The Book of Nothing

by John D. Barrow

These possibilities created considerable uncertainty for cosmologists until the mid-1960s. They were removed by an approach pioneered by Roger Penrose.32 He looked at the problem in a new way and considered the collection of all possible histories that were possible for all particles of matter and light rays. Bypassing all the problems of the shape and uniformity of the Universe and the ways of measuring time, Penrose showed that if Einstein’s theory is true, if time-travel is impossible, and gravity is always attractive, then so long as there is enough gravitating matter and radiation in the Universe, at least one of that collection of histories must have had a beginning – it cannot be continued indefinitely into the past. Observations showed that there was easily enough matter to meet the last condition33 and all forms of matter then known or hypothesised exhibited gravitational attraction.

  This deduction was remarkable in many respects. It managed to come up with such a strong and general conclusion because it gave up the idea that it was the infinite density – the ‘Big Bang’ itself – that characterised the beginning of a universe. Instead, it employed the simpler and more relevant idea of a history with a beginning – that the universe of space and time had an edge. It might be that the histories with a beginning are accompanied by infinite densities but that is a quite separate, and much more difficult, question which is still not fully answered.34 Also, it is only demanded that one past history have a beginning, not all of them. The simple expanding universes which describe our Universe so well today have the property that all the histories come to an end simultaneously at a finite time in the past when the density becomes infinite. Penrose’s approach tells us nothing about the nature of the beginning of the histories, only that they must occur when the assumptions he makes hold good.

  The interesting thing about the singularity that is predicted by these theorems is that there is no explanation as to why it occurs. It marks the edge of the Universe in time (see Figure 9.2). There is no before; no reason why the histories begin; no cause of the Universe. It is a description of a true creation out of nothing.

  Figure 9.2 Singularities are part of the edge of space and time. If we represent space-time as a sheet then this edge can be at places where the density of matter becomes infinite or even places where it remains finite because there are ‘holes’ in the sheet.

  These developments led to considerable interest amongst theologians and philosophers of science,35 who saw it as a demonstration that the Universe did have a beginning in time. From the mid-1960s until about 1978 these mathematical theorems were widely cited as evidence that the Universe had a beginning. However, it is important to realise that they are mathematical theorems not cosmological theories. The conclusions follow by logical deduction from the assumptions. What are those assumptions and should we believe them? Unfortunately, the two central assumptions are now not regarded as likely to hold good. We expect Einstein’s equations of general relativity to be superseded by an improved theory that successfully includes the quantum effects of gravitation. This new theory will have the property of becoming just like Einstein’s theory when densities are low, as they are now in the Universe. Indeed, recent superstring theories of elementary particles and gravity, which are the favourite candidates for an ultimate theory of all the forces of Nature, have the nice property of reducing to Einstein’s equations in a low-energy environment. It is widely expected that this new improved theory will not contain the singular histories that characterised Einstein’s theory, but until we have the new theory we cannot be sure.

  There is a more straightforward objection to the deduction of a beginning using the theorems of Penrose and Hawking. The central assumption is that gravity is always an attractive force. When the theorems were first proved this was regarded as an extremely sound assumption and there was no particular reason to doubt it. But things have changed. The rapid progress in our understanding of particle physics theories and the ways in which the forces of Nature are linked together has shown that we should expect Nature to contain forms of matter which respond repulsively to gravitational fields. Moreover, these fields are very appealing. They include amongst their number the scalar fields which drive inflation. Indeed, the whole process of inflation, through which the expansion of the Universe can be accelerated, is a consequence of the repulsive gravitational action of these fields. As a result, there has been a sea change in attitudes. Whereas up until the late 1970s it was widely accepted that all matter in the Universe should exhibit gravitational attraction and the assumptions of the singularity theorems hold good, since 1981 exactly the opposite has been believed: that it is unlikely and undesirable that all matter displays gravitational attraction. Indeed, the recent observations of the acceleration in the expansion of the Universe today, if correct, demonstrate that there exists matter which displays gravitational repulsion. It is the cosmological vacuum energy that contributes a repulsive lambda force to the gravitational force of Newton.36

  The logic of the singularity theorems is that if their assumptions hold then there must be a singularity in the past. If the assumptions do not hold, as we now believe is most likely, then we cannot conclude that there is no beginning – only that there is no theorem. Some universes with gravitationally repulsive matter still have beginnings where the density is infinite, but they don’t need to. We have already seen one spectacular example that appears to evade the need for a beginning. The self-reproducing eternal inflationary universe almost certainly has no beginning. It can be continued indefinitely into the past.

  Thus the old conclusions of the singularity theorems are no longer regarded by cosmologists as likely to be of relevance to our Universe. Crucial assumptions in those theorems – the attractive nature of gravitation, and the truth of Einstein’s general theory of relativity all the way back to the earliest times when energies are so high that quantum gravitational effects must intervene – are no longer likely to be true. What are the alternatives?

  NO CREATION OUT OF ANYTHING?

  “We are the music-makers

  And we are the dreamers of dreams,

  Wandering by lone sea-breakers,

  And sitting by desolate streams;

  World-losers and world-forsakers,

  On whom the pale moon gleams:

  Yet we are the movers and shakers

  Of the world forever, it seems.”

  Arthur O’Shaughnessy, ‘Ode’

  If the whole expanding Universe of stars and galaxies did not appear spontaneously out of nothing at all, then from what might it have arisen? One option that has an ancient pedigree is that it had no beginning. It has always existed. A persistently compelling picture of this sort is one in which the Universe undergoes a cyclic history, periodically disappearing in a great conflagration before reappearing phoenix-like from the ashes.37 This scenario has a counterpart in modern cosmological models of the expanding universe. If we consider closed universes which have an expansion history that expands to a maximum and then contracts back to zero (see Figure 9.3), then there is a tantalising possibility. Here, we see a one-cycle universe that begins at a singularity and ends at one.38 But suppose the Universe re-expands and repeats this behaviour over and over again. If this can happen then there is no reason why we should be in the first cycle. We could imagine an infinite number of past oscillations and a similar number to come in the future. We are ignoring the fact that a singularity arises at the start and the end of each cycle. It could be that repulsive gravity stops the Universe just short of the point of infinite density or some more exotic passage occurs ‘through’ the singularity, but this is pure speculation.

  This speculation is not entirely unrestrained, though. Let us assume that one of the central principles governing Nature, the second law of thermodynamics, which tells us that the total entropy (or disorder) of a closed system can never decrease, governs the evolution from cycle to cycle.39 Gradually, ordered forms of matter will be transformed into disordered radiation and the entropy of the radiation will steadily increase. The result is to
increase the total pressure exerted by the matter and radiation in the Universe and so increase the size of the Universe at each successive maximum point of expansion,40 as shown in Figure 9.4. As the cycles unfold they get bigger and bigger! Intriguingly, the Universe expands closer and closer to the critical state of flatness that we saw as a consequence of inflation. If we follow it backwards in time through smaller and smaller cycles it need never have had a beginning at any finite past time although life can only exist after the cycles get big enough and old enough for atoms and biological elements to form.

  Figure 9.3 A one-cycle closed universe.

  For a long time this sequence of events used to be taken as evidence that the Universe had not undergone an infinite sequence of past oscillations because the build-up of entropy would eventually make the existence of stars and life impossible41 and the number of photons that we measure on average in the Universe for every proton (about one billion) gives a measure of how much entropy production there could have been. However, we now know that this measure does not need to keep on increasing from cycle to cycle. It is not a gauge of the increasing entropy. Everything goes into the mixer when the Universe bounces and then the relative number of protons and photons gets set by physical processes that occur early on. One problem of this sort might be that of black holes. Once large black holes form, like those observed at the centres of many galaxies, including the Milky Way, they will tend to accumulate in the Universe from cycle to cycle, getting ever more massive until they engulf the Universe, unless they can be destroyed at each bounce or become separate ‘universes’ which we can neither see nor feel gravitationally.

  Figure 9.4 A many-cycle closed universe in which the cycles increase in size.

  A curious postscript to the story of cyclic universes was recently discovered by Mariusz Dbrowski and myself. We showed that if Einstein’s lambda force does exist then, no matter how small a positive value it takes, its repulsive gravitational effect will eventually cause the oscillations of a cyclic universe to cease. The oscillations get bigger and bigger until eventually the Universe becomes large enough for the lambda force to dominate over the gravity of matter. When it does so, it launches the Universe off into a phase of accelerating expansion from which it can never escape unless the vacuum energy creating the lambda stress were to decay away mysteriously in the far future (see Figure 9.5). Thus the bouncing Universe can eventually escape from its infinite oscillatory future. If there has been a past eternity of oscillations we might expect to find ourselves in the last ever-expanding cycle so long as it is one that permits life to evolve and persist.

  Figure 9.5 A many-cycle universe is eventually transformed into an expanding universe by the presence of a lambda force.

  Another means by which the Universe can avoid having a beginning is to undergo the exotic sequence of evolutionary steps created by the eternal inflationary history that we explored in the last chapter. There seems to be no reason why the sequence of inflations that arise from within already inflating domains should ever have had an overall beginning. It is possible for any particular domain to have a history that has a definite beginning in an inflationary quantum event, but the process as a whole could just go on in a steady fashion for all eternity, past and present.

  One of the most interesting features of research efforts in modern cosmology is the way in which the creation-out-of-nothing tradition influences the direction in which cosmologists look for mathematical models of the early Universe. The singularities predicted by the theorems of Hawking and Penrose in the 1970s were happily accepted by many cosmologists as a real prediction of Einstein’s theory of gravitation, even though they were really just predicting that the theory had to cease being a good descriptor of the Universe at some finite time in the past, when densities became too high for the quantum effects of gravity to be ignored any longer. In other areas of physics, the appearance of predictions that physically measurable quantities become infinite is always a signal that the theory has ceased to be applicable to the circumstance to which it is being applied. A refinement is necessary to make the equations applicable to a wider range of physical phenomena. Yet the appearance of an infinity in the density of matter and a beginning to space and time was regarded as acceptable to many scientists. The breakdown of prediction was often interpreted as a consequence of the Universe having a beginning rather than as an incompleteness of the theory. This is perhaps because the picture created by having a ‘beginning’ for the Universe is one with which most Westerners feel comfortable because of the religious traditions in which they have been raised.

  For similar reasons, there often seems to be more opposition to the idea of a universe that has always existed. The steady-state cosmology of Herman Bondi, Fred Hoyle and Thomas Gold attracted much opposition from scientists and non-scientists alike. That opposition came from opposite ends of the religious spectrum. Some Christians opposed it because it denied the reality of sudden creation out of nothing whilst the Stalinist regime in the Soviet Union disliked it because it denied the possibility of progress and evolution towards a better world.

  At first, the absence of a beginning appears to be an advantage to the scientific approach. There are no awkward starting conditions to deduce or explain. But this is an illusion. We still have to explain why the Universe took on particular properties – its rate of expansion, density, and so forth – at an infinite time in the past.

  There are several specific candidates for the something out of which the present expansion of the Universe might have emerged. Figure 9.6 shows some of the alternatives. They are very different conceptually and in their metaphysical ramifications, but they are all entirely compatible with all our observations of the Universe’s current and past behaviour.

  Figure 9.6 Some of the different ‘beginnings’ to our Universe that are consistent with observations of its present state.

  THE FUTURE OF THE VACUUM

  “Then star nor sun shall waken,

  Nor any change of light:

  Nor sound of waters shaken,

  Nor any sound or sight:

  Nor wintry leaves nor vernal,

  Nor days nor things diurnal,

  Only the sleep eternal

  In an eternal night.”

  Algernon Swinburne42

  We have seen how the vacuum energy of the Universe may prevent the Universe from having a beginning, may influence its early inflationary moments and may be driving its expansion today, but its most dramatic effect is still to come: its domination of the Universe’s future. The vacuum energy that manifests itself as Einstein’s lambda force stays constant whilst every other contribution to the density of matter in the Universe – stars, planets, radiation, black holes – is diluted away by the expansion. If the vacuum lambda force has recently started accelerating the expansion of the Universe, as observations imply, then its domination will grow overwhelming in the future. The Universe will continue expanding and accelerating for ever. The temperature will fall faster, the stars will exhaust their reserves of nuclear fuel and implode to form dense dead relics of closely packed cold atoms and concentrated neutrons, or large black holes. Even the giant galaxies and clusters of galaxies will eventually follow suit, spiralling inwards upon themselves as the motions of their constituent stars are gradually slowed by the outward flow of gravitational waves and radiation. All their stars will be swallowed up in great central black holes, growing bigger until they have consumed all the material within reach. Ultimately, all these black holes will evaporate away by the Hawking evaporation process, producing a universe that contains a sea of non-interacting, fairly structureless collections of stable elementary particles and radiation. Or perhaps they do not evaporate completely, but leave a tiny relic of stable matter, or something more exotic, like a wormhole connection into another universe (or another part of our own Universe), or even a true singularity. Nobody knows.

  The most fascinating thing about the cosmic vacuum energy is that, ultimately, it wins out over
all other forms of matter and energy in the struggle to determine the shape of space and the rate of expansion of the universe. No matter what the structure of the universe in its earlier days before the vacuum energy comes to dominate, just as all ancient roads led to Rome so all ever-expanding universes approach a very particular accelerating universe, called the de Sitter universe after Willem de Sitter, the famous Dutch astronomer who discovered it was a solution of Einstein’s theory of general relativity in 1917. It is distinguished by being the most symmetrical possible universe.

  This property of an accelerating universe, that it loses all memory of how it began, is sometimes called the ‘cosmic no hair property’. This curious terminology is chosen to capture the fact that all the accelerating universes become the same: they retain no individual distinguishing features (hairstyles, metaphorically speaking). This inexorable slide towards the same future state signals that there is a loss of information taking place when the universe starts accelerating. The expansion is so fast that the information content of signals sent across the universe gets degraded as fast as possible. Everything looks smoother and smoother; all differences in the rate of expansion from one direction to another are expunged at a rapid rate; no new condensations of matter can appear out of the cosmic matter distribution; local gravitational pull has lost the last battle with the overwhelming repulsion of the lambda force.

  This has important consequences for any consideration of ‘life’ in the far future. If life requires information storage and processing to take place in some way, then we can ask whether the Universe will always permit these things to occur. When the vacuum energy is not present, and so the expansion does not ultimately accelerate, Freeman Dyson,43 Frank Tipler and I44 showed that there are a range of possibilities open for this rather basic form of ‘life’ to perpetuate itself. It can store information in elementary-particle states that are vastly better information storage repositories than those used for storing data in our present computers. In order to continue to process information indefinitely, living systems need to create and sustain deviations from perfect uniformity in the temperature and energy of the Universe.45 This may always be possible when the accelerating vacuum energy is not present. Tiny deviations in the way in which the Universe is expanding from one direction to another can be exploited to make radiation cool at slightly different rates in different directions. The gradient in temperature thereby created can then be used to do work or process information. This does not, of course, mean that life in any shape or form will survive46 for ever, let alone that it must survive for ever, merely that it is logically and physically possible given the known laws of physics in the absence of a vacuum energy permeating the Universe.