The Book of Nothing

by John D. Barrow

  You might not like it. You might wish that it would simply go away. But unfortunately, as yet, there seems to be no good reason to exclude it.

  Until quite recently, most physicists who worried about this problem were looking for a missing insight to prove that lambda must be zero. They were persuaded of the rightness of this approach by the unnatural situation that is created by the existence of a force like this that ‘just happens’ to become noticeable in the Universe around the epoch when we are living in the Universe, about fourteen billion years after the expansion began. But we have just witnessed a change of attitude. Astronomers have found strong evidence for the existence of a non-zero lambda force. Its size means that it has come to govern the rate at which the Universe is expanding at about the time when galaxies were still forming – what astronomers would call ‘quite recently’. From the theoretician’s point of view this is very odd. Lambda not only exists, but has a special value that makes it come into play near the epoch when life develops in the Universe. The only consolation is that, if these observations are correct, there is now a very special value of lambda to try to explain. The right explanation has a very particular target to shoot at. One can imagine a lot of spurious arguments that manage to ‘explain’ why lambda is zero but not so many that can come up with the unusual observed value.

  Inflation has solved a lot of our other puzzles; can it help us with lambda? Unfortunately, it is hard to see how inflation can help. We have already seen how the lambda stress is like a vacuum energy in the Universe. If we look at our potential energy landscape for the scalar field that is driving the inflationary expansion we can relate the presence of lambda to a special property of its topography. In the examples that we have drawn (like Figure 8.5, for example), the level of the minimum that defines the true vacuum state has been placed at a zero value. But there was no reason to do that. It was just artistic licence. The final minimum energy value could have been placed at any level above the zero line. Our knowledge of physics does not tell us where it should be. However, if this level is above the zero line, as in Figure 8.14, then it will leave an energy in the Universe that behaves exactly like the lambda stress. Its height above the zero line will determine the magnitude of the lambda force.

  When one looks at the numbers, the situation becomes even more perplexing. The effect of lambda grows steadily with respect to the familiar Newtonian force of gravity as the Universe gets bigger. If it is only recently becoming the dominant force, after billions of years of expansion of the Universe, it must have started out enormously smaller than the Newtonian force. The distance of that final minimum energy level in Figure 8.14 from the zero line in order to explain the value of lambda inferred from the supernova observations is bizarre: roughly 10−120 – that is, 1 divided by 10 followed by 119 zeros! This is the smallest number ever encountered in science.

  Figure 8.14 The height of the minimum above the zero line determines the residual value of the lambda stress in the Universe.

  Why is it not zero? How can the minimum level be tuned so precisely? If it were 10 followed by just 117 zeros, then the galaxies could not form. Extraordinary fine tuning is needed to explain such extreme numbers. And, if this were not bad enough, the vacuum seems to have its own defence mechanism to prevent us finding easy answers to this problem. Even if inflation does have some magical property which we have so far missed that would set the vacuum energy exactly to zero when inflation ends, it would not stay like that. As the Universe keeps on expanding and cooling it passes through several temperatures at which the breaking of a symmetry occurs in a potential landscape, rather like that which occurs in the example of the magnet that we saw at the beginning of the chapter. Every time this happens, a new contribution to the vacuum energy is liberated and contributes to a new lambda term that is always vastly bigger than our observation allows. And, by ‘vastly bigger’ here, we don’t just mean that it is a few times bigger than the value inferred from observations, so that in the future some small correction to the calculations, or change in the trend of the observations, might make theory and observation fit hand in glove. We are talking about an overestimate by a factor of about 10 followed by 120 zeros! You can’t get much more wrong than that.

  All our puzzles about whether or not lambda exists and, if so, what is responsible for giving it such a strange value, are like questions about the inflationary scalar field’s potential landscape. Why is its final vacuum state so fantastically close to the zero line? How does it ‘know’ where to end up when the scalar field starts rolling downhill in its landscape? Nobody knows the answers to these questions. They are the greatest unsolved problems in gravitation physics and astronomy. The nature of their answers could take many forms. There could exist some deep new principle that links together all the different forces of Nature in a way that dictates the vacuum levels of all the fields of energy that feel their effects. This principle would be unlike any that we know because it would need to control all the possible contributions to lambda that arise at symmetry breakings during the expansion of the Universe.19 It would need to control physics over a vast range of energies.

  Alternatively, there could be a less principled solution in which the lambda stress is determined completely randomly. Although huge values of lambda are the most probable and persistent, they give rise to a universe that expands too fast too early for stars and galaxies and astronomers ever to appear. If we were casting our eye across all possible universes displaying all possible values of the lambda stress, it could be that those, like our own, with outlandishly small values are self-selected from all the possibilities by the fact that they are the only ones that permit observers to evolve. In fact, if lambda were just one hundred to a thousand times bigger than the observations claim, the sequence of events that led to us might well be prevented. Bigger still and they definitely would be. This type of approach, while it may be true, can never predict or explain the exact value of lambda that we have observed, because life is not so sensitive to the value of lambda that, say, doubling its value would make life impossible.

  FALLING DOWNSTAIRS

  “… but we shall all be changed, in a moment, in the twinkling of an eye …”

  St Paul20

  The picture of many vacuums that may characterise the forces and interactions of Nature gives rise to the possibility of inflation. There are many options as to how the change from one ephemerally stable vacuum to another true vacuum might occur and we have no knowledge as yet of the identity of the scalar field which might be the culprit.21 In this way of looking at vacuum, we have so far imagined that the vacuum state in which we now find ourselves is a deep and stable one, a ‘true’ vacuum. The lowest of the low.

  What if we are not in such a vacuum basement? It is entirely possible that the state of the Universe in which we find ourselves is that of a temporarily stable, or ‘false’, vacuum. Instead of being on the ground floor of the vacuum landscape, we may be higher up, in a state that is only stable for a period of time. That period is pretty long, because the Universe seems to have possessed the same general laws and properties for about fourteen billion years. But one day things may change very suddenly, without the slightest warning. The situation could be like that pictured in Figure 8.15. If inflation left us lodged in on the shallow ledge in the potential landscape shown in Figure 8.15, then we might suddenly find ourselves nudged over the brink and on the way down to a lower minimum. That nudge might be supplied by very high energy events in the Universe. If collisions between stars or black holes generated cosmic rays of sufficiently high energies, they might be able to initiate the transition to the new vacuum in a region of space.22 The properties of the new vacuum will determine what happens next. We could find ourselves suddenly falling into a vacuum state in which all particles have zero mass and behave like radiation. We would disappear in a flash of light without warning.23 The way in which our form of biochemical life relies on rather particular coincidences between the strengths and properties of
the different forces of Nature means that any change of vacuum state would very likely be catastrophic for us. It would leave us in a new world where other forms of life might be possible but there is no reason why they should be a small evolutionary step away from our own biochemical forms.

  Figure 8.15 A potential energy landscape with many shallow minima may gradually evolve downstairs from one minimum to another over billions of years. We may not yet have reached the bottom.

  This picture of the vacuum landscape is a speculative one. We do not know the overall form of the landscape well enough to be able to tell whether we are already on the ground floor or whether there are other vacuums downstairs into which the states of matter in our locale can fall, either accidentally or deliberately. As one contemplates this radical possibility of an unannounced change in some of the basic properties of the forces of Nature, it is tempting to portray it as the ultimate extension of the idea of punctuated equilibrium that Niles Eldridge and Stephen Jay Gould24 have promoted. They proposed the course of biological evolution by natural selection on Earth proceeds by a succession of slow changes interspersed by sudden jumps rather than as a steady ongoing process. Indeed, we can characterise it as a movement through a landscape with many hills and valleys in which a force is dragging someone along. The pattern of change under these circumstances is for a slow climb up each hill but when the top is reached there will be a sudden jump across to the side of the next hill and another spell of steady hill-climbing (see Figure 8.16). If the Universe follows this lead there may be a shock for our descendants in aeons to come. As with the puzzle of why the lambda force should come into play so close to our time, so we might regard it as unlikely that the epoch at which the fall ‘downstairs’ could occur should be close to the time of human existence in the Universe – unless, of course, there is a link with lambda, or the presence of life can do something inadvertent to precipitate the great fall downstairs. Prophets of doom: do not give up hope.

  Figure 8.16 A typical evolution in a landscape with many minima when there is a force acting. The dog climbs the slopes slowly to the top and then suddenly jumps across to a point on the next ascent and begins slowly climbing uphill again.25

  BITS OF VACUUM

  “Cats, no less liquid than their shadows,

  Offer no angles to the wind.

  They slip, diminished, neat, through loopholes

  Less than themselves.”

  A.S.J. Tessimond26

  At the start of this chapter, we described a vacuum landscape which was three-dimensional. Imagine a Mexican hat with a shallow valley at the top of the hat and an entire circle of minima all at the same level at the bottom of the hat’s brim, as in Figure 8.2. It is possible to move around the circle of vacuum states in the trough at the bottom of the hat without changing energy. In 1972, the British physicist Tom Kibble27 realised that the possible existence of vacuums with continuous interrelationships of this sort meant that changes in their shape could occur as the Universe cooled, which would create structures in the Universe which retained memory of the energy of the Universe at the time when they formed. They are pieces of vacuum. Depending on the shape and pattern of the possible multiple vacuums they could have three simple forms. There can be lines of vacuum energy, either closed loops or never-ending lines, called ‘cosmic strings’.28 There can be sheets of vacuum energy which extend for ever, called ‘walls’, and there can be finite-sized spherical knots of vacuum energy called monopoles. The strings have a thickness given by the quantum wavelength corresponding to the energy of the Universe when the symmetry breaking that created them took place. Similarly, walls are sheets of vacuum energy with a thickness determined by this quantum wavelength.

  These three vacuum structures have proved to be perennially fascinating to astronomers ever since their possible existence was first recognised. It was soon realised that if they could exist then their impacts on the Universe are very different. Walls were only an optional structure in the theories of matter at very high energies that were being explored. This was fortunate because walls are a disaster for the Universe. A single vacuum wall stretched across the visible Universe would exert a devastating gravitational force on the expansion of the Universe and produce huge differences in the intensity of radiation from different directions in the Universe. Evidently, from our observations of the smoothness of the radiation and the expansion, we can conclude that we are not in the presence of cosmic domain walls. This deduction is an example of how an astronomical observation can provide a constraint on the possible properties of the unified theory of the forces of Nature at very high energies which are beyond the reach of the energies attainable by direct experiments.

  The next candidate to be considered is the monopole. These are far more problematic. Unlike walls, monopoles appeared to be inevitable in any reasonable theory of how the Universe changed from the hightemperature environment of the Big Bang to the present low-temperature world that we inhabit. If the forces of electricity and magnetism are to exist in our world today then monopoles must be formed in the early Universe. Alas, their presence is another potential disaster. A monopole should form inside every region that light signals have had time to cross from the beginning of the expansion of the universe to the time when the monopoles can appear. Such regions are very small because monopoles are very massive by the standards of elementary particles, and appear in pairs when the universe is very energetic and very young. This means that the region of the universe that eventually expands to become the fifteen-billion light-year expanse that we call the visible Universe today will contain a huge number of these monopoles. When we add up the masses of all the monopoles that we should find, their total mass turns out to be billions of times greater than that of all the stars and galaxies put together. This is not the Universe that we live in. Indeed, it is not a universe that we could live in.

  In the mid-1970s, this ‘monopole problem’ was a serious dilemma for physicists trying to develop a unified theory of the different forces of Nature. The candidate theories had many attractive features that offered explanations for particular properties of the Universe, most notably why it displayed such an overwhelming excess of matter over antimatter. But they all predicted a monopole catastrophe. Experimental physicists, on the other hand, didn’t see these monopoles. What happened to them?

  It was this problem that first led Alan Guth, then at Stanford University, to the theory of the inflationary Universe. He saw that initiating a period of accelerated expansion would solve the monopole problem in the same way that it solved the problem of the smoothness of the Universe. The inflationary surge of acceleration enabled the whole of our visible Universe to expand from a region that was once small enough for light signals to keep it smooth and coordinated except for the small zero-point fluctuations. A monopole forms every time a mismatch occurs in the direction in which vacuum energy fields are pointing when the universe cools to the energy level of the monopoles. Mismatches produce ‘knots’ in the vacuum energy that manifest themselves as monopoles. These knots can only be ironed out over regions that are small enough for light signals to traverse in the time before the appearance of the monopoles. Guth saw that inflation would enable the whole of our visible Universe today to be encompassed by a region that was once small enough to contain perhaps only one knot of vacuum energy and a single monopole. Their effect on the expansion of our visible Universe would then be utterly negligible and we have a natural explanation for the mysterious cosmic scarcity of monopoles.

  What Guth was proposing was that the monopoles are not prevented from forming (as many others were trying to find ways of demonstrating at the time), nor were they annihilated in some way after they formed (as others had also tried to show): they are just moved so far by the expansion that they are beyond the horizon of our visible Universe today. Just as the smoothness of our visible Universe is a reflection of the smoothness of the small domain from which it inflated so its lack of monopoles derives from the smooth, unknotted
character of the vacuum fields within the same domain.

  Historically, the prime motivation for devising the theory of inflation was the resolution of the monopole problem. An added initial bonus was to provide an explanation for the smoothness and flatness of the visible Universe. However, as time has gone on, the focus of interest has switched to the prediction of inflation that the zero-point fluctuations will be inflated to produce little irregularities from which galaxies can form, for it is here that a critical observational test of the theory will soon be made.

  This leaves one more vacuum structure for us to evaluate: the strings. Cosmic strings turn out to be far more interesting than walls or monopoles. Whereas walls and monopoles both threaten to overpopulate the Universe with unwanted mass, and have to be eradicated early on, cosmic strings are more subtle. They will start by threading the Universe with a great network of lines of vacuum energy, like a web of cosmic spaghetti. As the expansion of the Universe proceeds, the network behaves in a complicated fashion. Whenever intersections of string occur, the string reorganises itself by exchanging partners, as shown in Figure 8.17.

  The trend is for the network to produce lots of little loops of string at the expense of long lines of string that run across the Universe. Once a small loop is formed it is doomed to dissolve. It will oscillate and wriggle, gradually radiating all its energy away in the form of gravitational waves. If we think of Einstein’s picture of curved space, then the wiggling of the loops of string creates ripples in the geometry, which spread out at the speed of light, taking away the string’s energy like waves on a pond surface. In Figure 8.18 a computer simulation of an expanding box of cosmic strings is shown.

  The behaviour of the string network over the history of the Universe is tantalising. It appears that the presence of the loops and lines of string energy can act as seeds around which fluctuations in density can start to develop and from which ultimately galaxies might form. However, it is very difficult to calculate what would happen in detail. A host of complicated processes come into play and the fastest computers in the world are still unable to follow all these processes quickly and accurately enough to determine whether strings can produce real galaxies clustered in the patterns that we see. The acid test of such a theory is again provided by the pattern of fluctuations in the microwave radiation left over from the Big Bang. The gravitational field created by the evolving network of strings will leave its characteristic imprint in this radiation. It appears to have a signature that is quite different from that left by the inflated zero-point fluctuations which provide the rival theory. But not everyone agrees. So far, if the string predictions have been correctly calculated, the evidence of the ground-based detectors is beginning to turn against them, but it is early days. The predictions need to be more fully worked out by bigger computer simulations and elaborated, and only the satellite observations will be fully convincing checks.