Olbers' paradox: a contradiction between the presumably infinite universe and the dark night sky.

If the universe were infinite, then every possible line of sight would at some point end at a star, much as in a sufficiently large forest you can see nothing but trees no matter which way you look. As a result, the night sky should not be dark but rather blazing bright. Moreover, the energy of all that light would gradually increase the Earth's surface temperature up to about 6000 degrees Celsius (1083 degrees Fahrenheit).

It would be indeed astonishing if no one had noticed this obvious paradox before the German physician Wilhelm Olbers, who published it in 1826. In fact, Olbers was not the first to discover it. Several astronomers, including Kepler and Halley, had already entertained thoughts about it at earlier times.

What Olbers did do first is to provide an explanation, which he published along with the paradox. According to his explanation, the universe is not completely transparent, but is filled with fine dust that swallows up the light of the stars. That, however, can't be right; if such dust did exist, it would heat up to 6000 degrees itself due to the absorbed energy of light and would eventually begin to radiate light itself.

Astronomers attempted further explanations: The universe is not in fact infinite; or it is infinite but the stars are not evenly distributed*; or it is infinite but not Euclidian; or it is Euclidian but not temporally infinite, so that light emitted from the more distant stars still has not reached us. This last explanation best coheres with our current scientific knowledge. Moreover, the redshift weakens the light emitted by more distant stars, while the permanent expansion of the universe prevents the light of most stars from ever reaching us. Thus, we do not in fact see the entire universe but only a part of it — namely, the Hubble volume, which has a radius of 46 giga-lightyears. This volume contains about 100 billion galaxies — a lot of stars, but not enough to make the night sky blazingly bright.

* If stars had a fractal distribution - like cantor dust - the night sky would be dark even in a spatially and temporally infinite universe, as the light from far stars would be occluded by near stars.

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