By combinations of Newton's gravitation constant G, the velocity of light c and Planck's constant h or h/2π, a mass, a length and a time can be constructed:

Using modern values (NIST),

h = 6.626·10-34 J s, h/2π = 1.055·10-34 J s
G = 6.674·10-11 m3 kg-1 s-2
c = 2.998·108 m s-1

we get:

using h
using h/2π

Mass M

5.456·10-8 kg
2.176·10-8 kg
1.86·10-9 kg

Length L

4.051·10-35 m
1.616·10-35 m
1.38·10-36 m

Time T

1.351·10-43 s
5.391·10-44 s
4.60·10-45 s

 which are close to the results of Stoney.

Additional relations:

L / T = c

action = energy·time = M·L2 / T = M·L·c = h

The fundamental constants c, h, G may are corresponding to the physical theories visualized by the Cube of Theories (Bronshtein, Zelmanov, Okun):

 Cube of theories Bronshtein Zelmanov Okun

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