Olbers' paradox

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Olbers' paradox, described by the German astronomer Heinrich Wilhelm Olbers in 1823 (and then reformulated in 1826) and earlier by Johannes Kepler in 1610 and Halley and Cheseaux in the 18th century, is the paradoxical observation that the night sky is dark, when in a static infinite universe the night sky ought to be bright. It is one of the pieces of evidence for a non-static Universe such as the current Big Bang model. This paradox is sometimes also known as the "dark night sky paradox".

Contents

1 Assumptions
2 Explanations

2.1 Accepted explanation
2.2 Myths and alternative explanations

3 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 brightness of a surface is independent of its distance, so every point in the sky should be as bright as the surface of a star.

For stars to appear "uniformly distributed" in space they must also be uniformly distributed in time, because the further away one looks, the older is what one sees. 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. The current scientific consensus is that effects of general relativity relating to the Big Bang and the finite age of the Universe do indeed give a finite size for the observable universe, but that it is the astronomical redshift relationship which really explains the dark sky at night.

Explanations

Accepted explanation

The explanation of the paradox which is generally accepted by the scientific community points to the finite speed at which light travels through space. Given its finite speed, the light from the most distant star cannot have travelled a further distance, measured in light years, than the star itself is old. This explanation was first offered in 1848 by poet and writer Edgar Allan Poe, who observed:

"Were the succession of stars endless, then the background of the sky would present us an uniform luminosity, like that displayed by the Galaxy -–since there could be absolutely no point, in all that background, at which would not exist a star. The only mode, therefore, in which, under such a state of affairs, we could comprehend the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all."[link]

The most widely accepted model for the Big Bang would make the universe approximately 13.7 billion years old, so the furthest expanse that light could have possibly travelled since its creation is an equal number of light years. Thus, even if every infinite trajectory into space from the earth eventually passes through a star in the farthest regions of the universe, the light of all such stars beyond the maximum distance in which light has travelled since the origin of the universe will remain beyond visibility from earth. In reality this does not explain the dark sky, as the light from the Big Bang was incredibly intense, and was emitted in all directions. However the emission from the Big Bang is redshifted to microwave wavelengths due to general relativity, where it forms the cosmic microwave background radiation. So in reality the explanation for the dark night sky results from the redshifting of all light from distant objects, and not directly from the finite age of the Universe (although the redshifting process and the age of the universe are connected in most theories).

Myths and alternative explanations

An alternative explanation which is sometimes suggested by non-scientists 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 there is a bound on the distance from which light can reach the observer. However, this reasoning would 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.

A different resolution, which does not rely on the Big Bang theory, was offered by Benoit Mandelbrot. He postulated that if the stars in the universe were fractally distributed (e.g. like a Cantor dust), it would not be necessary to rely on the Big Bang theory to explain Olbers' Paradox. This model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred. This is merely a demonstration of the consequences of fractal theory, rather than a serious resolution of this paradox. Astronomical observers have found no evidence to support a fractal distribution of the stars.

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]".

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