### THE PHYSICAL CONTENT OF h‑SPACE THEORY

**GRAVITATIONAL ATTRACTION**

To understand the gravitational attraction we refer back to the idea from the section “Definition of relative motion of n=0‑objects(II)”−”,”+” and n=0-objects(I)”, where the density of undirected n=0-objects(I) around n=0-objects(II)”−”,”+” (i.e. electrons and positrons), ρ_{0},was shown to decreased. The magnitude of this decrease in density ρ_{M }is determined by the following equation and is inversely proportional to the square of the distance R:

ρ_{M} = MLq_{0}/Lq4πR^{2}

where R – distance measured in the length of n=0-object(I), M – the number of n=0-objects(II)”−”,”+” placed in a three-dimensional volume of the n=0-object(I), (Lq)^{3}.

The density gradient of undirected n=0-objects(I), which are moving relative to each other, means that electrons/positrons attract each other along the gradient, regardless of their charge (see “Definition of relative motion of n=0-objects(II)”−”,”+” and n=0‑objects(I)”). Accordingly, at a distance Rthe velocity Vof attraction of a body to a body consisting of n=0-objects(II)”−”,”+” in a three-dimensional volume of the n=0-object(I), (Lq)^{3}, in an amount equal to Mis determined by the following equation:

V = v_{0}ρ_{M} = v_{0}MLq_{0}/Lq4πR^{2}

The velocity of attraction at the distance R – ΔR,after start of movement from the distance R,is defined by the following sum of velocities, similar to the velocity of attraction/repulsion of pairs of n=0‑objects(II)”−”,”+”:

R − ΔR

V = (v_{0}MLq_{0}/Lq4π) Σ R^{−2}

R

where R − ΔR and R are distances measured by the length of n=0‑object(I), M– the number of n=0-objects(II)”−”,”+” placed in a three-dimensional volume of the n=0-object(I), (Lq)^{3}.

Based on the above, we can then calculate the density ρ_{M }for the physical body, composed of atoms and having a linear size equal to the length of n=0-object(I), i.e. ≈ 10^{-5} m. The number of atoms (linear size of the atom ≈ 10^{-10} m) in the volume of ≈ (10^{-5})^{3} m is equal to (10^{-5})^{3}/(10^{-10})^{3} ≈ 10^{15}. Each atom contains on average 100 to 1000 electrons and positrons. Thus, the entire amount of the electrons and positrons in a volume of ≈ (10^{-5})^{3} m^{3 }is equal to about 10^{17} – 10^{18}. To displace one n=0-object(I), the number of electrons/positrons must be equal to the ratio Lq/Lq_{0} – 10^{-5}/10^{-15}≈ 10^{10}. Then, to calculate the decrease in density ρ_{M}we have the following equation:

ρ_{M} = 10^{18}10^{−15}/10^{−5}4πR^{2 }= 10^{8}/4πR^{2}

where R is distance measured in the length of n=0‑object(I), Lq,

Next, we consider a physical body composed of atoms and having a linear size greater than the length of n=0-object(I), ≈ 10^{-5} m. This body can be represented as a sum of bodies whose linear dimensions are equal to the length of the n=0-object(I), ≈ 10^{-5} m. For each of these parts, a decrease in density of n=0-objects(I) ρ_{M}is defined not only by the number of electrons and positrons in the volume of this part, but also by the presence of electrons and positrons in neighboring parts of the body. However, the decreasing effect of adjacent parts is small since it is inversely proportional to the square of the distance. If the number of the electrons and positrons is the same in each part of the body (i.e. in the each volume of n=0‑object(I), ≈ (10^{-5})^{3} m^{3}), then for the approximate calculation of a decrease in density of n=0-objects(I)ρ_{M}we can use the entire length of this physical body as distance unit instead of the length of n=0-object(I). I.e. in the equation above the distance R can be measured in units equal to the linear size of the body. For accurate calculation, it is necessary to sum up the reducing effects on density of n=0-objects(I) ρ_{M}from the adjacent parts having a volume of n=0-object(I), ≈ (10^{-5})^{3} m^{3}.

Analogously as in the case of electrostatic interaction, the gravitational force has an upper bound, i.e. a maximum distance of the gravitational attraction, R_{max}.This distance corresponds to the minimum change in density equal to a single n=0-object(I). The lower boundary, i.e. the minimum distance of the gravitational attraction, R_{min}, corresponds to the length of an n=0-object(II)”-“, “+”. The maximum distance of the gravitational attraction, generated by physical body consisting of atoms, can be calculated as follows. The decrease of density, ρ_{M}, for such a body can be considered the same all along the linear size of a body – ρ_{M} = 10^{8}/4πR^{2}. Then, a linear body size L_{X}can be used as the unit of length to measure the distance R. This approximation is a minimum estimate of the decrease of density, ρ_{M}. From the equality of the density ρ_{M}to one (1 = 10^{8}/4πR^{2}),the maximum distance R_{max }is the square root of 10^{8}/8π, √(10^{8}/8π). As an example, we can determine the maximum boundary of gravitational attraction for the Earth, Jupiter and the Sun. For the Earth, the unit of length R is the Earth’s diameter, ≈ 10^{7} m. A calculation for the Earth gives a gravitational boundary of about 10 million kilometers, ≈ √(10^{8}/4π)х10^{7} ≈ 10^{3}х10^{7} m,which is about 14 times smaller than the distance from the Earth to the Sun (Fig. 22). For Jupiter, with a diameter 10 times larger than the Earth, the border will be about 100 million kilometers, ≈ √(10^{8}/4π)х10^{8} ≈ 10^{3}х10^{8} m, which is about 7 times less than the distance from Jupiter to the Sun. The value of the decrease in density of n=0-objects(I), ρ_{M}_{ }, for the Sun, ρ_{Sun },is different from that of a planet composed by atoms. In the section below, which discusses star formation, it was assumed that stars are composed of densely packed electrons and positrons, the same as atomic nuclei. This implies that the volume of n=0-object(I) contains the number of electron/positron equal to the ratio – (Lq)^{3}/(Lq_{0})^{3} = (10^{-5})^{3}/(10^{-15})^{3} = 10^{30}. From the above, to displace one n=0-object(I) the volume of n=0-object(I) must contain the number of electrons/positrons equal to the ratio Lq/Lq_{0}, 10^{-5}/10^{-15} ≈ 10^{10}. Accordingly, the decrease of the density of n=0-objects(I), ρ_{M}_{ }, can be up to 10^{20}. Since today the density of n=0‑objects(I), ρ_{0}, is equal to ≈ 10^{10}, it is reduced by the electrons/positrons of the Sun up to one n=0-object(I). I.e. for the stars today all n=0-objects(I) are displaced by electrons and positrons, and a decrease in density of n=0-objects(I), ρ_{M}_{ }, is equal to 10^{10}. From the equation 1 = ρ_{M}/8πR^{2}, the maximum distance R_{max}, in units of Sun diameters (10^{9} m), is the square root of 10^{10}/8π, i.e. ≈ 10^{4 }Sun diameters, or 10^{13 }meters (Fig. 22). This is comparable with the distance from the Sun to the Kuiper belt.

**Fig. 22**

If the distance between two bodies having masses of Mand N(where the masses are expressed as the amounts of n=0‑objects(II)”−”,”+” (electrons, positrons)), is less than the maximum distance of the gravitational attraction, then the velocity of gravitational attraction is proportional to the product of the masses:

R − ΔR

V = (v_{0}MNLq_{0}/Lq4π) ΣR^{−2}

R

where R − ΔR and R are distances measured by the length of n=0‑object(I), Lq; M and N – the numbers of n=0‑objects(II)”−”,”+” comprising the two bodies M and N.

Since gravity has boundary in the proposed model, the formation of galaxies is different and is not a result of gravitational contraction of the hydrogen masses (see section “Cosmology”).

Similar to the attraction shown between bodies (composed by electrons and positrons), non-zero-dimensional objects, like electromagnetic quanta (n=1-objects), will also be attracted by bodies consisted of electrons and positrons, as a result of the movement of undirected n=0‑objects(I) having density gradient created by bodies.

As described in the section “Electrostatics”, changes in the electrostatic field of moving charges does not act with the velocity of interaction, but instantly. This is because the velocity of attraction/repulsion of charges is determined by the spatial distribution of density of directed n=0-objects(I) between them, and follows an inverse square law. An inverse square law applies also for gravitational interactions, but there are some differences. In the case of charge interactions, the density of undirected n=0‑objects(I), ρ_{0}, determining the density of directed n=0‑objects(I), is constant with the motion of charges. In the case of gravity, the density of the undirected n=0-objects(I), which determines the interaction, is the density ρ_{M}of undirected n=0‑objects(I) replaced by the gravitating body. The process of displacement is not instantaneous, but occurs at a velocity that depends on the initial density of undirected n=0‑objects(I)ρ_{0}, and is comparable to the speed of light. Accordingly, a moving body displaces the undirected n=0-objects(I) from the body volume at velocity v_{0}ρ_{0}, and, consequently, there is a time delay in changing the gravitational attraction of the moving body. In another case, when one body is at a resting state and the other is moving, the resting body acts on the moving body instantly. The consequence of this mechanism of gravitation is that when a body moves faster than v_{0}ρ_{0}, the undirected n=0‑objects(I) will not be replaced by this body. The moving body will leave the area earlier than the n=0‑objects(I). As a result, the body moving at such a speed does not generate gravity. This relationship can be expressed in terms of the effective gravitational mass, M_{effective}, and resting mass, M, as follows: M_{effective} = M(1 − V/v_{0}ρ_{0}). If a body revolves around another body, the effective gravitational mass, M_{effective}, of a rotating body is: M_{effective} = M√(1 − V^{2}/(v_{0}ρ_{0})^{2}).

A consequence of the proposed mechanism of gravitation, which is based on the change in density ρ_{0}, is a change of the charge of an electron in a gravitational field, since the elementary charge is determined by the density of undirected n=0-objects(I), ρ_{0}. The increase of density ρ_{M}(increase of gravity) corresponds to a decrease in ρ_{0}, i.e. a decrease of the elementary charge. In the suggested theory, the observed gravitational redshift can be explained by a decrease in the density ρ_{0}, since, according to the equation for the generated quantum (see “Secondary formation of n≠0-objects“), its wavelength is inversely proportional to the density ρ_{0}.

λ = ^{1}L = Lv_{1}q_{0}3/4πρ_{0}((1/n^{2}) − (1/m^{2}))

The closer generating atoms are to a massive body, the lower is the density ρ_{0 }and, consequently, the longer the wavelength and the greater the shift of the observed spectral lines to the red region of the spectrum. From experimental data for light emitted at a distance rfrom a massive body (and received at infinity), the shift is approximately equal to:

z_{approx} = GM/c^{2}r

where z_{approx}– the shift of spectral lines under the influence of gravity (as measured by an observer at infinity), G – Newton’s gravitational constant, M – mass of the gravitating body, c – the speed of light, r – the radial distance from the center of the source body.

Another consequence of the proposed mechanism of gravitation is the existence of so-called black holes. By definition, a black hole is a region in space, which cannot emit light quanta due to the strong gravitational attraction. In the suggested theory, this is possible because of the reduction in density of undirected n=0‑objects(I), ρ_{0}, from 10^{10 }down to 1. This means that the velocity of gravitational attraction, v_{0}ρ_{0}, will be greater than the speed of light. As noted above, the decrease in density of undirected n=0-objects(I) by 10^{10 }times is typical for all stars, including the Sun. Thus, the velocity of Sun gravity is greater than the speed of light, and therefore we can say that Sun has a black hole inside. In addition, since the density of n=0‑objects(I) inside the Sun is minimal, i.e. equal to 1 (n=0-objects(I) are displaced by electrons/positrons) inside the Sun, the generation of electromagnetic rays is not possible, since the change in the density of n=0‑objects(I) is less than 1is not possible. The same is valid for all the stars. This follows from the equation for generated electromagnetic quanta, n=1-objects:

λ = ^{1}L = Lv_{1}q_{0}3/4πρ_{0}((1/n^{2}) − (1/m^{2}))

Therefore, stars are cold inside. Radiation occurs only at the surface, since there the density of n=0-objects(I) is greater than one.

**COMMENTS**

In the suggested theory, the cause of gravitational attraction is due to the presence of the density gradient of the vacuum particle (undirected n=0‑objects(I)). It is formed around the body because of the three-dimensional density distribution of the displaced vacuum particles from the volume of the gravitating body. As a result, a body will move along this density gradient of the vacuum particles towards the gravitating body. Thus, as in general relativity, the underlying basis of gravity is geometric, the existence of three-dimensional space. Unlike general relativity, the suggested theory posits that the various gravitational effects are explained not by time dilation, but by a change of density (about general relativity, see below) of the vacuum particles (undirected n=0-objects(I)) in three-dimensional Euclidean space.

In contrast to existing theories of gravitation, which describe interactions over unlimited distances, the proposed theory of gravitational attraction has a maximal boundary defined by the mass. Because of this, the gravitational interaction should be redefined as the gravitational attraction. If a body of greater mass can attract a body of lower mass, the body of lower mass may not be able to act on a body of greater mass if the latter body is far from the maximal boundary of gravity of the body of lower mass.

As described above, the electric charge is determined by the density of undirected n=0-objects(I), ρ_{0}. The increase of density ρ_{M}(increase of gravity) corresponds to a decrease in ρ_{0}, i.e. a decrease of the elementary charge. This means that magnetic interaction depends on the gravitational potential, i.e. it should be weaker at Earth surface than at the distance from it.