuous connection of existence and non-existence in dynamics. We note that no object (regularity) of existence or non-existence can be completely independent of any basic regularity, since otherwise the worldview becomes an open system.

It would seem that there are contradictions between infinite numerical series and the presence of Planck's constant, according to which the number of possible members in the universe should be finite. But this paradox is resolved by hierarchical construction, according to which the same object in different oppo-sites when viewed from different levels of the hierarchy

x0 = cos(x)X + sin(x)iX1, y0 = cos(ix)X1-sin(ix)X, x'0=ch(w)X -sh(w)X, y*=ch(w)iX +(1/i)sh(w)X, x'0=ch(w)X -sh(w)X, x'1=/y*= -ch(w)X +sh(w)X

has a different regularity. In other words, when we try to find all the cause-and-effect relationships in the movement of any object, we are not able to do this, because there are always previous interaction events that we have not taken into account. In addition, closed universe is ensured precisely due to the presence of oppo-sites, because breaks in one opposite are expressed through the magnitude of the other opposite and a constant in one opposite looks like the magnitude of motion giving continuity in the other opposite. And in motion, the object does not have an accurate location because of the continuity of movement. From here, a fleet-footed Achilles will never catch up with a leisurely turtle if the turtle is ahead of Achilles at the beginning of the movement. Therefore, having received a magnitude of an object as a discrete quantity, when considering it from the standpoint of its composition and in account of this object in representation of the highest in the hierarchy, we will already discover connections of object and its law of managing objects that are lower in the hierarchy. And so on we can do ad in-finitum, taking into account the need for the isolation of the universe and the principle that the smallest object in the hierarchy in one opposite is the biggest in the hierarchy in the other opposite. As a result, all possible laws are included in the universe, and it gives a constant magnitude. Otherwise, it would mean the absence of the isolation of the universe and the presence of miracles.

Considering the above, each of the two opposites of any object should be characterized by some magnitudes in the system of these basic functions. Let's one opposite of an object is being characterized by the value X, respectively, the other opposite of this object is characterized by the value iXi = Y, then we gets a system of equations with respect to x-objects of existence: x0 = cos(x)X + sin(x)Y, y0 = cos(x)Y- sin(x)X. (13)

The ratio (13) is a well-known formula for the rotation of the coordinate axis. In this case, this turn means a transition from existence to non-existence, and vice versa. Hence, the magnitude of the imaginary unit is also interpreted by turningi = exp(i^' 2) , which gives the orthogonality of opposites. It is clear that the transition is determined by the number of x-objects of existence transferred into non-existence.

If we now apply the principle of relativity and consider this system from non-existence with the equivalent transfer of objects from non-existence to existence, then this means not only replacing the argument of function of objects x by the argument of function w =ix, but we have another representation through the laws of the such objects also, taking into account transformations:

ch(w)=cos(ix), -sh(w)=isin(ix). (14)

In this case, we will get an object with four components in the form:

In other words, the basic functions of the decomposition of an object through sine and cosine, at the transition to the opposite, gave a decomposition through hyperbolic sine and cosine, and here we also have a representation in opposites, taking into account the imaginary unit.

That is, if we now apply the principle of relativity and consider the system (13) from non-existence, then this means not only replacing x on w =ix, but also the other representation of the objects: x"0 = ch(w)x0 - sh(w)x', x'1 = -sh(w)x0 + ch(w)x1. (16) Such coordinate transformations correspond to the Minkowski geometry and have an invariant quadratic form. If we take into account that the derivation of formulas for the Lorentz transformation also requires an invariant quadratic form [4], then if

chZ= y=(1-p2)-1/2, shZ= Py, (17)

we obtain a physical interpretation of formula (16) as a special case through the Lorentz transformations, which connect two systems moving relative to each other with a velocity v, if here the condition is got:

v/c = P = thZ. (18)

Here c is the speed of light. The assumptions made in formulas (17) and (18) are valid only from the point of view of showing the physical interpretation of formula (16), and at deriving the Lorentz-Einstein formulas; the final effect was to obtain an invariant quadratic form based on the constancy of the speed of light. In our case, on the contrary, the invariant form requires the constancy of the speed of light.

Thus, the Lorentz formulas are applicable only in the special case, since they do not fully meet the requirements of the law of opposites. The essence of the differences is that the formula (16) considers the movement with the speed of transformation of opposites into each other. According to the formulas (17) and (18), we are considering the variant of mutual displacement relative to each other of two objects with the velocity v, and not of opposites, but of objects of the same opposite. That's why A. Einstein could not describe an electromagnetic wave using Lorentz transformations. As it will be seen later in next articles of this journal, in our case, the electromagnetic components are expressed in terms of wave functions, and actually they are passing into sources of radiation and absorption in system of the opposite, and characterize by their magnitude the space-time curvature.

In this variant, motion along one of the coordinates with a velocity v is being considered, for example, along the x-axis. The velocity v in this case reflects the number of objects passing from non-existence into existence. Then x0 = ct, x1 = x. It is clear that the object is characterized here by a time interval calculated through units of the length x0 and x1. And if:

(x'0 )2 = (ch(w)x0 - sh(wy)2= =[(ch(w)x0]2-2ch(w)x0sh(w)x1+[sh(w)x1]2,

(x'1)2 =[(ch(w)^]2- (19)

2ch(w)x1sh(w)x0+[sh(w)x0]2. Then we have an invariant form:

(x0)2 - (x1)2 = (x'0)2 - (x'1)2 = const. (20)

Given that this form for each object remains invar-

iant in the system we have obtained, the conclusion follows: the sum of these forms from all objects will also be equal to a constant, which means it can be normalized to a level of unit.

Carefully analyzing equations (10) and (13), as well as taking into account the need to represent any object as a regularity, in accordance with equality (7) in [1], we can come to the following conclusion: if the sum of the magnitudes of all objects at the x0 coordinate corresponds to ch(w), and at the x1 coordinate is equal to sh(w), since otherwise there will be no closed system of the universe, then in this case we immediately get to an invariant form:

jj (x0)2 -jj (x1)2 =(chw)2 - (shw)2 = 1. (21)

1=1 <=1

If we take into account the known relations (13) to the argument of existence

w=ix , (22)

then we get the ratio

cos2 (x) + sin2 (x) = 1. (23)

Considering the functional magnitudes for existence and non-existence according to systems (11) and (12), we see that equations (13) and (16) reflect the universe in the unity of the interaction of existence and non-existence.

Thus, the dynamics of change between opposites, at the using of an imaginary unit, leads to an invariant general formula of the Universe in [1]), and it followed from the condition of mathematical equality of summation and subtraction in opposites. Let's write it out again:

[cos(x)]2 + [sin(x)]2 = (ch w)2 - (sh w)2. (24) Here, the arguments in the right and left sides of the equation differ not in magnitude, but in belonging, which leads to other opposite interpretation of functional relationships.

It should be noted that the formula (24) is evaluated by some critics not as equality, but as identity. Maybe this would be the case, if we did not take into account here the formula (22), which connects the arguments. For example, the electric and magnetic components are interconnected through Maxwell's equations, but the wave equations for the electric and magnetic components are considered separately, but this mathematical separation does not mean separation in physics.

An important conclusion follows from the obtained invariant form: if the system of existence is closed, then the system of non-existence is open (within a finite number of objects of the universe), and vice versa. This is a natural result of the law of opposites. Formula (24) reflects the logic of a closed system in which any sum and difference are unchanged, since nothing can disappear from the closed system of the universe or appear in closed system of universe because of the law of quantitative conservation, in which global opposites are always equal. Therefore, summation in one opposite means the subtraction in the other opposite, and vice versa, but the number of smallest objects in the opposites is always the same and is equal to a constant. Otherwise, it would mean miracles! The fact that the subtraction with squaring of functions for phys-

ical objects is an invariant form was known from Einstein's SRT and GRT, but the fact that the sum with squaring of functions for the same objects is also invariant is already our merit.

As noted above, formula (16) representing Minkowski geometry, and formulas (17), (18) which are representing Lorentz transformations, have invariant quadratic form. In this case, the question arises about which formulas are the truth of the universe. If we take into account that the Lorentz transformations were derived on satisfying only of the requirement of the invariant quadratic form, taking into account the interaction of two coordinate systems from one system of opposite, but the Minkowski geometry was obtained from satisfying the more global requirement of the axiom of the absence of miracles, then it is obvious that the true formulas of the universe are formulas (13) and (16). Moreover, formula (16) allows us to draw a deeper conclusion about the transformation of coordinates, associated with the fact that if the speed of transition from existence to nonexistence or vice versa is the maximum magnitude, then in direction of speed we have transformation of coordinate of length into coordinate of time, and vice versa. This does not mean that it is necessary to abandon formulas (17) and (18), since formulas (13) and (16) do not include the parameter of mutual motion of objects, and therefore for objects from one opposite (if we are taking into account their interaction) formulas (17) and (18) are simply irreplaceable. Moreover, in what follows, the connection between the Lorentz transformations and the circle formula will be shown. Coordinate transformation formulas (13) and (16) are nothing more than a reflection of the ongoing processes of changes in one common system of existence and non-existence. Formula (24) also implies another physical meaning of the geometry of Minkowski, associated with energy changes.

Physical interpretation of the formulas of the universe according to of the well-known invariant energy ratio and space-time transformations in view Einstein's SRT and Einstein's GRT

On base of the representation of one global opposite in the form of a circle equation (23), we present this formula with respect to an object in the universe in dynamics in the same opposite, where there is an interaction of opposites with magnitude of an exchange equal to the speed of light. Actually, when the object is being preserved, the dynamics of the interaction of opposite parts of the object, taking into account the observation from one selected opposite, will look normalized to the maximum magnitude of exchange (of velocity) in representation:

v2 + v12= c2=const. (25)

We will rewrite the resulting equation in other form:

V12= c2- v2. (26)

Next, we will perform the following transformations:

V12 = c2(1-v2/c2); v12/(1-v2/c2)= c2;

1/(1-v2/c2)= c2/v12;

1/[c2(1-v2/c2)]=1/v12. Then we will replace the variables and assume that

(27)

m=1/v1 , and a m0=1/c. As a result, we have:

m02/(1-v2/c2)= m 2. (28)

If we have the multiplication of both members of this equation onto the magnitude c4 (and it does not change the essence of the equation), then we get the Einstein energy formula squaring. Considering that Einstein's formula includes only two variables that give a closed system according to the circle formula, then they are opposites for each other (and it is similar to length and time, which are connected through the speed of light [4]), i.e. they can only be transformed into each other. And it follows from fact that these quantities cannot be expressed through the same form in single view, otherwise such a transformation cannot be fixed in any way due to the absence of differences between oppo-sites. Therefore, if one variable expresses the velocity v, then for the second variable we have representation in the role of mass and thus v1=1/m, and besides we are taking into account condition m0=h=1/c [1]. Thus, we determined the significance of the mass of rest of an electron (positron) through a magnitude inversely proportional to the speed of light (of exchange), and this magnitude equal the minimum discrete quantity -Planck's constant, and thereby we excluded the representation of mass outside the description through space and time. Note that the electron and positron are being preserved until annihilation, and there simply cannot be object with a rest mass less than the electron and positron. Accordingly, the representation of the magnitude (of object) depends on the system of observation in the hierarchy of the Universe with an inversely proportional relationship of opposites, which we have established in the form of a law of philosophy. It follows, that the mass of rest in one opposite is presenting the magnitude of exchange (velocity)in the other opposite, that is, in other words, as it will be understood later, the potential energy of one opposite is giving kinetic energy in the other opposite. Hence, in general, it follows that the mass of rest of an electron characterizes the magnitude of the exchange processes in an object at the speed of light in opposite system, and the kinetic energy of an electron in one system of opposite gives the added mass of rest in the other opposite system, taking into account the inversely proportional relationship.

It should also be noted that the transfer of the magnitude v2, out the left side of equation (25) from the sign of equality into the right side of equation in formula (26), is also giving a change of laws. And this means that in physics, unlike mathematics, it is not only impossible to arbitrarily do exchange of place of the variables of integration or differentiation, but also to transfer magnitudes from one part of equality to another part, because with this transfer it is necessary to take into account the change of representation in laws, taking into account the change of the place of observation.

Now we can approach the need to describe space and time in terms of Einstein's SRT and Einstein's GRT on the basis of the general formula of the universe.

We note that Einstein through the postulate about the constancy of the speed of light, actually legitimized the existence of two opposites in view of existence and non-existence as systems with their own space-time relations (of dependent and independent parts), where

quantitative changes occur between these systems as a result of movement. However, because A. Einstein did not know the principle of constructing the universe from simple to complex view according to logic on the basis of global opposites, he considered the need for the existence of SRT and GRT based on the exclusion of paradoxes in the laws of physics depending on the observation system from private object. This approach led him to contradictory conclusions, when in Einstein's SRT, motion have calculating in the relativity of two systems to each other, but in GRT it is impossible to do without an absolute system relative to which the speeds of movement will be measured. Therefore, we will first consider the general principles of Einstein's SRT and Einstein's GRT, because there is a contradiction in the used proofs, which lead to the presence of cosmological equations, black holes, teleportation, gravitational forces, nuclear forces and other alogisms. The complexity of the perception of Einstein's SRT and GRT lies in the fact that space and time are perceived by us, from life experience, as independent magnitudes. At the same time, it is assumed that there is:

1. Uniformity of space and time;

2. Isotropy of space;

3. The principle of relativity, that is, the full equality of all inertial systems of coordinates.

Indeed, mechanics convinces of the complete equality of all inertial systems, which is reflected in the well-known principle of Galileo's relativity. Galileo's principle of relativity is based on two assumptions [5]:

Time is absolute, that is, time is the uniform magnitude for all inertial systems of coordinates;

The velocities have summation as Euclidean vectors, that is, we have Euclidean space, where the object is described by three coordinates of lengths on each axis separately and independently of each other.

In this case, space and time have independence from each other. At the same time, we have three orthogonal directions for the space that are also independent of each other. From these assumptions we have the well-known Galilean transformations connecting two inertial systems of coordinates, for example, if one system has moving relative to the other system along the axis x with a velocity v, then we have the equation of motion in the form:

x=x0-vt0, y=y0, z=z0, t=t0. (29)

Accordingly, the velocities of the systems of coordinates are added and subtracted according to the orthogonal directions of coordinates. As is known, the equations of Newton's mechanics, for a closed system of material points with masses mi, with action between them of the forces Fiu(i^k), depending on relative distances, can be represented by:

Til ¿d2Ti , ,

(30)

.

Hence, we notice that the accelerations of the points, as well as the relative distances, are invariants of the Galilean transformations, since velocity is not included in the formula for the presence of forces:

(31)

As a result, the equations (30) are invariant with

respect to these transformations. However, in the case of the action of arbitrary forces, Newton's equations are only covariant (the concept of covariance will be disclosed somewhat later) with respect to the Galilean transformations and non-invariant forces should be considered as external, that is, a mechanical system cannot be considered closed.

As for the Maxwell-Lorentz electrodynamics equations, they turned out not to be covariant with respect to Galileo transformations, and all attempts to obtain the desired covariance by somehow changing the form of the equations did not bring success, because they led to a contradiction with experience. For example, the appearance of the full Lorentz force was associated with the presence of a speed difference in inertial systems of coordinates:

FJIop=qEy=q{E0x+1/c[VxB0z]}, Bz=B)z. (32) It is clear that, unlike formula (31), where the forces are determined by acceleration, this force is associated precisely with the presence of motion at the velocity v of one inertial system relative to another in-ertial system. But the paradox here also arose in the fact that the Lorentz force was being considered relative to a fixed system of coordinates. How is the representation of this force in a mobile inertial system? It turned out that when an observer was placed on a moving object vx=0, and at Bz=B0z, here simply cannot be any force, and it meant that the laws of physics in a mobile and stationary inertial systems differ from each other, but it was not being observed in practice. Another alo-gism is related to the fact that by virtue of the velocity vx, there is the presence of a Lorentz force that is perpendicular to the radial Coulomb force. The problem is being solved if we take into account the fact that the magnitude of B0z from a stationary absolute system is no longer the magnitude of Bz=B0z, that is, it is not correct to represent B0z in a mobile system in the same way as in a stationary system. Taking into account the formula (32), the magnetic induction from a static inertial system is converted into the electric force of the interaction of inertial moving systems (of objects) in the form of Ey= [vxB0]/c. That is, in fact, magnetic induction in a static inertial system looks like the intensity of the electric field in a mobile inertial system. Really, this phenomenon is called the electromagnetic continuum (that is, we have an analogue with the space-time continuum, which will show somewhat below in next articles). In fact, Lorentz's law excludes the existence of Newton's first law, that is, no object of the universe can be represented through an inertial system that has a completely closed independent representation, because there is always movement (change) relative to something. That is, anybody (object) cannot be in a state of rest or uniform and rectilinear motion, and the object will always experience acceleration associated with the presence of the Lorentz force. At the same time, the presence of force is always associated with acceleration and a change in the representation of the object. In other words, there are always objects relative to which the selected object has motion, and electromagnetic forces are inherent for any object of the universe, and unlike the description of some unknown forces according to Newton's mechanics, we must consider specific forces.

Hence, it was necessary to deal with the cause of the formation of the forces themselves, which make the interconnection of all objects of the universe. However, scientists initially proposed the solution of the problem due to the existence of some kind of electromagnetic ether, which justified the non-covariance (a different kind of equations in a mobile and static system of coordinates), and in this case the Maxwell-Lorentz equations can be valid only in a single system of coordinates associated with the ether (that is, an absolute system of coordinates was introduced in this way). In any other inertial system of coordinates, the ether will has moving, and this should affect the field equations. In other words, in any "ethereal" theory, the existence of an

"ethereal wind" is assumed, which means that the field equations must contain as a parameter the velocity of the system of coordinates in question relative to the ether. Thus, the idea of the ether turns out to be incompatible with Galileo's principle of relativity, as the following thought experiment clearly proves it.

Let's consider an electromagnetic wave generated by a point source of light at time t=0, and we must know what its propagation will look like in two inertial systems moving relative to each other at speed v. Let's say the system £ is connected to a stationary ether, but the system £* has moving along the axis X at a speed v, so that at the moment of time t = 0, their initial points coincide with the position of the source of light.

Fig.l.

Then at the moment of time t=T>0, the light will reach the points located at a distance R=cT from the initial coordinate r=0. Therefore, in the £ system, the wave front equation has the form:

x2+y2+z2-c2T2=0, ....

x2+y2= c2T2-z2. (33)

It should be noted that the first equation of the electromagnetic wave in (33) refers to purely wave processes without corpuscular properties, but the second equation in (33) 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 must have a connection with the general formula of the universe (22) in any inertial coordinate system. However, let's continue, and in the system £* by the moment of time t=T, the position of the source will shift along the X axis by the length (vT) and the equation of the same wave surface will take the form (Fig. 1):

(x*+vT)2+y*2+z*2-c2T2=0. (34)

Thus, in the systems £ and £*, the wave front equation looks different. But, as is well known from the theory of differential equations in private derivatives, we have the characteristic wave surface, and its form is determined only by the coefficients of the corresponding equations. Therefore, the electromagnetic field equations, as a result of solving which the corresponding wave fronts (33) and (34) are obtained, should also have the different view (in other words, the electromagnetic wave equation should have a view that takes into account the speed of motion), and it indicates their non-covariance. So, the "ethereal" concept of the electromagnetic field negates the Galilean principle of relativ-

ity and allows for the possibility of experimental detection of the ethereal wind. Therefore, Michelson's experiment was set up to detect the motion of the ether relative to the motion of the Earth [6], based on the fact that the ether must have a directional velocity vector of its motion. However, it was not possible to detect the ethereal wind in experiment; it gave rise to doubts about the validity of the "ethereal concept". In addition, we note that in the ethereal concept, the magnetic component in the formula (32) remains unchanged in any system of coordinates and is associated with the presence of ether. Hence there is no relativity of the representation of magnetic and electric components depending on motion, that is, there is no electromagnetic continuum. And thus, by choosing a system of coordinates for Vx = 0, and for Bz = B0z, it is possible to remove the Lo-rentz force, which means that the laws of physics depend on the system of coordinates, but it is not observed in practice. Hence, we have the need to return to the principle of relativity and to the statement that electromagnetic phenomena are described by the same Max-well-Lorentz equations in all systems of coordinates, and it was realized by Einstein in his special theory of relativity (SRT).

As you know, the SRT was based on Einstein's statement about the constancy of the speed of light in any inertial system of coordinates (the principle of relativity), this actually means that the laws of physics do not depend on the inertial system of coordinates, and any physical law is related to the law of conservation of energy (quantity), otherwise the miracle of emergence from nothing. That is, for an observer in a moving system, the laws of physics are exactly the same as for an observer in another system of coordinates, and in this case, it is not clear which system consider mobile system (everything is relative) and which system consider

static system. If we proceed from the concept of the electromagnetic ether, based on the Galilean transformations, then Einstein's conception of postulation seem contradictory to the true approach. It is enough to consider the mental experience with light, from which we can make sure in it. In fact, the front of wave of the light in the system £ at moment t=T will have the form of a sphere of radius R=cT with the center at point r=0. However, according to Einstein's conception, in the system £*, the front of the same wave of light should, be represented by a sphere of the same radius cT, but centered at the point r*=0* (Fig. 2). Thus, the wave fronts of the same wave of light in different systems of coordinates do not coincide (there is no simultaneity of events). At first glance, it seems that to resolve this "ob-

y

I r

<>

\ \

\ o\ 0* \

vious" contradiction, one must either abandon the principle of the constancy of the speed of light, that is, assume that the laws of physics are different for inertial systems, and then the speed of light depends on the speed of the source, or return to the "ethereal" concept. The resolution of contradictions, according to scientists, lies in careful consideration of the paradox, and in the assumption that the reason for its occurrence lies in the implicit use of the idea of absolute time rooted in our consciousness. That is, about the representation of time in look of a linear constant magnitude (in fact, it is an immutable constant that is actually closed into itself), when we tacitly assume t*=t and identify the principle of relativity with the requirement of covariance with respect to Galileo transformations.

Fig. 2.

In this case, we must refuse the condition t*=t and assume that t*=f(t, x), as proposed by Lorentz. Then it becomes obvious that the circles of electromagnetic wave propagation from the systems of coordinates £* and £, when the laws of physics are fulfilled in any in-ertial system of coordinates, should not coincide due to the relativity of the concept of motion with velocity v. In other words, there is no simultaneity of events in the systems of coordinates £* and £ by virtue of motion with a velocity v relative to each other. Thus on the observance of the principle of relativity, with the fulfillment of the laws of physics, the Lorentz transformations were derived in the form:

x*=(x-vt)/[1-(v/c)2]1/2=0, t*=(t-vx/c2)/[1- (35)

(v/c)2]1/2=0,

* *

y =y, z =z.

The inverse transformations are being obtained through replacing v on -v:

x=(x*+vt*)/[1-(v/c)2]1/2=0,

t=(t*+vx*/c2)/[1-(v/c)2]l12=0, (36)

* *

y=y*, z=z*.

In this case, it turns out that the moving body has reducing in the direction of its movement according to the law:

Z=/0[1-(v/c)2]1/2. (37)

At the same time, the clock (time) slows down:

T=T0/[1-(v/c)2]1/2. (38)

Practically, we have both a change in segment of time and a change in length, that is, at presence t*=f(t, x), there is also a dependence x*=f(t, x). Accordingly, we have invariance in the form:

It= l0[1-(v/c)2]1/2T0/[1-(v/c)2]1/2=const. (39) As a result, it turns out that the Lorentz transformations correspond to the closed interaction of two

global opposites, so the changing of the argument v does not affect the multiplication of two opposite magnitudes - in representation of length and time, and this means a space-time continuum. Indeed, this can be verified, since the Lorentz transformations are uniquely related to the equation of the circle. We will show this, and for this purpose we will use squaring of the formula (37):

l2=U? [1-(v/c)2]. (40)

Next, we can write:

l2/l02 +v2/c2=1. (41)

There are no units of dimension in this formula, and magnitudes have presentation as quantitative parameters of opposites, and in dynamics - as laws, because, only in the case of regularities it is possible to maintain this equality with numerical changes. It is easy to see that this equality corresponds to a well-known formula through laws in the form (22).

Really, these Lorentz transformations actually say that the representation of objects is determined by their connection in systems of coordinates, since length and time determine the object by their mutual changes. And this actually means that under the condition of the law of conservation of quantitative external exchange, the internal representation depends on the system of coordinates. As we will show below, the particle-wave representation also depends on the system of coordinates. If we were to take equation (38) for a similar transformation, then in this case we would find that length and time with respect to each other act through an argument with respect to velocity in the form of an inversely proportional relationship. If we replace the variables in (41), and instead of v/c is being entered the parameter in analog vl0/(cl0)=t0/t, we get:

№ +t02/t2=1. (42)

We can continue to replace variables, and it is often used in quantum mechanics. To do this, we multiply the member l2/^ by the member fo2/fo2, and the member t02/t2 by h2/h2. As a result, taking into account h2/U2=c2, and l2/t02=v2, k2/t2=vi2, we obtain a circle equation of the form (25). The orthogonality of the quantities v and v1 is not in doubt, since the initial variables were length and time.

Einstein's energy formula also directly corresponds to the expression in terms of hyperbolic functions of cosine and sine. Indeed, given the classical rel-ativistic relation between mass and energy, one can write:

E2 = c2p2 + M 2c4, (43)

At comparing with the formula (21) we have: (chZ)2 = E2/(M 2c4); (shZ)2 = c2p2/(M (44)

2c4).

From here we obtain a well-known invariant form, which has the view:

(chZ)2 = (shZ)2 + 1. (45)

Considering that the length and time of objects are connected by Lorentz-Minkowski transformations with the condition of the law of conservation of quantity between global opposites, it follows conclusion that the heterogeneity of space and time of objects depends on the rate of interaction of each object with other objects, that is, from the velocity of exchange (movement, change). Indeed, we consider the exchange between two objects of the universe (through systems of coordinates), which differ from each other due to the speed of movement (of change) of one object relative to the other. There are no other differences, and otherwise, in the absence of movement of objects in the universe, we have uniformity without the possibility of separation, that is, we have one common object. If there were no Lorentz-Minkowski transformations, then these objects would be independent, and it would be impossible to connect two objects through interaction, because there would be no exchange between them with the condition of the law of conservation of quantity (i.e. the laws of physics would depend on the system of coordinates). As we wrote earlier, there is no exchange - there is no interaction! In this case, the speed of movement acts as a factor of the difference between objects from each other, which actually leads to the heterogeneity of space and time. However, the fact of heterogeneity of objects also means the heterogeneity of the surrounding space and time, since objects have an expression through space and time, and if they did not have such an expression, they would be completely independent and closed into themselves without the possibility of their detection in space and time. But, what is the heterogeneity of the surrounding space and time for objects, we do not observe the movement of the surrounding space and time relative to itself? And here Einstein decided to express the heterogeneity of space and time through the so-called gravitational forces. Hence, the next postulation of Einstein, which was the basis of GRT, was the statement that the inertial mass is equal to the gravitational mass. Einstein justified this conclusion by the fact that an observer in a closed elevator cannot detect the difference in the formation of acceleration, that is,

this acceleration is due to gravitational acceleration, under the action of so-called gravitational forces, or due to acceleration from the using of external force that is associated with inertial mass. It is clear that the concept of mass in this case is also not defined (also as the concept of charge), as a result, the mass was divided into gravitational view and inertial view, and it was suggested that this is something contained in the spacetime field. By the way, this is approach where the concept of the existence of magnitude of substance (of matter) in space and time appeared, and Einstein derived his cosmological equation with the exception of the participation of electromagnetic forces in the form of a general covariant equation of the gravitational field [7]:

RaP~ U2gapR ~Xgap = 8nG / cXP •

(46)

where is the Ricci tensor, R is the Ricci scalar (the tensor contraction of the Ricci tensor), g^ is the

metric tensor, X is the cosmological constant (negligible at the scale of a galaxy or smaller), G is the universal gravitational constant, ^ - the energy density tensor of "ordinary" substance (of matter),that is, we have tensor of energy - impulse of matter.

The formula (46) is a nonlinear equation that leads to the impossibility of using the superposition principle in its solution, which corresponds to electromagnetic interaction. In fact, this is the equation of a static potential field, since there is no dynamics here and the problem of singularity (discontinuities) has not been solved. Accordingly, it is not possible to solve the problem of the interaction of electromagnetic and so-called gravitational forces on the basis of this equation (there is no exchange with a reciprocal transformation), although Einstein tried to create a unified field theory on the connection of gravitational and electromagnetic forces during his last 30 years. Here, in the presence of a spacetime curvature, the question arises about the interaction of this something in the form of mass (matter) in this space-time field, since the absence of interaction means the impossibility of detecting this something (mass). The only known way of interaction is related with exchange, and then there are questions: "What is this exchange related to? How is the mutual transformation of mass (matter) into space and time appear, and vice versa, and what is its necessity?" Actually, there was already a solution, since the equality of gravitational and inertial masses allowed Einstein to interpret the mass through a space-time curvature based on the speed of movement relative to some common initial system of coordinates, and this solved the problem of the emergence of mass. However, what is this absolute system of coordinates, and what is it physically connected with, if, according to the first Einstein's postulation, everything is relative? In fact, it turns out that GRT refutes SRT, because GRT requires a single system of coordinates, relative to which it is necessary to measure the elementary velocities of elementary objects to estimate the space-time curvature, but in SRT there cannot be such a system in principle, otherwise the laws of physics should have a difference depending on the system of coordinates. The problem is solved if we take into account that the universe is divided into two global

opposites (in physics it is being interpreted as length and time, and in philosophy as existence and non-existence), which are closed onto each other through the exchange with the speed of light. Actually, Einstein's postulation about the constancy of the speed of light (exchange) automatically follows from our theory about the isolation of the universe onto two global opposites with the fulfillment of the law of conservation of quantity. The connection of opposites through the speed of light was also introduced not by us, but it was done before us in accordance with the geometry of Minkowski according to the formula (5). So Einstein had to understand the necessity of two global opposites having symmetry in number and defining two opposite observation systems, and then the concept of mass would similarly that we have according to formula (28), from the magnitude of velocity in the system opposite, taking into account the inversely proportional relationship. In the future in next articles, it will also be shown that the Lo-rentz force also has a component associated with the speed of motion precisely due to the equation of the circle as a reaction force on the action. Thus, SRT and Einstein's GRT reflect the same law of the isolation of the universe, taking into account changes, but in two global opposites, at the same time there can be no "ethereal wind", because any change in length coordinates is transformed into time at the speed of light, that is, there is no direction of the "ethereal wind". Accordingly, in one global opposite, velocity reflects kinetic energy, but in the other global opposite - this potential energy by the rest mass. It is clear that any object in the universe must be characterized through potential and kinetic energy (otherwise object falls out of the universe), and here there must be dynamics of exchange with the transition of kinetic energy into potential energy, and, conversely, with the condition of the law of conservation of quantity. However, how can this problem be solved if the opposites are interconnected through an exchange velocity equal to the speed of light? The only way is to characterize an object through a closed and open representation, because, in the absence of an object in a closed view, it is impossible to isolate object into something separate, and in the absence of an open view, object has no interaction with other objects and then it is impossible to detect it in the universe. It is clear that, since the only way of interaction is through the change of views from the closed view to the opened view, and vice versa, it follows that the laws of physics should describe such transitions, which we will show in the next our articles this journal on the basis of the known laws of electrodynamics. Considering that kinetic motion is determined by the transfer of electromagnetic energy from object to the object, otherwise

the problem of breaks (of singularity) is not solved, and then it is necessary to focus on the analysis of the laws of electrodynamics and the conditions for the propagation of an electromagnetic wave in the future.

The conclusions:

1. We have shown the dynamics of using the imaginary unit as an attribute of the opposite to obtain the basic laws of the universe, taking into account the place of observation. At the same time, we have shown that the equality and interrelation of real and imaginary numbers was made even before us through the Schrodinger and Dirac equations. This also touches the connection of global opposites through the speed of light.

2. We have established the predominant role of the laws of physics over the laws of mathematics due to the fact that the laws of mathematics at subtracting, without taking into account the laws of physics, lead to the disappearance of objects from the universe, exclude the transition of quantity to a new quality, correspond to the possibility of creating a perpetual motion machine in one of the opposites, do not give a hierarchy of the construction of the universe taking into account the inversely proportional relationship.

3. We determined the relationship between the velocity and the mass of rest of the particle as opposites, which excluded the representation of the mass of rest as matter in space and time.

4. We have deduced the connection of the Einstein energy equation and the Lorentz transformations with the circle equation. That is, the laws of physics obtained in practice reflect the closed system of the universe into two global opposites.

References

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