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Olbers' paradox, also known as the dark night paradox or Olbers and Cheseaux's paradox, is a historical argument in astrophysics and physical cosmology that says the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe.

If the universe were static, homogeneous at a large scale, and populated by an infinite number of stars, any line of sight from Earth must end at the surface of a star and if light from an infinite distance could reach Earth, the night sky should be completely illuminated and very bright. This contradicts the observed darkness and non-uniformity of the night sky. The darkness of the night sky is one piece of evidence for a dynamic universe, such as the Big Bang model. That model explains the observed darkness by invoking expansion of the universe, which increases the wavelength of visible light originating from the Big Bang to microwave scale via a process known as redshift. Although he was not the first to describe it, the paradox is popularly named after the German astronomer Heinrich Wilhelm Olbers (1758–1840).

Edward Robert Harrison's Darkness at Night: A Riddle of the Universe (1987) gives an account 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 expound the Copernican system in English and also postulated an infinite universe with infinitely many stars. The paradox is commonly attributed to the German amateur astronomer Heinrich Wilhelm Olbers, who described it in 1823, but Harrison points out that Olbers was far from the first to pose the problem, nor was his thinking about it particularly valuable.

The first to publish a solution in scientific literature was Johann Heinrich von Mädler in 1858, suggesting that a finite age universe could resolve the paradox.

The paradox is that a static, infinitely old universe with an infinite number of stars distributed in an infinitely large space would be bright rather than dark. The paradox comes in two forms: flux within the universe and the brightness along any line of sight.

For example, one shell would stretch from 1,000,000,000 to 1,000,000,001 light years away. If the universe is homogeneous at a large scale, then there would be four times as many stars in a shell twice as far away, between 2,000,000,000 and 2,000,000,001 light years away. Thus the total light received from the second shell is the same as the total light received from the first shell. Thus the more shells, the more light; and with infinitely many shells, there would be an infinitely bright night sky. The flux form of the paradox is resolved because the flux is not infinite: the number of visible stars is limited by the age of the universe.

The line-of-sight version of the paradox starts by imagining a line in any direction in an infinite Euclidean universe. In such universe, the line would terminate on a star, and thus all of the night sky should be filled with light.

In 1848, John Herschel considered that Olbers' paradox could be resolved if stars were distributed non-uniformily. In 1896, Carl Charlier argued that Olbers' paradox and Seeliger's paradox indicated that the universe was finite, yet conceded that a hierarchical model could be an alternative.

The redshift hypothesised in the Big Bang model would by itself explain the darkness of the night sky even if the universe were infinitely old. The expansion of the universe causes the light from these distant stars and quasars to redshift, so that the total light flux from the sky remains finite.

"Olbers' paradox and the spectral intensity of the extragalactic background light".

Why is the sky dark? physics.org page about Olbers' paradox

Quick Facts

• In 1896, Carl Charlier argued that Olbers' paradox and Seeliger's paradox indicated that the universe was finite, yet conceded that a hierarchical model could be an alternative.
• The darkness of the night sky is one piece of evidence for a dynamic universe, such as the Big Bang model.
• That model explains the observed darkness by invoking expansion of the universe, which increases the wavelength of visible light originating from the Big Bang to microwave scale via a process known as redshift.
• The paradox is commonly attributed to the German amateur astronomer Heinrich Wilhelm Olbers, who described it in 1823, but Harrison points out that Olbers was far from the first to pose the problem, nor was his thinking about it particularly valuable.
• Although he was not the first to describe it, the paradox is popularly named after the German astronomer Heinrich Wilhelm Olbers (1758–1840).

Source material: Wikipedia - "Olbers' paradox". Adapted and summarized for DiscoverScroll. Original contributors are credited through the linked Wikipedia article. Read original on Wikipedia. CC BY-SA 4.0. Changes were made from the original.