The Book of Universes

I know it’s all in our minds, but a mind is a powerful thing.

Colin Cotterill¹

TWO MEN WALKING

I am always surprised when a young man tells me he wants to work at cosmology; I think of cosmology as something that happens to one, not something one can choose.

William H. McCrea²

The old gentleman walking down the street looked the same as ever – distinguished but slightly dishevelled, in a Bohemian style, a slow-walking European on an American main street, sad-faced, purposeful but not quite watching where he was going, always catching the attention of the locals as he made his way politely through the shoppers and the contra-flow of students late for lectures. Everyone seemed to know who he was but he avoided everyone’s gaze. Today, he had a new companion, very tall and stockily built, a little the worse for wear, untidy but in a different way to his companion. They were both deep in conversation as they made their way, walking and talking, oblivious of the shop windows beside them. The older man listened thoughtfully, sometimes frowning gently; his younger companion enthusiastically pressing his point, occasionally gesticulating wildly, talking incessantly. Neither spoke native English but their accents were quite different, revealing resonances with many places. Intent on crossing the street, they stopped, lingering at the kerbside as the traffic passed. The traffic lights changed and they continued quietly across the street, both momentarily concentrating on light, sound and relative motion. Suddenly, something happened. The taller man started to say something again, making a dart of his hand. The traffic was moving again now but the old man had stopped, dead in his tracks, oblivious to the cars and the hurrying pedestrians. His companion’s words had consumed his thoughts entirely. The cars roared past on both sides leaving the two of them marooned in their midst like a human traffic island. The old man was deep in thought, the younger one reiterating his point. Eventually, resuming contact with the moving world around them, but forgetful of where they had been going, the older man led them silently towards the pavement – the one they had stepped off a minute ago – and they walked and talked their way from whence they had come, lost in this new thought.

The two men had been talking about universes.³ The place was Princeton, New Jersey, and the time was during the Second World War. The younger man was George Gamow, or ‘Gee-Gee’ to his friends, a Russian émigré to the United States. The older man was Albert Einstein. Einstein had spent the previous thirty years showing how we could understand the behaviour of whole universes with simple maths. Gamow saw that those universes must have had a past that was unimaginably different to the present. What had stopped them both in their tracks was Gamow’s suggestion that the laws of physics could describe something being created out of nothing. It could be a single star; but it might be an entire universe!

FUNNY THINGS, UNIVERSES

History is the sum total of the things that could have been avoided.

Konrad Adenauer

What is the universe? Where did it come from? Where is it heading? These questions sound simple but they are amongst the most far-reaching that have ever been posed. Depending upon how much you know, there are many answers to the question of what we mean by ‘universe’.⁴ Is it just everything you can see out in space – perhaps with the space in-between thrown in for good measure? Or is it everything that physically exists? When you draw up the list of all those things to include in ‘everything’ you start to wonder about those ‘things’ that the physicists call the ‘laws of Nature’ and other intangibles like space and time. Although you can’t touch or see them, you can feel their effects, they seem pretty important and they seem to exist – a bit like the rules of football – and we had better throw them in as well. And what about the future and the past? Just focusing on what exists now seems a bit exclusive. And if we include everything that has ever existed as part of the universe, why not include the future as well? This seems to leave us with the definition that the universe is everything that has existed, does exist and will ever exist.

If we were feeling really pedantic we might take an even grander view of the universe, which includes not only everything that can exist but also everything that could exist – and finally, even that which cannot exist. Some medieval philosophers⁵ were drawn to this sort of completeness, adding everything that has existed, does exist and will not exist to the catalogue of what was, is and will be. This approach seems bent upon creating new problems in an area where there are enough already. Yet recently it has re-emerged in modern studies of the universe, albeit in a slightly different guise. Modern cosmologists are not only interested in the structure and history of our universe but also in the other types of universe that might have been. Our universe has many special and (to us at least) surprising properties that we want to evaluate in order to see if they could have been otherwise. This means that we have to be able to produce examples of ‘other’ universes so as to carry out comparisons.

This is what modern cosmology is all about. It is not just an exercise in describing our universe as completely and as accurately as possible. It seeks to place that description in a wider context of possibilities than the actual. It asks ‘why’ our universe has some properties and not others. Of course, we might ultimately discover that there is no other possible universe (whose structure, contents, laws, age and so forth are different in a way we can conceive of ) apart from the one we see. For a long time, cosmologists were rather expecting – even hoping – that would turn out to be the case. But recently the tide has been flowing in the opposite direction and we seem to be faced with many different possible universes, all consistent with Nature’s laws. And, to cap it all, these other universes may not be only possibilities: they may be existing in every sense that we attribute to ordinary things like you and me, here and now.

THE IMPORTANCE OF PLACE

And [Jacob] dreamed, and behold a ladder set up on the earth, and the top of it reached to heaven: and behold the angels of God ascending and descending on it.

Book of Genesis⁶

People have been talking about the universe for thousands of years. It was their universe, of course, not to be confused with ours. For many it would have been just the land as far as they could journey. Or maybe it was the night sky of planets and stars that could be seen with the naked eye. Most ancient cultures tried to create a picture or a story about what they saw around them, whether it be in the sky, on the ground or under the sea.⁷ This drawing of a bigger picture was not originally driven by an interest in cosmology, but was simply important to convince themselves, and others, that things had a meaning and they were part of that meaning. To admit that there were parts of reality about which they had no conception or control would have created a dangerous uncertainty. This is why ancient myths about the nature of the universe always seem so complete: everything has a place and there is a place for everything. There are no ‘maybes’, no caveats, no uncertainties and no possibilities awaiting further investigation. They really were ‘theories of everything’, but they are not to be confused with science.

Your time and place on Earth influenced the sense you would make of the universe around you. If you lived near the Equator then the apparent motions of the stars each night were clear and simple. They rose, passed up and over your head throughout the night and then descended to set on the opposite horizon. Every night was the same and it felt as though you were at the centre of these celestial movements. But if you lived far from the Tropics the heavens looked very different. Some stars rose above the horizon and set later that night, they came straight up and over your head before falling back to the horizon. Others never rose or set and were always above the horizon. They seemed to trace out circles around a great centre in the sky, like they were pinned to a wheel turning on its axis. It must have made you wonder what was special about that place around which the stars turned. Many myths and legends about the great millstone in the sky were framed by the inhabitants of northern latitudes to make some sense of that great nightly swirl of stars.

Figure 1.1 The Earth’s rotation axis, running through the North and South Poles, is tilted at about 23.5 degrees with respect to the vertical perpendicular to the Earth’s orbital plane.

The reason for this variation in the appearance of the night sky around the world is a tilt of the axis around which the Earth rotates each day (Figure 1.1). As the Earth orbits the Sun, the line through the Earth’s North and South Poles⁸ around which it rotates each day is not perpendicular to the line its orbit traces. It is tilted away from the vertical at about 23.5 degrees. This has many remarkable consequences: it is the reason for the seasons. If there were no tilt then there would be no seasonal changes in climate; if the tilt were much larger then the seasonal variations would be far more dramatic. However, if you know nothing about the motion of the Earth around the Sun, or the tilt of its axis, and merely look at the stars in the sky each night, the tilt ensures that there will be a very different sky on view at different latitudes on Earth.

If we extend the line from the South to the North Pole out into space it points in a direction that we call the North Celestial Pole and away from the South Celestial Pole. As the Earth rotates, at night we will see the fixed stars apparently rotating past in the opposite direction across the sky. If they remain visible they will be completing a great circle on the sky each time the Earth completes a daily revolution. However, not all of these circular paths across the sky will be completely visible to us because part of the path will lie below our horizon. In Figure 1.2 we show what a sky watcher living at a latitude of L degrees in the northern hemisphere will see on a clear night.⁹

Figure 1.2 The celestial sky seen by astronomers who are located at a latitude of L degrees north. Only half of the sky is visible to them at any moment. Some stars, the north circumpolar stars, are so close to the North Celestial Pole that they never set below the horizon. A second group, around the South Celestial Pole, called the south circumpolar stars, are never seen by the same astronomers because they do not rise above the horizon.

Our sky watcher’s horizon divides the sky in half. Only the part of it above the horizon can be seen at any moment. Observing from a latitude of L degrees north means that the North Celestial Pole lies L degrees above the horizon and the South Celestial Pole lies L degrees below it. The Earth’s rotation makes the sky appear to rotate in a westerly direction around the North Celestial Pole. Stars are seen to rise on the easterly horizon and then move up the sky before reaching their highest point, or ‘zenith’, after which they descend and set on the westerly horizon.¹⁰

There are two groups of stars that are not seen to follow this nightly rise and fall in the sky. Stars inside a circle that extends L degrees from the North Celestial Pole complete their apparent circles in the sky without ever disappearing below the horizon. If the sky is clear and dark they can always be seen.¹¹ For European sky watchers today, they include the stars in the Plough and Cassiopeia groups. Conversely, there is a collection of southern stars within a circular region of the same extent around the South Celestial Pole which are never seen by the southern-hemisphere sky watcher in our picture. They never rise above his horizon.¹² This is why the constellation of the Southern Cross can never be seen from northern Europe. Crucially, we can see that the size of these regions of the sky that are always visible or invisible varies with the latitude of the sky watcher. As your latitude increases and you move away from the Equator, so the sizes of these regions increase as well. In Figure 1.3 we show how the sky would appear to sky watchers at three very different terrestrial latitudes.

At the Equator, the latitude is zero and there are no regions of ever-visible or never-visible stars. An equatorial sky watcher can glimpse every bright star, although the two Celestial Poles are lost in the haze down on the far horizons in practice. The stars rise and ascend to their highest points in the sky. As each star rises, its direction remains relatively constant and is an excellent navigational beacon for wayfaring on land or sea throughout the night. There is almost no sideways motion in the darkness and the sky seems to be very symmetrical and simple. Our sky watchers gain the impression that they are at the centre of things, beneath a celestial canopy of overarching and predictable motions that seem to be there for their convenience. The universe looks as if they are central to it.

At the extreme case of the North Pole, the latitude is 90 degrees and the visible stars neither rise nor set. They move in circles around the sky. The Celestial North Pole is directly overhead and all the stars circle around it. It looks like the focal point of the universe and we are directly beneath it.

At more temperate northerly latitudes, like that of ancient Stonehenge in Britain at 51 degrees, there is an in-between situation. Stars lying within 51 degrees of the Celestial Pole will be seen to complete concentric circles on the sky with the Pole as their centre. Other stars will rise above the horizon, ascend to their zeniths, then descend and set. The sky appears extremely lopsided. Different stars follow different paths between their rising and setting. Most striking of all, though, is the great swirl of stars in the direction of the Celestial Pole, all circling it as if it is the hub of a great cosmic wheel (Figure 1.4). For those sky watchers who know nothing of astronomy, or the motion of the Earth, there seems to be a special place in the sky.

Figure 1.3 The appearance of the night sky seen from three different latitudes on Earth. It differs because of the change in position of the Celestial Pole around which the stars appear to rotate: (a) at the Equator; (b) at the latitude of Stonehenge in England; (c) at the North Pole.

This is one reason why there is a geographical dimension in the myths about the sky and the nature of the universe around us. Far from the Equator, in Scandinavia and Siberia, we find legends of the great circle in the sky: the millstone at whose centre the gods reside. The nearest star to the centre of the celestial swirl was given a special importance, hosting the throne of the sovereign of the universe around whom all the stars were arrayed.¹³

We will not be interested in tracing these myths any further here. We simply want to highlight how difficult it was to come up with a picture of the universe from an earthbound vantage point. There are significant biases that you will be unaware of when you know nothing about the stars and the rotation and orientation of the Earth.

Even when sophisticated early civilisations started making astronomical observations they still encountered the influence of our particular vantage point. We are confined to a small planet which, along with many other planets, orbits a star. Today we know about this solar system of planets and the hundreds of distant stars which have been found to have other planets around them (more than 500 at present). This familiarity makes it easy for us to forget how difficult it was to get away from an Earth-centred view and understand the motions of the other planets. As a very simple example of the difficulty, let’s think about our view from Earth of the motion of a planet like Mars. We will assume that both the Earth and Mars orbit around the Sun in circular orbits, and that the radius of the orbit of Mars is about one and a half times larger than that of the Earth’s orbit (Figure 1.5a). Earth takes one year to complete its orbit and we shall assume that Mars takes twice as long to complete its orbit. Now work out the difference between the two orbits as time passes. This tells us the apparent motion of Mars as seen from Earth. A graph of this is shown in Figure 1.5b.

Figure 1.4 A long-time exposure in the direction of the North Celestial Pole records the circular star trails around the Pole, which is located just above the top of the tree in the centre.

This curious heart-shaped loop with a cross-over (called a ‘limaçon’) is interesting. As we go from the top right towards the left, we see that Mars is moving away from the Earth. When it drops down to cut the horizontal axis at the point -5 the two planets are on opposite sides of the Sun and as far away from each other as possible. Then as Mars starts to return towards the Earth something very strange happens. Mars approaches the Earth and looks as if it is going to collide with it. But then it reverses its direction and moves away again, to resume its long period of motion away from the Earth. This ‘retrograde’ motion of Mars can be detected with the naked eye over a period of several nights during a period of close approach. We see that it arises each time the two planets are moving towards their distance of closest approach. If we look instead at one of the distant outer planets, like Saturn, whose orbit takes 29.5 Earth years to complete, there will be several occasions when the Earth–Saturn relative motion is in the vicinity of closest approach during each complete orbit of Saturn and there will be several loops in the picture of the apparent orbit.¹⁴

Figure 1.5 The apparent motion of the planet Mars observed from Earth. (a) The orbits of Earth and Mars, which are assumed to be circular, with the radius of Mars’s orbit approximately 1.5 times that of Earth’s. Mars takes about two years (687 Earth days) to complete its orbit. (b) The two-year orbit of Mars viewed from the Earth, traces out this looped, heart-shaped figure, called a ‘limaçon’. Mars moves away at first, reaching its maximum separation of -5 when the Earth and Mars are on opposite sides of the Sun. Mars then returns to its closest approach to Earth but suddenly reverses direction and moves away. Then it changes direction on the sky and starts to move away again.

The lesson we learn from this is that motions in the sky are very difficult to interpret if you do not have an overall picture – or theory – of the motions. An early astronomer watching Mars over two years would have seen it moving away from us, then towards us, before being apparently repelled and sent away again. What forces might be acting? Why does the motion change direction? These are difficult questions to answer if you are located on Earth, unaware that all the orbits (including your own vantage point) are revolving around the Sun at different rates.

ARISTOTLE’S SPHERICAL UNIVERSE

An expert is a person who avoids the small error as he sweeps on to the grand fallacy.

Benjamin Stolberg

A complicated picture of these apparent celestial motions arose because of a philosophical view of the universe introduced by Aristotle in about 350 BC in an attempt to simplify matters. Aristotle believed that the world did not come into being at some time in the past; it had always existed and it would always exist, unchanged in essence for ever. He placed a high premium upon symmetry and believed that the sphere was the most perfect of all shapes. Hence, the universe must be spherical. In order to accommodate the objects seen in the sky, and their motions, Aristotle proposed a complicated onion-skin structure containing no fewer than fifty-five nested spheres of transparent crystal, centred on the Earth, which is also assumed to be spherical in shape (an assumption that is very hard to reconcile with what he could see!). Each of the observed heavenly bodies was attached to one of these crystal spheres, which rotated at different constant angular speeds. Various extra spheres existed between those carrying the planetary motions. In this way, Aristotle could both explain observations and predict new things that might be seen. It had many features of a modern scientific theory – and many that are unrecognisable. The outer sphere of the stars in Aristotle’s picture was a realm where material things could not exist – a spiritual realm. All the motions we see were initiated by a Prime Mover acting at the boundary of this realm and causing the outer sphere to rotate. The rotation was then communicated inwards, sphere by sphere, until the whole cosmos was in perfect rotational motion. By tinkering with the speeds at which the different spheres rotated, many of the features of the night sky could be explained.

Figure 1.6 (a) A rotating sphere always occupies the same volume of space but other polyhedral shapes create a ‘void’ when they rotate. This Aristotelian ‘proof’ of the sphericity of the Earth is shown in Robert Recorde’s picture taken from his book Castle of Knowledge (1556). However, a wine-glass-shaped universe rotating about its vertical axis, shown in (b), also satisfies Aristotle’s requirement that its rotation leave and create no void region.

Aristotle’s philosophy was later absorbed and remoulded by medieval Christian thinkers who identified the Prime Mover with the God of the Old Testament and the outermost sphere with the Christian heaven. The centrality of the Earth was concordant with the central part played by humanity in the medieval world picture.

An important feature of the spherical shape for the Earth and all the other outer spheres was the fact that when a sphere rotates it does not cut into empty space where there is no matter and it leaves no empty space behind – see Figure 1.6a, which shows a sixteenth-century description by the eminent Tudor mathematician and physician, Robert Recorde (1510–58). A vacuum was impossible. It could no more exist than could an infinite physical quantity.¹⁵ A stationary spherical Earth always occupies the same portion of space as it rotates. If it were a cube this would no longer be true.¹⁶ In fact, in Aristotle’s argument the sphere isn’t the only possible shape a rotating Earth could have if it is not to leave or enter a void region of space. A wine glass will do just as well.¹⁷

Aristotle did not think of motion as being created by forces between objects in the way that we (following Newton) think of gravity. Forces were innate properties of the objects themselves; they moved in a manner that was ‘natural’ for them. Circular motion was the most perfect and natural movement of all.

PTOLEMY’S ‘HEATH ROBINSON’ UNIVERSE

I used to be an astronomer but I got stuck on the day shift.

Brian Malow¹⁸

We have already seen that in a solar system in which the Sun lies at the centre and all the planets orbit around it at different speeds you will see strange movements on the sky; other planets will seem to move backwards for a short period. This is an illusion created by our motion relative to those planets. We are all orbiting at different angular speeds and so we sometimes see other planets exhibit unusual counter-motions on the sky. Aristotle and his followers needed to explain those observations.

A solution to this challenging problem was first found by Claudius Ptolemy in about AD 130. It was the nearest thing to a ‘Theory of Everything’ in the ancient world and it lasted for more than 1000 years. Ptolemy’s task was to reconcile the complicated motions of the planets, and all their retrograde movements, with Aristotle’s rigid specifications that the Earth was at the centre of the universe. All the other bodies moved in uniform circular orbits at different constant angular speeds around the Earth, and no bodies in the universe can change their brightnesses or other intrinsic properties (Figure 1.7). This was quite a challenge.

Ptolemy addressed this huge problem in his book The Almagest (‘The Greatest’) by considering the circular orbit of a planet, or the Sun, around the Earth to trace out the motion of a point (or ‘deferent’ as it was termed). This point in its turn then acted as the centre of another smaller circular motion of that planet, called an ‘epicycle’, along which the planet moved.¹⁹ The overall motion of the planet looks like a circle with a continuous corkscrewing wiggle, shown in Figure 1.8

The overall motion of a planet like Mars relative to the Earth would be a circular orbit around a point that was itself orbiting the Sun in a circle. Ptolemy could have elaborated this further by adding further epicycles (circles moving in circular orbits) to the orbit of that planet around the Sun. More and more of these epicycles were added by his medieval successors as they sought for ever greater accuracy.²⁰

Figure 1.7 The universe model of Aristotle and Ptolemy.

There were a very large number of things that could be changed in order to make all the features of the moving planets, and the Sun, match observations very accurately. The retrograde motion seen from Earth is well described by the addition of the epicycles. For half of the planet’s orbit around its small epicycle it moves in the same sense as the motion around the deferent; but for the second half of the orbit around the epicycle it is moving in the opposite direction and we will observe a retrograde motion. The planet, as seen from Earth, would occasionally slow down, stop on the sky, and then reverse, before slowing down, stopping and then reverting to move in the opposite direction. This is a real retrograde motion and not an illusory one created by our different orbital speeds around the Sun.

Figure 1.8 Epicycles. A planet, P, moves in a small circle, the epicycle, whose centre, C, follows a larger circular orbit.

This early response to the complicated motions of the planets and the Sun relative to the Earth shows how difficult it is to arrive at a correct description of the universe from observation alone, or from a very general philosophical principle. If the Aristotelians had been more critical they would have had to grapple with other awkward problems. Why is the Earth not perfectly spherical? Why was the centrality of the Earth regarded as so important and yet other circular motions could take place in the epicycles which were not centred on the Earth? Why was the idea of displacing the centre of each planet’s deferent circle away from the Earth accepted? The displacement may have been small but the Earth is either at the centre of the universe or it isn’t.

COPERNICAN REVOLUTIONS

If the Lord Almighty had consulted me before embarking on creation thus, I should have recommended something simpler.

Alphonso X of Castile²¹

Ptolemy’s model of the universe, with the Earth at its centre, was an intricate human conception. It wasn’t right but it had so many ways of being tweaked to handle awkward new observations about planetary movements that it survived, largely unchallenged, until the fifteenth century. This elastic feature even led to the word ‘epicycles’ becoming a pejorative term to describe any slippery or overcomplicated scientific theory. If you have to keep adding new details into the workings of a theory to explain every new fact that comes along then your theory has little explanatory power. It is as if you have a new theory about cars which predicts that all cars are red. On Monday morning you step outside and see a black car, so you modify your theory to predict that all cars are red, except on Mondays when some are black. Lots of black and red cars pass by. All seems well. But then in the afternoon a green car drives by. Okay, all cars are red and black on Mondays except after noon, when some cars are green. You can see the way it’s going. This is a theory of cars that has a series of correcting ‘epicycles’. Every new fact is accommodated by a little modification so as to maintain the grand assumption you started out with. At some stage you should get the message and start again.

This is of course an exaggerated example. Ptolemy’s theory was more sophisticated. Each time an epicycle was added it introduced a new smaller correction to accommodate a finer detail of the observed motions. This theory was one of the first examples of a convergent approximation process in action. Each addition to the model is smaller than the last and produces a better description of the observations.²² It worked rather well for most purposes despite having the wrong overall picture of the solar system and the wrong celestial body (the Earth instead of the Sun) at its centre! It took a very persuasive case to turn the tide of opinion against it.

Nicolaus Copernicus is generally regarded as a revolutionary – the scientist who dethroned humanity from its central position in the universe. The reality has turned out to be more complicated and far less dramatic, and if he was a revolutionary at all, he was certainly a reluctant one.²³ Copernicus’s great book, De revolutionibus orbium coelestium (‘On the Revolutions of the Celestial Spheres’), was delivered to the printers in 1543, shortly before his death, and its impact was muted. Not many copies were printed and few of those were ever read. Yet, in time, Copernicus’s perspective became the rallying point for the transformation of our view of the universe. It would eventually displace the ancient Ptolemaic picture of a planetary system with the Earth at its centre in favour of a Sun-centred model that remains with us today.²⁴

The advances in printing during the early sixteenth century meant that Copernicus’s book could be printed with diagrams embedded in the text at the points where they are discussed. The most famous of his diagrams (see Figure 1.9) shows a simple model of the solar system with the Sun located at its centre. The outermost circle marks the boundary of the ‘immobile sphere of the fixed stars’ beyond our solar system. Each of the other six circles marks a sphere of motion for the orbits of the six, then-known, planets. Going from the outside inwards, they denote the planets Saturn, Jupiter, Mars, Earth (with its adjacent crescent Moon), Venus and Mercury, respectively. All follow circular tracks around the central Sun (Sol). The Moon was believed to move in a circle around the Earth.

The systems of Copernicus and Ptolemy were not the only pictures of the Sun and the planets that were on offer in the sixteenth and seventeenth centuries. Figure 1.10, taken from Giovanni Riccioli’s Almagestum Novum (‘The New Almagest’)²⁵ of 1651, nicely summarises the world pictures on offer to astronomers in the post-Copernican era. It shows six different models of the solar system (labelled I–VI).

Model I is the Ptolemaic system with the Earth located at the centre and the Sun’s orbit around it lies outside the orbits of Mercury and Venus.

Model II is the Platonic system, where the Earth is also central. The Sun and all the planets are in orbit around it but the Sun lies inside the orbits of Mercury and Venus.

Model III is the so called Egyptian system, in which Mercury and Venus revolve around the Sun, which, along with the outer planets, revolves around the Earth.

Model IV is the Tychonic system of the great Danish astronomer Tycho Brahe (1546–1601), in which the Earth is fixed at the centre and the Moon and the Sun revolve around the Earth but all the other planets revolve around the Sun. The orbits of Mercury and Venus are therefore partly between the Earth and the Sun, while the orbits of Mars, Jupiter and Saturn encircle both the Earth and the Sun.

Model V, called the semi-Tychonic system, was invented by Giovanni Riccioli himself. In his model the planets Mars, Venus and Mercury orbit the Sun, which, together with Jupiter and Saturn, orbits the Earth. Riccioli wanted to distinguish Jupiter and Saturn from Mercury, Venus and Mars because they were known to have moons like the Earth (the two moons of Mars had not yet been discovered) and so their orbits must be centred on the Earth rather than on the Sun.

Figure 1.9 Copernicus’s heliocentric picture of the solar system, published in 1543. The diagram is labelled in Latin and shows concentric spheres around the central Sun. The fixed outer sphere of the stars (I) surrounds rotating spheres (II–VII) containing the orbits of Saturn, Jupiter, Mars, Earth (with its Moon marked as a crescent lune), Venus and Mercury.

Model VI is the Copernican system we have just seen illustrated in Figure 1.9.

This selection of ancient astronomical views of the universe has taught us some simple lessons. It is not easy to understand the universe just by looking at it. We are confined to the surface of a particular type of planet in orbit, with others, around a middle-aged star. As a result, what we see in the night sky is strongly determined by where we are located on the Earth’s surface, when we look, and by any preconceptions we might have about where we should be in the grand scheme of things. Our world view predetermines our world model.

Figure 1.10 The six major world systems of 1651 shown by Giovanni Riccioli in his book The New Almagest.

As our view of the universe expanded so these problems got bigger too. In order to make progress we need to be able to describe and predict the celestial movements we see in our part of the universe. But, ultimately, we want to know what the whole universe is like. The first decisive steps in that direction were taken by astronomers in the eighteenth century. Let’s follow them next.

2	The Earnestness of Being Important

Symmetry calms me down. Lack of symmetry makes me crazy.

Yves Saint Laurent

SPECIAL TIMES AND SPECIAL PLACES

There isn’t a Parallel of Latitude but thinks it would have been the Equator if it had had its rights.

Mark Twain

Nicolaus Copernicus has given his name to an entire philosophy of the world. In science an ‘anti-Copernican’ view is a pejorative description of thinking that presumes the centrality of humanity. In astronomy, the Copernican ‘Principle’ is often invoked to add prestige to the idea that we should always assume our position in the universe is not specially privileged. Instead of thinking the Earth is the centre of the universe, like the ancients, we should assume that the universe is much the same everywhere and build our theories accordingly. And so the Earth is expected to be a typical planet orbiting a typical star in a typical galaxy in the universe.

While the removal of the Earth and humanity from the centre of the universe is an important general lesson for scientists, we have come to appreciate that it contains pitfalls of its own if over-zealously pursued. For while we have no reason to expect that our position in the universe is special in every way, we would be equally misled were we to assume that it could not be special in any way.

We now understand that life can only exist in regions of the universe that have certain features: obviously we could not exist at the centre of a star where no atoms could survive, or in a region of the universe where the density of matter is too low for stars to form.¹ If ‘typical’ places in the universe are ones that have an environment that does not allow life to develop and persist then we cannot be in a typical position. This simple moderation of the Copernican perspective plays a crucial role in the testing of predictions in modern cosmology.²

Location is not, as the estate agents say, everything. We must also consider our place in history. If the universe changes its overall properties with time, say, getting hotter or cooler as it ages, then we may find that stars and planets and life can only be supported during particular intervals of cosmic history. This type of bias is linked to many of the most significant features of the expanding universe we observe today. The universe appears very old because the building blocks of chemical complexity, nuclei of elements like carbon, nitrogen and oxygen, are made in the stars, by a slow process of nuclear burning that culminates in a supernova explosion which spreads those life-supporting elements into space. Eventually, those ingredients find their way into planets, and into you and me. This process of stellar alchemy takes billions of years to run its course. So we should not be surprised to find that our universe is so old. We could not exist in one that was significantly younger: it would not have had time to generate the building blocks needed for complexity of life.

In the future there will be a time when the last star exhausts its nuclear fuel and ‘dies’, collapsing into a dense endlessly cooling remnant, or a black hole. Perhaps this means there is a time after which no life can survive in the universe. Some people find this a very unsatisfactory state of affairs and believe that life will never die out.³ Certainly, life as we know it – carbon-based and biochemical – cannot survive indefinitely. But if we look at the direction in which our advanced technologies are evolving, there is hope. Continual miniaturisation allows resources to be conserved, efficiency to be increased, pollution to be reduced, and the remarkable flexibilities of the quantum world to be tapped. Very advanced civilisations elsewhere in the universe may have been forced to follow the same technological path. Their nano-scale space probes, their atomic-scale machines and nano-computers, would be imperceptible to our coarse-grained surveys of the universe. Their waste energy output would be small, leaving little trace. This may be the low-impact evolutionary path you need to follow in order to survive into the far, far future.

DEMOCRATIC LAWS

One law for all

Roman law

After Copernicus, his Sun-centric picture of our solar system was gradually refined and eventually described mathematically by a new theory of motion and gravity created by a young man from Lincolnshire, called Isaac Newton (1643–1727). Newton’s law of gravitation and three laws of motion dominated the way physicists and engineers understood the world for nearly 250 years. They transformed all previous pictorial descriptions of motion into a precise mathematical one. They provided equations (‘laws’ of change) whose solutions (the ‘outcomes’ of those laws) predicted successfully what we should see as time passes, the motions of the Moon, and the planets. One of those predictions was that the orbit of a planet around the Sun will not be circular, as Copernicus had assumed, but elliptical with the Sun located at one of the two focal points of the ellipse (Figure 2.1).

Newton’s three laws of motion can be paraphrased as follows:

First law: Bodies acted upon by no forces remain at rest or moving at constant speed in a straight line.

Second law: The rate of change of momentum of a body equals the force applied to it.

Third law: To every force there is an equal and opposite force of reaction.

These laws hide many remarkable insights. The first one refers to bodies acted upon by ‘no forces’. For who has ever seen such a body? It is an idealisation that Newton recognises as a fundamental benchmark. In the past, most people thought that bodies acted upon by no forces just slow down and stop. But Newton realised that the slowing is caused by the action of other forces, like friction and air resistance. He was acutely aware of all the forces at work in a given situation and was able to imagine what would happen if none of them were acting, an entirely idealistic situation.

Figure 2.1 An exaggerated elliptical orbit of a planet showing the location of the Sun at a focal point of the ellipse.

When Newton talks about bodies moving or being at rest, we could ask: ‘At rest relative to what?’ In fact, he refers all those motions to an imaginary fixed stage of space marked out by the distant stars which he takes to be unchanging and unmoving, and which became known as ‘absolute space’. Newton’s laws dictated how things moved around and acted out their parts on that stage. Nothing they did could ever change its fabric.

Newton realised that only special actors on this cosmic stage would see his simple laws to be true. They would need to move so that they did not accelerate or rotate relative to the far distant stars that fixed his unchanging ‘absolute’ space. Suppose that an astronaut looks out of the window of a rotating spaceship. He will see the distant stars rotating past in the opposite direction to the spin of the spaceship. These stars are rotating in circles and relative to him they are accelerating, but they are not being acted upon by any forces. So, for the spinning astronaut, Newton’s first law does not hold and the form of the second law of motion he deduced would become more complicated.⁴

Newton’s formulations of his laws of motion highlight the existence of a form of Copernican principle for the laws of Nature as well as for their outcomes. They required special observers, for whom the laws of motion look simpler than they do for everyone else. Yet surely the true laws of Nature, rightly expressed, should look the same for all observers, regardless of their motion or their position. No one should be privileged to find them simpler than everyone else.

Armed with Newton’s laws, physicists and astronomers could try to make sense of all the motions they saw in the heavens. They could try to understand the distributions of stars and how things got to be as they are today from simpler beginnings. They lacked the telescopic power that we possess today so their view of the cosmic landscape was limited in scope. Yet, gradually pictures were constructed that accounted for the distribution of stars and linked these astronomical pictures to what we know about physics and motion. And, crucially, they began to think about what Newton’s laws of motion might tell us about how the universe changes.

THE CHANGING UNIVERSE

Round like a circle in a spiral

Like a wheel within a wheel

Alan and Marilyn Bergman

In the centuries that followed Newton, our appreciation of the scope and scale of the universe grew steadily. Thomas Wright (1711–86), a clockmaker, self-taught astronomer, surveyor and architect from Durham in the north of England, was the first to seek a detailed picture of the Milky Way, the band of stars, gas, dust and light that had been known and admired by all who had studied the sky from ancient times.⁵ He recognised that the evidence provided by the early telescopes was showing that the sky was not randomly sprinkled with stars. Rather, they displayed very distinctive clustered patterns which we were a part of, looking outwards from inside of one of those clusters. What was the real three-dimensional pattern that gave the Milky Way its observed appearance?

Wright proposed two possibilities. The first imagined a clustering of stars in a disc of flat rings, rather like those we are familiar with around Saturn, circling around the centre of the Milky Way. The centre was the ‘centre of creation’ from which ‘all the laws of nature have their origin’. The second possibility was that the stars were clustered as if on the surface of a sphere. The Milky Way was a slice through the edge of this shell, reflecting the fact that we did not live near the centre of the galaxy (see Figure 2.2a).

Figure 2.2 (a) Thomas Wright’s model of the Milky Way galaxy in which the stars are uniformly distributed in a disc-shaped slab of space. (b) Wright’s never-ending universe containing an infinite number of galaxies that look like bubbles in infinite space. Both illustrations are from his 1750 book, An Original Theory of the Universe.

Wright’s imagination flew higher still. He could see no reason why there should be only one of these great collections of stars. He imagined an endless number of them all over the universe, each a centre of created stars, some spherical, some disc-like. The faint images all over the night sky suggested to him that they might all be Milky Ways, creating an ‘endless immensity . . . not unlike the known universe’, which is shown in Figure 2.2b.

Wright laid great stress on poetic and pictorial descriptions of the universe. He drew a large (3 x 2 square metres) plan of the universe illustrating a wide spectrum of astronomical phenomena, like eclipses and cometary orbits. He was also inspired to think of an unending universe of solar systems, each with its own system of planets orbiting around its central star, by John Milton’s mention of suns and other worlds in Paradise Lost