Since:

1) the gravitational field and the electromagnetic field are wave-like,

2) the electromagnetic field is a special case of the gravitational field, see:

Electric charge as a function of the moment of mass. The gravitational form of Coulomb`s law.

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

3) the gravitational field is quantized only in space,

4) the electromagnetic field is quantized in space and of time,

then for each given time reference at the coincidence of the wave spatial vectors of the standing gravitational wave and the traveling (standing) electromagnetic wave forms a gravitational-electromagnetic resonance, see:

Gravitational-electromagnetic resonance of the Sun as one of the possible sources of auroral radio emission of the planets in the kilometer range.

https://hal.archives-ouvertes.fr/hal-01232287v1

Gravitational-electromagnetic resonance of the Sun in the low-frequency of the radio spectrum of the Jupiter.

https://hal.archives-ouvertes.fr/hal-01326265v1

Planck’s universal proportions. Gravitational - electromagnetic resonance.

https://hal.archives-ouvertes.fr/hal-01329094v1

The building block of universe is quantum mechanics phenomenon, therefore the origination of everything must be QM, and gravity can not be exception. Gravity is not mechanical as Newton or Einstein stating, Gravity is Internal not external.

Article Gravity is an Internal Force

Dear Javad Fardaei, I agree with you that the basis of gravity is the quantum properties of matter at its micro-level. But the large-scale factor of the quantum gravitational properties of elementary particles is so small that at present and in the near foreseeable future, researchers do not and do not foresee the appropriate equipment for their study. Therefore, gravity since the creation of the general theory of relativity is usually described by its main property and manifestation at the mega and macroscopic levels of matter, namely, to deform, distort space. From here - the main instrumentation for the study and description of gravity became geometry. One of the main conclusions of my preprint is that the geometry of curved space under the influence of a gravitational field has a structure! Namely - the gravitational field of any gravitating object is a standing gravitational wave.

The spectrum of all radiating objects of the observed Universe (see preprint: Fig. 3,4,5) is modulated by an envelope whose wavelength is equal to the quantization step of the gravitational field of the radiating object, and which is proportional to its mass. By measuring the wavelength (frequency) of the envelope, we can accurately(!) estimate the mass of the radiating object.

Since there is gravitational-electromagnetic resonance, under certain conditions, gravitational-electromagnetic levitation (GEL) must exist. Co-authors of the preprint conducted a series of experiments to detect it. Experience as a whole was recognized as unsuccessful. Traces of GEL are found, which, nevertheless, do not allow us to unequivocally state the reliability of its existence. In a future experiment, it is necessary to significantly increase the output power of the generator of extremely high frequency oscillations and increase the accuracy of the measuring path.

According to the co-authors of the preprint, based of the work of the engine EM-drive are GER and GEL. If so, then the Chinese space experiment with EM - drive should have ended in failure. Since the experimental installation, in this case, is located at a significant distance from the center of gravity. The Chinese announced of the space an experiment with EM-drive, but they did not publish its results. Or I missed these results?

Preprint too at HAL:

Quantum of the gravitational field. Theoretical and experimental substantiation of gravitational electromagnetic resonance.

https://hal.archives-ouvertes.fr/hal-02553557

Gravity-electromagnetic resonance and the fact of energy transfer by a traveling electromagnetic wave create the prerequisites for creating renewable power sources.

The gravitational constant is a modified quantum of the gravitational field, it can be represented as: G = (lp / mp) * c^2 = (lp / mp) * hg, where lp, mp is the Planck length and Planck mass, and their ratio is the linear rarefaction of the Planck mass. That is, the gravitational constant is a product the quantum of the gravitational field hg per calibration coefficient is the universal Planck proportion.

If we determine the law of gravitation through the quantization steps S1, S2 of gravitating objects with mass m1, m2, then: F = G * [(m1 * m2) / (r ^ 2)] = Fp * [(S1 * S2) / (r ^ 2)] Where Fp is Planck's power. That is, it shows how much force F occupies the Planck force Fp.

Valery Timkov

Dear Valery,

You wrote: " A physically standing gravitational wave is a curvature, deformation of space under the influence of the gravitational field of a gravitating object." But the space is not material object. it can not "warp".

I liked your thoughts on the connection between gravity and electromagnetism. I believe that this is one and the same. If you find time, see the chapter on gravity in the book "Electromagnetic Gravity. Part 1" in my profile. The quantum value is also indicated there. But for this, two facts must be recognized.

1. An electromagnetic field is a dispersed medium that fills all space. And the electric and magnetic fields are flows of this medium. Analogy: air and wind with cyclones. And this is described in part 1.

2. Neutrino is the only elementary particle. All other are composites. (Part 1)

Are you interested in EM-drive? I am trying to use a Tesla transformer to create an electric field flux. But this is already in Part 3.

Yours

Valeriy Pakulin

PS

Please look at my site http://gravity.spb.ru

Valery Timkov the Big Bang and GTR are very weak and non-scientific theory that can not provide any answer for creation of well organized of billions of galaxies universe and origination of anything including mass, energy, force, gravity, color, taste, odor......

To just clarify few unprecedented things that might help you on this good question research. The Universe is made of two kinds of matter, chemical matter (all the element of periodic table), and non-chemical matter (particles). The smallest complete unit of universe is atom, anything smaller than an atom is particle. Atoms are well organized entity, like its mother nature universe, same atoms intent to get together (gravity) in space of universe, that why we know where the hydrogen, oxygen, carbon are in the space of the universe. But particle is much smaller than an atom, and they have no personality, this particle are dust, or dirt that is covering over the planets. for more detail Article Quantum Mechanics Gravity, Mechanical Gravity of Newton is Myth

Dear Valeriy Pakulin , thank you for the links to your work. I will definitely watch them. You state: ... "the space is not a material object" ... Here I fundamentally, categorically, and absolutely disagree with you. Real (!) Space, which is commonly called space-time, is a material object (!). The only thing I would adjust the name: space-energy. I will explain. In physics, astrophysics, cosmology, there are three fundamental, fundamental categories: 1) space, 2) mass-energy, 3) time. See link: Electric charge as a function of the moment of mass. The gravitational form of Coulomb`s law https://hal.archives-ouvertes.fr/hal-01374611v1 The inextricable connection and composition of these categories + initial conditions (a) + LIMITATIONS (!!!) (b) + the correct choice of a reference frame and methodology, as well as a set of observer tools (c) - give us ultimately a set of existing physical laws. Regarding the last paragraph, I want to emphasize: all hypotheses, for example, graviton, dark energy, and dark mass, string theory, ..., must necessarily be tested by practice, experiment, before that it is nothing more than mathematical simulacra of a real physical picture of the world. Moreover, each of the above hypotheses is not only not confirmed by experiment, but also has significant flaws in paragraphs. (a, b, c). In a triune bundle, space - energy (mass) - time, the last category is dependent on the first two. It is a composite characteristic of real space. The main properties of real space are: the absolute absence of straight lines in it, also including the coordinate axes, and the speed of movement of any material bodies and the maximum transmission rate of physical interaction cannot exceed the speed of light in vacuum. The absolute absence of straight lines and the unambiguous dependence of the radius of curvature of space on the magnitude of the gravitating mass in it is the essence of real space as a material object. In this case, the geometric picture of the deformed space under the influence of the gravitational field of the gravitating object (which rests or moves without acceleration) is a standing gravitational wave. Further. I think that the basic, that is, the maternal field for other types of fields is the gravitational field. The mechanism of its occurrence is at the quantum level of matter. Moreover, depending on the scale factor, the specifics of the motion of material carriers, and restrictions at different structural levels of matter, the gravitational field can be “reincarnated” into other types of fields. Regarding the compositeness of elementary particles - I agree. The electron and neutrino are in question. Yes, I'm interested in EM-drive. Do you have info on the Chinese space experiment with EM-drive?

Dear Valeriy Pakulin,

downloaded your book. Pre - interesting. I’ll look more closely.

Dear Javad Fardaei,

thank you for the link. I will work with her. As for the Big Bang and the general theory of relativity, I also have questions for them. For example, a completely structured observable Universe arose from a structureless point of singularity, that is, in fact, chaos. Nevertheless, to date, there is NO EXPERIMENTAL OBSERVATION that would refute these theories. Moreover, the main conclusions of these theories are regularly confirmed experimentally. In addition, physical laws, their limitations, and initial conditions make it possible to extrapolate their development both in the past and in the future. These extrapolations also do not contradict the main conclusions of the above theories.

Dear Valery Timkov It is very obvious that our vision through this massive of universe is limited, but it should not take us away from reality. the reason that the mechanical theory such as BB and GTR holding up to this date, it is because there is no other stronger theory exist, due to founder and supporters. But in reality the theory of BB can not answer any question, i.e. if the Universe has origination, everything else in it must have origination. that is including, Energy, mass, force, gravity, color, taste, odor, and many things that we observe. Unfortunately through the BB theory, science of physics is getting away from other science. To give you very clear example, the pandemic virus that the world is challenging is a good one. All the scientists are looking for medicine to fight with the virus. When we delve into the structure of this intelligent virus, it is made of few atoms and molecules. If our DNA is smart, and DNA of this virus is smart, atom must be smart, but the BB theory is considered as a accidental, mechanical universe, and by this theory definition of an atom is mechanical, yet our science of physics is supporting this non-scientific remark, all due to manmade science of BB and GTR. It is time to open our eye, and think out the box and shift the wrong foundation to a solid one. By wasting time to correct flawed theory would not take us to real science.

Dear Javad Fardaei,

I repeat, the Big Bang theory and the general theory of relativity, in agreement with experiment. This is the main criterion for the truth of any theory. In addition, they do not contradict the mainstream of modern physics - its Standard Model.

Einstein’s well-known formula for the total energy of the body, whose mass is m:

E = m * c ^ 2, can be expressed in terms of the step of its gravitational quantization S: E = Fp * S, where Fp is the Planck force, and also considering that the square of the speed of light in a vacuum is the quantum of the gravitational field: hg = c ^ 2, then by analogy with the Planck formula for the electromagnetic field, we can write: E = m * hg.

Dear Valery Timkov

The gravitational field is not "quantized".

I'm not quit sure what you mean by that. If you mean energy jumps, then it's no.

JES

Dear Stellan Gustafsson,

the presence of gravitational-electromagnetic resonance in nature, which in the preprint is substantiated both theoretically and EXPERIMENTALLY indicates that the gravitational field has a quantum-wave character, that is, it is quantized (!). I especially ask you to pay attention to Fig. 4 in the preprint. The quantum of the gravitational field is the square of the speed of light in a vacuum.

Dear Valery Timkov

As far as I know there is no experimental evidence for any quantum gravity!

But, there is a lot of theories around it.

JES

Dear Stellan Gustafsson,

please see the preprint. All your doubts will be explained:

Quantum of the gravitational field. Theoretical and experimental substantiation of the gravitational-electromagnetic resonance.

https://hal.archives-ouvertes.fr/hal-02553557v1

Here the main thing: the gravitational field has a quantum-wave character; the quantum of the gravitational field is the square of the speed of light in vacuum; the structure of the gravitational field of gravitating bodies that move without acceleration is a standing gravitational wave; if you imagine a gravitating body in the form of a point, then a standing gravitational wave is a combination of spherical equipotential surfaces embedded in each other, centered at this point, and spaced apart by a quantization step (gravitational wavelength); the quantization step is proportional to the mass of the gravitating body; the proportionality coefficient is the Planck proportion, namely the linear rarefaction of the Planck mass - that is, the ratio of the Planck length to the Planck mass; a quantum of a gravitational field is equal to the gravitational potential of a gravitating body at a distance of a quantization step from it; when the wave vectors of the standing gravitational wave and the traveling electromagnetic wave are equal, gravitational-electromagnetic resonance (GER) is observed; the presence of GER in nature is justified theoretically and confirmed experimentally; the emission spectrum of stars in their clusters is modulated by an envelope whose wavelength is equal to the quantization step of the radiating object, this makes it possible to accurately determine its mass - in this regard, repeatedly I especially ask you to pay attention to Fig. 4 in the preprint.

Dear Valery Timkov

I have seen your fig. 4 and I must say that to me this looks like an experimental problem, maybe some parasite or malfunctioning. I don't trust such a strange behaviour, it is too well behavied.

It will be necessary to have a confirmation from another group, before you can trust such a picture.

JES

Dear Stellan Gustafsson,

gravitational-electromagnetic resonance, which is shown in Fig. 1 - 5 obtained from various experimental(!) sources! Both in the conditions of a ground experiment (Fig. 1 - 2), and from various space stations (Fig. 3 - 5). In fig. 4, the gravitational-electromagnetic resonance of the Sun is presented most expressively, namely, it is clearly visible at a frequency of 202.97 kHz, which corresponds to the quantization step of the Sun of 1477.036 m. For more information and relevant figures on the issue of gravitational-electromagnetic resonance see here:

Gravitational-electromagnetic resonance of the Sun as one of the possible sources of auroral radio emission of the planets in the kilometer range.

https://hal.archives-ouvertes.fr/hal-01232287v1

Gravitational-electromagnetic resonance of the Sun in the low-frequency of the radio spectrum of the Jupiter.

https://hal.archives-ouvertes.fr/hal-01326265v1

Planck’s universal proportions. Gravitational - electromagnetic resonance.

https://hal.archives-ouvertes.fr/hal-01329094v1

Dear Valery Timkov

I think that you should avoid any mention of quantum physics, because what you are speaking about is EM-radiation (not photons). So, what you are speaking about is oscillation of charged particles in the atmosphere of the sun, emitting radio waves.

In such a scenario you detection of oscillations becomes more realistic.

JES

Dear Stellan Gustafsson,

with regard to quantum physics, please pay attention to the similarity of Planck's formula: E = h * ν; and Einstein's formulas: E = m * hg, where hg = c ^ 2 is the quantum of the gravitational field. As for the gravitational-electromagnetic resonance of stars and their clusters, then ALL of their spectrums of electromagnetic radiation is modulated by an envelope whose wavelength is the step of their gravitational quantization.

Dear Valery Timkov

As far as I know; the "detected photon" with the lowest energy had a wavelength some mm (CERN).

The quantum jump is an atomic phenomenon, directly connected with the photons associated wave.

At the scale in question, there are no photons, since the EM-wave is an independent phenomenon, where there is no quantum jumps (associated wave).

The EM-wave is continues, without any discontinuity.

JES

Dear Stellan Gustafsson,

a standing gravitational wave is a representation of the geometry of real space around a gravitating body that is stylized to a wave and adapted to our knowledge. The essence of this geometric picture is the curvature, deformation of space under the influence of the gravitational field of a gravitating body. And now the most important thing in the geometry of curved space - IT HAS A STRUCTURE. This structure consists of many equipotential spherical surfaces embedded in each other, which are separated from each other by a quantization step. If we number these spherical equipotential surfaces, starting from the one located at the center of gravity, then moving away from this center of gravity, their gravitational potentials will decrease as follows: on the surface of the first sphere there will be a potential that is equal to the quantum of the gravitational field (с ^ 2), on the surface of the second sphere, the gravitational potential will become 2 times less, the third - less than 3 times ... n the surface less than 1 / n. This means that two adjacent spherical layers will have different (!!!) gravitational energy density values ​​(!), And the equipotential surface between these layers is their section boundary. The essence of the process: let the source of electromagnetic radiation be at the center of gravity, then when the electromagnetic wave propagates, the electromagnetic wave will successively cross spherical layers with different energy properties. This will lead to the fact that its amplitude will be modulated, and the modulation depth and its wavelength will be determined by the mass of the radiating body, that is, its quantization step.

Dear Soudip Sinha Roy,

thank you for the link. Interesting.

Any body of the observable Universe can be unambiguously(!) determined using one of its three mutually related characteristics: of mass m, of quantization step S, and of time (delay) td of the propagation of the light signal c over a distance that is equal to the quantization step. Knowing one of the three characteristics, the other two can be determined through the Planck proportions, which are based on Planck's constants: of mass mp, of length lp, of time tp. For example,

if the mass m is known, then: S = (lp / mp) * m, td = (tp / mp) * m;

if the quantization step S is known, then: m = (mp / lp) * S, td = (tp / lp) * S = S / c; if the delay time td is known, then: m = (mp / tp) * td, S = (lp / tp) * td = c * td.

Then Einstein’s formula for the total energy of the body E has the form:

E = m * c ^ 2 = Fp * S = Fp * c * td.

Where Fp is Planck's power.

Or: E = (h * td) / (tp ^ 2).

Where h is Planck's constant.

We determine the Planck force through the gravitational constant G.

Then: Fp = (c ^ 4) / G. Then: E = [(c ^ 4) / G] * S = [(c ^ 5) / G] * td.

See the article:

Planck’s universal proportions. Gravitational - electromagnetic resonance.

https://hal.archives-ouvertes.fr/hal-01329094v1

And also a preprint:

Quantum of the gravitational field. Theoretical and experimental substantiation of gravitational electromagnetic resonance.

https://hal.archives-ouvertes.fr/hal-02553557

The building block of the Universe is quantum mechanics phenomenon. The Universe is holding pre-much very large number of unknown galaxies, and holding all its galaxies in very moderate distance, therefore it must universe is following certain criteria by its nature to put them in such manner, shape and distance. Thus, Gravity must be a Quantum mechanics remark or, gravity become Internal Not external as we think. All evidence shows this phenomenon as internal .

https://www.academia.edu/38373675/Creation_of_a_Quantum_Mechanic_Universe_and_its_Rotation.doc

Article Gravity is an Internal Force

It is known that the Schwarzschild radius (gravitational radius) determines the event horizon of any gravitating body, that is, determines the radius black hole.

The Schwarzschild sphere is located at a distance of two quantization steps from the center of gravity. See a preprint: Quantum of the gravitational field. Theoretical and experimental substantiation of gravitational electromagnetic resonance. https://hal.archives-ouvertes.fr/hal-02553557

It is known that the Hubble radius, that is, the radius of the observable Universe is two times smaller than the Schwarzschild radius, see formulas (76,77) in the preprint:

Analytical evaluation of the numerical values of the Hubble constant and main spatial-energy characteristics of the observable Universe.

https://hal.archives-ouvertes.fr/hal-02045149v3

The rhetorical question: can the observed Universe expand, like the Hubble sphere, while being a black hole?

Answer: The unambiguously observable Universe as the Hubble sphere cannot expand. Given the redshift from distant objects, the observable Universe can only rotate. See article: Rotating space of the Universe, as a source of dark energy and dark matter. https://hal.archives-ouvertes.fr/hal-01329145v1

The concept of the quantum-wave nature of the gravitational field does not contradict the general theory of relativity, but supplements it and develops it.

In particular, for example, the gravitational field has a structure in the form of standing gravitational waves. Mathematical description of standing gravitational waves - formulas (122 - 124) in the preprint:

Quantum of the gravitational field. Theoretical and experimental substantiation of gravitational electromagnetic resonance.

https://hal.archives-ouvertes.fr/hal-02553557

it is actually an analog of the equations of the general theory of relativity. These formulas show the redundancy of the mathematical apparatus of general relativity, and there is also no lambda calibration coefficient in these equations. The absence of the lambda coefficient in equations (122-124) turns the hypothesis of dark energy into absurdity.

Dear Valery Timkov ,

The gravitational field cannot be quantized! Only the variation of the gravitational field can be quantized the gravitation quantum depends on the length of (‘wave’)…

The before made statements were made onto the next article:

https://www.researchgate.net/publication/327201504_Gravity_a_paradym_shift_in_reasoning

https://www.researchgate.net/publication/321641934_A_2017_Fizikai_Nobel-dij_gravitacios_hullamai

https://www.researchgate.net/publication/313632704_AZ_ELMELETI_TUDOMANY_KENYES_JELENSEGE

https://www.researchgate.net/publication/277364319_Tenyekkel_igazolhato_a_gravitacio_valos_oka

Regards,

Laszlo Attila Horvath

According to

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

https://www.aanda.org/component/article?access=doi&doi=10.1051/0004-6361/201833910

https://www.aanda.org/articles/aa/pdf/forth/aa33910-18.pdf

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 S instead of the Einstein time-like and space-like interval in of the following form: S = r * [V(r) / c^2],

where V(r) is the gravitational potential of the gravitating object at a distance r from the center of gravity, c is the speed of light in vacuum, see preprint:

Quantum of the gravitational field. Theoretical and experimental substantiation of gravitational electromagnetic resonance.

https://hal.archives-ouvertes.fr/hal-02553557

or:

Preprint Quantum of the gravitational field. Theoretical and experime...

Lior Shamir in the latest version of the preprint based on numerous experimental data from various sources:

Multipole alignment in the large-scale distribution of spin direction of spiral galaxies https://arxiv.org/abs/2004.02963

showed that the observed Universe possibly rotates in 4 axes in complex alignment. On this basis, we can assume that: 1. The space of the observable Universe existed and rotated before the Big Bang around the center of gravity - the point of singularity. 2. The source and cause of the Big Bang was the collision of the observable Universe with the neighboring universe. See the article which shows that in the gravitational fractal of the Universe there can be more than 10 ^ 37 universes that are similar to the observed Universe:

FRACTAL STRUCTURE OF THE UNIVERSE. https://hal.archives-ouvertes.fr/hal-01330337v1

3. This collision led to a quadrupole rotation of the space of the observable Universe. It is possible that the observable Universe began a “dance” of merging with the neighboring universe. 4. The quadrupole rotation of the observable Universe led to the formation of the Coriolis force, which adds 6.8% to the kinetic energy of rotation of the space of the observable Universe. See article:

ROTATING SPACE OF THE UNIVERSE, AS A SOURCE OF DARK ENERGY AND DARK MATTER. https://hal.archives-ouvertes.fr/hal-01329145v1

The quantum of energy of the electromagnetic field ħ, the gravitational constant G and the Planck force Fp can be determined through the quantum of the energy of the gravitational field hg, as well as the Planck constants: of mass mp, of length lp, of time tp: ħ= mp· tp· hg; G = ( lp/mp)·hg; Fp = ( mp/lp)·hg; obvious: (hg)^2 = G·Fp.

Analysis of the formulas for the energy quantum of the electromagnetic field ħ = mp • ([lp ^ 2] / tp) = mp • lp • c = mp • tp • hg and the energy quantum of the gravitational field hg = [lp ^ 2] / [tp ^ 2] = c ^ 2, where c is the speed of light in vacuum, shows at first glance a paradoxical situation: the quantum of energy of the electromagnetic field depends on the mass, and the quantum of energy of the gravitational field does not depend on the mass, but depends only on the square of the speed of the limiting transfer of physical interaction in the observable Universe. The dependence of the quantum of energy of the electromagnetic field on the mass (more correctly on the moment of mass) follows from the fact that the electric charge of an electron e is a function of the moment of mass: e ^ 2 = (10 ^ 7) • α • mp • lp, where: α is a constant fine structure, see the article: ELECTRIC CHARGE AS A FUNCTION OF THE MOMENT OF MASS. GRAVITATIONAL FORM OF COULOMB'S LAW (*)

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

As for the quantum of energy of the gravitational field, we will conduct a mental hypothetical experiment. There are three fundamental physical quantities: length, mass (energy), time, on the basis of which most of the other fundamental physical quantities can be obtained. Can these quantities exist separately from each other? Obviously not, they cannot. Really. First of all, one can mentally imagine the existence of space separately from the mass (energy) and time, but mass (energy) and time cannot even mentally exist without space. In space, in which there is no mass (energy) and time, there is no concept of measurement, standard, dimensionality, and dimension. It is infinite in dimensionality and dimension. Let's imagine a hypothetical non-material point in this space. This point can be fixed or move only along straight lines with infinite speed (there is no concept of time). For any infinite space, you can think of such an infinite speed that this space will contract to a point. Conclusion - the speed of an immaterial point in ideal space can have only two values ​​- zero and infinity. It follows from what has been said that one can hypothetically represent a space in which there is no mass (energy) and time, but in reality, there is no such space. Let there be no mass (energy) in space, but time appears. Changes, measurements, and standards in such space are absent, therefore, even hypothetically, time cannot appear in it. Time is a complex characteristic of real space, in which there is the mass (energy). Let a material point appear in an ideal space with a mass equal, for example, to the baryon mass of the observable Universe 1.844 • 10 ^ 53 kg, see the preprint: Analytical evaluation of the numerical values ​​of the Hubble constant and main spatial-energy characteristics of the observable Universe (**).

https://hal.archives-ouvertes.fr/hal-02045149v3

Around this material point under the influence of its gravitational field, space will be curved. The picture of such a curved space is a set of nested equipotential spherical surfaces that are separated from each other by a quantization step, in this case, the character it is the Hubble radius 1.369 • 10 ^ 26 m (see **),

see the preprint:

Quantum of the gravitational field. Theoretical and experimental substantiation of gravitational electromagnetic resonance.

https://hal.archives-ouvertes.fr/hal-02553557v1

The concept of time appears in space, and the speed of movement can vary from 0 to a certain maximum value. Why can't speed be infinite in real space? Because in such a real space such a phenomenon as inhibition, obstruction, resistance to movement appears. In electromagnetism there is a certain analogy to this phenomenon - electrical resistance, its unit of measurement, ohm, can also be measured in units of measurement of speed (see *). Braking, obstruction, resistance to motion is caused by two factors: 1) the “viscosity” of real space, since in this space the mass (energy) density is nonzero, for example, for the Hubble sphere it is 1.72 • 10 ^ (- 26) kg ^ 1m ^ (-3); 2) the curvature of space. Let's do a thought experiment. Let gravity be only viscous and it does not bend space. Let's place a light source, for example, on the surface of a Hubble sphere. Then the light will propagate in all directions inside the Hubble sphere only along straight lines and its speed will depend only on the value of gravitational viscosity. We “turn on” the curvature of space by gravity, then the light will propagate exclusively along curved lines and in the limiting case, it will reach the opposite point on the Hubble sphere in a time that is pi times longer than for the case of only viscous gravitational space. In other words, the curvature of space increases the path of the light signal (and, accordingly, the time of its propagation) as many times as the chord is less than her the contracting arc.

Thus, the maximum possible transmission speed of physical interaction (the speed of light) fully takes into account both the viscosity factor of the gravitational field and the factor of space curvature under its action, this speed is one of the main characteristics of the gravitational field, and its square is the quantum of this field.

In the article:

FRACTAL STRUCTURE OF THE UNIVERSE

https://hal.archives-ouvertes.fr/hal-01330337v1

a hypothesis about the fractal hierarchical structure of the universe is proposed. In ascending order of the hierarchy, the following fractals of the universe are distinguished: nuclear, electromagnetic, gravitational. Between the nuclear and electromagnetic fractals, there is a borderline, transitional fractal - atomic. It can also be assumed that there are fractals of the universe that are older than its gravitational fractal, and there is a transition fractal between the electromagnetic fractal of the universe - that is, the observable Universe, as the Hubble sphere and the gravitational fractal of the universe. The space of this fractal has a toroidal shape and is located between the Hubble sphere and the Schwarzschild sphere (radius of the Schwarzschild sphere = 2 radii of the Hubble sphere). Since the maximum transfer rate of physical interaction in an atom is 137.035999 times less than the speed of light, then taking into account the decrease in the mass density (that is, gravitational viscosity) in the transition fractal, it can be assumed that the maximum transfer rate of physical interaction in it will be greater than the speed of light.

Hypothesis. Let the radius of an elementary particle, which can be determined experimentally, is equal to the gravitational radius of one of the equipotential surfaces of its gravitational field. The quantization step S of the gravitational field of an elementary particle, the mass of which is m, is:

S = (m*G)/(c^2) = m*(lp/mp). (**)

Where G is the gravitational constant, c is the speed of light in vacuum, lp, mp is the Planck length and mass. Then: for a proton

Spr = 1,2421158474963510*10^(-54) m.

The gravitational radius of a proton: RGpr = 2 * Spr = 2,484231694992702*10^(-54) m.

In the course of the experiments, numerous estimates of the proton radius Rpr were obtained, which range from 8,31*10^(-16) m to 8,751*10^(-16) m.

Then the equipotential surface of the gravitational field of the proton, the number of which 7*10^(38) coincides with the radius of the proton

Rpr = 8,694810*10^(-16) m.

Since in formula (**) the quantization step of the gravitational field is directly proportional to the mass, then based on the mass ratios (see CODATA 2018): proton and electron, proton and neutron, proton and muon, we obtain estimates of the values ​​of the electron radii

Re = 4,7353420*10^(-19) m,

of the muon

Rμ = 9,7914538*10^(-17) m,

of the neutron

Rn = 8,68284234*10^(-16) m.

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.

See the conference paper:

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

Conference Paper THE QUANTUM OF THE GRAVITATIONL FIELD. THE GRAVITATIONAL-ELE...

The gravitational field in relation to space-time has two fundamental properties: 1) bends it, 2) creates viscosity in it, as an obstacle (resistance) to motion.

The viscosity of the gravitational field does not make it possible to ensure movement in space-time with infinite speed. The maximum possible transmission rate of physical interaction, that is, the speed of light in a vacuum, is determined exclusively by the spatial and energy parameters of the Hubble sphere, as the observable Universe. The fact that the speed of light is a constant is solely a result of the fact that the observable Universe is limited. The limitedness of the observable Universe and, as a consequence, the constancy of the speed of light, speaks of the absence of dark energy in nature. The presence of redshift from distant objects of the observable Universe indicates the rotation of its space.

It is known that the energy EU of the observable Universe is:

EU = MUc2,

where MU is the mass of baryonic matter in the observable Universe, c is the speed of light in a vacuum.

On the other hand, according to the law "Universal Planck Proportions":

EU = FPRU,

where FP is the Planck force, RU is the radius of the observable Universe, that is, the Hubble radius.

Then:

c2 = (FP/MU)RU.

c = SQRT[(FP/MU)RU]. (*)

On the right side of formula (*), all operands that determine the main spatial and energy characteristics of the observable Universe are constants, therefore the speed of light is a constant. Let the space of the observable Universe expand under the action of the force of dark energy. Then the radius RU also increases. Which leads to an increase in the speed of light in a vacuum. In practice, we do not observe an increase in the speed of light in a vacuum, which means that the radius RU is constant. But we observe redshift from distant objects of the observable Universe. This is possible only when the space of the observable Universe rotates.

PS. in (*), all operands that determine the main spatial and energy characteristics of the observable Universe: the Planck force is equal to the force of gravitational compression of the observable Universe, see preprint:

"Analytical evaluation of the numerical values of the Hubble constant and main spatial-energy characteristics of the observable Universe."

https://hal.archives-ouvertes.fr/hal-02045149v3

Today the wave theory of the gravitational field is most fully and with a good mathematical apparatus presented in the series of works by S. Fedosin:

Physics / Essays / Fedosin / Maxwell-like gravitational equations

https://en.wikiversity.org/wiki/Physics/Essays/Fedosin/Maxwell-like_gravitational_equations#History

Traces of spatial parity violation were found in the polarization of the relict radiation.

Physicists Yuto Minami and Eiichiro Komatsu reported measurements of the cosmic birefringence angle based on data from the Planck mission in 2018. The value of the angle is 0.35 ± 0.14 degrees, which excludes zero with a statistical accuracy of 2.4σ, and the difference of this angle from zero indicates the swirling of the microwave background of the observable Universe, and hence of its entire space:

Yuto Minami and Eiichiro Komatsu

New Extraction of the Cosmic Birefringence from the Planck 2018 Polarization Date

https://arxiv.org/pdf/2011.11254.pdf

Conclusion. Lior Shamir, using experimental data obtained in the study of spiral galaxies (attention, matter!), Showed the presence of the twisted space of the observable Universe:

Multipole alignment in the large-scale distribution of spin direction of spiral

galaxies

https://arxiv.org/abs/2004.02963

Large-scale asymmetry between clockwise and counterclockwise galaxies revisited

https://arxiv.org/abs/2004.02960

Large-scale patterns of galaxy spin rotation show cosmological-scale parity violation and multipoles

https://arxiv.org/pdf/1912.05429.pdf

Asymmetry between galaxies with different spin patterns: A comparison between COSMOS, SDSS, and Pan-STARRS

https://arxiv.org/abs/1911.11735

Yuto Minami and Eiichiro Komatsu showed the curl of space on the experimental CMB data, which fills, permeates the entire space of the observable Universe. This means that the observable Universe is rotating.