Physics/Essays/Fedosin/Vacuum constants

Vacuum constants are physical constants associated with the fields existing in the free space under high vacuum. The values of these constants can be determined from the analysis of the interaction of fields with matter. Vacuum constants come in a variety of physical equations as necessary coefficients. Because of this, great importance is the refinement of these constants in special experiments.

Basic constants
Speed of light: $$c = 2.99792458\cdot 10^8 \ $$ m/s, as exact value. It has become a defined constant in the SI system of units.

Electric constant or vacuum permittivity: $$ \varepsilon_0 = 8.854187817\cdot 10^{-12} \ $$ F/m.

Speed of gravity $$c_g $$. It is supposed that $$c_g $$ equals to the speed of light.

Gravitational constant: $$ G = 6.67384(80) \times 10^{-11} \ \rm{m}^3 \ \rm{kg}^{-1} \ \rm{s}^{-2} = 6.67384(80) \times 10^{-11} \ {\rm N} \ {\rm m^{2}} \ {\rm  kg^{-2}}.$$

Derivative constants
Vacuum permeability: $$ \mu_0 = \frac{1}{\varepsilon_0 c^2}=4 \pi \cdot 10^{-7} = 1.2566370614 \cdot 10^{-6} \ $$ H/m in the SI system of units.

Electromagnetic impedance of free space:
 * $$ Z_0 = \mu_0 c = \sqrt{\frac{\mu_0}{\varepsilon_0}}= \frac{1}{\varepsilon_0 c} = 376.730313461 \ldots \Omega. $$

Since $$ \mu_0$$ and $$ c $$ have exact values the same is for impedance of free space:
 * $$ Z_0 = 119.9169832 \pi \quad \Omega. $$

Gravitoelectric gravitational constant: $$~\varepsilon_g = \frac{1}{4\pi G } = 1.192708\cdot 10^9 \quad \mathrm {kg \cdot s^2 \cdot m^{-3}}. $$

Gravitomagnetic gravitational constant: $$~\mu_g = \frac{4\pi G }{ c^2_g} = 9.328772\cdot 10^{-27}\quad \mathrm {m / kg} $$, if $$c_g =c$$.

Gravitational characteristic impedance of free space:
 * $$~\rho_{g} =\sqrt{\frac{\mu_g}{\varepsilon_g}} = \frac{4\pi G }{c_g}.  $$

If $$~ c_{g}=c,$$ then gravitational characteristic impedance of free space equals to:
 * $$~ \rho_{g0} = \frac{4\pi G }{c} =2.796696\cdot 10^{-18} \quad \mathrm {m^2/(s\cdot kg)}. $$

Constants $$ c $$, $$ \varepsilon_0$$, $$ \mu_0$$ and $$ Z_0$$ belong to selfconsistent electromagnetic constants, and constants $$ c_g $$, $$ \varepsilon_g$$, $$ \mu_g$$ and $$ \rho_{g} $$ belong to selfconsistent gravitational constants.

Vacuum constants are used for creation of natural units such as Stoney units and Planck units. For example, Stoney mass is connected with elementary charge $$ e $$:
 * $$m_S = e \sqrt{\frac{\varepsilon_g}{\varepsilon_0}} = e \sqrt{\frac{\mu_0}{\mu_g}} = e \sqrt{\frac{Z_0}{\rho_{g0}}}. $$

The Planck mass is connected with Dirac constant $$ \hbar $$:
 * $$m_P = \sqrt{\frac{ \hbar c}{G}} . $$

The Stoney length and the Stoney energy, collectively called the Stoney scale, are not far from the Planck length and the Planck energy, the Planck scale.

The modernized Le Sage’s theory
The vacuum constants in the modernized Le Sage’s theory can be expressed in terms of the parameters of the vacuum field and matter. It is assumed that the vacuum field contained in the electrogravitational vacuum consists of two components. The first component in the form of the graviton field is responsible for the emergence of gravitation, mass and inertia of bodies, and the second component in the form of the field of charged particles leads to electromagnetic interaction. In this case, the main active component is assumed to be the second component in the form of flows of charged particles of the praons type.

For cubic distribution of graviton fluxes in space the gravitational constant is given by the formula:
 * $$~G = \frac{ \varepsilon_c \sigma^2}{4\pi M^2_n}, $$

where $$~ \varepsilon_c = 7.4 \cdot 10^{35} $$ J/m3 is the energy density of the graviton field, $$~ \sigma = 5.6 \cdot 10^{-50} $$ m2 is the cross-section of  interaction between gravitons and the nucleon matter, $$~ M_n $$ is the nucleon mass.

Similarly, for the vacuum permittivity we obtain:
 * $$~\varepsilon_0 = \frac{ e^2}{\varepsilon_{cq} \vartheta^2 }, $$

where $$~ \varepsilon_{cq} = 4 \cdot 10^{32} $$ J/m3 is the energy density of the field of charged particles, $$~ \vartheta = 2.67 \cdot 10^{-30} $$ m2 is the cross-section of  interaction between the charged particles of the vacuum  and the nucleon matter, close to the proton cross-section, $$~ e $$ is the elementary charge.

Estimation of the concentration of charged particles as the concentration of relativistically moving praons gives the value $$ 4 \cdot 10^{87} $$ m–3.

The strong gravitational constant is also related to the vacuum field:
 * $$~G_a = \frac{ \varepsilon_c \vartheta^2}{4\pi M^2_n} = 1.514 \cdot 10^{29} $$m3•s–2•kg–1.

In the modernized Le Sage’s model it is assumed that gravitons for the ordinary gravitation are the particles of the praon level of matter, located two levels below the level of stars, which acquired their energy in the relativistic processes near nucleons. The strong gravitation is acting at the level of nucleons, and reasoning by analogy, gravitons for the strong gravitation should be the particles of the graon level of matter, which acquired their energy in the processes near praons. Gravitons can be both neutral particles, such as neutrinos and photons, and relativistic charged particles, similar in their properties to cosmic rays. The effective mass of all these particles is their relativistic mass-energy with regard to the large Lorentz factor. In particular, gravitons of the ordinary gravitation can be praons, accelerated by the strong fields near nucleons almost to the speed of light.