The Book of Nothing

by John D. Barrow

  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.

  “The idea of an omnipresent medium has considerable attractions for the scientist. It enables him, for example, to explain how such familiar phenomena as light, heat, sound and magnetism can operate over great distances and travel through a seemingly empty space.”

  Derek Gjertsen1

  NEWTON AND THE ETHER: TO BE OR NOT TO BE?

  “Nothing is enough for the man to whom enough is too little
.”

  Epicurus

  Newton’s studies of motion and gravity in the second half of the seventeenth century followed a trajectory that would lead to staggering success. He could explain the motions of the Moon and the planets, the shape of the Earth, the tides, the paths of projectiles, the variation of gravity with altitude and depth below the Earth, the motion of bodies when resisted by air pressure, and much else besides. Newton did this by making a spectacular imaginative leap. He formulated laws of motion in terms of an idealised situation. His first law of motion states that ‘Bodies acted upon by no forces remain at rest or in motion at constant velocity.’ No one had ever seen (or will ever see) a body acted upon by no forces, but Newton saw that such an idea provided the benchmark against which one could reliably gauge what was seen. Whilst others had thought that bodies acted upon by no forces just slowed down and stopped, Newton identified all the forces that were acting in any given situation, and thought otherwise. When no motion occurred it was because different forces were in balance, leaving zero net force acting on the body.

  Despite the power and simplicity of Newton’s ideas, there was an awkward assumption at their heart. Newton had to suppose that there existed something that he called ‘absolute space’, a sort of fixed background stage in the Universe upon which all the observed motions that his laws governed were played out. Newton’s famous laws of motion applied only to motions that were not accelerating relative to this imaginary arena of absolute space.2 Today, we might approximate it by mapping out an imaginary scaffolding using the most distant, most slowly changing astronomical objects that we can see, the quasars.

  Absolute space was a tricky notion. It was the linchpin of Newton’s theory but you couldn’t observe it, you couldn’t feel it and you couldn’t do anything to it. It begins to sound as mysterious and elusive as the vacuum itself. It carried with it the added difficulty of not explaining how gravity or light could be propagated through it. One answer to this riddle was to give up the notion that space was empty in between the solid objects dotted around within it and instead imagine that the ‘empty’ space between contained an extremely dilute fluid that filled its every nook and cranny like a uniform motionless sea. This fluid begins to look like a candidate to replace the entirely mathematical concept of ‘absolute space’ because motion can always be described as taking place relative to the tenuous fluid.

  This great unchanging sea filling all of space became known as the ether. It is reminiscent of the elastic substance, or pneuma, that the ancient Stoic philosophers proposed as a space filler, which played an active role in their attempts to understand the world. The spreading of sound outwards from its source was interpreted as a motion through the pneuma, like a wave through water. The familiarity of this analogy did much to encourage its adoption as a model for the permeability of all space. Its removal of the need to worry about real vacua ever again was an added attraction.

  Newton never displayed any great enthusiasm for the idea and adopted it with some reluctance for want of something more compelling. He recognised that the ether provided a convenient vehicle to understand some of the properties of light and the propagation of its effects through space, but the presence of a fluid would play havoc with the motions of the Moon and the planets. He understood the motions of bodies in liquids and other resisting media very thoroughly and protested that the presence of an all-pervading resisting medium would just retard the motions of the celestial bodies. Eventually, they would grind to a halt.

  Torricelli, Pascal and Boyle had investigated a number of properties of the local vacua they could apparently create in their mercury columns. They had shone light through them, and so deduced that light could penetrate the evacuated space; magnetic attraction was not inhibited either; radiative heat passed unimpeded through the jars of empty space; and bodies fell to the Earth under gravity just as they did in air.3 Newton was well aware of these features of ‘empty’ space and so wondered if perhaps it was not so empty after all, so that the heat and light could be propagated by the ‘vibrations of a much subtler medium than air, which after the air was drawn out remained in the vacuum’.4

  In trying to sustain this idea, Newton got himself in a very complicated tangle. His first thought was to view light as a stream of minute particles (which we would now call ‘photons’) that bounced off reflecting surfaces and behaved like the tiniest of perfectly elastic billiard balls. Unfortunately, both he and the Dutch physicist, Christiaan Huygens, had discovered that under some circumstances light did not behave like a stream of little billiard balls at all. Two light beams slightly out of phase with one another could be made to interfere and produce an alternation of dark and light bands. This behaviour is characteristic of waves but not of particles. It can be explained by adding two waves so that the peaks of one wave match the troughs of the other. Newton had observed more colourful consequences of the wavelike behaviour of light, like those we see in the colours created when light passes through oil on the surface of water or scatters off a peacock’s tail.

  The most useful guide to the issue was the behaviour of sound. Sound is propagated from one point to another by means of undulations in the intervening medium. When we shout across the room it is the vibrations of the molecules of air that carry the energy that we call sound from one place to another. This picture was one that physicists focused upon when thinking about how light moved through empty space. Unfortunately, unlike heat and light, sound was not something that was transmitted through the jars of vacuum that Boyle and others had been producing. The extraction of the air from the vacuum tube removed the very medium whose vibration could convey its effects to distant places. Although we see the Sun and feel the heat that it radiates to us through the intervening ‘empty’ space we can’t hear anything that happens on the surface of the Sun, despite the fantastic violence of those events.

  Newton’s first attempt to draw these two properties of light together was to imagine that bullets of light must create waves by hitting the ether, just as throwing a stone into water creates a train of waves moving outwards from the impact point. The light would be able to set up an undulatory motion in the ether fluid. Gravity would accelerate them until the accelerating force became equal to the resisting force of the ether and then they would move with constant speed. However, light moves so rapidly that the accelerating force would need to be unrealistically large in order to accelerate the light particles up to 186,000 miles per second so quickly.

  Newton was never fully persuaded of the cogency of this ethereal picture and continued to pose questions about the propagation of light and gravity through space without ever convincingly answering them. Newton would not allow himself to lapse into the ancient delusion that some innate property of things called ‘gravity’ was responsible for the distant action of one mass on another (for this would explain nothing). In his famous correspondence with Richard Bentley5 about the ways in which his work on gravity and motion could lend support to a new form of Design Argument for the existence of God based upon the precision and invariance of the laws of Nature themselves, rather than the fortuitous outworkings of those laws, Newton revealed his puzzlement at the way gravity could apparently act through a vacuum:6

  “It is inconceivable, that inanimate brute matter should, without the mediation of something else, which is not material, operate upon, and affect other matter without mutual contact; as it must do if gravitation, in the sense of Epicurus be essential and inherent in it … That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers.”


  One can imagine how problematic Newton’s picture of forces acting instantaneously at a distance must have been for many of his contemporaries to accept. The rival theory of planetary motion in Newton’s time was the vortex theory of Descartes. It viewed the Universe as a great whirlpool of swirling particles whose actions upon one another were conveyed by physical contact (Figure 4.1). Descartes denied that a vacuum existed in space and filled it with a transparent fluid, matière subtile, which became a key part of the Cartesian world view.

  This picturesque swirling image of the Universe had far more popular appeal than Newton’s austere mathematical clockwork. Everyone had seen eddies of turbulent water. The analogy was familiar and convincing: stirring water in one part of the bath tub would propagate effects across the surface to other parts of the water. Descartes appeared to offer a plausible mechanism whereby the effects of gravity could be communicated through space. Yet Descartes’ theory failed. It could not explain the observed motions of the planets, enshrined in Kepler’s famous ‘laws’. It was a lesson on the difference between human conceptions of what looks ‘natural’ and what is natural.8

  Figure 4.1 René Descartes’ system of vortices (1636).7 Each vortex represents a solar system in a never-ending expanse of solar systems. The centres of the vortices (at the points marked S, E and A) are stars that are shining because of the turbulent motions of the vortices. The sinuous tube passing across the top of the picture is a comet that is moving too fast to be captured by any of the solar systems.