Quantum of the gravitational field. Theoretical and experimental substantiation of gravitational electromagnetic resonance. Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev To cite this version: Valery Timkov, Serg Timkov, Vladimir Zhukov, Konstantin Afanasiev. Quantum of the gravitational field. Theoretical and experimental substantiation of gravitational electromagnetic resonance.. 2020. hal-02553557 HAL Id: hal-02553557 https://hal.archives-ouvertes.fr/hal-02553557 Preprint submitted on 24 Apr 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. UDC 001.5:53.02:53.05 Quantum of the gravitational field. Theoretical and experimental substantiation of gravitational electromagnetic resonance. Valery F. Timkov1*, Serg V. Timkov2, Vladimir A. Zhukov2, Konstantin E. Afanasiev2 1Institute of Telecommunications and Global Geoinformation Space of the National Academy of Sciences of Ukraine, Senior Researcher, Ukraine 2Research and Production Enterprise «TZHK», Researcher, Ukraine *Email: [email protected] Annotation. It is shown that gravitating objects that are at rest, or move without acceleration, create a standing gravitational wave in space. The length of this wave is a quantization step of the gravitational field. It is proportional to the mass of the gravitating object. The coefficient of proportionality is a value that is inverse to the linear density of the Planck mass, that is, proportional to the linear rarefaction of the Planck mass. A physically standing gravitational wave is a curvature, deformation of space under the influence of the gravitational field of a gravitating object. If we 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 embedded in each other, the radius of which changes away from the center of gravity by the value of the quantization step. It is shown that 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. Theoretical and experimental substantiation of the presence of gravitational-electromagnetic resonance (GER) in nature is given. This resonance arises when the wave vectors of a standing gravitational wave and an electromagnetic wave traveling in space are equal. GER is the basis for modulating the emission spectrum of stars and their clusters. The wavelength of the envelope of the spectrum is proportional to the mass of the radiating object. By measuring the wavelength of the envelope, one can accurately estimate the mass of the radiating object. Keywords: Maxwell-like equations of the gravitational field, the standing gravitational wave, the quantum of the gravitational field, the gravitational electromagnetic resonance, Planck constants. Introduction. The gravitational field has a wave character [1,2]. There are two types of gravitational waves: a gravitational wave traveling in space [3,4,5], which depends on time, and a standing gravitational wave [6,7,8], which does not depend on time. In both cases, the gravitational wave is a deformation of space, a change in its curvature under the influence of the mass of the gravitating body. A prerequisite for the existence of a gravitational wave traveling in space is a movement with the acceleration of massive objects [3]. This movement generates a wave-like change in the curvature of space-time, which propagates from accelerating objects with the speed of light in a vacuum in the form of traveling gravitational waves. A real source of gravitational waves traveling in space can be, for example, two black holes merging into one, which rotates around each other. Each of the black holes moving with acceleration emits traveling gravitational waves, but according to Newton’s third law, the forces with which they act on each other are balanced, therefore, as a result of the interference formed, these traveling gravitational waves are almost completely mutually quenched. According to the general theory of relativity, the source of traveling gravitational waves from merging black holes is the quadrupole moment of their accelerating composite mass [3,9], which is called chirp mass. A standing gravitational wave is a deformation, a curvature of the space around a gravitating object, which is represented as a set of fractal spherical equipotential surfaces embedded in each other with a common center that coincides with the center of mass of this object. The radius of the spheres varies with a step that is proportional to the mass of the gravitating object [6]. This step is called the length of the standing gravitational wave. A standing gravitational wave can be a modulation source of a traveling gravitational wave. Under certain conditions, a standing gravitational wave can be a source of gravitational-electromagnetic resonance. A prerequisite for this is the fact that the electromagnetic field is a special case of the gravitational field [10]. The technological condition for the existence of gravitational electromagnetic resonance is the equality of the wave vectors (wavenumbers) of the standing gravitational wave and the traveling (standing) electromagnetic wave. A standing gravitational field is quantized in space. 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. Maxwell-like equations of the gravitational field. Let a charged test particle, the charge and mass of which q and m respectively, are simultaneously in the electromagnetic and gravitational fields, then from the side of these fields on the test particle the forces act: electromagnetic Fe , gravitational Fg : Fe = q ( E + V B ), Fg= m ( E g + V k B g ), (1) where E is the vector of electric field strength, V is the velocity vector of the test particle, B is the vector of the magnetic induction of the magnetic field, () is the sign of the vector product, Eg is the vector of the gravitational field strength, Bg is the gravitomagnetic induction flux vector, k is the dimensionless correction coefficient which equals 1 in the Heaviside equations and 2 or 4 in the equations based on the general theory of relativity. Obviously, the dimension of the vector Eg in the formula (1) - has the dimension of acceleration and the dimension of vector Bg - of frequency. The Coulomb law for two charges q1 and q2 at a distance of r12 from each other and the law of gravity for two bodies, whose masses are m1 and m2 , and which are at a distance of from each other, have the form: q1 q 2 r 12 m1 m 2 r 12 FkeE= , FGg = , (2) rr12 12 rr12 12 where: kE is the proportionality factor (Coulomb's constant, or the electric force constant ), r12 is radius-vector, G is a gravitational constant. An analysis of equations (1,2) shows that the structures of the gravitational and electromagnetic fields are similar. Accordingly, the equations that describe these fields should be similar. The electromagnetic field is described by the Maxwell equations. Based on them, Heaviside [1] proposed a description of the gravitational field. These equations are called Maxwell-like Heaviside equations, or they are also called gravitoelectromagnetic equations. To form a description of the gravitational field in the form of gravitoelectromagnetic equations, we consider the Maxwell equations [11]: E = , (3) 0 B = 0, (4) B H E = − = − 0 , (5) tt 11E BJ =22 + , (6) 0c c t where: c is the speed of light in vacuum, is the charge density, 0 is the vacuum permittivity, 0 is the magnetic constant, H is the vector of the magnetic field strength, J is the electric current density. Based on Maxwell's equations (3,4,5,6) we obtain the wave equations of the electromagnetic field. To do this, vectorially multiply by the operator nabla the left and right sides of equation (5), we obtain: HDE 22 =−EHE =− =− =− =− , (7) 0 0( ) 0 022( 0) 0 0 t t t t t t where D is the electric displacement vector. Given that: 1 = , (8) 00 c2 EEE =( ) −2 , (9) we get: 2 2 1 E ( EE) − = − 22. (10) ct Since the divergence of the electric displacement vector in a dielectric medium satisfies the condition: D = 0, (11) then the divergence of the electric field vector in a homogeneous medium (for example, vacuum) satisfies the condition: E = 0, (12) then equation (10) takes the form: 1 2 E 2 E = − . (13) ct22 Vector equation (13) can be represented in the form of three scalar equations: 22 EExx1 2=− 2 2 x c t 22 EEyy1 2=− 2 2 (14) y c t 22EE1 zz=− . z2 c 2 t 2 Similarly, we can obtain the wave equation for the magnetic component H of the electromagnetic field: 2 2 1 H H = − 22, (15) ct 22 HHxx1 2=− 2 2 x c t 22 HHyy1 2=− 2 2 (16) y c t 22HH1 zz=− . z2 c 2 t 2 Equations (13) and (15) are homogeneous wave equations. Each scalar function in equations (14,16) of the projections of vectors E and H can be represented as a generalized function V , then we come to the Poisson equation: 1 2V 2V = − .