Natural Systems of Units

George Johnstone Stoney (1826 - 1911)

By combinations of Newton's gravitation constant G, the velocity of light c and the electric charge of the electron e, Stoney could construct a mass, a length and a time, using the cgs system of units (1 cm, 1 gram, 1 second): Using modern values (NIST),

e = 4.803·10-10 g1/2 cm3/2 s-1
G = 6.674·10-8 cm3 g-1 s-2
c = 2.998·1010 cm s-1

we get

Mass M = 1.86·10-6 g

Length L = 1.38·10-34 cm

Time T = 4.60·10-45 s

We can imagine the quantity of mass, but the length and the time are not corresponding to anything of our physical world.

L / T = c

action = energy·time = M·L2 / T = M·L·c = e2 / c
= 7.70·10-30 g cm2 s-1 = 7.70·10-37 Js

Planck constant h = 6.626·10-34 Js

cgs System of Units

Using cgs units Coulomb's law is The unity of charge (1 esu, 1 electrostatic unit) is defined as the charge on each of two bodies separated by 1 cm and attracting each other by a force of 1 dyne (1 dyne = 1 g cm s-2 = 1·10-5 N). Taking q1=q2=q and q2 = F r2 , we get

1 esu = 1 g1/2 cm3/2 s-1.

To convert the electrostac unity (1 esu) to Coulomb (1 C), the the unity of charge of the SI system, we use Coulomb's law and q2 = 4πε0 F r2 q2 = 4πε0 F r2 = 107/c2 AmV-1s-1 10-5 N 10-4 m2 = 10-2/c2 A2m2.

We get:

q = 1 esu = 10-1/c Am = 3.336·10-10 As = 3.336·10-10 C

e = 1.602·10-19 C = 4.803·10-10 esu = 4.803·10-10 g1/2 cm3/2 s-1

 SI CGS e 1.602·10-19 C e = 4.803·10-10 g1/2 cm3/2 s-1 G 6.674·10-11 m3 kg-1 s-2 G = 6.674·10-8 cm3 g-1 s-2 c 2.998·108 m s-1 c = 2.998·1010 cm s-1

 Web Links John D. Barrow: Das 1x1 des Universums. Campus Verlag, Frankfurt/New York, 2004. John D. Barrow: The Constants of Nature. Jonathan Cape, 2002.

Juergen Giesen
2009/9/10