Olbers’ Paradox

9 mins read

In a sense, this is the most beautiful piece of observational evidence for the Big Bang.

Staring out into the night sky, a very profound question can be asked: 

Why does it get dark at night?

You might think that this is a rather trivial question. After all, even a child knows that night falls when the sun sets below the horizon, and that since there is nothing else in the night sky anywhere near as bright as the sun we have to make do with the feeble reflected light from the moon and the even more feeble light from the distant planets and stars. 

It turns out this question is far more profound than it first appears. Indeed, for several centuries, astronomers have posed this question and it took them a long time to find the correct answer. It is known today as Olbers’ Paradox.

Here then is the problem: we have good reason to believe that even if the Universe is not infinite in size (and it may well be), it is so enormous that for all intents and purposes it goes on forever. Thus, in every direction we care to look out into space, we should see a star, and the sky should be even brighter than it normally becomes during the day; in fact, it should be so bright, all the time, that it should not even matter whether it is day or night.

Imagine that you are standing in the middle of a very large forest. So large in fact that you can assume it extends to infinity in all directions. Now try shooting an arrow horizontally in any direction. In this idealised situation the arrow must be allowed to keep on going in a straight line without ever dipping down to the ground until it hits a tree trunk. Even if it misses all the closer trees, the arrow must eventually hit one. Since the forest is infinite, there will always be a tree in the flight path of the arrow, however far away that tree may be.

Now imagine that our universe goes on forever with an infinity of stars evenly distributed throughout it. The light that reaches us from these stars is like the example of the arrow, but in reverse. For no matter where we look in the sky, we should always see a star in our line of sight. So there would not be any gaps where we do not see a star, and the whole sky should be as bright as the surface of the sun, all the time.

There are two immediate responses to this dilemma. Firstly, you might argue, surely very distant stars would simply be too faint for us to see. And anyway, stars are not evenly spread out in the sky – they are bunched up in clusters, and those clusters and grouped into galaxies. Neither of these issues matter. They just mean that the night sky should be as bright as an average galaxy, which is not quite as bright as the surface of a star but still bright enough to light up the night sky.

Incredibly, it has taken many centuries to solve this puzzle. The answer turns out to be one of the most profound truths about our universe that we have ever discovered. But in order to resolve the paradox satisfactorily, we must first see how it evolved through history.

Given how long astronomers have been aware of the paradox, it is somewhat surprising that it took till as recently as the 1950s for it to be attributed to, and named after, Heinrich Wilhelm Olbers, a 19th century physician and amateur astronomer from Bremen in Germany. In fact, the problem goes back to the 16th century and an Englishman by the name of Thomas Digges.

An infinite space with an infinite number of stars meant that Digges was inevitably led to asking the crucial question: why is the night sky dark? For Digges, however, there was no paradox. He just assumed that the distant stars were simply too faint to contribute any light.

What Digges was missing was a vital mathematical calculation that would have shown how his reasoning about the darkness of the night sky was in fact wrong. But that was to come later. In 1610 Johannes Kepler revisited the problem, but he argued the reason it was dark at night was simply because the Universe was finite in extent; the darkness between the stars was the dark outer wall enclosing the Universe. Over a century after Kepler, another astronomer, the Englishman Edmund Halley, revisited the problem and argued that in fact Digges’ original solution was correct: that the Universe is infinite, but that the distant stars are too faint to be seen.

A few years after this a Swiss astronomer by the name of Jean-Philippe de Cheseaux showed that this does not help resolve the problem. He proved using some neat geometry that if we imagine all the stars grouped into concentric shells around us, like layers of an onion, extending out to infinity – and assuming that on average the stars are all of the same brightness1 and they are distributed evenly throughout the Universe (which we know is not the case, but is nevertheless a reliable assumption to make for the purposes of this proof), then while the stars in the innermost shells will shine brighter, it turns out that shells further out, which due to being larger in volume contain more stars, have an overall brightness that is exactly equal to that of the inner shells. In other words, lots of more distant and therefore fainter stars contribute as much total light as fewer, nearer, and hence brighter ones. And so we return to Kepler’s argument that the Universe cannot be infinite or the night sky would not be dark.

Enter Heinrich Olbers, who again posed the problem of the darkness of the night sky in a paper he published 1823. But his solution was different. He was aware that the faintness of distant stars does not help resolve the puzzle. Instead, he argued that space is filled with interstellar dust and gas that would block the light from the more distant stars (or, as would now understand, the galaxies). What he failed to realise was that if the Universe has been around for long enough, then even this material would slowly heat up, due to the light it absorbs, and would therefore eventually shine with the same brightness as the stars (or galaxies) it obscures.

In any case, what is interesting is that Olbers’ posing of the problem and his proposed solution were pretty much ignored completely by other astronomers right up until the end of the 19th century. You see, by this point, not only did astronomers not know how far out the Universe extended, they didn’t even have good evidence that stars clustered in galaxies and that our Milky Way was but one of billions of galaxies extending to vast distances. This all changed in the first decades of the 20th century when one man gave science a new view on the nature of space and time.

Let us recap. The reason the night sky is dark is not because the Universe is finite in size; for all we know, it may go on forever. It is not because the distant stars are too faint; the further out we look, the more star-filled galaxies there should be, contributing their cumulative light to brightening up the gaps we can see between the stars of our own galaxy as we look out into space. It is not because the light from the furthest reaches of space is blocked from us by dust and gas that absorbs it; given enough time, this intervening matter will also glow as it gradually absorbs the light energy it is blocking from us. No, the reason for the darkness of the space is more simple and profound than any of these suggested solutions. It is because the Universe had a beginning.

It is the very finiteness of the speed of light that helps us resolve Olbers’ paradox. Since the Universe is 13.7 billion years old, we can only ever see those galaxies that are close enough to us for their light to have had time to reach us. The expansion of space complicates matters of course. A galaxy that we say is ten billion light-years away from us is one whose light has been travelling towards us for ten billion years. But during that time the space between us and that galaxy has been stretching, so the true distance to that galaxy is in fact several times greater than this. However, a galaxy twice as far away as this one is out of our range; its light is still in transit towards us and we cannot see it. So it cannot contribute any brightness to the night sky. We can only see out into space as far as the age of the Universe allows us to.

What we can see in the sky therefore is just a tiny fraction of the whole cosmos. We call this the ‘visible universe’ and we cannot, even with the most powerful telescopes, see beyond this horizon in space. And this is because it is also a horizon in time. The further out we look, the further back in time we are looking because what we are seeing is the light that left its origin billions of years ago and so we see it for what it was, not what it is. The edge of the visible universe is to us therefore also the earliest moment in time. And here is that final subtlety regarding the expansion of space. Even if an infinite static (not expanding) universe had suddenly popped into existence 13.7 billion years ago, we still would not be able to see beyond 13.7 billion light-years. So, it is not the expansion itself that stops us seeing to infinity. For if we could wait long enough in a static universe then the light from ever-further galaxies would eventually reach us. It is just that beyond the edge of our visible universe, the light will never outrun the expansion, like walking too slowly down an escalator that it is going up.

Scientists are often asked what proof they have that the Big Bang actually happened. They usually quote the three standard pieces of evidence I discussed earlier. But isn’t it so much easier, and in my view more persuasive, to turn Olbers’ Paradox on its head? Rather than saying that the reason it gets dark at night is because the Universe must have had a beginning and that there has therefore not been enough time for light beyond a certain distance to reach us, why not try out the argument the other way around? For if anyone wanted proof of the Big Bang they need only venture outside at night and ponder the darkness of space.

The real puzzle is that it took astronomers so long to figure this out.