606 DISCUSSION ON THE 
It has been pointed out by Sir Arthur Eddington that a static universe 
is unstable, and he proposed the problem of finding the possible causes of 
its expansion. He suggested that such a cause might be the formation of 
condensations. I obtained recently a solution of this problem, and the 
main results are as follows : 
When the expansion is already started, the effect of kinetic energy or 
pressure of radiation is quite negligible. On the contrary, pressure is the 
chief factor in the question of instability of a static universe. If the 
pressure wete rigorously zero, the expansion could never appear. But, 
if the pressure (or kinetic energy) is not zero, any diminution of pressure 
must start the expansion. For example, a world full of radiation starts 
expanding as soon as the radiation can transform itself into matter. 
When condensations exist or are formed, the problem is complicated 
by gravitational effects ; but it can be shown that the general expansion 
of the universe depends entirely on the density of kinetic energy or of 
pressure at the places where the gravitational influences of the con- 
densations cancel one another. I call these places (for brevity) ‘ neutral 
zones.’ Condensation in itself has no direct effect whatever on the 
stability of the universe: but condensations would necessarily induce a 
rarefaction at the neutral zone and so a diminution of the density of 
kinetic energy at the neutral zone ; and this must induce expansion. 
We can conclude that any general process of condensation, occurring 
in a world where the kinetic energy does not vanish, must induce expansion. 
Therefore, practically, the expectation of Sir Arthur Eddington is fully 
confirmed. For example, formation of stars out of a primeval gas starts 
the expansion ; formation of extra-galactic nebule out cf a uniform mass 
of gas or of stars starts the expansion. I think that these results add 
much weight to the fact that the actual velocity of expansion fixes a 
limit to the time scale of the evolution, as we must rule out of our specula- 
tions every process which would start a premature expansion of space. 
Even if we had no experimental evidence of the expansion of space, 
considerations of stability would fix a limit to the time-scale of evolution. 
The reason is that, if the universe has existed for too long a time, any 
general process of condensation would be contradictory to the actual 
value of the density of matter. Although this quantity is not known 
with great accuracy, its value may give some idea of the maximum scale 
of evolution. I find that any general process of condensation, even of 
very moderate intensity, cannot have happened earlier than a few 
hundred thousand million years ago. 
As stated by Sir James Jeans, this brings almost complete chaos into — 
the already chaotic problem of stellar evolution. A complete revision of 
our cosmological hypothesis is necessary, the primary condition being 
the test of rapidity. We want a ‘ fireworks’ theory of evolution. The 
last two thousand million years are slow evolution: they are ashes and 
smoke of bright but very rapid fireworks. 
I think that the key of the problem is afforded by the discovery of the 
cosmic rays. Cosmic rays are of enormous energy. Their intensity is 
estimated to be about one-tenth of that of the light coming to us from the 
stars. If these rays are really cosmic, their energy is much bigger than 
that of the light of the stars, because it must be of equal intensity all over 
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