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.

Contents

1 Assumptions 2 Explanations 3 Resolutions 3.1 References

Assumptions

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. The observed brightness of a surface is independent of its distance, and the apparent area of a star diminishes as the square of its distance, and the number of expected stars increases as the square of the distance. Thus, every point in the sky should be as bright as the surface of a star.

It should be noted that for stars to appear "uniformly distributed" in space they must also be uniformly distributed in time, because the further away one looks, the older what one sees is. On an infinite scale, this means the universe must be infinitely old with no dramatic changes in the nature of stars in that time.

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.

Explanations

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 explanation 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.

Resolutions

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. Some see the darkness of the night sky to be evidence in support of the Big Bang theory.

Even without the Big Bang theory and its redshift evidence, we may establish the finite age of the universe (in its present form) by a mathematical evaluation of Hydrogen. Assume that the amount of mass in stars divided by the total amount of mass in the universe is nonzero. After some length of time, any given star will convert too much Hydrogen into Helium (or heavier elements) to continue nuclear fusion. From this we conclude that in unit time, the amount of Hydrogen converted into Helium by a given star divided by the star's mass is nonzero. Combining this with the earlier statement, we conclude that the amount of Hydrogen converted into Helium by stars as a whole divided by the mass of the universe is nonzero. There is no known process that can return heavier elements to Helium in the necessary quantities, and any would probably violate the second law of thermodynamics. Therefore, the amount of time needed for stars to convert all of the Hydrogen in the universe into Helium is finite, and it will never change back. After this, only heavier-element-burning stars will exist (and these will die when they hit Iron, an event known as the heat death of the universe). This hasn't happened yet, so either the universe is of finite age, it has undergone major changes in its history, or there exists some highly exotic process (for which no direct evidence exists) that produces Hydrogen to keep it going.

A different resolution, 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, although recent satellite studies have found the cosmic microwave background radiation is isotropic to 1 part in 10000.

References

• Relativity FAQ about Olbers' paradox
• Astronomy FAQ about Olbers' paradox
• Cosmology FAQ about Olbers' paradox
• 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
• Scott, Douglas, and Martin White, "The Cosmic Microwave Background".

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".