[Physics FAQ] - [Copyright]

Updated 2004 by JCB.
Original by Scott Chase.

Olbers' Paradox

Why isn't the night sky uniformly at least as bright as the surface of the Sun?  If the Universe has infinitely many stars, then presumably it should be.  After all, if you move the Sun twice as far away from us, we will intercept one quarter as many photons, but the Sun's angular area against the sky background will also have now dropped to a quarter of what it was.  So its areal intensity remains constant.  With infinitely many stars, every element of the sky background should have a star, and the entire heavens should be at least as bright as an average star like the Sun.

(We say "at least as bright" because the stars of such a bright universe would begin to absorb heat from their neighbours, and precisely what happens when a star is heated is a technical matter for thermodynamic and nuclear theories.  We don't expect such stars to cool down, but neither do we expect them to heat up indefinitely.  Olbers' Paradox originated before physicists had developed the nuclear theory of how stars shine; thus, it was never concerned with how old the stars might be, and how the details of their energy transactions might affect their brightness.)

The fact that the night sky is not as bright as the Sun is called Olbers' paradox.  It can be traced as far back as Kepler in 1610, and was rediscussed by Halley and Cheseaux in the eighteen century; but it was not popularized as a paradox until Olbers took up the issue in the nineteenth century.

There are many possible explanations which have been considered.  Here are a few:

  1. There's too much dust to see the distant stars.
  2. The Universe has only a finite number of stars.
  3. The distribution of stars is not uniform.  So, for example, there could be an infinity of stars,
    but they hide behind one another so that only a finite angular area is subtended by them.
  4. The Universe is expanding, so distant stars are red-shifted into obscurity.
  5. The Universe is young.  Distant light hasn't even reached us yet.

The first explanation is just plain wrong.  In a black body, the dust will heat up too.  It does act like a radiation shield, exponentially damping the distant starlight.  But you can't put enough dust into the universe to get rid of enough starlight without also obscuring our own Sun.  So this idea is bad.

The premise of the second explanation may technically be correct.  But the number of stars, finite as it might be, is still large enough to light up the entire sky, i.e., the total amount of luminous matter in the Universe is too large to allow this escape.  The number of stars is close enough to infinite for the purpose of lighting up the sky.  The third explanation might be partially correct.  We just don't know.  If the stars are distributed fractally, then there could be large patches of empty space, and the sky could appear dark except in small areas.

But the final two possibilities are surely each correct and partly responsible.  There are numerical arguments that suggest that the effect of the finite age of the Universe is the larger effect.  We live inside a spherical shell of "Observable Universe" which has radius equal to the lifetime of the Universe.  Objects more than about 13.7 thousand million years old (the latest figure) are too far away for their light ever to reach us.

Historically, after Hubble discovered that the Universe was expanding, but before the Big Bang was firmly established by the discovery of the cosmic background radiation, Olbers' paradox was presented as proof of special relativity.  You needed the red shift to get rid of the starlight.  This effect certainly contributes, but the finite age of the Universe is the most important effect.

References: Ap. J. 367, 399 (1991). The author, Paul Wesson, is said to be on a personal crusade to end the confusion surrounding Olbers' paradox.

Darkness at Night: A Riddle of the Universe, Edward Harrison, Harvard University Press, 1987