Olbers' paradox

Olbers' paradox, described by the German astronomer Heinrich Wilhelm Olbers in 1823 and earlier by Johannes Kepler in 1610 and Halley and Cheseaux in the 18th century, is the paradoxical statement that in a static infinite universe the night sky should be bright. If the universe is assumed to be infinite, containing an infinite number of uniformly distributed luminous stars, then every line of sight should terminate eventually on the surface of a star. Because the observed brightness of a surface is independent of its distance, this means that every point in the sky should be as bright as the surface of a star.

Kepler saw this as an argument for a finite universe, or at least for a finite number of stars, but the argument is not convincing as will be shown below.

One explanation attempt is that the universe is not transparent, and the light from distant stars is blocked by intermediate dark stars or absorbed by dust or gas, so that only light from a finite distance away can reach the observer. However, this reasoning does not resolve the paradox. According to the first law of thermodynamics, energy must be conserved, so the intermediate matter would heat up and soon reradiate the energy (possibly at different wavelengths). This would again result in uniform radiation from all directions, which is not observed.

Another resolution that has been offered points to the fact that every star contains only a finite amount of matter and therefore shines only for a finite period of time, after which it runs out of fuel. This theory seems to have been first suggested by poet and writer Edgar Allan Poe. However, the paradox stands if one assumes that stars are constantly being created randomly across the infinite universe, shine for a finite period, and die.

The paradox is resolvable in a variety of ways. If the universe has existed for only a finite amount of time, as the prevalent Big Bang theory holds, then only the light of finitely many stars has had a chance to reach us yet, and the paradox breaks down. Alternatively, if the universe is expanding and distant stars are receding from us (also a claim of the Big Bang theory), then their light is redshifted which diminishes their brightness, again resolving the paradox. Either effect alone would resolve the paradox, but according to the Big Bang theory, both are working together; the finiteness of time is the more important effect.

In fact, the darkness of the night sky is nowadays taken to be evidence in support of the Big Bang theory.

Another explanation, which does not rely on the Big Bang theory, was offered by Benoit Mandelbrot. It holds that the stars in the universe may not be uniformly distributed, but rather fractally like a Cantor dust, thus accounting for large dark areas. It is currently not known whether this is true or not.

Note: The name Olbers already has an "s" on the end, so the possessive is Olbers' (or, alternatively, Olbers's). It is incorrect to write Olber's because his name was not "Olber".

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References:

• Relativity FAQ about Olbers' paradox (http://math.ucr.edu/home/baez/physics/Relativity/GR/olbers)
• Astronomy FAQ about Olbers' paradox (http://www.faqs.org/faqs/astronomy/faq/part9/section-17)
• Cosmology FAQ about Olbers' paradox (http://supernova.lbl.gov/~evlinder/umass/faqm#olber)
• Paul Wesson, "Olbers' paradox and the spectral intensity of the extragalactic background light", The Astrophysical Journal 367, pp. 399-406 (1991).
• Edward Harrison, Darkness at Night: A Riddle of the Universe, Harvard University Press, 1987