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Dictionary of the History of Ideas

Studies of Selected Pivotal Ideas
2 occurrences of Ancients and Moderns in the Eighteenth Century
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2 occurrences of Ancients and Moderns in the Eighteenth Century
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X. THE STEADY-STATE THEORY AND
OTHER COSMOLOGIES

We shall conclude our discussion of modern cos-
mologies with brief descriptions of theories that are
related to, but do not spring directly from, Einstein's
field equations, whether or not we place λ = 0. Of
these, the most popular, and one which, has been
strongly supported by outstanding cosmologists and
physicists, is the steady state or continuous creation
theory of Bondi and Gold (1948) and Hoyle (1948).
On the basis of what they call the perfect cosmological


568

principle, which is an extension of Einstein's cosmo-
logical principle, they assert that not only must the
universe present the same appearance to all observers,
regardless of where they are, but it must appear the
same at all times—it must present an unchanging as-
pect on a large scale. The immediate consequence of
this theory is that mass and energy cannot be conserved
in such a universe. Since the universe is expanding,
new matter must be created spontaneously and contin-
uously everywhere so as to prevent the density from
decreasing.

It can be shown from this theory that matter would
have to be created at a rate equal to three times the
product of the Hubble constant and the present density
of the universe, in order to keep things as they are.
One nucleon must be created per thousand cubic cen-
timeters, per 500 billion years to maintain the status
quo. Hoyle arrived at the same result by altering
Einstein's field equations.

Although the steady-state theory was very popular
because it eliminated entirely the question of the origin
of the universe, it was rejected by most cosmologists
because of its continuous creation and the consequent
denial of the conservation of mass energy. But the
strongest argument against the steady state theory is
the existence of the 3°K radiation, which shows clearly
that our universe has evolved from a highly condensed
state. In addition, the observed distribution of quasars,
radio sources, and other distant celestial bodies shows
that the density of matter in the universe was much
higher a few billion years ago than it is now. The
observational evidence seems weighted against the
steady-state theory.

Other general principles have been invoked to derive
cosmological theories. Perhaps the most ambitious of
these theories is that of Eddington (1946), who at-
tempted, in his later years, to deduce the basic con-
stants of nature by combining quantum theory and
general relativity. Starting from the idea that the re-
ciprocal of the square root of the cosmical constant
represents a natural unit of length in the universe, and
that the number of particles in the universe must de-
termine its curvature, he derived numerical values for
such constants as the ratio of the mass of the proton
to that of the electron, Planck's constant of action, etc.
But very few physicists have accepted Eddington's
numerology since his analysis is often obscure, difficult
to follow, and rather artificial. In any case, the exist-
ence of nuclear forces and new particles which Ed-
dington was unaware of when he did his work, and
which therefore are not accounted for in his theory,
destroys the universality which he claims for his theory.

During the period that Eddington was developing
his quantum cosmology, three other cosmological sys
tems were introduced: the kinematic cosmology of
Milne (1935) and the cosmologies of Dirac (1937) and
Jordan (1947). Although these theories are extremely
interesting and beautifully constructed, we can only
discuss them briefly here. Of all the cosmological theo-
ries that we shall have discussed in this essay, Milne's
is the most deductive, for instead of starting with the
laws of nature as we know them locally, and then
constructing a model of the universe based upon these
laws, he introduces only the cosmological principle and
attempts to deduce, by pure reasoning, not only a
unique model of the universe, but also the laws of
nature themselves. To do this, Milne had to assume
the existence of a class of ideal observers attached to
each particle of an ideal homogeneous universal sub-
stratum, which is expanding according to Hubble's law.

To carry out his analysis consistently, Milne had to
introduce two different times; a kinematic time which
applies to the ideal observer and which also governs
electromagnetic and atomic phenomena, and according
to which the universe is expanding; and a dynamic
time, so that a good deal of arbitrariness is inherent
in this theory, particularly at the boundary region
where we pass from one kind of time to another. But
the major objection to this theory arises from its basic
assumption that an absolute substratum exists in the
universe, and that a privileged class of observers is
associated with this substratum.

Although a cosmological principle of one sort or
another is at the basis of the cosmologies which we
have discussed here, other types of principles have also
been used. The most notable of these is that proposed
by Dirac in 1937 (and later in a slightly different form
by Jordan), according to which certain basic numbers
associated with matter and the universe are not con-
stant, as had been assumed in all previous cosmologies,
but vary with time. The numbers Dirac had in mind
are certain dimensionless quantities which are obtained
by taking the ratio of atomic quantities to cosmological
quantities of the same kind. Dirac expressed this prin-
ciple as follows: “All very large dimensionless numbers
which can be constructed from the important constants
of cosmology and atomic theory are simple powers of
the epoch.”

One consequence of this principle is that the univer-
sal gravitational constant would have to decrease with
time. But one can show, as E. Teller did (1948), that
this would lead to a sun that was much too hot during
the Cambrian period; the temperature of the earth
would then have been so high that its oceans would
have been boiling. Owing to this discrepancy, Dirac's
theory has generally been discarded, although, more
recently, C. Brans and R. H. Dicke have introduced
a variation of it, starting from a different point of view.