Why the night sky is dark

If the universe went on forever and had always existed, every line of sight would end on a star, and the night sky would glow like the surface of the Sun. It does not. The darkness is a measurement.

The puzzle

Picture space filled evenly with stars, out to infinity, for all time. Look in any direction: your line of sight travels outward and sooner or later hits a star. So the whole sky should be a wall of stellar surface, with no gaps.

Distance does not rescue you. A far star looks dimmer, but its disc also looks smaller, and the two effects cancel exactly: the brightness per patch of disc does not depend on how far away it is. A wall of distant discs is as bright as a wall of near ones. Yet the night is dark. That contradiction is Olbers' paradox, after Heinrich Olbers' 1823 paper on the transparency of space, though Kepler and Halley had worried about it long before and the name only stuck in the 1950s.

Why it is worth a minute

Because the answer is cosmology you can check without a telescope. The dark sky rules out an infinite, eternal, unchanging universe. Something must be finite.

Counting in shells

Divide space around you into thin shells of equal thickness, like the layers of an onion. A shell twice as far away has four times the area, so it holds four times as many stars. Each of those stars delivers a quarter of the light, because brightness falls with the square of distance. Four times the stars, a quarter of the light each: every shell contributes the same amount. Add up infinitely many shells and the total is infinite.

In practice near stars block far ones, so the sum does not go to infinity. It goes to a wall. Call the lookout limit the typical distance a line of sight travels before it hits a star. Beyond a few lookout limits, every gap has closed. The fraction of sky covered by stars out to a distance r starts at zero, rises, and flattens toward one. Set r in the interactive below.

What is finite

Here is the escape. Light has a speed, and the universe has an age. Light from a star too far away has simply not had time to reach us yet: roughly, anything beyond the age of the universe times the speed of light. So you see only out to a horizon, not to infinity. If the horizon is much closer than the lookout limit, most lines of sight end in nothing, and the sky is dark. Counted this way, the darkness means the stars have not been shining forever: the stellar system began at some finite time in the past.

The expansion of the universe helps too. Light from a receding source arrives stretched to longer wavelengths with less energy, so the most distant sources are dimmed and pushed out of the visible band. But the horizon and the finite time stars have existed do most of the work; redshift dims the sky by only a modest factor, nowhere near the enormous factor the paradox demands.

In one breath

Every shell of stars adds the same light, so an infinite, eternal universe would give a sky as bright as a star's surface. The sky is dark because the number of shells is finite. Light has had only a finite time to travel, and stars have existed only a finite time. The darkness overhead is the finite age of the universe, seen with your own eyes.