Physics/Essays/Fedosin/Stoney mass

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)&minus;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.