III. CONTRADICTIONS IN THE
NEWTONIAN COSMOLOGY
We first consider what is now called the Olbers
paradox, a remarkable
conclusion about the appear-
ance of the
night sky deduced by Heinrich Olbers in
1826. Olbers was greatly puzzled by
the fact that the
night sky (when no moon is present) appears as dark
as it does instead of as bright as the sun, which, he
reasoned, is how it
should appear if the basic New-
tonian
concepts of space and time were correct. In
deducing this paradox, Olbers
assumed the universe to
be infinite in extent, with the average density and
the
average luminosity of the stars to be the same every-
where and at all times. He assumed, further, that
space
is Euclidean and that there are no large systematic
movements of
the stars. With these assumptions we
can see, as Olbers did, that each
point of the night
sky should appear as bright as each point of the
surface
of the sun (or any other average star). The reason for
this is
that if the stars were distributed as assumed,
a line directed from our eye
to any point in space
would ultimately hit a star so that the whole sky
should
appear to be covered with stars.
Until quite recently this apparent paradox was taken
as a very strong
argument against an infinite Newtonian
universe (or at least against
Olbers' assumptions) but
E. R. Harrison (1965) has shown that Olbers' conclu-
sions are contrary to the principle of
conservation of
energy. To understand this, we first note that a star
(like the sun) can radiate energy at its present rate for
only a finite
time because only a finite amount of
nuclear fuel is available for this
release of energy. Now
if we assume that stars (or galaxies) are
distributed
everywhere the way we observe them to be in our part
of
the universe, it would take about 1023 years before
the radiation from
these stars would fill the universe
to give the effect deduced by Olbers.
But all stars
would have used up their nuclear fuel long before this
time and their luminosities would have changed drasti-
cally. Thus Olbers' assumption that the luminosities
of
the stars do not change during their lifetimes is not
tenable.
Harrison has shown that the radiation emitted
by stars in a period of about
1010 years (which, on the
basis of modern theories we may take as a
reasonable
estimate of the age of the universe) should give just
about
the kind of night sky we observe.
Although Harrison's analysis of the Olbers paradox
removes this flaw in a
static infinite Newtonian uni-
verse, another
difficulty, first pointed out by Seeliger
in 1895 and also by C. G.
Neumann, still remains. In
a static Newtonian universe (one which is not
expand-
ing), with stars (or galaxies)
extending uniformly out
to infinity, the gravitational force at each point
must
be infinitely large, which is contrary to what we actu-
ally observe. This difficulty with a Newtonian
universe
can be expressed somewhat differently by considering
the
behavior of the elements of matter in it. These
elements could not remain
fixed but would move to-
wards each other so
that the universe could not be
static. In fact, a Newtonian universe can
remain static
only if the density of matter in it is everywhere zero.
To overcome this difficulty Neumann (1895) and
Seeliger (1895) altered
Newton's law of gravity by the
addition of a repulsive term which is very
small for
small distances but becomes very large at large dis-
tances from the observer. In this way a
static, but
modified, Newtonian universe can be constructed.
We may also exclude a Newtonian universe of in-
finite extent in space but containing only a finite
amount of
matter. The principal difficulty with such
a universe is that, in time,
matter would become in-
finitely dispersed or
it would all coalesce into a single
globule—contrary to
observation.
