In physics , Natural scale is the scale, which connects with the mass of electron . The method of constructing of the scale is the same as for Planck scale and Stoney scale . Usually, the Natural scale now considered for definition of the gravitational force between electrons and has not appropriate attention that should be for the scale of matter.
The natural gravitational coupling constant is:
α
N
=
m
e
2
2
h
c
ε
g
=
1.7517846
⋅
10
−
45
,
{\displaystyle \alpha _{N}={\frac {m_{e}^{2}}{2hc\,\varepsilon _{g}}}=1.7517846\cdot 10^{-45},\ }
where
m
e
{\displaystyle m_{e}}
h
{\displaystyle h}
Planck constant ;
c
{\displaystyle c}
speed of light in vacuum;
ε
g
=
1
4
π
G
{\displaystyle \varepsilon _{g}={\frac {1}{4\pi G}}}
gravitoelectric gravitational constant ;
G
{\displaystyle G}
gravitational constant .
Fundamental units of vacuum [ edit | edit source ] The set of primary vacuum constants is: [1]
c
{\displaystyle ~c}
electric constant
ε
0
{\displaystyle ~\varepsilon _{0}}
speed of gravity
c
g
{\displaystyle ~c_{g}}
G
{\displaystyle ~G}
The set of secondary vacuum constants is:
The vacuum permeability :
μ
0
=
1
ε
0
c
2
{\displaystyle \mu _{0}={\frac {1}{\varepsilon _{0}c^{2}}}\ }
The electromagnetic impedance of free space :
Z
0
=
μ
0
c
=
μ
0
ε
0
=
1
ε
0
c
{\displaystyle Z_{0}=\mu _{0}c={\sqrt {\frac {\mu _{0}}{\varepsilon _{0}}}}={\frac {1}{\varepsilon _{0}c}}}
The gravitoelectric gravitational constant:
ε
g
=
1
4
π
G
{\displaystyle ~\varepsilon _{g}={\frac {1}{4\pi G}}}
The gravitomagnetic gravitational constant:
μ
g
=
4
π
G
c
g
2
{\displaystyle ~\mu _{g}={\frac {4\pi G}{c_{g}^{2}}}}
The gravitational characteristic impedance of free space :
ρ
g
=
μ
g
ε
g
=
4
π
G
c
g
.
{\displaystyle ~\rho _{g}={\sqrt {\frac {\mu _{g}}{\varepsilon _{g}}}}={\frac {4\pi G}{c_{g}}}.}
Natural scale units based on electron mass [ edit | edit source ] For the sake of completeness in the Table 1 the main Natural scale units in the form consistent with Tables for the Stoney scale and vacuum constants are presented.
Table 1: Base Natural scale units
Name
Dimension
Expressions
SI equivalent
Electron mass
Mass (M)
m
e
{\displaystyle m_{e}\ }
9.10938215
(
45
)
⋅
10
−
31
{\displaystyle 9.10938215(45)\cdot 10^{-31}}
Electron wavelength Length (L)
λ
N
=
h
m
e
c
{\displaystyle \lambda _{N}={\frac {h}{m_{e}c}}}
2.4263102175
(
33
)
⋅
10
−
12
{\displaystyle 2.4263102175(33)\cdot 10^{-12}}
Natural gravitational coupling constant
Dimensionless
α
N
=
m
e
2
2
h
c
ε
g
{\displaystyle \alpha _{N}={\frac {m_{e}^{2}}{2hc\varepsilon _{g}}}}
1.7517846
⋅
10
−
45
{\displaystyle 1.7517846\cdot 10^{-45}}
Natural fictitious gravitational torsion mass
Dynamic mass (L2 T −1 )
m
Ω
=
h
m
e
{\displaystyle m_{\Omega }={\frac {h}{m_{e}}}\ }
7.27339
⋅
10
−
4
{\displaystyle 7.27339\cdot 10^{-4}}
2 s −1
Natural torsion coupling constant
Dimensionless
β
N
=
m
Ω
2
2
h
c
μ
g
=
1
4
α
N
{\displaystyle \beta _{N}={\frac {m_{\Omega }^{2}}{2hc\mu _{g}}}={\frac {1}{4\alpha _{N}}}\ }
1.42757
⋅
10
44
{\displaystyle 1.42757\cdot 10^{44}}
Natural charge
Electric charge (Q)
q
N
=
2
h
c
ε
0
α
N
=
e
α
N
α
=
e
(
m
e
m
S
)
{\displaystyle q_{N}={\sqrt {2hc\varepsilon _{0}\alpha _{N}}}=e{\sqrt {\frac {\alpha _{N}}{\alpha }}}=e\left({\frac {m_{e}}{m_{S}}}\right)}
7.84854579
⋅
10
−
41
{\displaystyle 7.84854579\cdot 10^{-41}}
Natural electric coupling constant
Dimensionless
α
N
=
q
N
2
2
h
c
ε
0
{\displaystyle \alpha _{N}={\frac {q_{N}^{2}}{2hc\varepsilon _{0}}}\ }
1.7517846
⋅
10
−
45
{\displaystyle 1.7517846\cdot 10^{-45}}
Natural fictitious magnetic charge
Magnetic charge (L2 MT −1 Q−1 )
q
m
=
h
q
N
=
h
e
α
α
N
{\displaystyle q_{m}={\frac {h}{q_{N}}}={\frac {h}{e}}{\sqrt {\frac {\alpha }{\alpha _{N}}}}\ }
{
8.44229
⋅
10
6
{\displaystyle 8.44229\cdot 10^{6}}
Natural magnetic coupling constant
Dimensionless
β
N
=
q
m
2
2
h
c
μ
0
=
1
4
α
N
{\displaystyle \beta _{N}={\frac {q_{m}^{2}}{2hc\mu _{0}}}={\frac {1}{4\alpha _{N}}}}
1.42757
⋅
10
44
{\displaystyle 1.42757\cdot 10^{44}}
Natural gravitational impedance quantum
Gravitational impedance (L2 M−1 T −1 )
R
N
=
m
Ω
m
e
=
h
m
e
2
{\displaystyle R_{N}={\frac {m_{\Omega }}{m_{e}}}={\frac {h}{m_{e}^{2}}}\ }
7.98492
⋅
10
26
{\displaystyle 7.98492\cdot 10^{26}}
2 kg−1 s −1
Natural electromagnetic impedance quantum
Electrical impedance (L2 M−1 T −1 Q−2 )
R
e
=
q
m
q
N
=
h
e
2
α
α
N
{\displaystyle R_{e}={\frac {q_{m}}{q_{N}}}={\frac {h}{e^{2}}}{\frac {\alpha }{\alpha _{N}}}\ }
1.07562
⋅
10
47
{\displaystyle 1.07562\cdot 10^{47}}
The difference of Natural coupling constant
α
N
{\displaystyle \alpha _{N}\ }
fine structure constant
α
{\displaystyle \alpha \ }
Dirac large numbers and different numerology approaches. [2]
Actually, the relationship between fine structure constant and Natural coupling constant yields the Dirac number :
ξ
D
=
α
α
N
=
(
e
m
e
)
2
ε
g
ε
0
=
(
m
S
m
e
)
2
=
4.167
⋅
10
42
,
{\displaystyle \xi _{D}={\frac {\alpha }{\alpha _{N}}}=\left({\frac {e}{m_{e}}}\right)^{2}{\frac {\varepsilon _{g}}{\varepsilon _{0}}}=\left({\frac {m_{S}}{m_{e}}}\right)^{2}=4.167\cdot 10^{42},\ }
where
m
S
{\displaystyle m_{S}\ }
Stoney mass .
↑ Latest (2010) values of the constants [1]
↑ Ross McPherson. Stoney Scale and Large Number Coincidences. Apeiron, Vol. 14, No. 3, July 2007.
