Olbers' paradox

The Olbers' paradox refers to the contradiction between the prediction of a bright night sky and its actual dark appearance.

Term

The term was created by Hermann Bondi 1952. Heinrich Wilhelm Olbers formulated this problem in 1823, after it has already been considered by other researchers in connection with competing cosmological models. It affects world models that correspond to the perfect cosmological principle, that is, an infinitely extended universe postulate and take over large distances uniform distribution of stars in this one. Under these conditions, would have a correspondingly long time after the light of a star from any direction have reached Earth and the sky 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: Generic term paradox

Historical development of models

Due to the Copernican revolution developed various cosmologies, which differed in the fact that the star distribution they assume in the universe. Copernicus took in his work De revolutionibus Orbium Coelestium the view that the stars are in the outermost shell of the immovable universe. His model contains a finite number of stars in a finite distance from the sun, so it is inhomogeneous and hierarchical.

Thomas Digges (1546 - 1595) explained such a sphere of fixed stars for scientifically untenable and beat in A Perfit Description of the Caelestial Orbes a homogeneous distribution of stars in an infinite universe before. The supernova of 1572 was a star who had come closer from a distant, invisible zone and thus become visible to him. For Digges the " largest part of the stars invisible because of the distance. " Was

Also of Giordano Bruno (1548 - 1600) and in the Sidereus Nuncius by Galileo Galilei (1610 ) an infinite universe with an infinite number of suns was postulated in which the observed fixed stars are distant suns.

From these model conceptions followed the paradox, as described Johannes Kepler ( 1571-1630 ). He had thus a strong argument against the infinity of the universe (or against the infinite depth of the fixed stars ).

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

Olbers ' formulation

" ... Are really the whole infinite space suns exist, whether they be distributed at approximately equal distances from each other, or in a galaxy systems, their quantity is infinite, and since the whole sky would be just as bright as the sun. For each line that I can think of is pulled from our eye is necessary to meet any one fixed star, and so we would each point in the sky stellar light, so send sunlight ... "

Exact formulation

If the three-dimensional universe following properties 1 to 5 met, then the sky to the earth after infinite time is infinite light:

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

Illustrate the paradox olbersschen

To better illustrate the paradox, one can imagine the earth in the middle of a plain. If the universe were all built about the same and indefinitely large, the observer would see within the distance r ( comparable to a horizon line ) all the stars within this radius. In this case, the apparent size of the celestial body in proportion to the distance from the viewer. Increasing this line of sight to x (r x), then, the number of stars in a square, so x ² to be, although the star located therein to the root of x appear smaller. Comparing the " overall brightness " of the two radii, one finds that both correspond to each other. This means that regardless of how far an observer might look, the collective number would increase to visible stars on the horizon directly proportional to the distance. If we now also assume that the universe is infinitely large and the light would have unlimited time to reach us, this would mean that there could never be dark on Earth.

Historical explanations

In the history of the paradox, many proposals have been discussed, as was to be dissolved. The most obvious solution, the assumption that the light from distant stars is hindered in its spread and the dust and gas clouds absorb the starlight. This was proposed by Olbers solution. As John Herschel realized already that provides no explanation, because the clouds would heat up until their emission is equal to its absorption.

Benoît Mandelbrot discusses the Olbers' paradox in his book Fractal Geometry of Nature by 1977. In a hierarchical ( fractal) arrangement of masses in the universe, the paradox can be avoided, as the first writer Edmund Edward Fournier d' Albe ( 1868-1933 ) in his Book Two New Worlds of 1907 showed, where it arrived Fournier only on the demonstration of the principle, and not a realistic model. By Carl Charlier was in 1908 taken up in more realistic models in which the fractal dimension with the size scale varied, and also wanted to recognize such cluster structures in his maps of the galaxy distribution. Fournier announced in a physical argument ( an upper limit for the observed speed rating ) for a fractal dimension of the mass distribution is close to 1. Also Mandelbrot himself sees in these experiments less a model for a solution of the paradox, which he viewed through the standard cosmological models as solved, but first of view of a possible fractal arrangement of the galaxies in the universe. But studies of the distribution of galaxies on different scales refute a simple hierarchical model with a common fractal dimension ..

Resolution of the paradox

The condition of an infinitely large observable universe with an infinite number of stars, which was adopted in the formulation of the paradox is refuted. Observation data from projects like COBE and WMAP or probes show that the visible universe is spatially and temporally limited. Light can give us in finite time, in which the universe exists only for a finite wide range reach, in which only finitely have developed since the big bang many stars. In addition, stars have only a finite lifetime, which further restricts the number of stars whose light can reach us. Through interstellar dark clouds, the brightness of stars behind it is additionally reduced.

The now popular idea for explaining the dark night sky based on the general theory of relativity and the resulting current developed Lambda -CDM model of cosmology.

Today's statement by the dark night sky

Other effects are still observed for the explanation of the exact appearance of our night sky. The paradox was restricted to the light from stars, with most radiation quanta in the intergalactic medium dating back to the era of decoupling of the background radiation. This light was sent to the spectrum of an approximate blackbody temperature of 3000 K and would at free spread evenly illuminate the sky yellow / orange. That this is not the case, the expansion of the universe. The expanding space reduces the energy of the moving light through it, which consequently becomes long-wave. This effect is known as the cosmological redshift. As a result of this redshift the background radiation from the Big Bang has become so low in energy that it corresponds to the thermal radiation spectrum of a very cold (2.7 K) black body today. This very long-wavelength range is part of the microwave radiation. He is invisible to the human eye and therefore does not contribute to sky brightness.

The redshift would also explain a paradox olberssches in an infinite, expanding universe. Due to the olbersschen paradox so you can not exclude infinite universes. Also in the meantime for other reasons, the majority of astrophysicists regarded as refuted steady-state theory is in principle compatible with the Olbersschen paradox due to expansion.