# Physics/Essays/Fedosin/Stoney mass

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In physics, the Stoney mass (${\displaystyle m_{S}}$), is one of the base units in the system of natural units called Stoney units. It is a quantity of mass defined in terms of fundamental physical constants.

The Stoney mass is defined as:

${\displaystyle m_{S}=e{\sqrt {\frac {\varepsilon _{g}}{\varepsilon _{0}}}}={\sqrt {\alpha }}m_{P}=1.859\cdot 10^{-9}\ }$ kg,

where

${\displaystyle \varepsilon _{g}={\frac {1}{4\pi G}}\ }$, and ${\displaystyle G\ }$ is the gravitational constant,
${\displaystyle \varepsilon _{0}\ }$ is the electric constant,
${\displaystyle \alpha \ }$ = (137.035999074)−1 is the electric fine structure constant,
${\displaystyle e\ }$ is the elementary charge.

The Stoney mass is ${\displaystyle \alpha ^{-1/2}\approx 11.706}$ times less than the Planck mass ${\displaystyle m_{P}\ }$.

## History

Contemporary physics has settled on the Planck scale as the most suitable scale for a unified field theory. The Planck scale was however anticipated by George Stoney. [1]

The Stoney scale has been re-discovered by M. Castans and J. Belinchon[2], and by Ross McPherson, [3] in connection with the Large number coincidences.

## Stoney mass vs elementary electric charge

The elementary charge is a unit of the Stoney scale. The Coulomb force between two such charges is:

${\displaystyle F_{C}={\frac {1}{4\pi \varepsilon _{0}}}\cdot {\frac {e^{2}}{r^{2}}}.\ }$

The Newton force between two Stoney masses is:

${\displaystyle F_{N}={\frac {1}{4\pi \varepsilon _{g}}}\cdot {\frac {m_{S}^{2}}{r^{2}}},\ }$

From the equality of the above forces

${\displaystyle F_{C}=F_{N}\ }$

we find out the relationship between Stoney mass and Stoney charge:

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

Note that, George Stoney first proposed the term electron for the particle with elementary electric charge due to O’Hara [4] and Keller.[5]

## References

1. Stoney G. On The Physical Units of Nature, Phil.Mag. 11, 381-391, 1881
2. M. Castans and J. Belinchon(1998). Enlargement of Planck’s System of Absolute Units, arhiv: physics/9811018.
3. Ross McPherson. Stoney Scale and Large Number Coincidences. Apeiron, Vol. 14, No. 3, July 2007.
4. 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.
5. A. Keller (1984). The Infancy of Atomic Physics: Hercules in His Cradle, Oxford Uni. Press.