The Book of Nothing

by John D. Barrow

  One of things that we have seen in the struggle to make sense of the vacuum and its possible reality is a medieval willingness to conduct experiments, both thought-experiments which appeal to common experience and more contrived sequences of events which demand careful observation and interpretation. This appeal to the behaviour of the world as a source of reliable knowledge did not begin with Galileo, but with him it started to become the only trusted guide to the truth behind everyday things. This was not so much because other guides were mistrusted, merely that they were so hard to interpret clearly and reliably. The medieval philosophers like Bacon and Burley began a tradition of inquiry and a search for the vacuum that would be taken up by Galileo and his contemporaries with a brilliant acuteness. Nothing better displays the phase transition from natural philosophy to natural science.

  “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 spec
tacular 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).