How darkness at night appears to be telling us there was a beginning to time but is actually telling us something quite different
‘If the stars are other suns having the same nature as our sun, why do not these suns collectively outdistance our sun in brilliance?’
Johannes Kepler (Conversations with the Starry Messenger, 1610)
‘The only way in which we could comprehend the blackness our telescopes find in innumerable directions would be by supposing the distance of the invisible background so immense that no ray has yet been able to reach us.’
Edgar Allan Poe (‘Eureka’, 1848)
It is a crystal-clear night far away from the lights of any town or city. The stars are shining like diamonds. There are so many stars that they distract from the most striking feature of the night sky: it is black. Overwhelmingly black. It may seem like a trite observation. However, it is telling us something important about the Universe. The overwhelming majority of astronomers believe that it is telling us that the Universe has not existed for ever; that there was an instant when it came into being; that, in common with you and me and every creature on Earth, the Universe was born. But actually the world’s astronomers are dead wrong. The darkness of the sky at night is telling us something entirely different.
The person who first realised that such a commonplace observation of the sky might have something to tell us about the cosmos was the German astronomer Johannes Kepler, imperial mathematician to the emperor of the Holy Roman Empire. In 1610, he received a copy of Galileo’s best-seller The Starry Messenger, in which the Italian scientist documented the astronomical discoveries he had made with the newly invented telescope. They included mountains on the Moon and the four ‘Galilean’ moons of Jupiter. Kepler was so inspired by the book that he dashed off a letter to Galileo, which was later published as a short book. In Conversations with the Starry Messenger, Kepler not only underlined the importance of Galileo’s work but pointed out something that nobody else appeared to have noticed: the darkness of the sky at night is deeply surprising.
Most people, if asked why the sky is dark at night, would say that it is because there is no Sun and starlight is much weaker than sunlight. It takes a genius to realise that the reason it is black at midnight is far from obvious and may actually have something profound to say about the Universe.
Kepler’s reasoning was straightforward. If the Universe is infinite in extent so that its stars march on for ever, then between the bright stars in the night sky we should see more distant, fainter stars, and between them, stars even more distant and even more faint. It was like looking into a dense forest. Between the trunks of some nearby trees you see the trunks of more distant trees and, between them, the trunks of trees even further away. The view that confronts you is therefore of a solid wall of trees. Similarly, claimed Kepler, when we look out into the Universe, we should see a solid wall of stars.
It is possible to be more precise than this. Imagine the Earth is surrounded by spherical shells of space rather like the concentric skins of an onion. The further away a shell, the fainter the stars it contains. On the other hand, the further away the shell, the bigger it is, containing more stars. Well, the increase in the number of stars should exactly compensate for the stars getting fainter.1 In other words, every onion-shell of stars should contribute exactly the same amount of light to the terrestrial night sky. But this is disastrous. If the Universe goes on for ever, there are an infinite number of such shells. Add up the light coming from all of them and the answer is an infinite amount. Far from being dark at night, the sky should be infinitely bright.
Infinity – a number bigger than any other – is merely an abstract mathematical concept. Nothing in the real world is infinite in size. The conclusion that the night sky should be infinitely bright must therefore be wrong. There must be a flaw somewhere in the logic. And there is. Although the stars appear to be dimensionless pinpricks, in reality they are other suns, shrunken to mere specks by their immense distance. Each is a tiny disc – too small to see with the most powerful telescopes – but a disc nonetheless. Consequently, the discs of nearby stars obscure those of the faraway ones, just as nearby trees in a forest hide the faraway ones. This means the night sky should be papered entirely by the discs of stars. Although not infinitely bright, it should be as bright as the surface of a typical star.
Kepler believed the Sun was a typical star. Consequently, he concluded that the night sky should be as bright as the surface of the Sun. We know today that the Sun is not an average star. It is considerably more luminous than most. About 70 per cent of stars in the solar neighbourhood are ‘red dwarfs’, cool suns reminiscent of softly glowing embers. However, this hardly changes Kepler’s conclusion. Rather than being as bright as the surface of the Sun, the sky at night should be glowing blood red from horizon to horizon. ‘In the midst of this inferno of intense light’, said the Anglo-American cosmologist Edward Harrison, ‘life should cease in seconds, the atmosphere and oceans boil away in minutes, and the Earth turn to vapour in hours.’
Thankfully, the sky is not as bright as the surface of a typical star. It is about a trillion trillion trillion times fainter. The paradox that the night sky is dark when, logically, it should be bright ought to be called Kepler’s paradox. However, because it was popularised by a distinguished German astronomer called Heinrich Olbers in the early nineteenth century, it has instead become known as Olbers’ paradox.
When a prediction clashes with a cast-iron observation, clearly it is the prediction that is at fault. More than likely the assumptions that went into making the prediction need reexamining. Kepler’s most obvious assumption was that the Universe goes on for ever. If this is not true, then the paradox can go away. After all, there will be only a limited number of onion shells of stars contributing their starlight to the Earth’s night sky. It is easy to imagine the sky being filled with so little starlight as to appear black. This was actually Kepler’s solution to the dark-sky paradox. He abhorred the idea of an infinite Universe. It terrified him. It was monstrous. He therefore concluded, with some relief, that the Universe must be finite in extent.
If Kepler was right, the cosmos is not like an endless forest; it is akin to a localised clump of trees bounded at the rear by a dark wall. Because the clump is so small and sparse, we can see the dark wall behind. This is the blackness between the stars.
As a matter of fact, in the twentieth century astronomers did indeed discover that the Universe is finite – or at least the portion of the Universe from which we receive starlight. Recall Edwin Hubble’s 1929 discovery that the Universe is expanding, its constituent galaxies flying apart like pieces of cosmic shrapnel. If the expansion is imagined to run backwards, like a movie in reverse, there comes a time when all of creation is squeezed into the tiniest of tiny volumes. This was the beginning of time, the moment of the Universe’s birth, the Big Bang. According to the best current estimates, space, time, matter and energy exploded into being in the fireball of the Big Bang about 13.7 billion years ago.
The size of the Universe – or at least its effective size – is inextricably linked to its age. This is because light, though fast, is not infinitely fast, so it takes time for it to cross space.2 An interval of 13.7 billion years may seem an unimaginably huge tract of time, but it is simply not long enough for light, crawling snail-like across the vastness of space, to have made it to Earth yet from the most distant reaches of the Universe. Consequently, the only celestial objects we can see are those whose light has taken less than 13.7 billion years to reach us. Imagine them occupying a bubble of space – the ‘observable universe’ – centred on the Earth.
The observable universe is bounded by the ‘cosmic light horizon’. This is pretty much like the horizon at sea. We know there is more of the sea over the horizon. Similarly, we know there is more of the Universe over the cosmic light horizon, only its light has not got here yet. It is still on its way.
A light year is the distance light travels in a year.3 So an obvious conclusion to draw is that the distance to the cosmic light horizon must be 13.7 billion light years. However, this is incorrect since the Universe, in its first split second of existence, is believed to have undergone a brief, faster-than-light epoch of expansion. Because of this ‘inflation’, the distance to the light horizon is not 13.7 billion but about 42 billion light years.4
Of course, the Universe may be infinite in extent. In fact, in the inflationary picture it is effectively infinite. However, the combination of the finite age of the Universe and the finite speed of light reduces the volume of space from which we can receive light to a bubble 84 billion light years across. This cuts the amount of light arriving on Earth dramatically.5
Remarkably, the first person to realise that the night sky might be black because there were stars too far away for their light to have got to us was Edgar Allan Poe. In his imaginative essay ‘Eureka’, published in 1848, he wrote:
Were the succession of stars endless, then the background of the sky would present us a uniform luminosity since there could be absolutely no point, in all that blackness, at which would not exist a star. The only way in which we could comprehend the blackness our telescopes find in innumerable directions would be by supposing the distance of the invisible background so immense that no ray has yet been able to reach us.
It would seem, then, that the evidence that the Universe has a finite age – that it was born in a Big Bang – stares us in the face every night. In fact, it has been staring people in the face since the dawn of human history. Only nobody realised. Nobody guessed the true cosmic significance of dark sky at night.
It is a wonderful story. It is a neat resolution of a 400-year-old mystery. It is a story that 99 per cent of the world’s professional astronomers will trot out if you ask them. Unfortunately, it is not true.
In concluding that in an infinite Universe the night sky should be as bright as the surface of a typical star, Kepler made a hidden assumption: that stars are actually up to the job of filling the Universe with light. After all, for the night sky on Earth to appear bright, the empty space between the stars must be filled to the brim with starlight. All that can be deduced from the fact that the sky is dark at night, therefore, is that for some reason the stars have not yet succeeded in filling up the Universe with their light.
Light is constantly being pumped into empty space by countless trillions upon trillions of stars. But, as Douglas Adams pointed out in The Hitch Hiker’s Guide to the Galaxy: ‘Space is big. You just won’t believe how vastly, hugely, mind-bogglingly big it is.’ Consequently, it would take a very long time for space to fill with starlight like a bath filling to the brim with water. Exactly how long was calculated in 1964 by Edward Harrison. His answer was a whopping 100,000,000,000,000,000,000,000 years.6 This is much longer than the 13.7 billion years that the Universe has been in existence.
The darkness of the sky at night is therefore telling us not that the Universe was born – which would be a truly remarkable thing – but merely that it must be younger than the light fill-up time of 100,000,000,000,000,000,000,000 years. This is not a very useful constraint on the age of the Universe. Nevertheless, it was obtained at no cost, deduced from the most mundane observation of the sky at night.
Can we therefore conclude that we have come on the cosmic stage rather too early? And that if we were to wait patiently for 100,000,000,000,000,000,000,000 years, the night sky would indeed be as bright as the surface of the average star? Of course, after such a vast interval of time, the Earth would be long gone, most likely swallowed by the Sun, which itself would have winked out and died. But that is a minor detail. Imagine that, for the sake of argument, even after 100,000,000,000,000,000,000,000 years there is still a convenient vantage point from which to observe the Universe. Would the whole of space be glowing as brightly as the surface of a typical star? The answer is no. The reason is that not only would the Sun be long dead, all the stars would be long dead. They simply do not burn long enough.
This was something Kepler failed to realise. The idea that an energy source is needed to heat something and that eventually all energy sources are exhausted is a relatively recent one. At least, it was not appreciated before the nineteenth century. So far, the Sun has burned for about 5 billion years but it will run out of energy within another 5 billion years. Red dwarfs, which are much less massive than the Sun, live longer. Their fires are cooler, so they use up energy at a miserly rate and may survive for 100 billion years or more.7 But even this span of time pales into insignificance compared with the 100,000,000,000,000,000,000,000 years needed by the stars to fill the Universe to the brim with light.
It turns out that Kepler’s – or Olbers’ – paradox was never actually a paradox after all. The night sky could never be as bright as the surface of the average star because that would require the stars to fill up space with starlight, and they simply do not contain enough energy to create the required starlight. The night-sky paradox is telling us that either the Universe is younger than the time needed to fill it with light or that the stars have insufficient energy to make a bright sky. It turns out the latter is true. The sky is dark at night because there is not enough energy in the Universe. It is as simple as that. The stars are too feeble by far.
Since mass is a form of energy, it is possible to ask how much matter would have to be converted into light to fill the Universe with starlight. The answer is 10 billion times more matter than exists in the Universe. But stars do not convert 100 per cent of their mass into starlight, only about 0.1 per cent. Consequently, the stars fall short of being able to fill the Universe with starlight by a factor of about 10 trillion.
So if the darkness of the sky at night is telling us not that the Universe was born but merely that the stars are unutterably feeble, why discuss it at such length? Because it is a fascinating historical story, for one thing. Because if you know the true explanation for darkness at night, you will know something that 99 per cent of the world’s professional astronomers do not know. Because, sometimes, knowing why a wrong-headed argument is wrong-headed – and this one baffled the world’s best brains for 400 years – can itself illuminate important things. And because, actually, there does exist everyday evidence that tells us the Universe was born – this chapter will not be short-changing you – it is just not the darkness of the sky at night.
Tune your TV between stations. Some of the static, or ‘snow’, on the screen is caused by the microscopic jitter of electrons in the circuits of the TV. Some is from radio waves picked up from buildings, trees, the sky, keys turning in the ignition of cars, passing taxis, and so on. But about 1 per cent of the static is from radio waves which have come directly from the Big Bang itself. Before being intercepted by your TV aerial, they had been travelling for 13.7 billion years across space. And the last thing they touched before your aerial was the blisteringly hot fireball at the birth of the Universe.
The afterglow of the Big Bang fireball is in the air around us, which is why, at this very moment, your TV aerial is picking it up. Remarkably, 99.9 per cent of the light in the Universe is tied up in this ‘cosmic background radiation’, with only 0.1 per cent in the form of starlight. In fact, every sugar-cube-sized volume of space is currently being criss-crossed by about 300 photons from the Big Bang. Which makes it all the more incredible that the afterglow of the Big Bang was not discovered until 1965 – and then entirely by accident.
The credit goes to two young radio astronomers who were employed by Bell Telephone Laboratories in Holmdel, New Jersey. Though it may seem odd that a commercial company employed two astronomers, there was method in Bell Labs’ madness. By the early 1960s, the company had seen the future, and that future involved bouncing telephone signals around the world via satellites high in Earth orbit. This meant Bell Labs would have to develop the ability to detect faint radio signals from minuscule objects in the sky – which is where the radio astronomers came in. They too were in the business of trying to register faint sources of radio waves in the sky – for instance, distant galaxies. If Bell Labs employed some radio astronomers, went the reasoning, it stood to benefit from their specialist expertise.
In turn, Arno Penzias and Robert Wilson were attracted by the prospect of using a unique radio antenna. Bell Labs’ engineers had been using a giant ‘microwave horn’ at Holmdel to transmit and receive radio signals at a ‘microwave’ wavelength of 7.35 centimetres to and from the Telstar communication satellite. But when that project was finished, they abandoned the horn. Penzias and Wilson jumped at the chance to use it for astronomy. They were to be sorely disappointed, however.
Penzias and Wilson intended to use the Holmdel antenna – an ice-cream-cone-shaped horn the size of a railway carriage – to try and detect faint radio waves coming from cold hydrogen gas which they believed to be floating in space in the outer regions of our Milky Way. Since they expected the signal from such gas to be extremely weak, before they could make any astronomical observations they first needed to account for all the spurious sources of radio waves in the neighbourhood of their antenna so they could subtract them from what the antenna picked up. Everything warm – you, me, trees, buildings, the sky, and so on – emits radio waves from jiggling electrons.
Pretty soon, however, Penzias and Wilson hit a problem. After subtracting every source of spurious radio waves from their signal, they found that their horn was still registering a persistent radio hiss. It was present wherever they pointed the horn at the sky. And it was exactly the emission that would be expected from a body at an ultra-chilly –270°C – three degrees above ‘absolute zero’, the lowest temperature possible.
At first, Penzias and Wilson thought the anomalous hiss might be coming from New York City, which was just over the horizon from Holmdel. But when they pointed the horn away from New York, the hiss did not disappear. Then they thought it might be coming from electrons injected high into the atmosphere by a nuclear test the previous year. But as the months passed, the static did not fade as expected. They thought it might be coming from an unknown source within the Solar System. But as the Earth travelled around the Sun, changing its position relative to other bodies in the Solar System, the static did not change. They even thought the hiss might be the microwave glow from pigeon droppings. Two pigeons were nesting deep inside the horn – a cosy, warm place during the harsh New Jersey winter – and they had coated the interior with what radio engineers quaintly referred to as a ‘white dielectric material’. The material, better known as pigeon shit, glowed gently with microwaves. Penzias and Wilson ousted the pigeons, posting them in the company mail to another Bell Telephones site, then climbed into the horn with stiff brooms to sweep away the offending droppings. But after their hard work, they found to their dismay that the persistent static was still there.
What Penzias and Wilson had stumbled on – and this became clear only when they learnt of a nearby team at Princeton University, which by a bizarre coincidence was actually looking for it – was the leftover heat of the Big Bang. It had been the physicist George Gamow who had first realised that if the Universe had once been small, it must also have been hot. And if it had been hot, the heat must still be around today. After all, it had absolutely nowhere to go. It was bottled up in the Universe, which, by definition, is all there is. In 1948, Gamow’s students, Ralph Alpher and Robert Herman, realised that the expansion of the Universe over the past billions of years would by now have cooled down the heat of the Big Bang. At only a few degrees above absolute zero, it would appear not as visible light but as invisible microwaves. Microwaves – radio waves with a wavelength ranging from a few centimetres to a few tens of centimetres – were given out by all manner of celestial objects. But Alpher and Herman realised that the afterglow of the Big Bang would be distinguishable from all other sources. For a start, being cosmic in origin, it would be coming equally from all directions in the sky.8
What Penzias and Wilson had picked up was the leftover heat from the Big Bang – the afterglow of creation. It is so ubiquitous that if your eyes could see microwaves rather than visible light, at night the whole sky would appear to be glowing white from horizon to horizon. It would be like being inside a giant light bulb.9
This ought to ring a bell. Remember that for the night sky to be bright, the stars must fill empty space to the brim with starlight. In practice, however, this means them shining for 100,000,000,000,000,000,000,000 years, which is impossible, since they do not have the energy reserves necessary. But what is impossible for stars turns out to be possible for the afterglow of the Big Bang. Or at least once upon a time it was possible. In the fireball of the Big Bang, there was indeed sufficient energy for light to fill all of space. Today, since the Universe has become so much bigger, diluting and cooling the light of the fireball, there is no longer enough energy around. Yes, if you had microwave eyes, you would see all of space glowing – but they would have to be very sensitive microwave eyes.
But your TV is a very sensitive microwave receiver. Turn it on again and tune it between the stations. That static is telling you that the Universe has not existed for ever, that it was born in a Big Bang, that there was a beginning to time.
1. Basically, the intensity of starlight from a star drops off with the inverse square of its distance. So if it is twice as far away as a similar star, it is a quarter as bright; if it is three times as far away, it is a ninth as bright; and so on. On the other hand, the volume of a shell of space, which is directly related to the number of stars it contains, increases with the square of its distance. So if it is twice as far away, it contains four times as many stars; three times the distance, nine times as many; and so on. The two factors exactly compensate for each other (at least they do if space is not curved – but that’s another story).
2. The speed of light is more than a million times faster than a passenger jet, so you have to admire anyone who finds a way to measure it. Ole Christensen Röemer’s idea was to time light crossing a known distance. Since light spanned terrestrial distances too quickly for clocks to measure, the seventeenth-century Danish astronomer looked to the heavens. Imagine there is a clock out in space that strikes midday when the Earth in its orbit around the Sun is closest to the clock. Six months later, when the Earth is at its furthest, the clock will be delayed in striking because the light will have to travel across the diameter of the Earth’s orbit. Röemer’s genius was to find a celestial ‘clock’ – Jupiter and its moons. Instead of the striking of midday, he used the instant at which the moon Io went behind Jupiter. In 1676, he found that such ‘eclipses’ were delayed by 22 minutes (the modern figure is 16 minutes 40 seconds). Combining this with an estimate of the diameter of the Earth’s orbit, he calculated the speed of light as 225,000 kilometres per hour. Röemer’s measurement was accepted only when confirmed by James Bradley in 1729. His idea was to measure the speed of light relative to something else fast: the speed of the Earth as it orbited the Sun, which he knew. The Earth’s motion changed the apparent direction at which light arrived from stars just as your running through rain changes its direction. Bradley measured the shift in position of stars and concluded light travelled at 298,000 kilometres per second, which is almost exactly right.
3. Light actually travels at about 300,000 kilometres per second, or a billion kilometres an hour. Click your fingers. In the time it took you to do that, a ray of light could have made the round trip between Europe and America about 30 times over.
4. The speed of light is only the cosmic speed limit in Einstein’s special theory of relativity of 1905. Ten years later, Einstein generalised the theory to deal not only with bodies moving at constant speed with respect to each other but with bodies changing their speed, or accelerating. In his general theory of relativity – which also turned out to be a theory of gravity – space is a backdrop to which the galaxies are effectively nailed. And that backdrop can expand at any speed it likes.
5. The expansion of the Universe also stretches space and, with it, the wavelength of light. Imagine a wiggly line scrawled on a balloon becoming stretched when the balloon is inflated. This ‘red shift’ – so-called because the stretching shifts visible light to longer, ‘redder’ wavelengths – results in lower-energy light. It therefore plays a small role in reducing the light energy raining down on the Earth, though it falls far short of explaining why the sky is dark at night.
6. This estimate was made before the 1998 discovery that the Universe’s expansion is speeding up. In an ever-growing universe, filling up space with light is like filling up a bath with water as the bath grows bigger at a faster and faster rate.
7. See Chapter 4.
8. The reason for this is that the Big Bang happened everywhere in the Universe at once. This is difficult to visualise because, of course, every terrestrial explosion – be it the detonation of a stick of dynamite or a volcano – has a centre. The Big Bang explosion had no centre.
9. The ‘peak’ emission of the cosmic background radiation is actually at about a millimetre in wavelength, which is not in the microwave ‘band’. However, people persist in calling it the cosmic microwave background radiation because the earliest measurements, by Penzias and Wilson and others, were at microwave wavelengths.
Further reading:
Cosmology by Edward Harrison (Cambridge University Press, 1991).