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Dictionary of the History of Ideas

Studies of Selected Pivotal Ideas
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SUMMARY

At this point in our narrative, the reader may well
feel that modern cosmology is a welter of conflicting
theories, all of which contain some elements of truth,
but none of which gives a complete picture of the
actual universe. This, however, would be a wrong
conclusion to draw from the present state of affairs.
It is true that a few years ago this would have been
a fair assessment, since the observational evidence then
was far too meager to permit us to choose from among
the various cosmologies that stem from the basic field
equations. But even then, the common heritage of all
of these theories (the general theory of relativity) indi-
cated that the basic differences among them are more
apparent than real.

The situation in the early 1970's was quite different,
for a threshold had been reached for a cosmological
breakthrough; as we have seen, enough observational
evidence was available to show us that our universe
originated explosively, about ten to twenty billion years
ago, from a highly condensed state. Even though we
still could not decide unequivocally between an ex-
panding and an oscillating universe on the basis of the
observational evidence, the major problem of the origin
of the universe had been solved and we had a self-
consistent picture. It accounted not only for the reces-
sion and distribution of the distant galaxies but also
for many diverse phenomena, ranging from the back-
ground radiation all around us in space (the 3° K. iso-
tropic radiation which we have already discussed) to the
formation of the stars and the heavy elements.

The most remarkable thing about the state of matter,
whether in the form of stars or interstellar dust and
gas all around us, is that it points to some momentous
event that must have occurred some billions of years
ago and which led to the pronounced differentiation
that we see now. Starting from the “big bang,” to
which all these observations point, we can now arrange
the succession of events that led to the present state
of the universe into a well-ordered, meaningful, and
understandable sequence. After the original explosion,
when the temperature was still very high, about 30%
of the primordial neutrons and protons were fused into
He4, but the expanding gas cooled off much too rapidly
for elements above He4 to be built up in any appreci-
able quantities, and these had to wait for the stellar
ovens that were to be formed when the rapidly ex-
panding gas of hydrogen and helium was fragmented
into stars by turbulence and the gravitational forces.

The fragmentation of the original hydrogen-helium
gaseous mixture into galaxies and stars occurred when
the exploding universe had cooled off to very nearly
its present value—about two hundred million years
after the initial explosion. The density of matter and
radiation was then favorable for gravitational contrac-
tion to take over in local regions and to compress the
gas into huge clouds. This, however, could occur only
after another process had come into operation—the
natural and unavoidable fragmentation of the expand-
ing gas into local eddies. One can show that a stream
of gas becomes unstable against such a fragmentation
when the length of the stream exceeds a certain num-
ber whose value can be derived from hydrodynamical
theory. In an expanding universe this is bound to hap-
pen after the expansion has progressed beyond a given
point. The average size of the turbulent eddies that
are formed during this kind of fragmentation is deter-
mined by the speed and density of the expanding gas.

The details of this fragmentation process were
worked out many years ago by J. H. Jeans. According
to his calculation, we know that the expanding gas must
have broken up into fragments having an average size
equal to that of a typical galaxy. These galaxies in turn
also suffered fragmentation (on a smaller scale) by the
same process and the oldest stars were thus formed.
These oldest stars (about 8 billion years old) were
formed at the center of the galaxies; and that is where
we find them now, although they also constitute the
globular clusters that surround the core of a galaxy.

Since the very oldest stars were formed almost ex-
clusively from the primordial hydrogen and helium,
at least some of the heavy elements that we now ob-
serve all about us in the universe must have been
synthesized in the interiors of these stars as they
evolved. This, indeed, is the case, for we now know,
from the theory of stellar interiors, that thermonuclear
processes occur near the center of a star, resulting in
the transmutation of the light to the heavy elements.
When the oldest stars were first formed, they con-
tracted very rapidly until their central temperatures
reached about 10 million degrees, at which point ther-
monuclear energy was released with the transformation
of hydrogen to helium; this process kept the stars in
equilibrium and supplied them with their energy for
the first few billion years of their lives—in fact, until
about 12% of their hydrogen had been transformed into
helium.

The core of each star, consisting entirely of helium,
then began to contract quite rapidly under its own
weight, and the central temperature rose (in a few
hundred million years) to about 100,000,000 degrees.
At this high temperature, the helium nuclei in the core
were transformed to carbon—the first step in the
buildup of the heavy elements. This led to the forma-
tion of a carbon core which contracted still further,
resulting in still higher core temperatures. In fact, the
temperature in the core continued to increase until the
billion degree mark was reached, and the heavy ele-


570

ments, right up to iron, had been synthesized. But at
that point a drastic change occurred in the evolution
of the star, for very little of its nuclear fuel was left
to supply the energy required to support its own
weight. The star, which by this time had evolved into
a very large and luminous object, collapsed violently
and became a supernova, ejecting great quantities of
material from its outer regions.

Following the supernova explosion, the hot residual
core (consisting of such nuclei as iron, calcium, magne-
sium, and free electrons) continued to contract, finally
becoming a white dwarf of enormous density. It re-
mains in this stage when the outward pressure of the
free electrons just balances the gravitational contrac-
tion. But this is not so in all cases, and the star must
continue to contract beyond the white dwarf stage if
it is massive enough—ultimately becoming a very hot
neutron star, about ten miles in diameter. Although
such stars have not yet been observed directly, astron-
omers believe that they constitute some of the X-ray
sources now being observed and are the recently dis-
covered “pulsars.” But even neutron stars are not the
final stage of stellar evolution, for the theory of relativ-
ity tells us that such stars must continue to contract
until they disappear from sight.

But what of the material that was ejected from each
star that became a supernova? This was swirled into
the outer regions of the galaxy, where it became the
gas and dust that formed the spiral arms that we now
see. From this gas and dust—consisting not only of the
primordial hydrogen and helium, but also of such heavy
elements as carbon, oxygen, sodium, calcium, and
iron—the second generation, and hence younger stars
such as our sun, were formed. But something else
happened at the same time—planets were also formed.
It can be shown, as has been done by C. F. von
Weizsäcker, G. F. Kuiper, H. Urey, H. Alfvén, and
others, that the turbulences that must occur when a
star like the sun is formed by gravitational contraction,
from dust and gas, must lead to the formation of planets
at fairly definite distances from the star. This is in
agreement with the arrangement of the planets in our
solar system.

We thus see that the cosmological theories that stem
from Einstein's gravitational field equations agree with
the overall architectural and dynamical features of the
universe as we now observe them. At the same time,
these theories show us how the present state of the
universe has evolved from a highly condensed initial
state, and tell us what to expect in the future evolution
of the universe. Although many of the details are still
missing from this forecast, the dominant features are
clearly indicated, and we have every reason to believe
that we shall soon be able to answer most of the ques
tions about the universe that seemed so unanswerable
just a few years ago, for never before in the history
of science have so many capable scientists been work-
ing on this exciting problem.