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deutsch The Mysterious EddingtonDirac Number Different relations between atomic and cosmic quantities and fundamental constants are leading to the same large number in the order of magnitude of 10^{40}.
The electrostatic
force between an electron and a proton
and the
gravitational force = 2,27·10^{39} ^{For two electrons the ratio becomes} ^{ } 2. Lengths The "classic electron radius" r can be computed assuming that the energy W=m_{e}c^{2} is equal to the potential energy of the elementary charge e spread over a sphere of radius r: r = 3·10^{15} m The ratio of this "elementary length" to the radius of the universe R = c·t = 1·10^{26} m ^{is a number of the same order of magnitude as in (1).} 3. Times The light takes the time t to pass the elementary length This "elementary time" is contained in age of the universe T = 6,2·10^{17} s by a number of the same order of magnitude as in (1) and (2):
4. Particles The mass M of the universe 2,4·10^{51} kg to 2,0·10^{52} kg compared to the mass of a proton m_{p} = 1,67·10^{27} kg is the number of protons and the number of particles (protons and electrons) is This is nearly the square of the number found in (1), (2) and (3) !
By chance or not ? Dirac suggested in 1937 that this
coincidence could be understood if fundamental
constants  in particular, G  varied as the
Universe aged. Robert Dicke pointed out in 1957 and 1961
that the age of the universe, as seen by living
observers, cannot be random: The coincidence is is a
consequence of the fact that 'carbon is required to
make physicists' to observe the universe. The order
of magnitude of the lifespan of a main sequence star
(Sun: 10·10^{9} years) agrees with the result derived by
Dirac. Another
strange coincidence:
The ratio c^{2}/G (square of the
speed of light c divided by the gravitational
constant G) is nearly the same as the the ratio M/R
(mass M of the universe and radius R of the visible
universe): c^{2} /
G = M / R c^{2}/G
=
(2.998·10^{8}
m/s)^{2}/[6.674·10^{11} m^{3}/(kg
s^{2})] c^{2}/G = 1.4*10^{27} kg/m Computing the radius R of the visible universe by c and the age T of the
universe:
R = c·T and the mass M of the
universe by the number of nucleons n = 1.2*10^{80}
of mass m=1.67*10^{27} kg M = n·m
= 2.00·10^{53}
kg M/R
= 1.5·10^{27} kg/m c^{2}/G
=
M/R is equivalent to G·M/(R·c^{2})
=1 6.674·10^{11} m^{3}/(kg s^{2}) · 2.00 