Why Is the Night Sky Dark? Olbers' Paradox, Explained

Go outside on a clear night without a moon, and the sky is mostly black. You see a few thousand stars, with darkness between them. This seems too obvious to need an explanation. Yet for about four hundred years it was one of the hardest questions in astronomy. A simple and reasonable picture of the universe predicts the opposite. It predicts a night sky as bright as the surface of the Sun. So why is the night dark?

What Olbers’ paradox is

Olbers’ paradox is the name for this puzzle. A paradox is an argument that starts from reasonable assumptions and ends in a result that cannot be true. Here the assumptions are about the universe as a whole. For a long time, many astronomers imagined it like this:

1. The universe is infinite in size.
2. The universe is infinitely old and does not change.
3. Stars are spread more or less evenly through all of it.

If all three were true, the whole night sky would shine. The rest of this section shows why, in two ways. The first way uses a calculation, and the second uses a picture.

Why an endless universe should have a bright sky

For the calculation, imagine the stars around you sorted into thin shells, like the layers of an onion. Each shell is a little farther away than the one before.

Now compare two shells. The first is 10 light years away, and the second is 20 light years away. A light year is the distance light travels in one year.

• Each star in the far shell looks four times fainter. Its light has spread out over a sphere that is four times as large, because twice the distance means four times the surface.
• But the far shell contains four times as many stars. It also has four times the surface area, and the stars are spread evenly.
• So the two effects cancel. Four times as many stars, each four times fainter, give exactly as much light as the near shell.

The same is true for a shell at 40 light years, at 80, or at a billion. Every shell adds the same amount of light. In an infinite universe there are infinitely many shells, so the light keeps adding up.

The picture gives the same result in an easier way. Think of a large forest. If the forest is deep enough, every line of sight ends on a tree trunk, wherever you look. In the same way, if stars go on forever, every line of sight from Earth must end on a star. Nearer stars hide the stars behind them, so the total brightness does not become infinite. But the whole sky would be covered with the surfaces of stars, each one as bright as the Sun.

Who asked the question first

The puzzle is named after Heinrich Wilhelm Olbers, a doctor in the German city of Bremen. He worked as a doctor during the day and did astronomy at night. He was very good at it. He discovered two of the first four asteroids ever found, Pallas in 1802 and Vesta in 1807. In 1823 he wrote an article about the dark sky for an astronomical yearbook. Its title, “On the transparency of space”, shows what he thought the answer was.

But Olbers was not the first to ask the question. In 1610 the astronomer Johannes Kepler used the dark sky as an argument that the number of stars must be limited. Edmond Halley discussed the question in the 1720s. In 1744 the Swiss astronomer Jean-Philippe Loys de Chéseaux wrote a study of a comet. In it he concluded that an endless field of evenly spread stars would make the whole sky shine like the Sun. Both de Chéseaux and Olbers looked for something in space that absorbs the light on its way to us.

The most surprising early answer came from a poet. In 1848 the American writer Edgar Allan Poe published Eureka, a long essay about the universe that he called a prose poem. Poe looked for the answer in time, not in space:

Were the succession of stars endless, then the background of the sky would present us an uniform luminosity

In plain words, Poe says that the whole background of the sky would glow evenly if the stars went on forever. He then suggested why it does not. The light from the most distant regions, he wrote, has not yet had time to reach us. In 1901 the physicist Lord Kelvin worked out this idea with numbers.

Why the night is dark: the universe has an age

Modern cosmology, the science of the universe as a whole, confirms Poe’s idea. The answer depends on two facts.

The first fact is that the universe is not infinitely old. It began about 13.8 billion years ago. The second fact is that light is very fast, but not infinitely fast. Together, these facts mean that we can only see objects whose light has had time to reach us. Light from farther away is still on its way. So the onion does not go on forever. The shells stop where the travel time of light runs out.

A third fact makes the effect stronger. Stars do not shine forever either. Even within the region we can see, there is not nearly enough starlight to cover every line of sight. To fill the sky, stars would have to shine far longer than they actually live.

The expansion of the universe adds a smaller effect. It stretches the light of distant galaxies to longer wavelengths, which carry less energy. But the cosmologist Edward Harrison showed that the age of the universe matters most. Expansion alone would not make the sky dark.

There is one more surprise. The sky is not completely dark after all. If our eyes could see microwaves, a kind of light with very long wavelengths, the whole sky would glow evenly in every direction. This glow is called the cosmic microwave background. It is the cooled light of the hot early universe. In a way, the bright sky that the paradox predicted really exists. It has just shifted to wavelengths our eyes cannot see.

What a dark sky is good for

The paradox is useful in three ways.

• In science teaching. In cosmology courses, Olbers’ paradox is often the first step from looking at the sky to thinking about the universe as a whole. One everyday observation is enough to rule out a whole model of the universe.
• As a lesson in method. The paradox shows how a simple calculation can turn an “obvious” fact into evidence. The dark sky fits a universe that had a beginning. Anyone could observe it, long before telescopes could test the idea.
• As a habit for everyday claims. The paradox teaches you to ask a useful question: “If this theory were true, what should I already see?” If you do not see it, that absence is evidence too.

Suppose a trading strategy really beat the stock market every time. Then the people using it would appear among the richest investors. Suppose a miracle diet worked for everyone. Then nobody would need the next diet. This question takes a minute, and it catches a surprising number of bad ideas.

Common wrong answers, and the limits of the paradox

Two answers sound right, but neither works on its own.

The first wrong answer is “because space is mostly empty”. In an infinite and eternal universe, emptiness does not help. Distance fills every gap sooner or later, as in the forest.

The second wrong answer is “because dust absorbs the light”. This was Olbers’ own favourite answer. But in an eternal universe, the dust would absorb starlight until it became as hot as the stars. Then the dust itself would glow just as brightly. So absorption only delays the problem.

The real answer is a horizon. This is a limit to how far we can see, and the age of the universe sets it. This also shows the limit of the paradox. On its own, it was never a proof of the Big Bang. A dark sky fits any universe of limited age. Other evidence from the twentieth century was needed to show which universe we live in. This evidence was the expansion of the universe and the cosmic microwave background.

Go deeper

The classic book on the question is Edward Harrison’s Darkness at Night: A Riddle of the Universe (Affiliate Link), published by Harvard University Press in 1987. It follows every answer people have tried, from Kepler to modern cosmology. The dark sky may also make you wonder why the universe has exactly the properties it has. The Fine-Tuned Universe: Why Our Existence Seems Almost Impossible looks at that question through the physical constants.