Natural Systems of Units

Planck

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

 

George Johnstone Stoney : 1826 - 1911

Fundamental Quantum Cosmological Units and the Quantum Evolution of the Universe

Natural Systems of Units. To the Centenary Anniversary of the Planck System (pdf)

Trialogue on the number of fundamental constants (pdf)

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