# 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: [1] ${\displaystyle c=2.99792458\cdot 10^{8}\ }$ m/s, as exact value. It has become a defined constant in the SI system of units.

Electric constant or vacuum permittivity: [2] ${\displaystyle \varepsilon _{0}=8.854187817\cdot 10^{-12}\ }$ F/m.

Speed of gravity ${\displaystyle c_{g}}$. It is supposed that ${\displaystyle c_{g}}$ equals to the speed of light.

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

## Derivative constants

Vacuum permeability: ${\displaystyle \mu _{0}={\frac {1}{\varepsilon _{0}c^{2}}}=4\pi \cdot 10^{-7}=1.2566370614\cdot 10^{-6}\ }$ H/m in the SI system of units.

Electromagnetic impedance of free space:

${\displaystyle Z_{0}=\mu _{0}c={\sqrt {\frac {\mu _{0}}{\varepsilon _{0}}}}={\frac {1}{\varepsilon _{0}c}}=376.730313461\ldots \Omega .}$

Since ${\displaystyle \mu _{0}}$ and ${\displaystyle c}$ have exact values the same is for impedance of free space:

${\displaystyle Z_{0}=119.9169832\pi \quad \Omega .}$

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

Gravitomagnetic gravitational constant: ${\displaystyle ~\mu _{g}={\frac {4\pi G}{c_{g}^{2}}}=9.328772\cdot 10^{-27}\quad \mathrm {m/kg} }$, if ${\displaystyle c_{g}=c}$.

${\displaystyle ~\rho _{g}={\sqrt {\frac {\mu _{g}}{\varepsilon _{g}}}}={\frac {4\pi G}{c_{g}}}.}$

If ${\displaystyle ~c_{g}=c,}$ then gravitational characteristic impedance of free space equals to: [3] [4]

${\displaystyle ~\rho _{g0}={\frac {4\pi G}{c}}=2.796696\cdot 10^{-18}\quad \mathrm {m^{2}/(s\cdot kg)} .}$

Constants ${\displaystyle c}$, ${\displaystyle \varepsilon _{0}}$, ${\displaystyle \mu _{0}}$ and ${\displaystyle Z_{0}}$ belong to selfconsistent electromagnetic constants, and constants ${\displaystyle c_{g}}$, ${\displaystyle \varepsilon _{g}}$, ${\displaystyle \mu _{g}}$ and ${\displaystyle \rho _{g}}$ 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 ${\displaystyle e}$:

${\displaystyle m_{S}=e{\sqrt {\frac {\varepsilon _{g}}{\varepsilon _{0}}}}=e{\sqrt {\frac {\mu _{0}}{\mu _{g}}}}=e{\sqrt {\frac {Z_{0}}{\rho _{g0}}}}.}$

The Planck mass is connected with Dirac constant ${\displaystyle \hbar }$:

${\displaystyle m_{P}={\sqrt {\frac {\hbar c}{G}}}.}$

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 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. [5]

For cubic distribution of graviton fluxes in space the gravitational constant is given by the formula: [6]

${\displaystyle ~G={\frac {\varepsilon _{c}\sigma ^{2}}{4\pi M_{n}^{2}}},}$

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

Similarly, for the vacuum permittivity we obtain: [7]

${\displaystyle ~\varepsilon _{0}={\frac {e^{2}}{\varepsilon _{cq}\vartheta ^{2}}},}$

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

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

The strong gravitational constant is also related to the vacuum field:

${\displaystyle ~G_{a}={\frac {\varepsilon _{c}\vartheta ^{2}}{4\pi M_{n}^{2}}}=1.514\cdot 10^{29}}$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.

## References

1. CODATA value: Speed of Light in Vacuum. The NIST reference on Constants, Units, and Uncertainty. NIST.
2. Latest (2010) values of the constants [1]
3. J. D. Kraus, IEEE Antennas and Propagation. Magazine 33, 21 (1991).
4. Raymond Y. Chiao. "New directions for gravitational wave physics via “Millikan oil drops”, arXiv:gr-qc/0610146v16 (2007).PDF
5. Fedosin S.G. The Force Vacuum Field as an Alternative to the Ether and Quantum Vacuum. WSEAS Transactions on Applied and Theoretical Mechanics, ISSN / E-ISSN: 1991-8747 / 2224-3429, Volume 10, Art. #3, pp. 31-38 (2015).
6. Fedosin S.G. The graviton field as the source of mass and gravitational force in the modernized Le Sage’s model. Physical Science International Journal, ISSN: 2348-0130, Vol. 8, Issue 4, pp. 1-18 (2015). http://dx.doi.org/10.9734/PSIJ/2015/22197.
7. Fedosin S.G. The charged component of the vacuum field as the source of electric force in the modernized Le Sage’s model. Journal of Fundamental and Applied Sciences, Vol. 8, No. 3, pp. 971-1020 (2016). https://dx.doi.org/10.5281/zenodo.845357.