- main stoney scale units
Boltzmann's constant, kB (or simply k) = 1.
Dielectric constant[1]:
F m-1
Magnetic constant:
H m-1
Electrodynamic velocity of light:
m s-1
Electrodynamic vacuum impedance:
Ohm
Dielectric-like gravitational constant:
kg s2 m-3
Magnetic-like gravitational constant:
m kg-1
Gravidynamic velocity of light:
m s-1
Gravidynamic vacuum impedance:
m2 kg-1 s-1
The above fundamental constants define naturally the following relationship between mass and electric charge:
![{\displaystyle m_{S}=e{\sqrt {\frac {\epsilon _{G}}{\epsilon _{E}}}}=e{\sqrt {\frac {\mu _{E}}{\mu _{G}}}}=e{\sqrt {\frac {\rho _{E0}}{\rho _{G0}}}}\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/818ee649de5d5a5947e66b90886ab5772938857d)
And since:
![{\displaystyle \alpha =\ {\frac {e^{2}}{\hbar c\ 4\pi \varepsilon _{0}}}\ =\ {\frac {e^{2}c\mu _{0}}{2h}}={\frac {k_{\mathrm {e} }e^{2}}{\hbar c}}={\frac {1}{137.035999}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e7c6e5e66eaa132033570970d9df3800ea3f5b81)
Since the Bohr radius equals:
![{\displaystyle a_{0}={\frac {4\pi \epsilon _{0}\hbar ^{2}}{m_{e}e^{2}}}={\frac {\hbar }{m_{e}\,c\,\alpha }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/772f48b4edfac88e5dc67d49f0086a8b9fe3feee)
And the Bohr scale velocity equals:
(velocity of electron in Bohr atom)
Therefore the above fundamental constants also define the reduced Planck's constant as:
(ℏ = twice the angular momentum of hydrogen electron = energy * time)
Since the Rydberg constant equals:
![{\displaystyle R_{\infty }={\frac {\alpha ^{2}m_{e}c}{4\pi \hbar }}={\frac {\alpha ^{2}}{2\lambda _{e}}}\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/be2766ea984c9749f75a39a920f2141407b42223)
Therefore the Frequency of the hydrogen electron equals:
(freq * wavelength = velocity)
The Bohr magneton is defined in SI units by
![{\displaystyle \mu _{\mathrm {B} }={{e\hbar } \over {2m_{\mathrm {e} }}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/873741222e26d80325e64f8ba6dad1801cd306a1)
If the electron is visualized as a classical charged particle literally rotating about an axis with angular momentum
, its magnetic dipole moment
is given by:
![{\displaystyle {\vec {\mu }}={\frac {-e}{2m_{e}}}\,{\vec {L}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b48af3752f5d0680766de365396ebfbea3a80f1c)
Here the charge is
where
is the elementary charge. The mass is the electron rest mass
. Note that the angular momentum
in this equation may be the spin angular momentum, the orbital angular momentum, or the total angular momentum. It turns out the classical result is off by a proportional factor for the spin magnetic moment. As a result, the classical result is corrected by multiplying it with a correction factor.
![{\displaystyle {\vec {\mu }}=g\,{\frac {-e}{2m_{e}}}\,{\vec {L}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e571ec23de1d3790a31f59e97e8e2592aaf352d9)
The dimensionless correction factor g is known as the g-factor. Finally, it is customary to express the magnetic moment in terms of the Planck constant and the Bohr magneton:
![{\displaystyle {\vec {\mu }}=-g\mu _{B}{\frac {\vec {L}}{\hbar }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2ce5cac0221a577ec3bec1ed0838ce3dd05fb819)
Here
is the Bohr magneton and
is the reduced Planck constant.
The Bohr radius including the effect of reduced mass can be given by the following equation:
,
the Classical electron radius equals:
(lambda = Compton wavelength)
Rydberg energy(equal to 1/2 Hartree):
(binding energy of the hydrogen electron)
Gravitational units
[edit]
Stoney mass:
kg,
where
is Planck mass.
Stoney gravitational fine structure constant:
![{\displaystyle \alpha _{GS}={\frac {m_{S}^{2}}{2hc\epsilon _{G}}}=\alpha =7.29973506\cdot 10^{-3}\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/c76b5e54e203122dbf927f18299743e62ee88da1)
Stoney "dynamic mass", or gravitational magnetic-like flux:
J s kg-1
Stoney scale gravitational magnetic-like fine structure constant[2]
![{\displaystyle \beta _{GS}={\frac {\phi _{GS}^{2}}{2hc\mu _{G}}}={\frac {1}{4\alpha }}=34.259009\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/ad2765fb1d45e094c456f92418dbdcab7150f1c8)
Stoney gravitational impedance quantum:
J s kg-1
Stoney charge:
C
Stoney electric fine structure constant: (the speed of the electron in a Bohr atom)
![{\displaystyle \alpha _{ES}={\frac {q_{S}^{2}}{2hc\epsilon _{E}}}=\alpha .\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/cddcafca7c21758d5fc4a979a9105210d225f792)
Stoney magnetic charge, or flux:
Wb
Stoney scale magnetic fine structure constant[2]
![{\displaystyle \beta _{MS}={\frac {\phi _{MS}^{2}}{2hc\mu _{E}}}={\frac {1}{4\alpha }}=34.259009\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/818e39034927cc085f5413c8f77d8e4550c073e9)
Stoney electrodynamic impedance quantum:
Ohm
is the s.c. von Klitzing constant.
Table 1: Secondary Stoney units
Name
|
Dimension
|
Expressions
|
SI equivalent with uncertainties[1]
|
Stoney wavelength
|
Length (L)
|
|
1.188 60 × 10-33 m
|
Stoney time
|
Time (T)
|
|
3.964 74 × 10-42 s
|
Stoney classical radius
|
Length (L)
|
|
1.380 45 × 10-36 m
|
Stoney Schwarzschild radius
|
Length (L)
|
|
2.760 90 × 10-36 m
|
Stoney temperature
|
Temperature (Θ)
|
|
1.210 49 × 1031 K
|
Stoney scale static forces
[edit]
Electric Stoney scale force:
![{\displaystyle F_{S}(q_{S}\cdot q_{S})={\frac {1}{4\pi \epsilon _{E}}}\cdot {\frac {e^{2}}{r^{2}}}={\frac {\alpha _{SE}\hbar c}{r^{2}}},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/f40ce20c3d029ce8a7ff064b4c654839bb74314d)
Gravity Stoney scale force:
![{\displaystyle F_{S}(m_{S}\cdot m_{S})={\frac {1}{4\pi \epsilon _{G}}}\cdot {\frac {m_{S}^{2}}{r^{2}}}={\frac {\alpha _{SG}\hbar c}{r^{2}}},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/c1f7deba696bebd8d8201e30522f525a1bea096b)
Mixed (charge-mass interaction) Stoney force:
![{\displaystyle F_{S}(m_{S}\cdot q_{S})={\frac {1}{4\pi {\sqrt {\epsilon _{G}\epsilon _{E}}}}}\cdot {\frac {m_{S}\cdot e}{r^{2}}}={\sqrt {\alpha _{G}\alpha _{E}}}{\frac {\hbar c}{r^{2}}}={\frac {\alpha \hbar c}{r^{2}}},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/ff3d01159d8f894f20acd6afd690f66223753527)
where
is the mixed fine structure constant.
So, at the Stoney scale we have the equality of all static forces which describes interactions between charges and masses:
![{\displaystyle F_{S}(q_{S}\cdot q_{S})=F_{S}(m_{S}\cdot m_{S})=F_{S}(m_{S}\cdot q_{S})={\frac {\alpha \hbar c}{r^{2}}}.\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/12d6af466a53a81df9c7525d8a13e8e5e39f3a13)
Stoney scale dynamic forces
[edit]
Magnetic Stoney scale force:
![{\displaystyle F_{S}(\phi _{MS}\cdot \phi _{MS})={\frac {1}{4\pi \mu _{E}}}\cdot {\frac {\phi _{MS}^{2}}{r^{2}}}={\frac {\beta _{SE}\hbar c}{r^{2}}},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/3576db88919e2f75995ff5a6767a70ba4ac85d08)
Gravitational magnetic-like force:
![{\displaystyle F_{S}(\phi _{GS}\cdot \phi _{GS})={\frac {1}{4\pi \mu _{G}}}\cdot {\frac {\phi _{GS}^{2}}{r^{2}}}={\frac {\beta _{SG}\hbar c}{r^{2}}},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a80842b36457ddf05b9d3941e5b98854adb0fd1e)
Mixed dynamic (charge-mass interaction) gorce:
![{\displaystyle F_{S}(\phi _{MS}\cdot \phi _{GS})={\frac {1}{4\pi {\sqrt {\mu _{G}\mu _{E}}}}}\cdot {\frac {\phi _{MS}\cdot \phi _{GS}}{r^{2}}}={\sqrt {\beta _{G}\beta _{E}}}{\frac {\hbar c}{r^{2}}}={\frac {\beta \hbar c}{r^{2}}},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/66d1b936b4f20c3dbeb956d594927cf21f543aa0)
where
So, at the Stoney scale we have the equality of all dynamic forces which describes interactions between dynamic charges and masses:
![{\displaystyle F_{S}(\phi _{MS}\cdot \phi _{MS})=F_{S}(\phi _{GS}\cdot \phi _{GS})=F_{S}(\phi _{MS}\cdot \phi _{GS})={\frac {\beta \hbar c}{r^{2}}}.\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/f2d4eebabcc8029f52c60ce77e662f77305c08af)
Derived Stoney scale units
[edit]
Name
|
Dimensions
|
Expression
|
Approximate SI equivalent
|
Stoney area
|
Area (L2)
|
|
m2
|
Stoney volume
|
Volume (L3)
|
|
m3
|
Stoney momentum
|
Momentum (LMT-1)
|
|
kg m/s
|
Stoney energy
|
Energy (L2MT-2)
|
|
J
|
Stoney force
|
Force (LMT-2)
|
|
N
|
Stoney power
|
Power (L2MT-3)
|
|
W
|
Stoney density
|
Density (L-3M)
|
|
kg/m3
|
Stoney angular frequency
|
Frequency (T-1)
|
|
rad s-1
|
Stoney pressure
|
Pressure (L-1MT-2)
|
|
Pa
|
Stoney current
|
Electric current (QT-1)
|
|
A
|
Stoney voltage
|
Voltage (L2MT-2Q-1)
|
|
V
|
Stoney electric impedance
|
Resistance (L2MT-1Q-2)
|
|
Ω
|
Stoney gravitational charge current
|
Gravitational current (MT-1)
|
|
kg s-1
|
Stoney gravitational charge voltage
|
Gravitational voltage (L2T-2)
|
|
m2 s-2
|
Stoney gravitational charge impedance
|
gravitational impedance (LT-2)
|
|
m s-2
|
Stoney electric capacitance per unit area
|
Electric capacitance (L-2M-1T2Q2)
|
|
F m-2
|
Stoney electric inductance per unit area
|
Electric inductance (L2MT-2Q-2)
|
|
H m-2
|
Stoney gravity capacitance per unit area
|
Gravitational capacitance (L-4MT2 )
|
|
m-4 kg s2
|
Stoney gravity inductance per unit area
|
Gravitational inductance (M-1)
|
|
kg-1
|
Stoney particle radius
|
Length (L)
|
|
m
|
Stoney particle area
|
Area (L2)
|
|
m 2
|
In physics, Stoney scale units are units of measurement named after the Irish physicist George Johnstone Stoney, who first proposed them in 1881. They are an example of natural units, i.e. units of measurement designed so that certain fundamental physical constants are normalized to unity. The constants that Stoney units normalize are the following.
Each of these constants can be associated with at least one fundamental physical theory: c with special relativity, εG with general relativity and Newtonian gravity, e and εE with electrostatics, and k with statistical mechanics and thermodynamics.
Stoney units have profound significance for theoretical physics since they simplify several recurring algebraic expressions of physical law by nondimensionalization. They are particularly relevant in research on unified theories such as quantum gravity.
Contemporary physics has settled on the Planck scale as the most suitable scale for the unified theory. The Planck scale was however anticipated by George Stoney.[3]
James G. O’Hara[4]
pointed out in 1974 that Stoney’s derived estimate of the unit of charge, 10−20 Ampere (later called the Coulomb), was 1⁄16 of the correct value of the charge of the electron. Stoney’s use of the quantity 1018 for the number of molecules presented in one cubic millimetre of gas at standard temperature and pressure. Using Avogadro’s number 6.0238×1023, and the volume of a gram-molecule (at s.t.p.) of 22.4146×106 mm3, we derive, instead of 1018, the estimate 2.687×1016. So, the Stoney charge differs from the modern value for the charge of the electron about 1% (if he took the true number of molecules).
Stoney scale and Planck scale are intermediate between microscopic and cosmic processes and it was soon realized that either could be the right scale for a unified theory. The only notable attempt to construct such a theory from the Stoney scale was that of H. Weyl, who associated a gravitational unit of charge with the Stoney length[5][6].
[7]
and who appears to have inspired Dirac’s fascination with LNH[8].
However, Weyl’s dogmatic adherence to the principle of locality reduced his theory to a mathematical construct with some non-physical implications. The Stoney scale thereafter fell into such neglect that it should to be re-discovered by M. Castans and J. Belinchon[9], and by Ross McPherson[10]
For a long time the Stoney scale was in the shadow of the Planck scale (something like a "deviation" of it). However, after intensive investigation of gravity by using the Maxwell-like gravitational equations during last decades, became clear that Stoney scale is independent scale of matter. Furthermore, it is the base of the contemporary electrodynamics and gravidynamics (classical and quantum). Due to McDonald[11]
first who used Maxwell equations to describe gravity was Oliver Heaviside[12]
The point is that in the weak gravitational field the standard theory of gravity could be written in the form of Maxwell equations[13]
It is evident that in 19th century there was no SI units, and therefore the first mention of the gravitational constants possibly due to Forward (1961)[14]
In the 1980s Maxwell-like equations were considered in the Wald book of general relativity[15] In the 1990s Kraus[16] first introduced the gravitational characteristic impedance of free space, which was detailed later by Kiefer[17], and now Raymond Y. Chiao[18] [19] [20] [21] [22] who is developing the ways of experimental determination of the gravitational waves.
Fundamental units of vacuum
[edit]
Dielectric constant[1]:
F m−1
Magnetic constant:
H m−1
Electrodynamic velocity of light:
m s−1
Electrodynamic vacuum impedance:
Ohm
Dielectric-like gravitational constant:
kg s2 m−3
Magnetic-like gravitational constant:
m kg−1
Gravidynamic velocity of light:
m s−1
Gravidynamic vacuum impedance:
m2 kg−1 s−1
Considering that all Stoney and Planck units are derivatives from the ‘’vacuum units’’, therefore the last are more fundamental that units of any scale.
The above fundamental constants define naturally the following relationship between mass and electric charge:
![{\displaystyle m_{S}=e{\sqrt {\frac {\varepsilon _{G}}{\varepsilon _{E}}}}=e{\sqrt {\frac {\mu _{E}}{\mu _{G}}}}=e{\sqrt {\frac {\rho _{E0}}{\rho _{G0}}}}\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/ba5324bc263215f3714f5d7f9074909dba8fa940)
and these values are the base units of the Stoney scale.
Primary Stoney units
[edit]
Gravitational Stoney units
[edit]
Stoney mass:
kg,
where
is Planck mass.
Stoney gravitational fine structure constant:
![{\displaystyle \alpha _{GS}={\frac {m_{S}^{2}}{2hc\varepsilon _{G}}}=\alpha =7.29973506\cdot 10^{-3}\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/6ade29940cb46db72fa4e75746252fe2dfa17b46)
Stoney "dynamic mass", or gravitational magnetic-like flux:
J s kg−1
Stoney scale gravitational magnetic-like fine structure constant[2]
![{\displaystyle \beta _{GS}={\frac {\varphi _{GS}^{2}}{2hc\mu _{G}}}={\frac {1}{4\alpha }}=34.259009\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/837b1e631376886483d2a60e603613af96e64733)
Stoney gravitational impedance quantum:
J s kg−1
Electromagnetic Stoney units
[edit]
Stoney charge:
C
Stoney electric fine structure constant:
![{\displaystyle \alpha _{ES}={\frac {q_{S}^{2}}{2hc\,\varepsilon _{E}}}=\alpha .\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b368488acfab17382967262eceb9c68c52cc97f7)
Stoney magnetic charge, or flux:
Wb
Stoney scale magnetic fine structure constant[2]
![{\displaystyle \beta _{MS}={\frac {\varphi _{MS}^{2}}{2hc\mu _{E}}}={\frac {1}{4\alpha }}=34.259009\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/efa5732feb01e0f5abaa325babd7142318f11650)
Stoney electrodynamic impedance quantum:
Ohm
is the s.c. von Klitzing constant.
Secondary Stoney scale units
[edit]
All systems of measurement feature base units: in the International System of Units (SI), for example, the base unit of length is the meter. In the system of Stoney units, the Stoney base unit of length is known simply as the ‘’Stoney length’’, the base unit of time is the ‘’Stoney time’’, and so on. These units are derived from the presented above primary Stoney units, which are arranged in Table 1 so as to cancel out the unwanted dimensions, leaving only the dimension appropriate to each unit. (Like all systems of natural units, Stoney units are an instance of dimensional analysis.)
Used keys in the tables below: L = length, T = time, M = mass, Q = electric charge, Θ = temperature. The values given without uncertainties are exact due to the definitions of the metre and the ampere.
Table 1: Secondary Stoney units
Name
|
Dimension
|
Expressions
|
SI equivalent with uncertainties[1]
|
Stoney wavelength
|
Length (L)
|
|
1.188 60 × 10−33 m
|
Stoney time
|
Time (T)
|
|
3.964 74 × 10−42 s
|
Stoney classical radius
|
Length (L)
|
|
1.380 45 × 10−36 m
|
Stoney Schwarzschild radius
|
Length (L)
|
|
2.760 90 × 10−36 m
|
Stoney temperature
|
Temperature (Θ)
|
|
1.210 49 × 1031 K
|
Derived Stoney scale units
[edit]
In any system of measurement, units for many physical quantities can be derived from base units. Table 2 offers a sample of derived Stoney units, some of which in fact are seldom used.
As with the base units, their use is mostly confined to theoretical physics because most of them are too large or too small for empirical or practical use and there are large uncertainties in their values
Table 2: Derived Stoney units
Name
|
Dimensions
|
Expression
|
Approximate SI equivalent
|
Stoney area
|
Area (L2)
|
|
m2
|
Stoney volume
|
Volume (L3)
|
|
m3
|
Stoney momentum
|
Momentum (LMT −1)
|
|
kg m/s
|
Stoney energy
|
Energy (L2MT −2)
|
|
J
|
Stoney force
|
Force (LMT −2)
|
|
N
|
Stoney power
|
Power (L2MT −3)
|
|
W
|
Stoney density
|
Density (L−3M)
|
|
kg/m3
|
Stoney angular frequency
|
Frequency (T −1)
|
|
rad s−1
|
Stoney pressure
|
Pressure (L−1MT −2)
|
|
Pa
|
Stoney current
|
Electric current (QT −1)
|
|
A
|
Stoney voltage
|
Voltage (L2MT −2Q−1)
|
|
V
|
Stoney electric impedance
|
Resistance (L2MT −1Q−2)
|
|
Ω
|
Stoney gravitational charge current
|
Gravitational current (MT −1)
|
|
kg s−1
|
Stoney gravitational charge voltage
|
Gravitational voltage (L2T −2)
|
|
m2 s−2
|
Stoney gravitational charge impedance
|
gravitational impedance (LT −2)
|
|
m s−2
|
Stoney electric capacitance per unit area
|
Electric capacitance (L−2M−1T2Q2)
|
|
F m−2
|
Stoney electric inductance per unit area
|
Electric inductance (L2MT −2Q−2)
|
|
H m−2
|
Stoney gravity capacitance per unit area
|
Gravitational capacitance (L−4MT2 )
|
|
m−4 kg s2
|
Stoney gravity inductance per unit area
|
Gravitational inductance (M−1)
|
|
kg−1
|
Stoney particle radius
|
Length (L)
|
|
m
|
Stoney particle area
|
Area (L2)
|
|
m 2
|
Stoney scale forces
[edit]
Stoney scale static forces
[edit]
Electric Stoney scale force:
![{\displaystyle F_{S}(q_{S}\cdot q_{S})={\frac {1}{4\pi \varepsilon _{E}}}\cdot {\frac {e^{2}}{r^{2}}}={\frac {\alpha _{SE}\hbar c}{r^{2}}},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/9ede36d559f9c503cf96f7ce5fd053b360de822a)
where
is the electric fine structure constant.
Gravity Stoney scale force:
![{\displaystyle F_{S}(m_{S}\cdot m_{S})={\frac {1}{4\pi \varepsilon _{G}}}\cdot {\frac {m_{S}^{2}}{r^{2}}}={\frac {\alpha _{SG}\hbar c}{r^{2}}},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/d17a480ac37e97e5bb9abcae0cbcf14e93b3f3ca)
where
is the gravity fine structure constant.
Mixed (charge-mass interaction) Stoney force:
![{\displaystyle F_{S}(m_{S}\cdot q_{S})={\frac {1}{4\pi {\sqrt {\varepsilon _{G}\varepsilon _{E}}}}}\cdot {\frac {m_{S}\cdot e}{r^{2}}}={\sqrt {\alpha _{G}\alpha _{E}}}{\frac {\hbar c}{r^{2}}}={\frac {\alpha \hbar c}{r^{2}}},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/4c2b5f41a24c08c916612f8dbb6585a2c4239625)
where
is the mixed fine structure constant.
So, at the Stoney scale we have the equality of all static forces which describes interactions between charges and masses:
![{\displaystyle F_{S}(q_{S}\cdot q_{S})=F_{S}(m_{S}\cdot m_{S})=F_{S}(m_{S}\cdot q_{S})={\frac {\alpha \hbar c}{r^{2}}}.\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/12d6af466a53a81df9c7525d8a13e8e5e39f3a13)
Stoney scale dynamic forces
[edit]
Magnetic Stoney scale force:
![{\displaystyle F_{S}(\varphi _{MS}\cdot \varphi _{MS})={\frac {1}{4\pi \mu _{E}}}\cdot {\frac {\varphi _{MS}^{2}}{r^{2}}}={\frac {\beta _{SE}\hbar c}{r^{2}}},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/1c2888abd44cc8ec6810fb45478e5f16a230b3e5)
where
is the magnetic fine structure constant.
Gravitational magnetic-like force:
![{\displaystyle F_{S}(\varphi _{GS}\cdot \varphi _{GS})={\frac {1}{4\pi \mu _{G}}}\cdot {\frac {\varphi _{GS}^{2}}{r^{2}}}={\frac {\beta _{SG}\hbar c}{r^{2}}},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/00bd12446b20e1a121df1a5c6aa8533a3c497860)
where
is the magnetic-like gravitational fine structure constant.
Mixed dynamic (charge-mass interaction) gorce:
![{\displaystyle F_{S}(\varphi _{MS}\cdot \varphi _{GS})={\frac {1}{4\pi {\sqrt {\mu _{G}\mu _{E}}}}}\cdot {\frac {\varphi _{MS}\cdot \varphi _{GS}}{r^{2}}}={\sqrt {\beta _{G}\beta _{E}}}{\frac {\hbar c}{r^{2}}}={\frac {\beta \hbar c}{r^{2}}},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/56980960ba090f60ca82f5f1e29727ffcdbe8dd0)
where
So, at the Stoney scale we have the equality of all dynamic forces which describes interactions between dynamic charges and masses:
![{\displaystyle F_{S}(\varphi _{MS}\cdot \varphi _{MS})=F_{S}(\varphi _{GS}\cdot \varphi _{GS})=F_{S}(\varphi _{MS}\cdot \varphi _{GS})={\frac {\beta \hbar c}{r^{2}}}.\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/dfb557750f62c67043cf19266fc83c8a3927592f)
For the sake of completeness in the Table 3 presented the main Planck units in the form consistent with above tables for Stoney scale.
Table 3: Base Planck units
Name
|
Dimension
|
Expressions
|
SI equivalent with uncertainties[1]
|
Other equivalent
|
Planck mass
|
Mass (M)
|
|
2.176 44(11) × 10−8 kg
|
1.220 862(61)× 1019 GeV/c2
|
Planck wavelength
|
Length (L)
|
|
1.013 56 × 10−34 m
|
|
Planck gravity fine structure constant
|
Dimensionless
|
|
1
|
|
Planck "dynamic mass"
|
Dynamic mass (L2T −1)
|
|
3.043 96 × 10−26 m2 s−1
|
|
Planck "dynamic mass" fine structure constant
|
Dimensionless
|
|
1/4
|
|
Planck time
|
Time (T)
|
|
3.386 86 × 10−43 s
|
|
Planck charge
|
Electric charge (Q)
|
|
1.875 545 870(47) × 10−18 C
|
11.706 237 6398(40) e
|
Planck electric fine structure constant
|
Dimensionless
|
|
1
|
|
Planck "magnetic charge"
|
magnetic charge (L2MT −1Q−1)
|
|
3.532 90 × 10−16 Wb
|
|
Planck "magnetic charge" fine structure constant
|
Dimensionless
|
|
1/4
|
|
Planck gravity impedance quantum
|
Gravitational impedance (L2M−1T −1)
|
|
1.398 35 × 10−18 m2 kg−1 s−1
|
|
Planck electromagnetic impedance quantum
|
Electrical impedance (L2M−1T −1Q−2)
|
|
1.883 65 × 102 Ω
|
|
As could be seen from the table, the main difference between Stoney and Planck units - the fine structure constants. For example, the wave vacuum impedance in the Planck scale will be:
![{\displaystyle \rho _{EP}={\sqrt {\frac {\mu _{E}}{\varepsilon _{E}}}}=2\alpha \cdot {\frac {h}{e^{2}}}=2\cdot {\frac {h}{q_{P}^{2}}}.\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/c5d90d2ea1ed0eb1bc57e21cf76e943948aeb6a5)
This is due to the difference in fine structure constants. Actually, the relationship between "static" and "dynamic" forces in the Planck scale is:
![{\displaystyle {\sqrt {\frac {F_{Pst}}{F_{Pdyn}}}}={\sqrt {\frac {\alpha _{P}}{\beta _{P}}}}=2\alpha _{P}=2,\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/f2718daf29bc001be46e83d6bc13a85288d3aaa0)
but in the Stoney scale it will be:
![{\displaystyle {\sqrt {\frac {F_{Sst}}{F_{Sdyn}}}}={\sqrt {\frac {\alpha _{S}}{\beta _{S}}}}=2\alpha _{S}=2\alpha .\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b10490c568dd0737b613a27673a9fb834c468487)
Natural scale units based on electron mass
[edit]
For the sake of completeness in the Table 4 presented the main Natural scale units based on electron mass in the form consistent with above tables for Stoney scale.
Table 4: Base Natural scale units
Name
|
Dimension
|
Expressions
|
SI equivalent with uncertainties[1]
|
Other equivalent
|
Electron mass
|
Mass (M)
|
|
9.109382 15(45) × 10−31 kg
|
5.109989 10(13) × 10−1 MeV
|
Electron wavelength
|
Length (L)
|
|
2.42631021 75(33) × 10−12 m
|
|
Natural gravity fine structure constant
|
Dimensionless
|
|
1.751 12 × 10−45
|
|
Natural "dynamic mass"
|
Dynamic mass (L2T −1)
|
|
7.273 39 × 10−4 m2 s−1
|
|
Natural "dynamic mass" fine structure constant
|
Dimensionless
|
|
1.427 57 × 10+44
|
|
Natural charge
|
Electric charge (Q)
|
|
7.848 545 79 × 10−41 C
|
|
Natural electric fine structure constant
|
Dimensionless
|
|
1.751 12 × 10−45
|
|
Natural "magnetic charge"
|
magnetic charge (L2MT −1Q−1)
|
|
8.442 29 × 106 Wb
|
|
Natural "magnetic charge" fine structure constant
|
Dimensionless
|
|
1.427 57 × 1044
|
|
Natural gravity impedance quantum
|
Gravitational impedance (L2M−1T −1)
|
|
7.984 92 × 1026 m2 kg−1 s−1
|
|
Natural electromagnetic impedance quantum
|
Electrical impedance (L2M−1T −1Q−2)
|
|
1.075 62 × 1047 Ω
|
|
Note that, the Natural scale has different values for the fine structure constants (as the Planck scale does).
However, this difference is so high, that this scale now is the base for the LNH and different numerology approaches [10].
Actually, the relationship between Stoney and Natural fine structure constants yields the s.c. Dirack number:
![{\displaystyle \xi _{D}={\frac {\alpha _{S}}{\alpha _{N}}}=\left({\frac {e}{m_{0}}}\right)^{2}{\frac {\varepsilon _{G}}{\varepsilon _{E}}}=\left({\frac {m_{S}}{m_{0}}}\right)^{2}=4.167\cdot 10^{42}.\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/992fed2a154080d7a0a5834175936612112d3054)
Weak interaction Natural scale units
[edit]
The weak scale of Natural units is based on the neutrino mass. As is known, neutrinos are generated during the annihilation process, which is going through intermediate positronium atom.
The effective mass of the positronoum atom is:
![{\displaystyle m_{Bp}={\frac {m_{e}m_{p}}{m_{e}+m_{p}}}=0.5m_{N},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a2dac6a66c8663c90b98c4a2c8347d9b03ed98e4)
where
are electron and positron mass respectively.
The energy scale for the positronium atom is:
![{\displaystyle W_{Bp}={\frac {\hbar ^{2}}{2m_{Bp}a_{Bp}^{2}}}=\left({\frac {\alpha }{2}}\right)^{2}\cdot m_{N}c^{2}=m_{WN}c^{2},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/2e8d5430d89a486a434a3053f8db8ad4432bb85a)
where
is the length scale for positronium, and
is the upper value for the neutrino mass, and
is the weak interaction force constant (or weak fine structure constant).
Table 5: Base weak Natural scale units
Name
|
Dimension
|
Expressions
|
SI equivalent with uncertainties[1]
|
Other equivalent
|
Neutrino mass
|
Mass (M)
|
|
1.21273 70 × 10−35 kg
|
|
Neutrino wavelength
|
Length (L)
|
|
1.88225 05 × 10−7 m
|
|
Weak interaction force constant
|
Dimensionless
|
|
1.77231 68 × 10−10
|
|
Weak gravity force constant
|
Dimensionless
|
|
3.1047 2 × 10−55
|
|
Weak Natural "dynamic mass"
|
Dynamic mass (L2T −1)
|
|
5.4637 3 × 10−0 m2 s−1
|
|
Weak Natural "dynamic mass" force constant
|
Dimensionless
|
|
3.1047 2 × 10+53
|
|
Weak Natural time
|
Time (T)
|
|
6.0792 2 × 10−16 s
|
|
Weak Planck scale units
[edit]
The primordial level of matter has two standard scales: Planck (defines the Planck mass) and Stoney (defines the Stoney mass).
However, it has the third primordial scale that could be named as the weak interaction scale, which has the following force constant:
![{\displaystyle \alpha _{W}=({\frac {\alpha }{2}})^{4},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/c178091402592b7467048cb1f634cc0faf84b359)
that is the same as in the weak natural scale.
The weak primordial mass will be:
kg,
where
is the Planck mass.
The weak primordial wavelength is:
m
The weak primordial time is:
s
Work function and Universe scale
[edit]
The standard definition of the work function in the strength field is:
![{\displaystyle A_{\lambda }=F_{\lambda }\cdot \lambda ={\frac {\hbar c}{\lambda }}={\frac {m_{\lambda }c^{2}}{2\pi }}.\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/890dabf6d5736f8a7067ab9ef5052448e5b6fbde)
So, the complex weak displacement work in the weak natural force will be:
![{\displaystyle A_{NWW}=F_{WN}\cdot \lambda _{W}=\alpha _{W}\alpha _{N}\cdot {\frac {\hbar c}{\lambda _{W}}},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/2bb8d3c0649e33b0cf334ebfd663e425661b048c)
where
![{\displaystyle F_{WN}={\frac {m_{WN}^{2}}{2hc\epsilon _{G}}}=\alpha _{W}\alpha _{N}\cdot {\frac {\hbar c}{r^{2}}}\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/93090884f87004ef053e410d842102595147e8ba)
is the weak natural force, and
is the weak Planck wavelength.
Considering the Universe bubble as the minimal energy scale:
![{\displaystyle W_{U}=h\nu _{U}={\frac {\hbar c}{\lambda _{U}}},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/f37faadd7c0e14104965af0f4ae318058e55ed03)
where
is the Universe wavelength, and equating the above energies, we derive the following fundamental relationship:
![{\displaystyle {\frac {\lambda _{W}}{\alpha _{W}\alpha _{N}}}={\frac {\lambda _{U}}{2\pi }},\ }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b99d5a7edd5cd19494b42a6f5216853241b14e67)
from which the Universe length parameter could be derived:
m
which value is consistent with the 15 billion years.
- ^ a b c d e f g Latest (2006) values of the constants [1]
- ^ a b c d
Yakymakha O.L.(1989). High Temperature Quantum Galvanomagnetic Effects in the Two- Dimensional Inversion Layers of MOSFET's (In Russian). Kyiv: Vyscha Shkola. p.91. ISBN 5-11-002309-3. djvu
- ^ Stoney G.
On The Physical Units of Nature, Phil.Mag. 11, 381–391, 1881
- ^
J.G. O’Hara (1993). George Johnstone Stoney and the Conceptual Discovery of the Electron, Occasional Papers in Science and Technology, Royal Dublin Society 8, 5–28.
- ^
K. Tomilin, “Natural System of Units”, Proc. of the XX11 International Workshop on High Energy Physics and Field theory, (2 000) 289.
- ^
H. Weyl, “Gravitation und Elekrizitat”, Koniglich Preussische Akademie der Wissenschaften (1918) 465–78
- ^
H. Weyl, “Eine Neue Erweiterung der Relativitatstheorie”, Annalen der Physik 59 (1919) 101–3.
- ^
G. Gorelik, “Herman Weyl and Large Numbers in Relativistic Cosmology”, Einstein Studies in Russia, (ed. Y. Balashov and V. Vizgin), Birkhaeuser. (2002).
- ^
M. Castans and J. Belinchon(1998). “Enlargement of Planck’s System of Absolute Units”, preprint: physics/9811018
- ^ a b
Ross McPherson. Stoney Scale and Large Number Coincidences. Apeiron, Vol. 14, No. 3, July 2007
- ^
K.T. McDonald, Am. J. Phys. 65, 7 (1997) 591–2.
- ^
O. Heaviside, Electromagnetic Theory (”The Electrician” Printing and Publishing Co., London, 1894) pp. 455–465.
- ^
W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addison–Wesley, Reading, MA, 1955), p. 168, 166.
- ^ R. L. Forward, Proc. IRE 49, 892 (1961).
- ^ R. M. Wald, General Relativity (University of Chicago Press, Chicago, 1984).
- ^ J. D. Kraus, IEEE Antennas and Propagation. Magazine 33, 21 (1991).
- ^ C. Kiefer and C. Weber, Annalen der Physik (Leipzig) 14, 253 (2005).
- ^ Raymond Y. Chiao. "Conceptual tensions between quantum mechanics and general relativity:
Are there experimental consequences, e.g., superconducting transducers between electromagnetic and gravitational radiation?" arXiv:gr-qc/0208024v3 (2002). [PDF
- ^ R.Y. Chiao and W.J. Fitelson. Time and matter in the interaction between gravity and quantum fluids: are there macroscopic quantum transducers between gravitational and electromagnetic waves? In Proceedings of the “Time & Matter Conference” (2002 August 11–17; Venice, Italy), ed. I. Bigi and M. Faessler (Singapore: World Scientific, 2006), p. 85. arXiv: gr-qc/0303089. PDF
- ^ R.Y. Chiao. Conceptual tensions between quantum mechanics and general relativity: are there experimental consequences? In Science and Ultimate Reality, ed. J.D. Barrow, P.C.W. Davies, and C.L.Harper, Jr. (Cambridge:Cambridge University Press, 2004), p. 254. arXiv:gr-qc/0303100.
- ^ Raymond Y. Chiao. "New directions for gravitational wave physics via “Millikan oil drops” arXiv:gr-qc/0610146v16 (2009). PDF
- ^ Stephen Minter, Kirk Wegter-McNelly, and Raymond Chiao. Do Mirrors for Gravitational Waves Exist? arXiv:gr-qc/0903.0661v10 (2009). PDF