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Olbers's paradox

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Not to be confused with Oberth paradox.
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.
As more distant stars are revealed in this animation depicting an infinite, homogeneous, and static universe, they fill the gaps between closer stars. Olbers's paradox says that because the night sky is dark, at least one of these three assumptions must be false.

Olbers's paradox, also known as the dark night paradox or Olbers and Cheseaux's paradox, is an 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. In the hypothetical case that the universe is 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 hence the night sky should be completely illuminated and very bright. This contradicts the observed darkness and non-uniformity of the night sky.[1]

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

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Edward Robert Harrison's Darkness at Night: A Riddle of the Universe[2] (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.[3] Kepler also posed the problem in 1610, and the paradox took its mature form in the 18th-century work of Halley and Cheseaux.[4] 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,[2]: 227  and that Edgar Allan Poe's essay Eureka (1848) curiously anticipated some qualitative aspects of Kelvin's argument:[1]

Were the succession of stars endless, then the background of the sky would present us a 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.[5]

The paradox and resolution

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See also: Redshift and expansion of the universe

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.[1] The paradox comes in two forms: flux within the universe and the brightness along any line of sight. The two forms have different resolutions.[6]: 354 

A view of a square section of four concentric shells

The flux form can be shown by dividing the universe into a series of concentric shells, 1 light year thick. A certain number of stars will be in the shell, say, 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 second shell between 2,000,000,000 and 2,000,000,001 light years away. However, the second shell is twice as far away, so 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. That 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.[7]

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, bue every point in the sky would still be like the surface of a star.[8]

The flux form is resolved by the finite age of the universe: the number of concentric shells in the model above is finite, limiting the total energy arriving on Earth.[6]: 355 

Another way to describe the flux version is to suppose that the universe were not expanding, and always had the same stellar density; then the temperature of the universe would continually increase as the stars put out more radiation. After something like 1023 years, the universe would reach the average surface temperature of a star. However, the universe is only 1012 years old, eliminating the paradox.[4]: 486 

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. This version is known to be correct but the result is different in our expanding universe governed by general relativity. The termination point is on the surface of last scattering where light from the Big Bang first emerged. This light is dramatically redshifted from the energy similar to star surfaces down to 2.73K. Such light is invisible to human observers on Earth.[6]: 355 

Recent observations suggesting that the estimated number of galaxies based on direct observations is too low by a factor of ten do not materially alter the resolution but rather suggest that the full explanation involves a combination of finite age, redshifts, and UV absorption by hydrogen followed reemission in near-IR wavelengths also plays a role.[9]

See also

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References

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  1. ^ a b c Overbye, Dennis (3 August 2015). "The Flip Side of Optimism About Life on Other Planets". The New York Times. Retrieved 29 October 2015.
  2. ^ a b Harrison, Edward Robert (1987). Darkness at Night: A Riddle of the Universe. Harvard University Press. ISBN 9780674192713.
  3. ^ Hellyer, Marcus, ed. (2008). The Scientific Revolution: The Essential Readings. Blackwell Essential Readings in History. Vol. 7. John Wiley & Sons. p. 63. ISBN 9780470754771. The Puritan Thomas Digges (1546–1595?) was the earliest Englishman to offer a defense of the Copernican theory. ... Accompanying Digges's account is a diagram of the universe portraying the heliocentric system surrounded by the orb of fixed stars, described by Digges as infinitely extended in all dimensions.
  4. ^ a b Unsöld, Albrecht; Baschek, Bodo (2001). The New Cosmos: An Introduction to Astronomy and Astrophysics. Physics and astronomy online. Springer. p. 485. Bibcode:2001ncia.book.....U. ISBN 9783540678779. The simple observation that the night sky is dark allows far-reaching conclusions to be drawn about the large-scale structure of the universe. This was already realized by J. Kepler (1610), E. Halley (1720), J.-P. Loy de Chesaux (1744), and H. W. M. Olbers (1826).
  5. ^ Poe, Edgar Allan (1848). "Eureka: A Prose Poem". Archived from the original on 26 April 2008.
  6. ^ a b c Peacock, J. A. (28 December 1998). Cosmological Physics (1 ed.). Cambridge University Press. doi:10.1017/cbo9780511804533. ISBN 978-0-521-41072-4.
  7. ^ Byrd, Gene; Chernin, Arthur; Teerikorpi, Pekka; Valtonen, Mauri (2012). Paths to dark energy: theory and observation. Berlin: de Gruyter. pp. 49–50. ISBN 978-3110258783.
  8. ^ D'Inverno, Ray (1992). Introducing Einstein's Relativity (PDF). Oxford University Press. ISBN 9780198596868.
  9. ^ Conselice, Christopher; Wilkinson, Aaron; Duncan, Kenneth; Mortlock, Alice (20 October 2016). "The Evolution of Galaxy Number Density at z < 8 and its Implications". The Astrophysical Journal. 830 (3): 83. arXiv:1607.03909. Bibcode:2016ApJ...830...83C. doi:10.3847/0004-637X/830/2/83. S2CID 17424588.

Further reading

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Library resources about
Olbers's paradox
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