Olbers paradox

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Graphic illustration of the Olbers paradox

The Olbers Paradox (alternative spelling of Olbers Paradox ) shows the resulting contradiction in predicting a bright night sky and its actual dark appearance.

term

The term was created by Hermann Bondi in 1952. Heinrich Wilhelm Olbers formulated this problem in 1823 after it had already been considered by other scientists in connection with competing cosmological models . It concerns world models that correspond to the perfect cosmological principle , i.e. That is, to postulate an infinitely extensive universe and assume in this a star distribution even over great distances . Under these conditions, after a correspondingly long time, the light of a star should have reached the earth from every direction and the sky should appear at least as bright as the star's surface. This contradicts the observation of a dark night sky and was a historical argument against such models.

See also: umbrella term paradox

Historical development of the models

Thomas Digges homogeneous star distribution in his A Perfit Description of the Caelestiall Orbes .

As a result of the Copernican change , different cosmologies developed, which differed in the distribution of stars in the universe they assumed. In 1543, in his work De revolutionibus orbium coelestium, Copernicus took the view that the stars are in the outermost immobile shell of the universe. His model contains a finite number of stars at a finite distance from the sun, so it is inhomogeneous and hierarchical.

Thomas Digges declared such a fixed star sphere to be scientifically untenable and in 1576, in A Perfit Description of the Caelestial Orbes, proposed a homogeneous distribution of stars in an infinite universe. The supernova of 1572 was a star for him, who had come closer from a distant, invisible zone and thus become visible. For Digges, "most of the stars were invisible because of the distance."

Also by Giordano Bruno and Galileo Galilei in Sidereus Nuncius (1610) an infinite universe with an infinite number of suns, it was postulated in the observed fixed stars are distant suns.

The paradox as described by Johannes Kepler in 1610 followed from these model ideas . He thus had a strong argument against the infinity of the universe (or against the infinite depth of the fixed star sky).

In the 18th century the paradox was also dealt with, for example it was mentioned by Edmond Halley in 1720 and Jean-Philippe de Chéseaux , and Johann Heinrich Lambert also knew it.

Olbers' formulation

“If there are really suns in the whole of infinite space, they may now be at roughly equal distances from one another or distributed in Milky Way systems, then their number becomes infinite, and the whole sky should be as bright as the sun. Because every line that I can imagine drawn by our eye will necessarily meet some fixed star, and therefore every point in the sky would have to send us fixed star light, that is, sunlight. "

Exact formulation

If the three-dimensional universe fulfills the following properties 1 to 5, then the sky on earth is infinitely bright after infinite time:

  1. It is infinitely extended in every direction.
  2. All stars have a finite size and luminosity.
  3. The number of stars in a sphere with a radius around the earth approaches infinitely like ( homogeneous star distribution on a cosmological scale).
  4. The number of stars in each section of this sphere goes towards infinity as ( isotropy on a cosmological scale in the homogeneous star distribution).
  5. The stars and the universe do not change at any time (static universe).

The statements mentioned in conditions 1 and 2 were already generally accepted in the 16th century, the finite lifespan of stars was not yet known. The star distribution postulated by Digges, which can be described as homogeneous and isotropic on large scales as in conditions 3 and 4, was a direct reaction to the spatially inhomogeneous star distribution of Copernicus. If an eternal lifetime of the stars is assumed, an infinite amount of light would already have reached the earth.

Illustration of the Olbers paradox

Forest as an analogy to the Olbers paradox: in every (horizontal!) Line of sight there is a tree.

To better illustrate the paradox, imagine the earth in the middle of a plane. If the universe were constructed roughly the same everywhere and of unlimited size, the observer would see all stars within this radius within the distance r (comparable to a horizon line). The apparent size of the celestial body decreases proportionally to the distance from the observer. If you increase this line of sight by x (r + x) , the number of stars in it increases quadratically, i.e. by x² , although the stars in it appear smaller by the root of x . If you compare the “total brightness” of the two radii, you can see that both correspond to each other. This means that regardless of how far an observer might look, the collective number of visible stars on the horizon would increase in direct proportion to the distance. If one also assumes that the universe is of unlimited size and that light has unlimited time to reach us, this would mean that it could never get dark on earth. This means that the same temperature on earth as at any other point in the universe would have to prevail as on the sun of approx. 6000 K.

Historical explanations

In the history of the paradox, many proposals have been discussed as to how to resolve it. The most obvious solution is the assumption that the light of distant stars is hindered in its propagation and that dust and gas clouds absorb the starlight. That was the solution proposed by Olbers. As John Herschel already recognized, this does not provide an explanation, since the clouds would heat up until their emission equals their absorption.

Benoît Mandelbrot discusses the Olbers paradox in his book Fractal Geometry of Nature from 1977. With a hierarchical ( fractal ) arrangement of masses in the universe, the paradox can be avoided, as the writer Edmund Edward Fournier d'Albe (1868–1933) first did in his Book Two New Worlds from 1907 showed that Fournier was only concerned with demonstrating the principle and not with a realistic model. This was taken up by Carl Charlier in 1908 in more realistic models in which the fractal dimension varied with the size scale, and who also wanted to recognize such cluster structures in his maps of the galaxy distribution. Fournier also gave a physical argument (an upper limit on the observed stellar velocity) for a fractal dimension of the mass distribution close to 1. Even Mandelbrot himself sees in these experiments less a model for a solution to the paradox, which he regards as solved by the cosmological standard models, but rather first views of a possible fractal arrangement of the galaxies in the universe. Investigations of the galaxy distribution on different scales refute a simple hierarchical model with a common fractal dimension.

Resolution of the paradox

The condition of an infinitely large observable cosmos with an infinite number of stars, which was assumed in the formulation of the paradox, has been refuted. Observation data from projects and probes such as COBE and WMAP show that the visible universe is limited in space and time. Although nothing speaks against the assumption of an infinitely expanded universe, since the universe has a finite age and light only propagates at a finite speed , since the Big Bang only light can reach us from a finitely large area. In addition, stars only have a finite lifespan, which further limits the number of stars whose light can reach us.

The idea that is widespread today to explain the dark night sky is based on the general theory of relativity and the current lambda CDM model of cosmology developed from it.

Today's explanation of the dark night sky

To explain the exact appearance of our night sky, there are other effects to consider. The paradox was limited to the light from stars, whereas most of the radiation quanta in the intergalactic medium originate from the era of the decoupling of background radiation . This light was emitted with the spectrum of an approximately black body with a temperature of 3000 K and would illuminate the sky evenly yellow / orange if it spread unhindered. That this is not the case is due to the expansion of the universe. The expanding space reduces the energy of the light moving through it, which becomes longer-wave as a result. This effect is called cosmological redshift . As a result of this red shift, the background radiation from the Big Bang has become so low in energy that today it corresponds to the thermal radiation spectrum of a very cold (2.7 K) black body. This very long-wave range belongs to microwave radiation. It is invisible to the human eye and therefore does not contribute to the brightness of the sky. The light of distant galaxies is also shifted by the expansion of the universe into infrared, which is invisible to humans, which creates the infrared background.

Even if the majority of astrophysicists now assume the steady-state theory , which has meanwhile been disproved for other reasons , the undisputed redshift due to the expansion is sufficient in principle to solve the Olbers paradox, regardless of the assumption of a big bang.

literature

chronologically

  • Gerhard Vollmer : Why does it get dark at night? The Olbers Paradox as an epistemological case study. In: Heinz-Dieter Ebbinghaus and Gerhard Vollmer (eds.): Thinking on the move. Wissenschaftliche Verlagsgesellschaft, Stuttgart 1992, pp. 183–199.
  • Paul Wesson: Olbers' paradox and the spectral intensity of the extragalactic background light . In: The Astrophysical Journal . tape 367 , 1991, pp. 399-406 (English).
  • Edward Harrison: The dark night sky riddle. in: The Galactic and Extragalactic Background Radiation. Proceedings of the 139th. Symposium of the International Astronomical Union, held in Heidelberg. Dordrecht, Boston, 1990, pp. 3-17.
  • Edward Harrison: Darkness at Night: A Riddle of the Universe . Harvard University Press 1987.
  • Stanley L. Jaki : The Paradox of Olbers' Paradox. A Case History of Scientific Thought. Herder & Herder, 1969. (Real View Books, Pinckney, Missouri 2000. ISBN 1-892548-10-0 ).
  • Wilhelm Olbers: About the transparency of space. In: Astronomisches Jahrbuch für 1826. P. 110–121. (Reprinted in: Wilhelm Olbers, his life and works. Published by C. Schilling on behalf of the descendants. Berlin 1894.) online .

Web links

Commons : Olbers' paradox  - collection of images, videos and audio files

α-Centauri Videos:

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English:

Footnotes and individual references

  1. ^ Edward Harrison: Olbers' Paradox in recent times. (Pp. 33–46) in: Bruno Bertotti u. a. (Ed.): Modern Cosmology in Retrospect. Cambridge 1990, p. 38 ; Gerhard Günther: Comments on the philosophy of heaven. in: Rolf Fechner, Carsten Schlüter-Knauer (eds.): Existence and cooperation. P. 133
  2. ↑ Schilling: Wilhelm Olbers, seine Leben und seine Werke, 1894, p. 133 ( online )
  3. ↑ "It was his belief that the distances to the stars varied that at first seemed to be consistent with the new star being a faint one close to the Earth." JJ O'Connor, EF Robertson: Thomas Digges. @University of St Andrews, Scotland (accessed March 23, 2014); s. a. Michael Weichenhan: “Ergo perit coelum…” The supernova of 1572 and the overcoming of Aristotelian cosmology. Stuttgart 2004, p. 588
  4. ↑ "the greatest part rest by reason of their wonderful distance invisible to us", quoted from Michael Weichenhan: "Ergo perit coelum ..." Stuttgart 2004, p. 587/588 ( online only p. 587, accessed March 23, 2014); s. a. Harry Nussbaumer: Revolution in the sky: how the Copernican turn changed astronomy. Zurich 2011, p. 91
  5. ↑ Kepler Dissertatio cum nuncio sidereo galilei , 1610, German Diederichs 1918 (Otto Bryk), English by Edward Rosen: Keplers conversation with Galileos Sidereal Messenger , New York, Johnson Reprint, 1965, p. 34.
  6. ↑ Paolo Rossi: The Birth of Modern Science in Europe. translated Munich 1997, p. 175
  7. ↑ Halley is quoted in Benoît Mandelbrot The fractal geometry of nature , Freeman 1983, p. 92 Chapter 9 is devoted to the discussion of the paradox, there called Blazing Sky Effect .
  8. ↑ Schilling: Wilhelm Olbers, seine Leben und seine Werke, 1894, p. 135 ( online )
  9. ↑ on Fournier d'Albe: Mandelbrot, Fractal Geometry of Nature , loc.cit., P. 396
  10. ↑ Charlier How an infinite world can be constructed , Arkiv för matematik, Astronomi och Fysik, Vol. 4, 1908, pp. 1–15 (English in Vol. 16, 1922, pp. 1–34)
  11. ↑ Peebles Principles of Physical Cosmology , Princeton University Press 1993, pp. 209-224