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Dictionary of the History of Ideas

Studies of Selected Pivotal Ideas
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III. CONTRADICTIONS IN THE NEWTONIAN COSMOLOGY
  
  
  
  
  
  
  
  
  
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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.


556

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.