This article is from the Astronomy FAQ, by Joseph Lazio (jlazio@patriot.net) with numerous contributions by others.
If the Universe were infinitely old, infinite in extent, and filled
with stars, then every direction you looked would eventually end on
the surface of a star, and the whole sky would be as bright as the
surface of the Sun. This is known as Olbers' Paradox after Heinrich
Wilhelm Olbers (1757--1840) who wrote about it in 1823--1826 (though
it had been discussed earlier). A common suggestion for resolving the
paradox is to consider interstellar dust, which blocks light by
absorping it. However, absorption by interstellar dust does not
circumvent this paradox, as dust reradiates whatever radiation it
absorbs within a few minutes, which is much less than the age of the
Universe.
The resolution of Olbers' paradox comes by recognizing that the
Universe is not infinitely old and it is expanding. The latter effect
reduces the accumulated energy radiated by distant stars. Either one
of these effects acting alone would solve Olbers' Paradox, but they
both act at once.
 
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