Olbers' paradox

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In astrophysics and physical cosmology, Olbers' paradox is the argument that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. It is one of the pieces of evidence for a non-static universe such as the current Big Bang model. The argument is also referred to as the "dark night sky paradox." The paradox states that at any angle from the Earth the sight line will end at the surface of a star, so the night sky should be completely white. This contradicts the darkness of the night sky and leads many to wonder why we do not see only light from stars in the night sky (see physical paradox).

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History

Harrison (1987) is the definitive account to date of the dark night sky paradox, seen as a problem in the history of science. According to Harrison, the first to conceive of anything like the paradox was Thomas Digges, who was also the first to exposit the Copernican system in English and may have been the first to postulate an infinite universe with infinitely many stars. Kepler also posed the problem in 1610, and the paradox took its mature form in the 18th century work of Halley and Cheseaux. The paradox is commonly attributed to the German amateur astronomer Heinrich Wilhelm Olbers, who described it in 1823, but Harrison shows convincingly that Olbers was far from the first to pose the problem, nor was his thinking about it particularly valuable. Harrison argues that the first to set out a satisfactory resolution of the paradox was Lord Kelvin, in a little known 1901 paper,[1] and that Edgar Allan Poe's essay Eureka (1848) curiously anticipated some qualitative aspects of Kelvin's argument:

The Paradox

The paradox is that a static, infinitely old universe with an infinite number of stars infinitely far away would be bright rather than dark.

To show this we divide the universe in to a series of concentric shells, 1 light year thick (say). Thus a certain number of stars will be in the shell 1,000,000,000 to 1,000,000,001 light years away, say. If the universe is homogeneous at a large scale, then there would be four times as many stars in a second shell between 2,000,000,000 to 2,000,000,001 light years away. However, the second shell is twice as far away, so each star in it would appear four times dimmer than the first shell. Thus the total light received from the second shell is the same as the total light received from the first shell.

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