Dictionary of the History of Ideas Studies of Selected Pivotal Ideas |

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3 | I. |

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7 | V. |

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III. CONTRADICTIONS IN THE NEWTONIAN COSMOLOGY |

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Dictionary of the History of Ideas | ||

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*III. CONTRADICTIONS IN THE*

NEWTONIAN COSMOLOGY

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.

Dictionary of the History of Ideas | ||