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Dictionary of the History of Ideas

Studies of Selected Pivotal Ideas
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We saw in the last section that placing λ = 0 se-
verely restricts the number of models, and that these
models represent ages that are somewhat too small for
stellar evolutionary comfort. For this reason, a group
of investigators, particularly Lemaître, Eddington,
Robertson, Tolman, and McVittie, in the early days (all
independently of each other and without knowledge
of Friedmann's work) and Gamow (1946) later, con-
structed various models with λ different from zero.
There are many more such models than one can obtain
with λ = 0, and among them are both the expanding
and oscillating types, as we have already noted. The
most popular of these models during the earlier period
of this work is the one first proposed by Lemaître in
1927 and strongly supported by Eddington. This is the
expanding II model listed in Table I, for which both
λ and k are positive. In this model the universe is
always closed and finite and began its expansion from
some finite nonzero value of R. But the moment of
the beginning of the expansion was not the moment
of zero time (that is, the moment of the origin of the
universe) because in this model the universe could have
remained in a nonexpanding, static state for as long
as one might desire—in fact, for an infinite time in
the past.

Since this model starts expanding from a static
model, both Lemaître and Eddington assumed this
initial static model to be the original Einstein static
model. In this model the value of λ and the radius R
are chosen (in relationship to the mass M of the uni-
verse) in such a way as to give a closed spherical
universe in which the cosmical repulsion is just bal-
anced by the gravitational attraction. However, this
Einstein universe is unstable, as we have already noted,
so that any initial expansion reduces the density and
causes this model to expand still more, with further
reduction in density, and so on. The expansion thus
proceeds faster and faster until the universe is infinitely
expanded and the density is everywhere zero. On the
other hand, a slight compression could have caused the
Einstein model to have contracted indefinitely, finally
ending up as an infinitely condensed point of matter.

If, then, we accept this Lemaître-Eddington picture,
the universe was in a static Einstein state for an infinite
time in the past and then at some finite time in the
past, for some unknown reason, began to expand, at-
taining its present rate of expansion after a few billion
years. Although Eddington never abandoned this con-
cept and fought for it vigorously to the end of his life,
Lemaître revised his thinking in 1931 and replaced this
type II expanding model by a type I expanding model.


As we can see from Table I, three possible models of
the universe can be constructed with λ positive and
k = 1: an oscillating type, an expanding I type, and
an expanding II type. If we reject the last of these
(which corresponds to the original Lemaître-Eddington
model, which we have just discussed) we still have the
oscillating and the expanding I models.

The reason Lemaître replaced the expanding II
model by the expanding I model is that he had no
reasonable explanation for the start of the initial ex-
pansion of the actual universe from an Einstein static
state. Although his own theoretical investigations and
those of McCrea and McVittie (1931) strongly sug-
gested that any local condensation of the matter in
the Einstein static universe (for example, the formation
of a single galaxy or star) would cause it to start ex-
panding, these investigations left unanswered the
question as to why other galaxies were formed. If
expansion began after the formation of a single galaxy,
the density of the universe would immediately begin
to decrease and other condensations into galaxies would
be precluded. This would mean, of course, that the
cosmological principle defined in Section V would be
untenable, since the distribution of matter in the
neighborhood of this initial condensation would be
different from that elsewhere in the universe. More-
over, it is difficult to see how the heavy elements such
as iron, lead, and uranium could have originated in
an Einstein static-state universe, since we know from
nuclear theory that the formation of such elements
from hydrogen in great abundance requires extremely
high temperatures and pressures. This means that the
entire universe, or at least parts of it, must have passed
through a high temperature-high pressure phase. Thus
the very existence of the stars and heavy elements
argues against the Einstein static state as the initial
phase of our present universe.

Owing to these difficulties, inherent in the assump-
tion that our present universe evolved from an Einstein
static universe of finite radius, Lemaître introduced the
assumption that we live in an expanding universe of
type I, which began its expansion from a highly con-
densed state. He referred to this initial condensation
as the primordial atom or nucleus and assumed that
a vast, radioactive explosion occurred in this atom and
that what we now see in the recession of the galaxies
all about is the result of this explosion. In this picture,
the expanding universe is always finite in size, but
closed like a sphere. The initial condensed state (that
is, the Lemaître primordial atom) may be pictured as
having been present for an infinite time in the past
or we may suppose that the universe began its life in
the Einstein static state and then collapsed violently
into a primordial atom from which it began to expand.
According to Lemaître, this expansion carried the uni-
verse back to its initial Einstein state, but it did not
stop there. Its velocity of expansion carried it beyond
this static phase, and after that its expansion proceeded
with ever increasing speed.

Whether we are discussing an Einstein-Friedmann
expanding model, with λ = 0; or an oscillating model,
with λ = 0; or a Lemaître model, with λ > 0 and
k = +1 (expanding II or oscillating), we are dealing
with a group of models that are referred to as the “big
bang” models of the universe, since all of them picture
the universe as having originated explosively from a
point. The term “big bang” was first introduced by
Gamow (1948) who, together with Alpher and Herman
(1950), sought to account for the origin of the heavy
elements by supposing that they were formed from the
original protons and neutrons in the very early and
very hot stage of the explosion. According to this
picture of the origin of the universe, neutrons were
the principal components of the original material
ejected from the primordial atom or point source. Some
of these neutrons quickly decayed into protons and
electrons, and these protons then captured other neu-
trons to build up the heavy elements. This whole
buildup of heavy elements must have occurred during
the first thirty minutes after the initial explosion, for
the temperature of this primordial material dropped
very rapidly after that and everything then remained

Gamow's theory was very appealing at first since
no other theory of the elements was available then;
the theory of stellar structure and evolution had not
yet reached a point of development where it could
be shown that heavy elements can be and are built
up inside stars, as they evolve from structures like the
sun into red giants like Antares and Betelgeuse, with
their internal temperatures rising to billions of degrees.
Gamow's theory of the buildup of the heavy elements
during the first thirty minutes of the life of the universe
had to be discarded, however, since there are no stable
nuclei of atomic masses 5 and 8, so that neutron cap-
ture alone could not have bridged the nuclear gap
between the light and heavy nuclei. Even if some heavy
nuclei were formed by neutron capture in this early
fireball stage of the universe (and all nuclei capture
neutrons very readily) a half hour would hardly have
been long enough for the heavy elements to have been
formed in their present abundances. Since we now
know that the heavy elements can all be baked in the
stellar furnaces at various stages of evolution, this phase
of the Gamow “big bang” theory is not essential and
one can discard it without invalidating the overall

If we then accept this Lemaître-Gamow hot “big


bang” hypothesis, the universe must have passed
through a very high temperature phase (about 1010 to
1011 degrees K) soon after the initial explosion, and
some observable evidence of this may still be around.
That this should be so was first pointed out by Gamow
himself, who argued that there must have been a con-
siderable amount of very hot black body radiation
present in this initial phase of the universe and most
of it must still be around, but in a very much red-shifted
form. He estimated that its temperatures would now
be 6°K. Without knowing about Gamow's suggestion,
Dicke proposed the same idea in 1964 (he called it
the “primordial fireball radiation”) and later, in collab-
oration with Peebles, Roll, and Wilkinson (1965), dem-
onstrated that the initial hot black body radiation (at
a temperature of 1010 degrees K) must now be black
body radiation (at a temperature of 3.5°K). The general
idea behind this deduction is the following: if the
universe was initially filled with very hot black body
radiation (that is, of very short wavelength), this radia-
tion would remain black body radiation during the
expansion of the universe, but it would become redder
and redder owing to the Doppler shift imparted to it
by the expansion. This is similar to radiation that is
reflected back and forth from the walls of an expanding
container. This 3.5°K black body radiation was de-
tected by Penzias and Wilson in 1965 and has since
been verified by other observers. It is present in the
form of isotropic, unpolarized microwave background
radiation in the wavelength range from 1/10 to 10 cm.

One other residual feature of the “big bang” should
still be visible, or at least amenable to verification—the
present helium abundance. During the initial fireball
period when the temperature was considerably larger
than 1010 degrees K, the thermal electrons and neu-
trinos that were present would have resulted in very
nearly equal abundances of neutrons and protons.
When the temperature of the fireball dropped to 1010
degrees K these neutrons and protons would have
combined to form deuterium, which, in turn, would
have been transformed into He4, and no heavier ele-
ments would have been formed. Two questions then
arise. (1) Is the helium that we now observe all about
us, in our own galaxy and in others, still this primordial
helium? (2) If so, what can this tell us about the models
of our universe?

The evidence relating to the first question is some-
what ambiguous because we know that helium burning
occurs during the giant stage of a star's evolution, so
that some of the original helium must certainly have
been transformed into heavy elements in stellar inte-
riors, and thus disappeared. But we may assume that
the helium that is found in stellar atmospheres is pri-
mordial and the evidence here is that although there
is an overall helium abundance of about 25%, some
stars have been observed with very weak helium lines.
In spite of these, however, the overall evidence favors
the 25% abundance, which is in agreement with the
“big bang” hypothesis.

Taking all of the observed data into account (the
3°K black body radiation and the helium abundance)
the preponderance of the evidence favors the “big
bang” theory and points to an age of at least 1010,
i.e., ten billion years for our universe. The observed
helium abundance (if we accept 25% as the primeval
abundance) also indicates that the density of matter
in the universe must be at least 4 × 10-31 grams per
cc. But if the density of matter in the universe is no
larger than this, we run into difficulty with the obser-
vations on the rate at which the expansion of the
universe is decelerating. We have already noted that
Humason, Mayall, and Sandage have given a value for
this deceleration which indicates that the universe must
ultimately stop expanding and begin to collapse. This
means that the correct model of the universe is an
oscillating one, rather than expanding, but, as we have
seen, this requires the density of matter to be about
10-29 gms/cc, as compared to the observed density of
7 × 10-31

In spite of this, the evidence for an oscillating uni-
verse has been greatly strengthened recently by the
analysis of the distribution of quasars and of quasi-
stellar radio sources in general. Since these objects
(according to their red shifts) are at enormous distances
from us, they give us the rate of expansion of the
universe in its earliest stages. By comparing this with
the present rate of expansion, we obtain a very reliable
value for the deceleration, which shows the universe
to be oscillating. To account for the discrepancy be-
tween the observed and required density of matter for
such a model of the universe, we must suppose that
there are large quantities of dark matter in inter-
galactic space—in the form of hydrogen clouds, black
dwarf stars, and streams of neutrinos. But until we have
direct evidence of this, we cannot be sure about the
validity of the oscillating model.