On the problem of the unified field theory

Proceeding from the dialectical law “negation of negation”, a unified picture of the physical world is proposed, in which the nodal points of development are the planetary systems of the macro and micro world, which differ from each other in the density of matter by ~ 1012 times. In the systems, the inverse quadratic laws of gravitation of masses operate, with constants, respectively, 6.674.10-8 and 1.847.1028 cm3 / gs2, which set the orbital motion of bodies and elementary particles relative to each other. Orbital distances in systems are expressed by quantum equations in which they are proportional to the squares of integers. The equations also include the constants of gravitation, mass and speed of axial rotation of the central bodies. In addition, the orbital distances are inversely proportional to the square root of the corresponding radiation rates characteristic of each system. The motion of bodies in both systems obeysKepler's third law, which is essentially a "glue" of macro and micro systems, linking changes in the nature of orbital motion in micro systems with the type of aggregate and phase transitions of substances in macro systems.

Undoubtedly, the physical world is one, there is something in it that unites it, makes it, one, whole. In an attempt to find this unifying principle, the problem of a unified field theory arose. Her main devotee wasA. Einstein. Here is his statement on this matter: “Now the problem of the unified nature of gravitational and electromagnetic fields is especially vividly worried about the minds. A thought striving for the unity of theory cannot be reconciled with the existence of two fields, which by their nature are completely independent of each other. Therefore, attempts are being made to construct such a mathematically unified field theory in which the gravitational and electromagnetic fields are considered only as different components of the same unified field, and its equations, if possible, no longer consist of logically independent members”.

However, despite numerous attempts, it was not possible to create a unified field theory. Gradually, the direction of thoughts began to drift towards the "theory of everything" [1]. In this regard, it is advisable to return to the origins of the problem statement [2] and analyze the issue of the unifying principle of the physical world.

The failure, in our opinion, was based on the wrong choice of the starting position. What to take as primary - the field source, the field itself or an interacting system consisting of the field source, the field itself and the law of their interaction. The choice of separately electric and gravitational fields as the initial one predetermined the departure from the solution of the problem.

After Rutherford-Bohr's discoveries of the planetary structure of the atom, which repeated the solar system in miniature, it became clear that the planetary principle of the structure of the world is universal, and that these two systems should be taken as the basis for comparing and constructing a single physical picture of the world. There appeared stable concepts of the macro and micro world (the solar system and the atom).

Below is a hypothesis that gives a more generalized approach to the problem of unified field theory. This approach is based on a comparison of the properties of these systems and the regularities of Hegel's dialectics, in particular the dialectical law of "negation of negation", in which the development process is considered as a repetition of some properties at the nodal points of the process at a higher qualitative level. This is a general philosophical law and you need to have remarkable abstract thinking (scientific fantasy) and courage to apply it for specific scientific purposes. Below is an attempt to apply this law to solve the problem under consideration.

The first nodal point of the law of denial of negation will be considered the world around us, the solar system, which has a planetary structure. Then it is natural to assume that the other nodal point will be the planetary system of the atomic world. And here the question arises about the direction of the development of the material world. Where is the "arrow of time" directed from the solar system to the world of the atom or vice versa? This question of the direction of evolutionary development is solved according to R. Clausis, taking into account the change in entropy. In the process of development of the material world, its entropy grows.At which nodal point is the entropy higher?

In the previous chapter 16 it was shown that the formation of cosmic bodies with an extremely high density (~ 1012 g / cm3) occurs due to the "fall" of electrons onto the nucleus of an atom and the fusion of nuclei. This process occurs due to the loss of potential energy of electrons for radiation and an increase in their orbital speed. In this case, there is an increase in entropy. Thus, the process of development of the material world is directed towards the formation of denser space objects with less internal energy.

Now, to be convinced of the physical unity of the systems of the macro and micro world, let us perform a comparative analysis of both systems. The glue for the solar system (macro world) is the force of gravity F, expressed by Newton's law:

where: G is the gravitational constant, M1 and M2 are the masses of interacting bodies, R is the distance between bodies. As it turned out [3, 4, 5, 6], the inverse quadratic law of gravitation also operates in the world of atoms, but with the gravitational constant g by 36 decimal orders of magnitude greater than the Newtonian constant:

where: f is the force of micro gravitational interaction in the atom, m1, m2 and r are the masses of interacting particles and the distance between them.

The microgravitational constant g has been determined by several methods. First of all, it was calculated - 3.84.1028 cm3 / gs2, according to the unique direct tens metric measurements of the force of interaction of crossed platinum filaments with a diameter of 1.0 mm, performed by BV.Deryagin [4].

When calculating the energy of formation of chemical bonds, it was shown [7] that the true value of the constant lies in the range of 0.428 • 1028 - 2.126.1028 cm3 / g s2. The most accurate value of the constant of microgravity was obtained by calculating according to the equation ofKepler's third law [8] for 10 chemical elements located in different parts of the periodic table of chemical elements. The average value of the constant of microgravity was obtained, equal to g = 1.847. 1028 ± 0.045 cm3 / s2g.

The calculation of the value of g by the formula for the orbital velocity, into which it enters, is clear and convincing for understanding. The formula is:

where v is the orbital velocity, g is the micro gravity constant, m is atomic mass, d is Dalton, r is the radius of the orbit on which the electron revolves.

Let's consider the calculation using the example of a hydrogen atom. The minimum radiation frequency for hydrogen is observed in the Humphrey series of 0.02424.1015 s-1. It is logical to assume that this frequency refers to an electron orbiting in the extreme surface orbit, the radius of which is equal to the radius of the hydrogen atom 110 pm. The atomic mass of hydrogen is 1.008. d = 1,661.10-24 g. Substituting the given values of the quantities into equation (4), we obtain the value of the micro gravity constant g = 1.843.1028 cm3 / gs2, which is close in magnitude to the value given above.

The micro gravitational constant g is the same unifying principle for the objects of the micro world, like the constant G in Newton's law.

Another bond for the solar system and the atomic system is the law of orbital distances, which includes almost all the parameters that characterize both systems.

where r is the radius of the orbit, k is a constant characteristic of a given atom, n is the main quantum number or in expanded form:

where: r is the radius of the allowed orbits of the atom, n is the quantum number (a series of integers), g is the micro gravity constant equal to 1.847.1028 cm3 / gs2, m is the mass of the atomic nucleus, c is the speed of light, ω is the frequency of rotation of the nucleus, c-1.

Orbital distances in the solar and satellite systems are expressed [9] by a similar formula:

where R is the orbital distance, km is a constant characteristic of a given planetary macro system, n is a series of integers (principal quantum number) or in expanded form:

where: R is the orbital distance, n is the principal quantum number (a series of integers), G is the gravitational constant, M and T are the mass and period of axial rotation of the central body, C is the propagation speed of gravitational radiation, equal to 0.25.109 cm / s.

The identity of equations (1) and (2), in our opinion, speaks of a deep analogy between the systems under consideration and the existence of common laws underlying them.

Bodies interacting according to equation (1) and (2) are in mutual orbital motion and obeyKepler's third law:

where: M is the mass of the central body, T is the period of revolution of the orbital body.

This is essentially the third "clamp", which acts both in the solar system and in the atomic system, but also closely links the changes in these systems that take place during aggregate and phase transitions of substances.

In the macrocosm, a new approach to the problem of aggregate and phase transitions is possible if we take as a basis the assumption that particles of matter (atoms, molecules) interact with each other with their masses according to the inverse quadratic law of gravitation. Therefore, in all states, they are in orbital motion relative to each other [11]. In this case, the aggregate and phase transitions are linked to the nature of the orbital motion, changes in the orbits along which the particles move. For example, a transition from a real gas (superheated vapor) to a saturated state means a change in the orbit from hyperbolic to parabolic. The transition to a liquid state is caused by the change of an open parabolic orbit to a closed elliptical and circular orbit. In both cases, we are dealing with a change in the state of aggregation, which coincides with a first-order phase transition.

Fig. 1. Types of orbits depending on the orbital speed (potential energy of the orbit, distance between bodies): O- center of a circular orbit, O- center of an elliptical orbit, P- perigee (periapsis) of the orbit, A- apogee (apocenter) of the orbit, r- radius of a circular orbit , r1 is the radius of the circular orbit of the "inner" ellipse, a is the semi-major axis, e = Oe / OR is the eccentricity of the orbit, v is the orbital velocity, 1 is the elliptical orbit (the "inner" ellipse), 1.1 is the circular orbit of the "inner" ellipse, 2- circular orbit, 3- elliptical orbit, 4- parabolic orbit, 5- hyperbolic orbit, 6- circular orbit with the radius of the semi-major axis of the ellipse, energetically equivalent to the elliptical orbit.

The transition from a liquid to a solid state, following the accepted logic, occurs when the orbital motion of particles changes from circular to elliptical along the trajectory of an ellipse inscribed in a circular orbit. Finally, when the solid body cools and, accordingly, the energy of the orbit along which the orbital motion in the solid body is reduced, the orbit at very low temperatures inevitably turns into a circular one due to energy loss, but with a smaller radius see curve 1.1 compared to the previous circular orbit, see curve (2) in Fig. 1. This last transformation corresponds to a second-order phase transition. That is, a second-order phase transition is a phase transition in a solid, caused by a change in an elliptical orbit to a circular orbit when the solid is cooled to a certain temperature - the temperature of the second-order phase transition of a given substance.

In orbital motion, the determining parameter is the distance between interacting particles in the system. For given masses of gravitating particles, it determines the orbital speed and type of the orbit and, therefore, the type of aggregate state. Thus, the distance between particles in the micro world can serve as an unambiguous criterion and sign of a particular state of aggregation. True, this unambiguity is violated when the parameter of the orientation of the interacting particles comes into play. This occurs when the particle shape deviates from the spherical shape. For example, during crystallization, the distance between particles prescribed by the laws of orbital motion is violated due to the formation of strong intermolecular bonds that act asymmetrically. A typical example here is the aggregate transition "liquid water - ice". It is also a 1st order phase transition.

There is a confusion of concepts, and even a misunderstanding of the differences between aggregate and phase transitions. In the light of the above considerations, it seems logical to link the phenomenon of the aggregate transition with a change in the distance between particles, that is, with the type of orbits in the orbital interaction. And the phenomenon of a phase transition - with different orientations of molecules during the phase transition, but within the same type of orbital interaction.

In this case, the emergence of several phase states of a substance in the same state of aggregation, for example, in a solid or liquid crystal, becomes understandable. In general, the "orbital" approach to the problem of aggregate and phase transitions, as will be shown below, allows one to give an exhaustive description of phase transitions of the 1st and 2nd order and to establish their place in the overall chain (picture) of aggregate and phase transitions.

If the solid body continues to cool, the energy of the elliptical orbit will decrease, the axes of the "inner" ellipse will decrease, and ultimately the elliptical orbit (curve 1, Fig. 1) will turn into a circular orbit (curve 1.1). Such a change in the nature of the orbital motion macroscopically, it can be assumed, is expressed in the form of a second order phase transition. This assumption is supported by three circumstances.

First. The transformation of an elliptical orbit into a circular one occurs in a solid state at a low temperature, which is typical for some cases of second-order phase transitions (changes in magnetic properties, the appearance of superconductivity).

Second, small circular orbits, see Fig. 1, curve 1.1, should contribute to a decrease in electrical and hydrodynamic resistance, which corresponds to the phenomena of superconductivity and super fluidity observed during phase transitions of the second kind.

And, finally, the third: the transformation of anisodiametery elliptical orbits into circular ones explains the increase in the fragility of solids, their transition to a powdery state, so that we can talk about the fifth type of the state of aggregation - the powdery state of aggregation of substances.

It is clear that the change in the nature of the orbits with a decrease in their energy is prescribed by the inversely quadratic law of gravitation and therefore is general, universal. Therefore, on the basis of the foregoing, it can be assumed that the second-order phase transition is also universal in nature, that each substance undergoes this transition when the temperature decreases in a certain temperature range by changing the type of orbit from elliptical to circular. However, the changing properties (superconductivity, super fluidity, magnetization, brittleness) and the transition temperature range depend on the individual characteristics of the substance, although the general rule set by the transition from elliptical orbits to less energy-intensive circular orbits should be preserved in all cases.

Now let us demonstrate the operation of the considered laws in a wide range of atomic parameters. Let's start with extreme cases with the shortest-wave series of X-rays and the structure of the uranium atom, which has the highest atomic mass.

The α1 X-rays in the K series of the uranium atom have the shortest wavelength of 0.01259 nm. Therefore, we can assume that such a wavelength (frequency) corresponds to the minimum quantum number n = 1 and the radius of the orbit, that is, in accordance with equation (4) for the first orbit k = r. In turn, knowing the wavelength λ, we calculate the radius according to the equations ofKepler's third law, which in relation to atomic systems have the form:

where λ is the wavelength, ν is the frequency of radiation, c is the speed of light, r is the radius of the orbit, g is the constant of micro gravity, m is atomic mass, d is Dalton.

Substituting the above values of the quantities into equation (9), we obtain the radius of the first orbit of the uranium atom, from which X-rays of the Kα1 series occur, r = 0.069 pm. The radii of other orbits are calculated according toBohr's equation (4) by multiplying by the square of the quantum number corresponding to the orbit, see Table 1. For example, for the next X-ray L series at n = 2, the wavelength λcal = 0.1011 nm was obtained with the reference value λexp = 0.07479, and for the M series at n = 3, respectively, λcal = 0.3412 nm and λexp = 0.3329 nm. For other series at n = 4, 5, 6, and 7, good agreement between the calculated and experimental data was also obtained, see columns 6 and 7 in Table 1.

Satisfactory coincidence is also observed for the calculated and experimental values of the atomic radii characterizing the length of chemical bonds and the size of the atom, see columns 2 and 3. The bond lengths calculated using equations (1) and (2) are 89.42 and 104.9 pm. The experimental values almost coincide with these values and are 89 and 104 pm, respectively. The calculated length of the covalent bond is 139.7 pm, the experimental value is 142 pm. Finally, the calculated radius of the uranium atom of 152.4 pm practically coincides with the experimental value of 153 pm.

The reliability of the model of the structure of the uranium atom is confirmed by the coincidence of the radiation frequencies calculated by theBalmer-Rydberg equation and the frequencies calculated by the equation of Kepler's third law, in which the radius r calculated by theBohr equation (4) was used.

TheBalmer-Rydberg equation expresses the change in radiation frequencies depending on two series of quantum numbers ni and nj:

Here c is the speed of light, R0 isRydberg's constant, which for a long time was known only for hydrogen. In several works [12] it was shown that the Rydberg constant for a chemical element is its first ionization energy. For uranium, it is equal to 7.11 eV or 11.39.10-12 erg or in reciprocal centimeters ν0 = ν / s = 0.5734.105 cm-1. Thus, it is possible to calculate the frequencies using theBalmer-Rydberg equation for uranium and compare them with the frequencies calculated using the Bohr equations (4) andKepler's third law (9). The results of such calculations are presented in table 1 columns 4, 5, 6 and 7.

Frequencies and wavelengths in columns 4 and 5 for quantum numbers 24-47 were calculated according toKepler's third law equations (9) and (10) using the value of the radius calculated according to Bohr's equation (1). TheBalmer-Rydberg equation was used to calculate the characteristic frequencies and wavelengths, which can be compared with those calculated according toKepler's third law. The latter include limiting and head frequencies.

The limiting frequencies are realized when the second quantum number nj = ∞ and are calculated by the equation:

For the uranium atom, two limiting frequencies are realized: for ni = 1 ν = 1.719.1015 s-1 and for ni = 2 ν = 0.4298.1015 s-1, see column 5. Calculation by the equation forKepler's third law gave close values, respectively

Head frequencies in each series of radiation are calculated using theBalmer-Rydberg equation and correspond to the first (head) quantum number nj in order. Column 5 shows the head frequencies obtained for ni = 1, nj = 2: 1.289.1015 and for ni= 2, nj = 3: 0.2388.1015 s-1, which quite accurately coincide with the frequencies calculated by the equation ofKepler's third law, respectively 1.205.1015 and 0.2437.1015 s-1

The data presented unambiguously indicate the compatibility of the results obtained by the equations ofKepler's third law using the microgravitational constant g and the classical equation of atomic physicsBalmer-Rydberg, which confirms the adequacy of the proposed microgravitational model of the atomic structure.

1. E. Berkovich, "Trinity Option - Science" No. 5 (299), March 10, 2020 and No. 6 (300), March 24, 2020.

2.P.S. Laplace, Statement of the World System, Leningrad, Ed. "Science", 1982, Chapter 18, On Molecular Attraction, pp. 226-256.

4. B.V.Deryagin, N.V. Churaev, V.M. Muller, Surface Forces, 1985, Ed. "Science", p106.

6. J.N. Israelachvily, Intermolecular and Surface Forces, 3rd edn N.Y. Acad. Press, 2011, p. 151.

7. AT. Serkov, MB. Radishevsky, AA. Serkov, Hypothesis-2, On the change of the scientific paradigm in natural science, Moscow, 2016, VINITI, p. 38.

8. AT. Serkov, A.A. Serkov, http://www.sciteclibrary.ru/rus/catalog/pages/11885.html; http://www.sciteclibrary.ru/eng/catalog/pages/11886.html

10. AT. Serkov, MB. Radishevsky, AA. Serkov, Hypothesis-2, On the change of the scientific paradigm in natural science, Moscow, 2016, VINITI, p. 13

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