THE QUANTUM OF THE GRAVITATIONAL FIELD. THE GRAVITATIONAL-ELECTROMAGNETIC RESONANCE. PHYSICAL NATURE OF THE QUANTUM OF THE GRAVITATIONAL FIELD.

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THE QUANTUM OF THE GRAVITATIONAL FIELD.

THE GRAVITATIONAL-ELECTROMAGNETIC RESONANCE. PHYSICAL NATURE OF THE QUANTUM OF THE GRAVITATIONAL FIELD.

Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev

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Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev. THE QUANTUM OF THE GRAVITATIONAL FIELD. THE GRAVITATIONAL-ELECTROMAGNETIC RESONANCE.

PHYSICAL NATURE OF THE QUANTUM OF THE GRAVITATIONAL FIELD.. X-th Interna- tional Scientific and Practical Conference ”Technical Regulation, Metrology, Information and Trans- port Technologies, Ministry of Education and Science of Ukraine; - Ministry of Economic Development, Trade and Agriculture of Ukraine; - Odessa State Academy of Technical Regulation and Quality; - Mining and Metallurgical Academy. Stanislaw Staszyc in Krakow, Poland; - University of Bielsko- Biala, Poland; - Precarpathian National University. V. Stefanika; - State Service of Ukraine for Food Safety and Protection consumers; - Agency for Standardization, Certification and Trade Inspection under the Government of the Republic Tajikistan, Republic of Tajikistan; - Belarusian State Insti- tute of Metrology, Republic of Belarus; - Łód �� Technical University, Poland; - University of Lodz, Poland; - Međimurje Polytechnic in Čakovec, Republic of Croatia; - National Aviation University; - National Technical University of Ukraine ”Kyiv Polytechnic Institute named after Igor Sikorsky ”; - Tallinn Technical University, Republic of Estonia; - University of the North, Republic of Croatia; - Petro Mohyla Black Sea National University; - PJSC Odesakabel; - NGO ”Union of Consumers of Ukraine”; - Engineering Academy of Ukraine; - International Academy of Information Technologies, Republic of Belarus; - International Academy of Standardization; - Technical Committee for Standard- ization TC 90 ”Measuring instruments for electrical and magnetic quantities ”; - Technical Committee for Standardization TC 163 ”Quality of educational services”, Oct 2020, Odessa, Ukraine. pp.33 - 39.

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Одеська дер жавна академія технічно го регулювання та яко сті

Збірник наукових праць Х Міжнародної науково-практичної конференції

КВАНТ ГРАВІТАЦІЙНОГО ПОЛЯ. ГРАВІТАЦІЙНО-

ЕЛЕКТРОМАГНИТНИЙ РЕЗОНАНС. ФІЗИЧНА ПРИРОДА КВАНТА ГРАВІТАЦІЙНОГО ПОЛЯ.

Тімков В.Ф.¹, Тімков С.В.², Жуков В.О.², Афанасьєв К.Є.²

1 - кандидат технічних наук, доцент, старший науковий співробітник, Інститут

телекомунікацій та глобального геоінформаційного простору Національної академії наук України, Київ, Україна.

2 - науковий співробітник, науково-виробниче підприємство «TZHK»,Одеса, Україна.

Анотація – усі гравітуючі об'єкти спостережуваного Всесвіту створюють в просторі-часі стоячу гравітаційну хвилю. Довжина цієї хвилі є кроком квантування гравітаційного поля.

Вона пропорційна масі гравітуючого об'єкта. Коефіцієнтом пропорційності є величина, яка дорівнює лінійному розрідженню маси Планка. Фізично стояча гравітаційна хвиля - це викривлення, деформація простору-часу під дією гравітаційного поля гравітуючого об'єкта.

Якщо уявити гравітуючий об'єкт як матеріальну точку, то геометрична картина стоячої гравітаційної хвилі може бути уявлена як сукупність ієрархічних вкладених одна в одну сферичних еквіпотенційних поверхонь, радіус яких при віддаленні від центру гравітації змінюється на величину кроку квантування. Стояча гравітаційна хвиля має квантовий характер. Квантом гравітаційного поля є квадрат швидкості світла у вакуумі. Квант

гравітаційного поля дорівнює гравітаційному потенціалу гравітуючого об'єкта на відстані від нього рівному кроку квантування. Перша еквіпотенційна поверхня від центру гравітації має гравітаційний потенціал, який дорівнює кванту гравітаційного поля, далі, в міру віддалення від центру гравітації, гравітаційний потенціал на еквіпотенційних поверхнях зменшується обернено пропорційно їх номеру. Експериментальним доказом квантово-хвильової природи гравітаційного поля є наявність в природі гравітаційно-електромагнітного резонансу.

Фізичною природою кванта гравітаційного поля є кінематична гравітаційна в'язкість простору-часу.

Ключові слова – квант, квантування гравітаційного поля, стояча гравітаційна хвиля, потенціал, резонанс.

THE QUANTUM OF THE GRAVITATIONL FIELD. THE

GRAVITATIONAL-ELECTROMAGNETIC RESONANCE. PHYSICAL NATURE OF THE QUANTUM OF THE GRAVITATIONAL FIELD.

Valery F. Timkov¹, Serg V. Timkov², Vladimir A. Zhukov², Konstantin E.

Afanasiev²

1 – Candidate of Technical Sciences, Docent, Senior Researcher, Institute of Telecommunications and Global Geoinformation Space of the National Academy of Sciences of Ukraine, Kyiv, Ukraine.

2 – Researcher, Research and Production Enterprise «TZHK»,Odessa, Ukraine.

Abstract – All gravitating objects of the observed Universe create a standing gravitational wave in space-time. The length of this wave is a quantization step of the gravitational field. It is proportional to the mass of the gravitating object. The proportionality coefficient is a value that is equal to the linear rarefaction of the Planck mass. A physically standing gravitational wave is a curvature, deformation of space-time under the influence of the gravitational field of a gravitating object. If you imagine a gravitating object as a material point, then the geometric picture of a standing gravitational wave can be represented as a set of hierarchical spherical equipotential surfaces

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embedded in each other, the radius of which, when moving away from the center of gravity, changes by the magnitude of the quantization step. A standing gravitational wave has a quantum character. The quantum of the gravitational field is the square of the speed of light in a vacuum. The quantum of the gravitational field is equal to the gravitational potential of the gravitating object at a distance from it equal to the quantization step. The first equipotential surface from the center of gravity has a gravitational potential, which is equal to the quantum of the gravitational field, then, as you move away from the center of gravity, the gravitational potential on equipotential surfaces decreases inversely with their number. The experimental proof of the quantum-wave nature of the gravitational field is the presence of gravitational-electromagnetic resonance in nature.The physical nature of the quantum gravitational field is the kinematic gravitational viscosity of space-time.

Keywords – quantum, quantization of the gravitational field, standing gravitational wave, potential, resonance.

Formulation of the problem. The electromagnetic field is a special case of the gravitational field. The electromagnetic field is quantized. Is the gravitational field quantized?

Purpose of the study. Theoretical and experimental substantiation of the quantum nature of the gravitational field.

1. Introduction.

It was shown in [1 - 8] that the stationary gravitational field can be represented in the form of Maxwell-like Heaviside equations:

g,

g

E 

 r  

(1) Br_g 0,

(2) _g B^g ^g H^g ,

E t t

  

    

 

r r

r (3)

1₂

g ,

g g g

B J E c t

 ^

   



r r r

(4) where: Er_g

is the vector of the gravitational field strength, Br_g

is the gravitomagnetic induction flux vector, _g is the mass density, G is the gravitational constant, J_g is the mass current density or mass flux, in [kg m s¹ ^{ }² ¹], c is the speed of light in vacuum, _g is the gravitoelectric constant, _g is the gravitomagnetic constant.

Based on equations (1-4), the wave equations of the gravitational field can be obtained:

2 2

1 1

g .

g g

g

E E

c t  

    

 r r

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² g ¹₂ ² ₂^g g g⁾^.

B B J

c ^ t 

   



r r r

(6) Equations (5 - 6) show that the stationary gravitational field has a wave character.

2. Quantum of the Gravitational Field.

Based on equations (5 - 6), taking into account the constraints and initial conditions, the equation of the gravitational potential for a material point and a symmetric sphere can be obtained:

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^{( )} ^, V r GM

 r (7) where: Mis the mass of material point, or a symmetric sphere, ris the distance from

the center of gravity to the current point at which we determine of the gravitational potential.

It is known [9] that the total energy E of any body, whose mass M can be represented as:

EMc²F S_P , (8) where: ^F^P is Planck’s force, S is the radius of curvature of space, curved under the

influence of the body’s gravitational field.

From:

F S^P₂ .

M  c (9) Then the formula (7) can be represented as:

( ) GM GF S^P₂ .

V r  r  rc (10) We represent in formula (10) the values of the gravitational constant G and the

Planck's force F_P through Planck's constants: of the mass ^m^P^,of length l_P,of time

P,

t then:

3

2

2 2 2 2

( ) ^P ^P ^{P P} .

P P P

GF S l m l S

GM S

V r c

r rc m t t rc r

    (11) Formula (11) suggests that the structure of the potential of the gravitational field, the

strength of the gravitational field, as well as the structure of the potential energy of the gravitational field are of a quantum nature. This means that if a material body is represented in the form of a point whose mass is equal to the mass of the body, then the gravitational field around this material point can be represented as a set of

equipotential spherical surfaces embedded in each other whose radius varies in increments equal to the value of the radius of curvature of space S, which proportional to body mass and is determined by the formula [9]:

^P .

P

S l M

m (12) The square of the speed of light in a vacuum is the energy quantum of the

gravitational field. Denote: h_g c², then the formula (12) can be represented as:

( ) _g S. V r h

 r (13) The set of spherical equipotential surfaces around the material point form a kind of

standing gravitational wave, at which the wavelength is equal to the length of the quantization step S, and the wave vector is directed towards the material point. The physical essence of a standing gravitational wave is a deformation, a curvature, a peculiar ripple of space under the influence of a gravitational field. It is constant in time, but variable in space.

The first equipotential surface from the center of gravity has a gravitational potential, which is equal to the quantum of the gravitational field, then, as you move away from

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the center of gravity, the gravitational potential on equipotential surfaces decreases inversely with their number.

3. The Gravitational-Electromagnetic Resonance

Considering that the electromagnetic field is a special case of the gravitational field [10], the structure of which has the character of a standing gravitational wave for all material objects of the Universe, then under certain conditions, gravitational- electromagnetic resonance is possible [9,11,12]. The condition for the existence of gravitational-electromagnetic resonance is the equality of wave vectors (and in particular wave numbers) of a standing gravitational wave and a traveling

electromagnetic wave. If we expand the equation of gravitational potential (13) in Fourier series, and the Maxwell equations for the electromagnetic field in waveguides and resonators are presented in the form of Hamilton equations, it turns out that the wave numbers of the gravitational field and the electromagnetic field are equal under certain conditions, which confirms the presence of the nature of gravitational-

electromagnetic resonance. The presence of gravitational-electromagnetic resonance in nature is confirmed experimentally: under terrestrial conditions [9] Fig. 1, in the space [13] Fig. 2.

Fig.1. Gravitational-electromagnetic resonance in terrestrial conditions [9].

Fig. 2. Gravitational electromagnetic resonance in the space [13].

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According to [14], in the observable Universe with a speed that is close to the speed of light, much less than 1% of the substance moves. This means that in many

practical problems of physics, cosmology, and astrophysics, it is more correct to use the space-energy interval instead of the Einstein time-like and space-like interval in of the following form:

² ( ). S rV r

 c (14) The presence of the gravitational-electromagnetic resonance in nature confirms the

quantum nature of the gravitational field.

4. The Physical Nature of the Quantum of the Gravitational Field.

Gravitational viscosity, as inhibition of motion, is the property of a real gravitating space-time to resist the movement of one part of it relative to another.

By analogy with the concept of the viscosity of liquids and gases, we will distinguish between dynamic gravitational viscosity and kinematic gravitational viscosity. For the observable Universe, as the Hubble sphere, the dynamic gravitational viscosity is equal to the gravitational energy density of baryonic matter _U , and the kinematic gravitational viscosity _U is equal to the ratio of the dynamic gravitational viscosity to the mass density of baryonic matter _U . The gravitational energy density of baryonic matter _Uis [8,9]:

3 ^{P U} ,

U U

U

P F R

   V (15) where P_U is the pressure of the gravitational field of the baryonic matter of the

observable Universe, R_U this is the radius of the Hubble sphere, V_U this is the volume of the Hubble sphere. For the observable Universe, as the Hubble sphere, it is true:

2 P2 , U U

P

U P

M R P

F m l

T t

  (16) where M_U is the mass of the baryonic matter of the observable Universe, T_U is the Hubble time.

It is shown in [15] that for the Hubble constant: H 67.55770 ^0.02329(km s/ ) /Mpc, the values of the baryonic matter mass of the observable Universe, the Hubble radius and the Hubble time are as follows:

1.8442238245 ·1053 ,

MU   kg R_U 1.3692928247 ·10 ²⁶m, 4.5674692213 ·1017 .

TU   s

Then:

44 1 1 2

1.210335838886277672100 10 ,

FP  kg m s^ V_U 1.0754187557553 10 ⁷⁹m³^,

26 1 3.

1.7148890 10

U kg m

   ^ ^

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On each point of the surface of the Hubble sphere, the gravitational field of baryonic matter presses with a force equal to the Planck force [16], then:

10 1 1 2

2 5.136926649254362 10 .

4

P P

U

U U

F F

P kg m s

S R ^ ^{ }

    (17)

Where from:

-9 1 1 2

1.54107799477 .

3 630 10

U PU kg m s

    ^{ } (18)

Then:

2 2

2 16 2 2

2 2 8.98645900 10 .

U U P

U

U U P

R l

c m s

T t

 ^ ^ ^ ^ ^ ^ ^ (19)

The physical nature of the quantum of the gravitational field of the baryonic matter of the observable Universe is the kinematic gravitational viscosity of this field.

The maximum possible transfer rate of physical interaction in the observable Universe, as the Hubble sphere, which is equal to the speed of light in vacuum, is completely determined by its space-energy characteristics and, first of all, by the kinematic viscosity of the gravitational field of the baryonic matter of the observable Universe.

5. Conclusion.

The gravitational field has a quantum-wave character. The quantum of the gravitational field is the square of the speed of light in a vacuum. The gravitational field has a structure. This structure is a standing gravitational wave. A standing gravitational wave is a curvature, a deformation of space-time under the influence of the gravitational field of a gravitating object. The geometric picture of a standing gravitational wave can be represented as a set of hierarchical spherical equipotential surfaces embedded in each other, which are separated from each other (and the first from the center of gravity) by a quantization step. The first equipotential surface from the center of gravity has a potential that is equal to the quantum of the gravitational field, then when moving away from the center of gravity the gravitational potential of equipotential surfaces decreases inversely with their number. In most practical tasks, it is convenient to replace the time-like and space-like interval with the space-energy interval. The physical nature of the quantum of the gravitational field of the baryonic matter of the observable Universe is the kinematic gravitational viscosity of this field.

6. References (ЛІТЕРАТУРА).

[1] Heaviside, O.: "A gravitational and electromagnetic analogy", The Electrician, v. 31, Part I p.p.

281–282, Part II p. 359, 1893.

[2] Agop, M., Buzea, C.Gh., Ciobanu, B.: "On Gravitational Shielding in Electromagnetic Fields.", 1999,

https://arxiv.org/html/physics/9911011

[3] Clark, S.J., Tucker, R.W.: "Gauge symmetry and gravito-electromagnetism. ", Classical and Quantum Gravity., 17 (19): 4125–4157,

arXiv:gr-qc/0003115

[4] Mashhoon, B., Gronwald, F., Lichtenegger, H.I.M.: "Gravitomagnetism and the Clock Effect.", Lect.Notes Phys. Lecture Notes in Physics., 562, pp. 83–108, 2001,

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arXiv:gr-qc/9912027

[5] Mashhoon, B.: "Gravitoelectromagnetism: A Brief Review.", 2008, arXiv:gr-qc/0311030

[6] Fedosin, S.G.: “The General Theory of Relativity, Metric Theory of Relativity and Covariant Theory of Gravitation: Axiomatization and Critical Analysis.”, International Journal of Theoretical and Applied Physics (IJTAP), ISSN: 2250‒0634, Vol. 4, No. I, pp. 9-26 (2014).

[7] Behera H., Barik, N.: “Attractive Heaviside-Maxwellian (Vector) Gravity from Special Relativity and Quantum Field Theory.”, 2017,

ArXiv 1709.06876v2.

[8] Landau, L.D., Lifshitz, E.M.: “The theory of fields.”, Nauka, Moscow, p.p. 91 – 119, p 462, 1973, In Russian.

[9] Timkov, V.F., Timkov, S.V., Zhukov, V.A.: “Planck’s universal proportions. Gravitational - electromagnetic resonance.”, International scientific-technical magazine: Measuring and computing devices in technological processes, ISSN 2219-9365, 3 (52), p.p. 7 - 11, 2015.

http://nbuv.gov.ua/UJRN/vott_2015_3_3 https://hal.archives-ouvertes.fr/hal-01329094v1

[10] Timkov, V.F., Timkov, S.V., Zhukov, V.A.: “Electric charge as a function of the moment of mass. The gravitational form of Coulomb`s law.”, International scientific-technical magazine:

Measuring and computing devices in technological processes, ISSN 2219-9365, 3 (56), pp.27 –32, 2016.

http://nbuv.gov.ua/UJRN/vott_2016_3_4.

https://hal.archives-ouvertes.fr/hal-01374611v1

[11] Timkov, V.F., Timkov, S.V., Zhukov, V.A.: “Gravitational-electromagnetic resonance of the Sun as one of the possible sources of auroral radio emission of the planets in the kilometer range.”, International scientific-technical magazine: Measuring and computing devices in technological processes, ISSN 2219-9365, 4 (53), p.p. 23 – 32, 2015.

[12] Timkov, V.F., Timkov, S.V., Zhukov, V.A.: “Gravitational-electromagnetic resonance of the Sun in the low-frequency of the radio spectrum of the Jupiter.”, International scientific-technical magazine: Measuring and computing devices in technological processes, ISSN 2219-9365, 2 (55), p.p. 198 –203, 2016.

[13] Parrot, M., and others,: “Propagation characteristics of auroral kilometric radiation observed by the MEMO experiment on Interball 2”, J. GEO R-S P, 106(A1), p.p. 315-325, 2001.

[14] Planck Collaboration, Aghanim, N., et al. (2018). "Planck 2018 results. VI. Cosmological parameters". Retrieved 18 July 2018.

[15] Timkov, V.F., Timkov, S.V., Zhukov, V.A., Afanaciev, K.E.: “The method for increasing the accuracy of some fundamental physical constants”, Collection of scientific articles of the 9th International Scientific and Practical Conference "Technical Regulation, Metrology, Information and Transport Technologies", Odessa State Academy of Regulation and Quality, pp. 132 - 145, Odessa, 2019.

https://osatrq.edu.ua/wp-content/uploads/2019/11/ikhconf.pdf https://hal.archives-ouvertes.fr/hal-02390730v1

[16] Timkov, V.F., Timkov, S.V., Zhukov, V.A..: “Rotating space of the universe, as a source of dark energy and dark matter”, International scientific-technical magazine: Measuring and

computing devices in technological processes, Khmelnitsky national university, Khmelnitsky, Ukraine, 2015, 52 (3), pp.200 - 204.