Olbers' paradox

thumb|As more distant stars are revealed in this animation depicting an infinite, homogeneous, and static universe, they fill the gaps between closer stars. Olbers' paradox says that because the night sky is dark, at least one of these three assumptions must be false.|alt=In this animation depicting an infinite and homogeneous sky, successively more distant stars are revealed in each frame. As the animation progresses, the more distant stars fill the gaps between closer stars in the field of view. Eventually, the entire image is as bright as a single star.

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. Modern cosmological models do not make all of these assumptions.

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 resulting microwave radiation background has wavelengths much longer (millimeters instead of nanometers), which appear dark to the naked eye. Although he was not the first to describe it, the paradox is popularly named after the German astronomer Heinrich Wilhelm Olbers (1758–1840).

History

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. 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 points out 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,

The paradox and resolution

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.

thumb|A view of a square section of four concentric shells

Flux form

The flux form can be shown by dividing the universe into a series of concentric shells, 1 light year thick. For example, one shell would stretch from 1,000,000,000 to 1,000,000,001 light years away. A certain number of stars will be in each shell. 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. However, since the second shell is twice as far away, each star in it would appear one quarter as bright as the stars in the first shell. Thus the total light received from the second shell is the same as the total light received from the first shell. Thus each shell of a given thickness will produce the same net amount of light regardless of how far away it is. The light of each shell adds to the total amount. Thus the more shells, the more light; and with infinitely many shells, there would be an infinitely bright night sky.

If intervening gas is added to this infinite model, the light from distant stars will be absorbed. However, that absorption will heat the gas, and over time the gas itself will begin to radiate. With this added feature, the sky would not be infinitely bright, but every point in the sky would still be like the surface of a star.

The flux form assumes a static universe of infinite age. With a finite age, only a limited volume of the universe contributes to light on Earth, resolving the paradox.

References

External links

Relativity FAQ about Olbers's paradox
Astronomy FAQ about Olbers's paradox
Cosmology FAQ about Olbers's paradox
Why is the sky dark? physics.org page about Olbers's paradox
Why is it dark at night? A 60-second animation from the Perimeter Institute exploring the question with Alice and Bob in Wonderland