The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe - John D. Barrow (2002)

Chapter 3. Constructing Nothing

“On the empty desk sat an empty glass of milk.”

BBC Radio 31

THE SEARCH FOR A VACUUM

“Nature, it seems, is the popular name
for milliards and milliards and milliards
of particles playing their infinite game
of billiards and billiards and billiards.”

Piet Hein, Atomyriades

While writers like William Shakespeare were plumbing the depths of the moral vacuum, others were seeking to create nothing less than a real physical vacuum. For more than two thousand years philosophers had argued fervently about the reality of a physical vacuum: the possibility that there could be a region of space that contains absolutely nothing. Both Aristotle and Plato denied, for quite different reasons, that such a vacuum could exist but other ancient thinkers disagreed. The Roman philosopher Lucretius was convinced that matter was composed of small constituent particles, which we would call ‘atoms’, and that the basic nature of the Universe was a motion of these atoms in the void that lay between them.

This picture of Nature, that we now call atomism,2 led its seventeenth-century supporters to countenance the existence of a vacuum in situations that were amenable to experimental investigation. Nor was it quite so mysterious as the theologians had claimed. It could be envisaged as the endpoint of a sequence of mechanical processes that sucked the contents out of a jar. As more of the contents were extracted so the closer did the inside of the jar come to resembling one which could be said to contain nothing at all. Of course, from the perspective of a sceptical philosopher this experiment might appear a little oversimplified. Even though all the air might be removed from the jar its interior could not be said to contain nothing. It was still subject to the laws of Nature. It remained part of the universe of space and time. One could still argue with justification that a perfect vacuum could never be created. For the pragmatist this claim would be supported by the manifest impossibility of extracting every last atom from the jar. For the natural philosopher a last-ditch defence was still available by appeal to a subtle distinction between jars that were completely empty and jars that were merely empty of everything of which they might be emptied. Nevertheless, the ensuing search for a physical vacuum was visually dramatic and it changed for ever the question of the character of that vacuum. It was now to become primarily a scientific question to which there were scientific answers.

The most fruitful investigations of the vacuum were conceived by seventeenth-century scientists investigating the behaviour of gases under pressure. If a container was to be evacuated of its contents, then the only way to get all the air out of the container was by sucking it out. This required the creation of a pressure difference between the inside and the outside of the container. A pump was needed and such devices existed for the pumping of water on ships and farms. In 1638 Galileo wrote3 that he had noticed that there was a limit to how high he could pump water using a suction pump. It would rise by ten and a half metres but no higher. He tells us about the problem of trying to pump water up from a cistern when its level had fallen too low:

“When I first noticed this phenomenon I thought the machine was out of order; but the workman whom I called in to repair it told me the defect was not in the pump but in the water which had fallen too low to be raised through such a height; and he added that it was not possible, either by a pump or by any other machine working on the principle of attraction, to lift water a hair’s breadth above eighteen cubits; whether the pump be large or small this is the extreme limit of the lift.”

Evidently Galileo was far from being the first to notice this irritating fact of agricultural life. There must have been farm workers and labourers trying to siphon water out of flooded trenches all over Europe who had come to appreciate it the hard way. Consequently there was good reason to devise suction pumps which could overcome this limit. As these machines improved they stimulated scientists to investigate why they worked at all. They were led to appreciate that if air could be removed from a closed space then the evacuated region would tend to suck things into it. At first this appeared to confirm Aristotle’s ancient precept that ‘Nature abhors a vacuum’: create an empty space and matter will move so as to refill it. Yet Aristotle maintained that this happened because of a teleological aspect to the working of the world. He expected matter to be drawn to fill the vacuum because it had that end in view. This is quite different from the type of explanation sought by Galileo. He was seeking a definite cause or law of Nature that would predict the future from the present physical state of affairs.4 Galileo saw that there was something unsatisfactory about using the inability of water pumps to raise water above some definite height as evidence for Nature’s abhorrence of a vacuum. For why did Nature’s level of abhorrence reach such a height (‘eighteen cubits’) and no further?

Galileo’s interest in the vacuum was not really philosophical. He was content to believe that it was impossible to make a true vacuum. For his purposes it was enough to produce a region that was almost empty. The reason for his interest in such a region is not hard to find. His deep insights into the behaviour of bodies falling under gravity had led him to recognise that air resistance played an important role in determining how things would fall under the pull of gravity. If objects of different mass, or of different size, are dropped simultaneously in a vacuum (where there is no air resistance to impede their fall to the ground), then they should experience the same acceleration and reach the ground at the same moment. Legend has it that Galileo performed this experiment by dropping objects from the Leaning Tower of Pisa, but historians regard this as rather unlikely to have been the case. However, in reality, in the Earth’s atmosphere a stone and a feather certainly do not hit the ground simultaneously if released together because of the very different effects of air resistance upon them. By producing a good vacuum, Galileo could get a better approximation to the true vacuum where his idealised laws of motion were predicted to hold exactly. In fact, this experiment with a falling feather and a rock was one of the first things that was done by the first Apollo astronauts to walk on the Moon for all to see on television. In the absence of an atmosphere to resist their motion, the two objects hit the ground together, just as Galileo predicted. This type of experiment was first carried out in less ideal conditions by the French scientist, Desaguliers, in 1717, as a demonstration for Isaac Newton at the Royal Society in London. Instead of a feather and a stone he used a guinea coin5 and a piece of paper. The Philosophical Transactions of the Royal Society reported that

“Mr Desaguliers shew’d the experiment of letting fall a bitt of Paper and a Guinea from the height of about 7 foot in a vacuum he had contrived with four glasses set over one another, the junctures being lined with Leather liquored with Oyle so as to exclude the Air with great exactness. It was found that the paper fell very nearly with the same Velocity as the Guinea so that it was concluded that if so great a Capacity could have been perfectly exhausted, and the Vacuum preserv’d, there would have been no difference in their time of fall.”

The puzzle of the water pumps was solved in 1643 by one of Galileo’s students, Evangelista Torricelli, who worked as his secretary in 1641–2 and eventually succeeded him as the court mathematician to the Tuscan Grand Duke Fernando II, a post he held until his premature death in 1647, when aged only thirty-nine. Torricelli realised that the Earth’s atmosphere carried a weight of air which bore down on the Earth and exerted a pressure at its surface. It was this ‘atmospheric pressure’ that he suspected, but could not rigorously prove, was the real reason why air tended to fill up any vacuum that we try to create. Using water was a cumbersome (although cheap) way to carry the investigations further. Eighteen cubits is about 10.5 metres and this is a tall order to study in a laboratory. But if he could use a liquid that was much denser than water, then the maximum height it could be pumped would be smaller. The densest liquid of all is the liquid metal, mercury. It is almost fourteen times denser than water and so we would expect that the maximum height it could be raised would be fourteen times less than that for water, giving a convenient height of just 76 centimetres of mercury. Using mercury, Torricelli6 constructed the first simple manometer without even needing a pump to raise the mercury, as shown in Figure 3.1.

He took a straight glass tube that was longer than 75 centimetres, sealed at one end by the glassblower but left open at the other. Using a bowl of mercury he filled the tube right to the top, sealed the open end with his finger, and then inverted the tube to stand upright with its open end under the surface of the mercury in the bowl (see Figure 3.1). When he removed his finger, the mercury level dropped down the tube. Every time you do this experiment at sea level, no matter how wide the tube, the level taken by the mercury is approximately 76 centimetres above the surface of the mercury in the bowl.7

The remarkable thing about Torricelli’s experiment was that for the first time it appeared to create a sustained physical vacuum. When the tube was first filled with mercury there was no air within it. Yet after the tube had been inverted the mercury fell, leaving a space in the sealed tube above it. What did it contain? No air could get in. Surely it must be a vacuum. On 11 June 1644 Torricelli wrote to one of his friends, Michelangelo Ricci, revealing some of his thoughts about the profound implications of his simple experiment:9

Figure 3.1 Two examples of Torricelli’s barometer.8 The column of mercury in each vertical tube is balanced by the pressure of the atmosphere on the surface of the mercury in the dish. At sea level the height is about 76 cm.

“Many people have said that it is impossible to create a vacuum; others think it must be possible, but only with difficulty, and after overcoming some natural resistance. I don’t know whether anyone maintains that it can be done easily, without having to overcome any natural resistance. My argument has been the following: If there is somebody who finds an obvious reason for the resistance against the production of a vacuum, then it doesn’t make sense to make the vacuum the cause for these effects. They obviously must depend on external circumstances … We exist on the bottom of an ocean composed of the element air; beyond doubt that air does possess weight. In fact, on the surface of the Earth, air weighs about four hundred times less than water … the argument that the weight of air such as determined by Galileo is correct for the altitudes commonly inhabited by man and animals, but not high above the mountain peaks; up there, air is extremely pure and much lighter than the four hundredth part of the weight of water.”

The reason for the behaviour of the column of mercury in Torricelli’s tube is that the force exerted by the weight of air in the atmosphere above the bowl of mercury acts on the surface of the mercury and causes the mercury to rise up the tube to a level at which its pressure balances that exerted by the air on the surface of the mercury bowl. Actually, the height of the mercury column is only approximately equal to 76 centimetres. It varies as the weather conditions change and from place to place on the Earth’s surface. These changes reflect the change in atmospheric pressure created by the winds and other changes in the density of the atmosphere that are produced by variations in temperature. When we see a weather map in a newspaper or on the television it will display isobars which trace the contours of equal pressure. These effects of weather on the pressure exerted by the atmosphere allowed Torricelli’s device to provide us with the first barometer. We notice also in his account to Ricci that he has realised that the result of his experiment depends upon the altitude at which it is conducted. The higher one climbs, the less atmosphere there is above and the lower the air pressure weighing down on the mercury column.

Torricelli was a talented scientist with many other interests besides air pressure. He determined laws governing the flow of liquids through small openings and, following in the footsteps of his famous mentor, deduced many of the properties of projectile motion. Not merely a theorist, he was a skilled instrument maker and lens grinder, making telescopes and simple microscopes with which to perform his experiments, and he made a considerable amount of money by selling them to others as well.

Torricelli’s simple experiment led eventually to the acceptance of the radical idea that the Earth was cocooned in an atmosphere that thinned out as one ascended from the Earth’s surface and was eventually reduced to an empty expanse that we have come to call simply ‘space’ or, if we keep going a bit further, ‘outer space’. This dramatic background stage for life on Earth provided the beginning for many reassessments of humanity’s place and significance in the Universe. Copernicus had published his startling claims that the Earth does not lie at the centre of the solar system about one hundred years before Torricelli’s work. The two are closely allied in spirit. Copernicus moves us from a central location in the Universe while Torricelli reveals that we and our local environment are made of a different density of material than the Universe beyond. We are isolated, swimming in a vast emptiness. Later, we shall find that this emptiness of space has remarkable consequences for us and for the possibility of life in the Universe.

Spurred on by Torricelli’s demonstrations and suggestions, other scientists around Europe started to investigate the empty space at the top of the mercury column, to discover its hidden properties, subjecting it to magnets, electric charge, heat and light. Robert Boyle10 in England used simple ‘vacuum pumps’ constructed by Robert Hooke to evacuate much larger volumes than those naturally produced by Torricelli and studied what happened to mice and birds placed in jars as they were gradually evacuated of air.11 He appears to have escaped the attentions of the seventeenth-century equivalent of the Animal Liberation Front.

Boyle was extremely wealthy. His family were substantial Irish land-owners in County Waterford. His serious study of science began in earnest after graduating from Eton in 1639 when he first read Galileo’s works whilst making a grand European tour with his private tutor. Upon his return he established himself in Dorset and began his impressive experimental scientific work. Later, he would move to Oxford and become one of the founding fellows of the Royal Society. Boyle had no need to seek grant support. He inherited a large fortune which allowed him to buy expensive pieces of scientific equipment and hire skilled technicians to help maintain and modify them. Boyle sought to exorcise the notion that the vacuum at the top of Torricelli’s barometer possessed a suction that was drawing the mercury up the tube in accord with traditional Aristotelian beliefs about the tendency for Nature to remove a vacuum. Such a notion was not held without reason. If you put your finger over the end of a glass tube, it did feel as if it was being slightly sucked up into the tube because it was difficult to remove it. Boyle laid the foundations for a straightforward explanation for the height of the mercury in terms of the difference in pressure between the atmosphere and the ‘vacuum’ inside the tube. Rival Aristotelian theories proposed that there was an invisible ropelike structure, called a funiculus (from the Latin funis, for rope), which pulled on the mercury, preventing it falling to the bottom of the tube. Boyle was able to demonstrate the superiority of the air pressure theory by using it successfully to predict the level attained by the mercury when the outside pressure was changed to different values.12

The most spectacular experiment inspired by Torricelli’s work was conducted in 1654 by Otto von Guericke,13 a German scientist who for thirty years was one of the four mayors of the German city of Magdeburg (Figure 3.2).

This civic status was of great help to him in making a memorable public display of the reality of the vacuum. His celebrated ‘Magdeburg Hemispheres’ demonstration involved carefully building two hollow bronze hemispheres which fitted closely together to form a good seal. A pump was requisitioned from the local fire service and attached to a valve on one of them so that the air could be sucked out after they were joined together to form a spherical shell. After much pumping Von Guericke announced to his audience that he had created a vacuum. Moreover, Nature was rather happy with it. Far from shunning or trying to remove it, as the ancients were so fond of preaching, Nature strenuously defended the vacuum against any attempt to destroy it! Just so that no one could miss the point, two teams of eight horses were harnessed together and hitched up to each hemisphere and then driven off in opposite directions in order to tear the hemispheres apart. They failed! Then Von Guericke opened the valve to let the air back in and the hemispheres could be effortlessly separated. They don’t do experiments like that any more! Actually, the two teams of eight horses proved rather hard to handle and required six trials before he could get each team member pulling in the same direction at the same time. The two Magdeburg hemispheres can still be seen in the Deutsches Museum in Munich (Figure 3.3).

Figure 3.2 Otto von Guericke.14

The result of all this work was to convince scientists that the Earth was surrounded by a substantial body of air which exerted a significant pressure on its surface. By carefully studying its effects, it was possible to explain all sorts of behaviours of gases and liquids in detailed mechanical terms rather than merely ascribing them to the vague notion that ‘Nature abhors a vacuum’ as the ancients did. Historians of science have highlighted the mundane study of air pressure as a turning point in our study of Nature; teleological notions of the ‘inclinations’ in the natural order of things brought about by mysterious occult forces were superseded by explanations that used only the concepts of matter and motion.

Figure 3.3 The Magdeburg Hemispheres Experiment.15

Von Guericke was a practical engineer of great ingenuity. He both liked and invented machines. But he was still fascinated by the ancient philosophical questions about the reality of the vacuum and their implications for the Christian doctrine of the creation of the world out of nothing. In his account of his experimental investigations he devotes a substantial section16 to airing his views about the void, which have a strong affinity to the medieval scholastic ideas that formed the philosophical tradition in which he worked. Von Guericke’s book is rather overblown. He has something to say about just about everything under the sun, and a good deal about things above it as well. His position in local government ensured that there would be an effusive dedication by one of the local noblemen. Indeed, Johannes von Gersdorf is moved to poetry in his tribute to the experimenter of Magdeburg, ‘the most distinguished and excellent gentleman, Otto von Guericke’:

“To delve into the manifold mysteries of nature
is the task of an inquiring and fertile mind.
To follow the tortuous paths of nature’s wondrous ways
is work more difficult and not designed for everyone.
You, Distinguished Sir, Magdeburg knows as its Burghermaster
as well as an outstanding researcher in the field of science.
Whether one speaks with you informally or studies your work alone,
he will soon confirm your genius openly and without a feeling of doubt.
May I make a small joke? While you prove quite clearly that a vacuum exists
in your Book, there is not a vacuum to be seen!”

For Von Guericke everything that existed could be put into one of two classes: it was either a ‘created something’ or an ‘uncreated something’. There could be no third way: no class that we can call ‘nothing’. Since ‘nothing’ is the affirmation of something and the opposite of something else, it must be a something. Thus it falls into the category of either the ‘created somethings’ or the ‘uncreated somethings’; or maybe, he feels, ‘nothing’ has a call on belonging to both categories. Thus an imaginary animal like a unicorn is nothing in the sense of being non-existent; that is, it is not a thing. But because it exists as a mental conception it is not absolutely nothing. It has the same type of existence as a human thought. Thus it qualifies as a created something. Von Guericke wanted to view the Nothing that was before the World was made as an uncreated something, so that he could say that before the World was created there was Nothing, or equally, there was an uncreated something. In this way he guards against sounding like a heretic.

Von Guericke summarised his lyrical philosophy of the void in a great psalm in honour of Nothing (Nihil). It gives a flavour of thinking that one would not have immediately associated with down-to-earth experimental demonstrations that the vacuum could be controlled by air pumps. It is worth reading at length. He joins various concepts of Nothing, empty space and imagined space together into one and the same concept, for

“everything is in Nothing and if God should reduce the fabric of the world, which he created, into Nothing, nothing would remain of its place other than Nothing (just as it was before the creation of the world), that is, the Uncreated. For the Uncreated is that whose beginning does not pre-exist; and Nothing, we say, is that whose beginning does not pre-exist. Nothing contains all things. It is more precious than gold, without beginning and end, more joyous than the perception of bountiful light, more noble than the blood of kings, comparable to the heavens, higher than the stars, more powerful than a stroke of lightning, perfect and blessed in every way. Nothing always inspires. Where nothing is, there ceases the jurisdiction of all kings. Nothing is without any mischief. According to Job the Earth is suspended over Nothing. Nothing is outside the world. Nothing is everywhere. They say the vacuum is Nothing; and they say that imaginary space – and space itself – is Nothing.”17

Von Guericke believed that space was infinite and likely to be populated by many other worlds like our own. He used the idea of the infinite world to support his argument that there is really no difference between real and imagined space. For, although we might think that unicorns inhabit only an imaginary space, he argues that if space is infinite then we are reduced to imagining some of its properties, just like we are the unicorns. In fact, Von Guericke equated infinite space, or Nothing, the uncreated something, with God.

A TALE OF TWO NOTHINGS

“It is hard to think of any modern parallel to the shiver of horror engendered by the mere suggestion to a man of the seventeenth century that a vacuum could effortlessly exist and be maintained; a materialist forced to admit irrefutable evidence of life after death might offer a fair analogy.”

Alban Krailsheimer18

It is well to remember that these great experiments with air pressure focused attention on the problem of two Nothings. There was the abstract, moral or psychological ‘nothing’, juggled with by playwrights and philosophers. It was a Nothing entirely metaphysical in nature; one that you didn’t have to worry about if you didn’t want to. It could stay as poetry. Set in stark prosaic contrast was the problem created by the attempts to create a real physical vacuum in front of your very eyes by evacuating glass tubes or metal hemispheres. This vacuum exerted forces and could be used to store energy. This was a very useful Nothing.

The seventeenth-century thinker who did most to join the two conceptions together was a polymath with diverse, seemingly contradictory, interests who liked to engage with problems that possessed a hint of the impossible or the fantastic. Some of those interests were physical, some were mathematical, while others were entirely theological. Blaise Pascal was born in the French town of Clermont in 1623. He died only thirty-nine years later, but in that short space of time he laid the foundations for the serious study of probability, constructed the second mechanical calculating machine, made significant discoveries about the behaviour of gases under pressure, and found new, important results in geometry and algebra. Finally, his most famous work was his unfinished collection of fragmentary ‘thoughts’, the Pensées,19 that remained incomplete at the time of his early death. All this was achieved from unpromising beginnings. Pascal’s mother died when he was just three years old, leaving the young boy at the mercy of his father’s theories of education. They moved to Paris where Etienne, a successful lawyer, decided to educate his rather sickly son himself in isolation from other children. Although Pascal Senior was an able mathematician, he was determined that his son should not study mathematics until he reached the age of fifteen, and all mathematics books were removed from their house. Not content with the diet of Latin and Greek that resulted, the young Pascal gradually came in contact with friends of his father who shared an interest in mathematics. Not to be denied, he evaded his father’s educational restrictions by rediscovering a number of geometrical properties of triangles for himself at the age of twelve. Surprised, his father relented and gave him a copy of Euclid’s book of geometry to work with. Soon afterwards the family uprooted and moved to Rouen where his father had been appointed tax collector for the region. The young Pascal prospered there. At the age of sixteen he presented his first mathematical discoveries of new theorems and geometrical constructions to a regular meeting of Paris mathematicians convened by Mersenne, one of the most notable number theorists of the day. His first published work, on geometry, appeared just eight months later. So began Pascal’s career of invention and discovery (see Figure 3.4).

Pascal’s interest in air pressure and the quest to create a perfect vacuum began in 1646. Unfortunately, this work threw him on to a collision course with the views of René Descartes, the most influential French natural philosopher of his day. In Rouen, Pascal came to hear of Torricelli’s remarkable experiments, conducted a few years before. Teaming up with Pierre Petit, a fortifications engineer and friend of his father, he began a series of telling experiments.20 The most important was planned by Pascal and carried out by his brother-in-law, Florin Périer. It sought to demonstrate the claims that Torricelli was making in his letter to Ricci about the thinning out of the Earth’s atmosphere at high altitude. On 15 November 1647 Pascal wrote to Périer asking him to compare the mercury levels in a Torricelli tube at the base and at the summit of a local mountain:

Figure 3.4 Blaise Pascal.21

“if it happens that the height of the quicksilver [mercury] is less at the top than at the base of the mountain (as I have many reasons to believe it is, although all who have studied the matter are of the opposite opinion), it follows of necessity that the weight and pressure of the air is the sole cause of this suspension of the quicksilver, and not the abhorrence of the vacuum: for it is quite certain that there is much more air that presses on the foot of the mountain than at its summit.”22

After a delay of several weeks due to bad weather, Périer gathered together his team in the convent garden in the town of Clermont. He prepared two identical tubes of mercury, adopting the same method as Torricelli had used. The heights of the mercury columns were measured carefully in the presence of an audience of local worthies and verified to be identical. The local priest was then left in charge of one of the mercury columns while Périer’s team headed for the summit of Mount Puy-de-Dôme in the Auvergne, 1465 metres above sea level. They read the height of mercury at different altitudes on their ascent and at the summit itself. Mission accomplished, they returned to the convent to check that the height of mercury in their instrument was the same as the one left in the priest’s care. It was. The change in level between the convent and the mountain top was a clear 8.25 centimetres.

What these measurements established for the first time, on 9 September 1648, was that the pressure of air decreased as one ascended the mountain. This result had a tremendous impact on all involved. Pascal wrote that the experimenters ‘were carried away with wonder and delight’. The fact that the effect which they discovered was so large inspired one of them, Father de la Mare, to look for the difference in mercury level when he took a barometer from ground level to the top of the 39-metre-high tower of the cathedral of Notre Dame de Clermont. The difference was 4.5 millimetres: small but still quite measurable. When Pascal heard the result he repeated the experiment in the tallest buildings in Paris, finding a similar measurable trend: the taller the building the bigger the pressure drop at the top. He soon realised that sensitive measurements of the variation of pressure with altitude could be used to determine altitude if a detailed enough understanding of the correlation between atmospheric pressure and altitude could be obtained independently. In the 350 years since Pascal’s first measurements we have built up a detailed picture of the Earth’s tenuous atmosphere (see Figure 3.5). Subsequently, he discovered that the barometric level at one place could change with the weather conditions, a fact that our modern use of the barometer exploits. A modern weather map, laced with isobars, is shown in Figure 3.6.

Figure 3.5 The change in the nature of the Earth’s atmosphere up to an altitude of 1000 kilometres above sea level.23

Pascal maintained that the empty space at the top of the mercury tube was a real vacuum. Pascal’s opponents were not especially interested in the practical implications of pneumatics and hydraulics, but they were concerned about the philosophical implications of such a claim, not least because they were being made by a young man of twenty-three who possessed no formal academic qualifications, merely an extremely stubborn and persistent character. In Italy, Torricelli’s group worked on many experiments between 1639 and 1644 but they did not pursue their researches any further, probably for fear of opposition by the Church – Giordano Bruno was burned at the stake in 1600 and Torricelli’s mentor, Galileo, remained under house arrest by the Inquisition in the nine years before his death in 1642. But Pascal, encouraged by Mersenne, who had learned of the experiments carried out in Rome, held no such fears despite his deeply religious inclinations. He improved and extended Torricelli’s experiments in many ways. He experimented with water and red wine and various oils, as well as mercury. These required large, often spectacular, experiments with long tubes and huge barrels to be performed in the streets of his home town. This showmanship did not endear him to his conservative opponents.

Figure 3.6 A weather map showing isobars, contour lines of equal atmospheric pressure. Winds blow from high to low pressure areas.24

Pascal faced opposition to the recognition of the reality of a physical vacuum on two fronts. The traditionalist Aristotelians had long exercised a strong influence on physics and they denied the possibility of making a vacuum. They explained the observed changes in Nature by ‘tendencies’ which really explained nothing at all; things grew because of a life force, objects fell to earth because of a property of heaviness. This was just a name game that could make no decisive predictions about what would happen in situations never before observed. But the Aristotelians were not the only ones to deny the possibility of a vacuum. The Cartesians, followers of Descartes, followed a unified natural philosophy which attempted to deduce the behaviour of the physical world in mathematical terms, by means of specific universal laws. However, this modern-sounding initiative did not allow space to be discussed without matter being present. Space requires matter just as matter requires space. These properties of the world were axiomatic to the Cartesian system and ruled the vacuum out of court ab initio. Unfortunately, Pascal’s meetings with Descartes to discuss the significance of his spectacular mountain-top experiments on air pressure did not go well. Descartes maintained that he had actually proposed that experiments of this sort be performed, but refused to admit that they established the existence of a real physical vacuum, as Pascal always claimed. Pascal did not create a good impression, because after his visit Descartes wrote to Huygens in Holland that he had found Pascal to have ‘too much vacuum in his head’!

Pascal ended up entering a public debate, conducted in print, with Descartes’ Jesuit tutor Père Noël. Noël sought to defend the non-existence of the vacuum on the ground laid out by his pupil, but also on the ground that the all-pervasive sovereignty of God prevented a vacuum forming anywhere, for this would require an abnegation of the Almighty’s power. Noël attacked Pascal’s interpretation of his experiment, making a fine linguistic distinction between a vacuum and ‘empty space’ when it came to evaluating the content of the mercury tube, denying that the space in the tube was the same vacuum that Aristotle had denied could exist:

“But is this void not the ‘interval’ of those ancient philosophers that Aristotle attempted to refute … or rather the immensity of God that cannot be denied, since God is everywhere? In truth, if this true vacuum is nothing other than the immensity of God, I cannot deny its existence; but likewise one cannot say that this immensity, being nothing but God Himself, a very simple spirit, has parts one separate from the other, which is the definition I give to body, and not that you attribute to my authors, taken from the composition of matter and form.”25

Pascal did not rise to the bait being dangled here to tempt him into a theological debate about the nature of God with a member of the Jesuits which would have resulted in him being tarred with the same brush as the atheistic atomists like Democritus (the ‘ancient philosophers’ that Noël mentions). Reclaiming the moral high ground, his reply to Noël cleverly sidestepped the problem with Jesuitical skill:

“Mysteries concerning the Deity are too holy to be profaned by our disputes; we ought to make them the object of our adoration, not the subject of our discussions: so much so that, without discussing them at all, I submit entirely to whatever those persons decide who have the right to do so.”26

As other commentators began to see the close connection between Pascal’s experiments and the ancient questions concerning the vacuum and the void, Pascal’s writings started to stress the ‘equilibrium’ and ‘balance’ that the experiments displayed rather than the emptiness. But he was circumspect in his views. His unpublished papers show that he held much firmer opinions than he voiced at the time. In his private writings we find him asking himself about the sense of the Aristotelian abhorrence of the vacuum:

“Does Nature abhor the vacuum more on top of a mountain than in a valley, and even more so in wet weather than in sunshine?”

Despite the down-to-earth nature of Pascal’s study of air pressure, his results had deep and (for some) disturbing implications. His theory of air pressure explained why the height of Torricelli’s mercury column should fall as the experiment was carried to high altitude: only the weight of air above the experiment is exerting pressure on the surface of the mercury in the bowl. Suppose that we kept on going – the change in the mercury level has so far been finite, does it not imply that the atmosphere may be finite in mass, surrounding the Earth like a hollowed-out sphere? This would mean that there was ultimately a vacuum out in space, surrounding and enclosing us. Noël argued that it led us to the dangerous conclusion that if this useless vacuum existed in outer space beyond us then it would mean that some of God’s creation was of no use. Yet Pascal’s arguments won the day. Not until the last half of the twentieth century would it be appreciated how the vastness of the Universe is necessary for the existence of life on a single planet within it.27

HOW MUCH OF SPACE IS SPACE?

“In the United States there is more space where nobody is than where anybody is. That is what makes America what it is.”

Gertrude Stein28

Fred Hoyle once said that ‘space isn’t remote at all. It’s only an hour’s drive away if your car could go straight upwards.’29 The work begun by Torricelli with such mundane equipment culminated in the discovery that the Earth is surrounded by a gaseous atmosphere that becomes increasingly dilute the further we go from the Earth’s surface. Pascal was drawn to speculate what this might ultimately mean for the nature of outer space beyond. Was a true vacuum encircling us or was there simply a medium that grew sparser and sparser beyond the Sun and the planets? In Pascal’s time it was not possible to appreciate the enormity of this problem. Today’s picture of the Universe allows us to discern the nature of outer space in considerable detail. What we have found is doubly surprising. Matter is organised into a hierarchy of systems of increasing size and decreasing average density. In ascending order of size, there are planets, groups and clusters of stars, and systems of hundreds of billions of stars which come together to form galaxies like our own Milky Way galaxy; then we find galaxies gathered together into clusters that can contain thousands of members and these clusters can be found gravitating together loosely in vast superclusters. In between these regions of greater than average density in the Universe, gas molecules and specks of dust are to be found. The average density of a planet or a star like the Sun is close to one gram per cubic centimetre, which means about 1024 atoms per cubic centimetre. This is roughly the density of things we encounter around us. This is vastly greater than the average density of the Universe. If we were to smooth out all the luminous material in the visible universe then we would find only about one atom in every cubic metre of space. This is a far better vacuum than we can make in any terrestrial laboratory by artificial means. There are about one hundred billion galaxies within this visible universe30 and the average density of material within a galaxy is about one million times greater than that in the visible universe as a whole, and corresponds to about one atom in every cubic centimetre.

Counting up the visible matter in the Universe is only part of the accounting that needs to be done if we are to have a complete inventory of the contents of space. Some matter reveals itself by its luminosity but all matter reveals itself by its gravity. When astronomers study the motions of stars in galaxies and galaxies in clusters they find a similar story. The speeds of the moving stars and galaxies are too great for the galaxies and clusters to remain locked together by gravitational attractions between their constituents unless there is about ten times more matter present in some dark unseen form. This is not entirely unexpected. We know that the formation of stars will not be a perfectly efficient process. There will be lots of material that does not get swept up into regions that become dense enough to create the conditions needed to initiate nuclear reactions and start shining. The major mystery is what form this matter takes. It is known to astronomers as the ‘dark matter problem’. The obvious first idea that the dark material is just like other matter – atoms, molecules, dust, rocks, planets or very faint stars – does not seem to work. There is a powerful limit on how much material of that sort – luminous or non-luminous – there can be in the Universe in order that the nuclear reactions that produce the lightest elements of helium, deuterium and lithium in the early stages of the Universe give the observed abundances. So we are forced to accept that the dark material that dominates the content of outer space must be another form of matter entirely. The favourite candidate is a population of neutrino-like particles (called WIMPS = weakly interacting massive particles), heavier than ordinary protons and more numerous.31 They do not take part in nuclear reactions so they avoid the limit on their abundance imposed by the behaviour of nuclear reactions in the early stages of the Universe’s history. Such particles are suspected to exist as part of the complement of elementary particles of matter but they would not have been visible in particle physics experiments so far. The theory of the expanding Universe allows the abundance of these particles to be calculated exactly in terms of their mass. If such hypothetical particles do supply the dark matter needed to hold galaxies and clusters together, then we will soon know. They will be detectable in a few years’ time in deep underground experiments devised to catch them as they fly through the Earth. A few detections should be made each day in each kilogram of specially designed detection material.

Atoms and molecules, and even neutrino-like particles, are far from all there is pervading outer space. Radiation exists in all wavelengths. The most pervasive and the most significant contributor to the total energy density of the Universe is the sea of microwave photons left over from the hot early stages of the Universe. As the Universe has expanded, these photons have lost energy, increased in wavelength and cooled to a temperature only 2.7 degrees above absolute zero. There are about 411 of these photons in every cubic centimetre of space. That is, there are roughly one billion of these photons for every atom in the Universe.

Our detailed probing of the distribution of matter and radiation in the Universe shows that, as we survey larger and larger volumes of the Universe, the density of material that we find keeps falling until we get out beyond the dimensions of clusters of galaxies (see Figure 3.7). When we reach that scale the clustering of matter starts to fade away and looks more and more like a tiny random perturbation on a smooth sea of matter with a density of about one atom in every cubic metre. As we look out to the largest visible dimensions of the Universe we find that the deviations from perfect smoothness of the matter and radiation remain at a low level of just one part in one hundred thousand. This shows us that the Universe is not what has become known as a fractal, with the clustering of matter on every scale looking like a magnified image of that on the next larger scale. The clustering of matter appears to peter out before we reach the limit of our telescopes. This is a reflection of the fact that these large aggregates of matter take time to assemble under the influence of gravitational attractions. There is only a finite time available for this process and so its extent is limited.

Figure 3.7 The observed clustering of about a million galaxies in the Universe.

The Universe appears to be a system of very low density wherever we look. This is no accident. The expansion of the Universe weds its size and age to the gravitational pull of the material that it contains. In order that a universe expands for long enough to allow the building blocks of life to form in the interiors of stars, by a sequence of nuclear reactions, it must be billions of years old. This means that it must be billions of light years in extent and possess a very small average density of matter and a very low temperature. The low temperature and energy of its material ensures that the sky is dark at night. Turn off our local Sun and there is just too little light around in the Universe to brighten the sky. The night is dark, interspersed only by pinpricks of starlight. Universes that contain life must be big and old, dark and cold. If our Universe was less of a vacuum it could not be an abode for living complexity.

In showing what the state of space is today we have rushed ahead to the present. But the vector from Pascal to the Big Bang was not so short. In the next chapter we begin to see what happened to the vacuum in between, how it was transmogrified, banished, restored and ultimately transfigured. We shall find that the concept of the vacuum and the search for evidence for its existence continued to play the same central role in science and philosophy in the nineteenth and twentieth centuries as it did at earlier times.