Olber's Paradox

It is well-know and observed that the night sky is dark. Why isn't the night sky as uniformly bright as the surface of the Sun? If the Universe has infinitely many stars, then it should be. That is, if the Universe is static, uniform, and infinite, we should expect that every direction our line of sight should intercept a star. After all, if you move the Sun twice as far away from us, we will intercept one-fourth as much light, since the Sun will subtend one-fourth as much angular area. So the surface brightness remains constant. With infinitely many stars, every direction on the sky should eventually intercept a star, and the entire heavens should be a bright as the sun. We should have the impression that we live in the center of a hollow black body whose temperature is about 6000 degrees Centigrade. This is Olbers' paradox. It can be traced as far back as Kepler in 1610. It was rediscussed by Halley and Cheseaux in the eighteen century, but 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:

There's too much dust to see the distant stars.
The Universe has only a finite number of stars.
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.
The Universe is expanding, so distant stars are red-shifted into obscurity.
The Universe is young. Distant light hasn't even reached us yet.

The first explanation is wrong. In a black body, the dust will absorb starligh and 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. In an infinite time the dust will heat up so that it radiates like a star. So this idea is bad.

The premise of the second explanation may technically be correct. The philosopher Immanuel Kant suggested we live in an Island Universe in that most of the Universe is empty and black but there is a grouping of stars, where we are and which we called the Milky Way Galaxy. However, in the 1920 Edwin Hubble had shown that there were many galaxies outside of our own Milky Way. Now we know that there are at least as many external galaxies as there are stars in the Milky Way (roughly 100 billion). We also know in principle that there are many more galaxies which we cannot see. Thus the number of stars, finite as it might be, may 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 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 times the speed of light. Objects more than about15 billions years old are too far away for their light to have reached us yet.

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 (an SR effect) to get rid of the starlight from the visible. We now actually view the effect of expansion as stretching of the wavelength of light as space stretches. Thus visible light is shifted to longer and longer wavelengths, thus the "red shift". 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

updated: 24-Apr-1996