The Book of Nothing

by John D. Barrow

  Evidence has steadily mounted to such an extent that the existence of black holes is regarded as established beyond all reasonable doubt by astronomers. The trick is to catch a black hole in orbit around another luminous star.44 The orbit of the visible star will betray the presence of an unseen companion and the star will have material steadily pulled from its outer regions by the companion’s gravitational pull. This material will be heated to millions of degrees Kelvin as it swirls down into the plughole produced by the black hole. At these temperatures there will be a profuse emission of X-rays from the heated material, colliding with other particles, on its inspiralling trajectory. When it nears the horizon surface the wavelength of the flickering of these X-rays will tell us the size of surface they are disappearing into. Black holes have a very particular relationship between their mass and the size of their event horizon. The information obtained from the motion of the visible star and the flickering of the X-rays enables this relationship to be checked. A number of such ‘X-ray binary systems’ are now known and they provide very strong evidence that black holes result when very massive stars end their careers and collapse in upon themselves.

  Up until 1975 this picture of black holes was regarded as the full story. Things went into black holes. They never came out. But then the picture changed in a dramatic way. Stephen Hawking45 asked what would happen if a black hole was placed in a quantum vacuum. Remember what we have just seen when the Casimir plates are placed in a quantum vacuum. The sea of vacuum fluctuations of all wavelengths is affected. Now imagine what would happen if a black hole were introduced. If a virtual particle-antiparticle pair appeared very close to the horizon then one of the particles could fall inside the horizon surface while the other stayed outside. The virtual particles would become real; the outgoing particle would be detected by a distant observer and the black hole would appear to be radiating particles from all over its horizon surface.46 This process should be happening continuously and the net result is that all black holes will slowly evaporate away. Black holes are not truly ‘black’ when the quantum vacuum is taken into account. Further investigation revealed that the radiation of vacuum particles followed the laws of black-body thermodynamics originally discovered by Planck. Black holes were black bodies. Sadly, the rate at which particles are expected to be radiated is very slow when black holes are as large as those seen in X-ray binary star systems. In order for Hawking’s radiation process to be visible,47 we would have to encounter black holes which are only about the mass of a large mountain or asteroid. Their horizon size is equal to that of a single proton! These ‘mini’ black holes cannot form today when stars die. But they can be formed in the dense environment of the Big Bang if it is irregular enough. If they were, then these mountain-sized black holes would be in the final stages of evaporation today. The climax of the process will be a dramatic explosion that would show up as a burst of high-energy gamma rays accompanied by radio waves arising from the fast-moving electrons emerging from the explosion at speeds close to that of light. They would radiate 10 gigawatts of gamma-ray power for a period of more than forty billion years and could be seen many light years away. Radio telescopes could see the radio waves from one of these atomic-sized explosions occurring two million light years away in the Andromeda galaxy.

  Observers have searched for evidence of black-hole explosions but none has yet been found. All we can say is that if exploding mini black holes do exist then they are few and far between, with no more than one occurring per year in every sphere of space, one light year in diameter.

  The Hawking radiation process is of great significance for our understanding of the way in which the great laws underlying Nature are interwoven. It is a unique example of a process which is both relativistic, quantum, gravitational, and thermodynamic. Again, we see that its existence is a direct consequence of the reality of the vacuum and the sea of fluctuations within it. The steep gradient in the gravitational force field near the horizon of the black hole pulls the virtual pairs apart and prevents them annihilating back into the vacuum. They become real particles at the expense of the energy of the gravitational field of the black hole.48

  In this chapter we have seen the vacuum move to centre stage in our story. Its existence and universality turn out to underlie the workings of all the forces of Nature. It influences the strengths of the electromagnetic, weak and strong forces of Nature, and links the force of gravity to the quantum character of energy. Each of these influences provides us with observational evidence for the reality of the quantum vacuum and the fluctuations that support it. These successes have flowed from a new conception of the vacuum that gives up the ancient picture of the vacuum as completely empty space. In its place is the more modest view that the vacuum is what is left when everything is removed from space that can be removed. What is left is the lowest energy state available. Remarkably, this means that the vacuum might change, steadily or suddenly. If it does then it can alter the complexion of the entire Universe. In the next chapter we see how.

  “Why is there only one Monopolies Commission?”

  Screaming Lord Sutch1

  VACUUM LANDSCAPE APPRECIATION

  “The Grand Old Duke of York

  He had ten thousand men,

  He marched them up to the top of the hill,

  And he marched them down again.”

  Nursery Rhyme

  The subtleties and unexpected properties of the quantum vacuum elevated it to play a leading role in fundamental physics in the mid-1970s. Since then its position has become increasingly wide-ranging and pivotal. Every day sees new research papers about some aspect of the vacuum posted on the electronic web sites that physicists use to announce their new work to colleagues all over the world.2 What has given rise to this explosion of interest? The adoption of a definition of the vacuum that requires it to be only a state of minimum energy is the answer. It immediately opens up a number of extraordinary possibilities.

  The first question that we might pose about the vacuum as minimum energy state is, ‘Why should there be only one of these minimum energy states?’ The energy ‘landscape’ could contain many undulations, valleys and hills, just like a real terrain. These undulations could be very regular, like a corrugated roof or an egg box, with many different minima, each having the same minimum value for the energy (see Figure 8.1). This scenario suggests two new possibilities: if there can be many vacuums then we have to decide in which one of them our Universe is going to end up; also, we would like to know if it is possible to change vacuums in some way, by jumping from one minimum to the other.

  In the example we have drawn in Figure 8.1, the different vacuums correspond to minima of the same depth. We could add a further dimension of possible variation to the situation by marking the position of the vacuum on a two-dimensional surface and its depth by the height above it. This is like a real landscape on the Earth’s surface in which the height above or below sea level defines the altitude at each location. When this extra dimension is added it becomes possible for a continuous line of points to be vacuums at the same height for the system. A simple example is shown in Figure 8.2, where the vacuums form a ring on the floor. In the middle of the ring is a maximum so that the overall shape of the energy landscape is rather like a Mexican hat.

  We can imagine still more unusual situations. We have drawn all the minima to lie at the same levels but there is no need for this. The vacuums are just defined by the presence of a local minimum in the landscape. There is no reason why they all need to be at the same level. If there is one which has a lower energy value than the others we will call it the ‘true’ or ‘global’ vacuum. Also, the minima can differ in other, more subtle respects. The curvature of the terrain in their immediate vicinities can be different (see Figure 8.3). So, the terrain can rise steeply or gradually as we move away from the minimum. If you find yourself in a steep-sided vacuum it will be harder to escape compared than from the shallow-sided sort.

  Figure 8.1 A vacuum landscape
with many local minima of equal depth.

  Figure 8.2 A continuous circle of minima of the same depth.

  When we looked at some of the effects of vacuum polarisation on the strengths of the measured forces of Nature in the last chapter we saw how the temperature of the environment in which forces act matters. Thus we might well expect that our energy landscapes depend on temperature. As the temperature changes, the shape of the landscape can change very significantly. Both the number of vacuums may change as well as their depths. Some can even cease to be minima if the landscape changes very dramatically.

  An interesting example of this process is provided by magnetism. The magnetisation energy of a bar of iron has a pattern of variation that is strongly dependent upon the temperature of the metal. When an iron bar is heated above a particular temperature of 750 degrees Celsius, called the Curie temperature, it displays no magnetic properties. There is no North and South magnetic pole on the bar. The high temperature has randomised the directions of all the atomic configurations in the iron and so there is no overall directionality to the bar’s properties. As the bar is allowed to cool below the Curie temperature a spontaneous magnetisation takes place: the bar ends up with a North magnetic pole at one end and a South magnetic pole at the other. If you repeat this heating and cooling process a number of times you will not necessarily find that the North magnetic pole always lies at the same end of the magnet. We can understand what is happening by looking at the energy landscape above and below the Curie temperature as shown in Figure 8.4.

  Figure 8.3 Landscape with different minima and different gradients.

  Above the Curie temperature, there is a single minimum vacuum state for the bar. It is symmetrically placed with the minimum at zero so there is no preference for one direction (right) of the bar over another (left). The minimum is a steep-sided valley into which everything will roll no matter where it starts out up the valley and this tells us that it doesn’t matter how our piece of iron started out. Once it is hot enough it will enter this minimum unmagnetised state and lose memory of any previous magnetised state. However, as the bar cools below the Curie temperature something unusual happens. The magnetisation-energy landscape changes from having a single central valley into one with two valleys and a peak in between. The original minimum has turned into a precarious maximum, whilst two new deeper minima have appeared, equidistant on either side of the central maximum. What does this mean for our iron bar? It means that the symmetrical unmagnetised state has become unstable. The system will roll off down into one of the two new minima. There is an equal chance of going either way and this corresponds to the bar being magnetised with the right-hand end or the left-hand end as the magnetic North pole of the resulting bar magnet. This transition from a state where the minimum that the system resides in is symmetric about the zero value to one in which it is asymmetrical is a common phenomenon in Nature and it is called symmetry breaking.

  Figure 8.4 The variation of magnetisation of a metal bar with temperature. (a) Above a critical temperature there is a single stable minimum (P) with no preferred directions. (b) Below the critical temperature two minima of equal depth appear and the previous stable minimum turns into an unstable maximum. A point located there will eventually roll into one of the two asymmetrical minima (P and P′) and the bar will have a magnetic North pole at one end and a magnetic South pole at the other.

  The phenomenon of symmetry breaking reveals something deeply significant about the workings of the Universe. The laws of Nature are unerringly symmetrical. They do not have preferences for particular times, places and directions. Indeed, we have found that one of the most powerful guides to their forms is precisely such a requirement. Einstein was the first to recognise how this principle had been used only partially by Galileo and Newton. He elevated it to a central requirement for the laws of Nature to satisfy: that they appear the same to all observers in the Universe, no matter how they are moving or where they are located. There cannot be privileged observers for whom everything looks simpler than it does for others. To countenance such observers would be the ultimate anti-Copernican perspective on the Universe.3 This democratic principle is a powerful guide to arriving at the most general expression of Nature’s laws. Yet, despite the symmetry of the laws of Nature, we observe the outcomes of those symmetrical laws to be asymmetrical states and structures. Each of us is a complicated asymmetrical outcome of the laws of electromagnetism and gravity. We occupy particular positions in the Universe at this moment of time even though the laws of gravity and electromagnetism are completely democratic with respect to positions in space. One of Nature’s deep secrets is the fact that the outcomes of the laws of Nature do not have to possess the same symmetries as the laws themselves. The outcomes are far more complicated, and far less symmetrical, than the laws. Consequently, they are far more difficult to understand. In this way it is possible to have a Universe governed by a very small number of simple symmetrical laws (perhaps just a single law) yet manifesting a stupendous array of complex, asymmetrical states and structures that might even be able to think about themselves. In the last decade, there has been an enormous upsurge of interest in trying to understand the asymmetrical outcomes of symmetrical laws. The availability of inexpensive fast computers has greatly facilitated this activity because the complexities of the asymmetrical outcomes are generally too great for unaided human calculation to reveal what is happening in full detail.

  THE UNIFICATION ROAD

  “Encyclopaedia Britannica full set, no longer needed due to husband knowing everything.”

  Personal ad, Lancashire Post4

  The joining together of the forces of Nature is made possible by the variation in their strengths as the temperature rises. This process sees a coming together first of the electromagnetic and weak forces to create a single electroweak force when temperatures reach about 1015 degrees Kelvin. If we carry on charting the strengthening of this force together with the weakening of the strong force, then a second unification is implied when temperatures reach a level of about 1027 degrees Kelvin. Above this so-called ‘grand unification’ temperature there is a single symmetrical force, but below it there is a breaking of this symmetry to create the different strong and electroweak forces.5

  This change of symmetry as the temperature falls will be reflected in the behaviour of all the material in the Universe during its very early stages. We can imagine the Universe expanding away from a Big Bang where the initial temperatures and energies are high enough to maintain complete unification of the strengths of the strong and electroweak forces. As the temperature falls below a particular value, these forces separate and go their different ways.

  This perspective upon the change of forces during the very early Universe focused the attention of high-energy physicists and cosmologists upon some of the unusual things that might happen if these changes occurred in special ways. In particular, if the elementary particles in the Universe underwent a change of vacuum state, from a high to a low level, then it could make the whole Universe behave in novel and very attractive ways.

  In gradually exploring the ramifications of these ideas for the Universe, interest has focused upon the consequences of a hypothetical type of matter existing in the early Universe. In order to avoid being too specific we call this a ‘scalar’ field. This means that at any point of space, and at any time, this field has only one attribute – its magnitude or intensity (a ‘scale’). For example, the density of printer’s ink on this page is a scalar field. The temperature in a room is a scalar field. But wind velocity is not a scalar because it is determined by a magnitude and a direction at every point and moment of time.

  In the earliest stages of the Universe’s history the temperature will be very much higher than today and we could expect new forms of matter to be formed which possess a diverse range of vacuum landscapes. Let’s pick on one of these energy fields. This field could have any number of vacuum states of different levels. It need not correspond exactly to any
field that we can observe today because it could have decayed away into radiation and other particles during the early stages of the Universe but, ultimately, our unified theory of all the forces of Nature should tell us what it is. Fields like this will possess two types of energy: a kinetic part associated with their motion, and a potential energy associated with their location. A simple analogy is provided by a swinging clock pendulum. When the bob is swinging through its lowest point it is moving at its fastest and its energy is entirely kinetic. As it rises up to its highest point it gradually slows down: its kinetic energy is transformed into potential energy as the bob works to overcome the downward force of gravity. Momentarily, when it stops at its highest point, before beginning its downward motion, its energy is entirely potential.

  Energy fields in the early Universe can behave like the pendulum. When the kinetic part of the energy is the largest, the field will change very quickly, but when the potential energy is largest it will change very slowly. Now suppose that the types of changes in the potential shape that we have just been looking at could come into play during the first moments of the Universe’s expansion. The scalar field could begin at high temperatures in a single stable vacuum state like that shown in Figure 8.5, but when the temperature falls below a particular value, Tc, a new vacuum state could appear at much lower energy.