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:

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.

If the universe were infinite and filled with stars in a uniform distribution, then every line of sight would terminate on the surface of a star and should be bright. To be sure, those further away would be fainter, but there would be more of them. Careful analysis suggests that the sky should be as bright as the surface of an average star.

Noting that the night sky is obviously not that bright, there are two lines of explanation. First, the universe appears to be of finite age and that light from stars at an infinite distance would not have reached us in the age of the universe. Second, we observe that the universe is expanding and that stars further away from us are receding at a faster rate. The result of this expansion is that the light from more distant stars is Doppler shifted more toward the red and beyond a certain distance would not contribute significantly in the visible region of the electromagnetic spectrum.

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