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From the field equations of the
GTR,
Einstein had, for a plane expanding universe (Einstein- de Sitter
universe),
deduced the relation [16], p. 107ff (Fig.
2 on p. 11):
(6)
(
= coupling constant in the field equations of the GTR, r
= average mass density of the universe,
h = H/c = 1/ tH
c
= 1/R = Hubble expansion)1
1)
For further explanations, see Annex II
Remark: The inflation- enhanced
big bang model postulates, the total matter came into existence in the
very early universe and since has remained constant. If this was
correct,
the value h in eq. (6) would, because of k
= constant, M = constant and
r ~ R
-3 , have to obey to the relation h ~ R
-3/2 (h2 ~ R
-3, which cannot be explained logically. As the
following
deliberations show, this deficiency can be solved in a very natural and
surprising way.
By conversion of eq. (6), we receive:
(7)
(G = gravitation constant, M = total
mass of the universe, R = radius of the universe, c = speed of light in
vacuum)
Sstrikingly, this relation also
is pertinent to a black hole, if for R the Schwarzschild radius Rs
and
for M the mass of the black hole Ms
are
substituted(GMs /Rs
c 2
= ½). Therefore,
the expansion speed of the universe
must at least correspond to the vacuum light speed c, in order to
escape
the gravitation collapse into a universal black hole.
Linkage of time and speed of light
According to the foregoing
results,
the speed of light would decrease with the progress of time t which, on
a superficial glance, interferes with the principle of the constancy of
the speed of light.
But: a „universal
natural constant“ is defined by the requirement that its measured
value
is equally large in any location and at all times, and that it can only
be found empirically and not by means of a theory.
By choosing a suitable time
parameter,
we can bring the speed of light into accordance with this definition
or,
as Einstein had written[4], p. 30: „ One can, for completing the
time
definition, use the principle of the constancy of the vacuum speed of
light.“
In the Special Theory of Relativity
STR), the „absolute“ Newton time finally had to be given up, since it
could
not be brought into accordance with the axiom, confirmed by
observations,
that the speed of light is a universal constant.
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