# 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]