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
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.