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The Paradox: Why is the
sky dark at night?
At first, this seems like a
silly question. It’s dark at night because the Sun has set, and
the Moon and stars are too dim to produce much light. But
Kepler, Halley, and Cheseaux before Olbers pointed out that if
we assume the Universe is infinite, and there is an infinite
number of stars, as was generally accepted, then each spot of
the sky should be occupied by starlight.
In 1826 Olbers published his
paradox questioning why the sky is dark at night. He noted that even though more distant stars are fainter, there are more
of them (Olbers, 1826). If we move the Sun four times further
from us, we will receive 1/16 the amount of light, but the Sun
will subtend one-quarter of the area, and its intensity is
unchanged. In fact, assuming that other stars have surface
temperatures the same as the Sun (~5800 K), then we should see
the sky as if we are in the center of a hollow black body whose
temperature is about 6000 K (Chase, 2004;
Struve, 1963). The
sky should be as bright as the Sun in all directions at all
points.
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Solutions to the Paradox
Olbers’ Paradox has bedeviled astronomers
and physicists since the 18th century, and it
continues to be examined in a serious fashion even in the 21st
century (Maddox, 1991). Phillipe de Cheseaux (1718-1751), a
wealthy Swiss landowner, mathematician, and astronomer, was one
of the first persons to examine the paradox in a formal manner
and offer what appeared to be a reasonable solution. He
proposed there is some absorption of starlight en route to the
Earth. Olbers gave essentially the same explanation and felt
the stars had not been shining forever (Moore, 2002). PG Tait
writing in the 1881 Encyclopedia Britannica stated the
paradox represented a finite Universe (Struve, 1963). By the
latter part of the 19th century and the beginning of
the 20th century, it was realized that absorption of
starlight offers no explanation, because the absorbing material,
mainly gas and dust, will simply heat up and emit the same
amount of radiation, albeit in a somewhat different form (Chase,
2004; Struve, 1963).
Other classical explanations include a)
there is only a finite number of stars in the Universe, b) the
distribution of stars is not uniform, and stars are hiding
behind each other, and c) the Universe is too young to allow
distant starlight to reach us. Sir John Herschel offered the
explanation of a “hierarchical” Universe in which stars form
galaxies, which in turn form galaxy clusters, and so forth
without end. The result being that stars are not uniformly
distributed in the Universe (Sky & Telescope, 1992).
The classical explanations fail to solve
the paradox. Stars and galaxies are not uniformly distributed
on small orders of scale, but there are a near infinite number
of stars and galaxies visible to us. When the Universe is
looked at on the largest scale of 100’s of megaparsecs, it is
uniform. Thus, we ought to see the light of galaxies if not
individual stars in all directions.
The sky between the stars and galaxies is
actually not totally dark. There is approximately 0.0003
ergs/cm/sec of energy coming to the Earth in the sky between
stars and galaxies. This is equivalent to a 25th
magnitude star per square arc second of sky (Wesson, 1989).
Modern cosmology in the 1980’s explained the paradox by the
expansion of the Universe and the finite age of galaxies. As
galaxies recede from us, their light is dimmed, because more
photons are spread over an increasingly large volume. Also,
their light is redshifted so the intrinsic energy of the photons
reaching us is slowly but steadily diminishing (Wesson, 1989).
Since the speed of light c is finite, there is only a finite
sphere of the Universe we are able to see. The finite age of
the Universe limits our ability to see a larger volume of space,
because light has only been traveling to us a finite time.
Thus, the galaxy formation surface we are able to view contains
a very large number but a finite number of galaxies. Contrary
to what Olbers thought, we do not see an ever increasing number
of light sources as we peer ever deeper into the sky (Wesson,
1989) (figure 1):
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