# Physics/Essays/Fedosin/Stoney mass

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In physics, the Stoney mass ($m_{S}$ ), 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:

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

where

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

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

The Stoney scale has been re-discovered by M. Castans and J. Belinchon, and by Ross McPherson,  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:

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

The Newton force between two Stoney masses is:

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

From the equality of the above forces

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

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

$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  and Keller.