The Book of Nothing: Vacuums, Voids, and the Latest Ideas about the Origins of the Universe - John D. Barrow (2002)

Chapter 9. The Beginning and the End of the Vacuum

“It has indeed been said that the highest praise of God consists in the denial of him by the atheist, who finds creation so perfect that it can dispense with a creator.”

Marcel Proust1

BEING OUT OF NOTHINGNESS

“The human race, to which so many of my readers belong, has been playing at child’s games from the beginning … The players listen very carefully and respectfully to all that the clever people have to say about what is to happen in the next generation. The players then wait until all the clever men are dead and bury them nicely. They then go and do something else. That is all. For a race of simple tastes, however, it is great fun.”

G.K. Chesterton2

Why is there something rather than nothing? Some regard such questions as unanswerable, some go further to claim that they are meaningless, whilst others claim to provide the answers. Science has proved a reasonably effective way of finding out about the world because it confines itself, in the main, to questions about ‘how’ things happen. If it does ask the question ‘why’ it is generally about an aspect of things that can be answered if one is in possession of a full description of how a certain sequence of events occurs, what causes what, and so on. As one digs deeper to the roots of scientific theories one finds that there is a foundation of a sort that we call laws of Nature, which govern the behaviour of the most elementary particles of Nature. The identities of these particles, the things they are able to do, and the ways in which they can combine are like axioms whose consequences we can test against the facts of experience. To some extent we may find that it is very difficult to imagine how things could be otherwise because the properties of the laws become closely bound up with the nature of the populations of identical elementary particles that they govern. Some laws only act upon particles with particular attributes. But in other respects it is possible for us to envisage a universe that was slightly different from our own. So far, we have not found a theory that requires there to be only one possible universe. This question boils down to one about the nature of the vacuum landscape for the ultimate theory of the Universe. If there is a single valley in this landscape, then there is a single possible vacuum state and one possible set of values for the constants of Nature that define it. If there are many valleys, and so many vacua, then the constants of Nature are not uniquely specified by one possibility. They can exist with different values and, as we have seen in the last chapter, they may even do so elsewhere in our Universe now. Hence there has emerged a more modest version of the great ontological question, ‘Why is there something rather than nothing?’ which physicists are able to comment on in a meaningful way. From their perspective, certain aspects of the world may be inevitable or be necessary features of any universe that is going to contain living observers.

The matters of science which are relevant to our great question are those studied by cosmologists and physicists. The study of the Universe has revealed it to be expanding. Tracing its history backwards for billions of years leads us to a moment when densities and temperatures would become infinite, and further backtracking using this description is impossible. This leads us to consider the serious possibility that it may have had a beginning at a finite time in the past. This is only an extrapolation and needs to be examined far more closely if it is to be taken seriously, but let us for the moment take it seriously enough to follow the argument a little further. If the expansion did have a beginning then we are faced with further questions: is this ‘beginning’ merely the start of the expansion of the Universe that we see today or is it the Beginning, in every sense, of the entire physical Universe? And, if it is the latter, does it include just the matter and energy in the Universe, or the entire fabric of space and time as well? And, if space and time come into being, what of the laws and symmetries and constants of Nature, as we like to call them; do they appear as well? Lastly, if some or all of these things must come into being at some identifiable moment of history, what do they come into being from, why, and how?

There are ancient traditions of humans asking great ‘why’ questions about the nature and end of existence. A large fraction of the readers of these pages will live in societies that have been strongly influenced by the Judaeo-Christian tradition and the ideas that it generated in order to harmonise its writings and doctrines with our early knowledge of the physical world. The doctrine of the Universe having been created out of nothing (creatio ex nihilo) is almost unique to the Christian traditions. A survey of the mythological beliefs of the world reveals surprisingly few basic cosmological scenarios, despite a veneer of exotic actors and fantastic memorable mechanisms.3

The idea of a ‘created’ universe is most commonly found as a re-shaped or reconstructed universe, usually being fashioned out of a state of chaos or a structureless void. Alternatively, the world may ‘emerge’ from some other state, for which there are a multitude of candidates. It can spring new-born from some primeval womb, or be fished out of the dark waters of chaos by a heroic diver. It may hatch from a pre-existent egg or emerge from the union of two world parents. Elsewhere, we find versions of the story of a clash between some superhero and the forces of darkness and evil, out of which the world is born. All these pictures have close links to human experiences of human childbirth, battles with rivals, animal reproduction and fishing for food. The emergence of something from nothing, like the birth of a child, is accompanied by pain and effort. It is often opposed, but ultimately it succeeds. Not all these examples are straightforward. As time passes mythological accounts tend to become increasingly complex. More and more facts come to light about the world and new questions are asked. Answers can usually only be provided by embroidering the story further. Explanations grow more elaborate.

Other traditions can be found in which the Universe does not begin at all: it always was. These traditions often have a cyclic picture of time and history that owes much to the seasonal cycles exploited by agricultural societies and the cycles of human life and death.4 Thus, while the ultimate reality continues from a past eternity to a future eternity, the Earthly world will die only to be reborn, rising like a phoenix from the ashes of its predecessor. The pattern of human cosmological stories is summarised in Figure 9.1.

In these accounts the language of creation, in the artistic or practical sense, is often used to describe the bringing into being of the observed state of the world. In most cases the raw materials were given and the creative process fashioned order from chaos. No inquiry was made into the origin of the materials themselves. The origin of the world out of the union of two gods offers scope for contemplating the appearance of something where once there was nothing, in the same way that a new child is not just a rearrangement of pre-existing things. However, the idea of making something from nothing was compromised by the pre-existence of the gods. The offspring owed something to them just as the offspring of a human union displays characteristics of its parents. These stories always drew a veil over the question of how there could be a transition from absolutely nothing to something. No tradition addresses this question. All have something emerging from something else, usually aided by an act of will by a superhuman intermediary. The impression that one gets from these stories is that the idea that the world began was not too difficult to accept, but it was impossible to comprehend the idea that it could have ‘begun’ in any sense other than having changed from something else into what it now appears to be. Nothing, as we have seen, is a very difficult concept to grasp. Here, it was easy to sidestep it.

Figure 9.1 The common patterns of cosmological traditions.

CREATION OUT OF NOTHING

“In the beginning there was Aristotle,
And objects at rest tended to remain at rest,
And objects in motion tended to come to rest,
And soon everything was at rest,
And God saw that it was boring.”

Tim Joseph5

There is a popular notion that the Christian tradition of the creation of the Universe out of nothing is simply that God made the Universe appear out of nothing at a moment in the finite past. Everything that constitutes the world – space, time, matter, laws of Nature – sprung into being at once out of nothing at all. These things were not fashioned out of some simpler, less ordered or chaotic mess. They were created, not formed out of something else.

Almost all of the statements in the last paragraph have a number of different variants and interpretations. Yet the detailed nature of the traditional doctrine of creation out of nothing is far less specific and cosmological. One suspects that the religious ideas have gradually become far more specific and well defined with the advent of twentieth-century cosmology and the fairly precise picture that it gives of the expanding Universe and its apparent beginning. Although some modern theologians seek to reconcile the ancient tradition of creation out of nothing with contemporary cosmological ideas,6 it is good to recall that the doctrine of creation out of nothing did not arise in Christian tradition in order to make assertions about astronomy and cosmology as we now understand them. Its primary objectives were to make a statement about the relationship between God and the Universe; to assert that there was meaning and purpose to the world, that it was dependent upon God, and to distinguish clearly between Christian beliefs and those of other belief systems that were current at the time when the early Church was developing its theology.7 In particular, it proclaimed that Nature was not the same thing as God; this was an important distinction that served to make the worship of idols or nature-gods appear futile. It also sought to make a theological point about the power of God. Creation rather than formation out of pre-existing stuff asserted that no help was needed from other sources; God controlled matter’s existence as well as its orderly patterns.

These aims were of far greater significance than any desire to underpin the idea that the world came into being at a definite moment in time.8 Yet it is this latter idea that often seems to be of primary interest to many modern apologists trying to reconcile science and Christianity.9 This polemical use of a doctrine of creation out of nothing is certainly not new. It was first developed in order to distinguish its adherents from other philosophies and beliefs, both current and inherited, in the Graeco-Roman worlds. Thus, whereas the followers of Plato subscribed to the shaping of some pre-existent world of matter into its present form by the action of a demiurge, Christianity affirmed a creation out of no pre-existent material at all. Aristotle, by contrast, argued for the past eternity of the world rather than its sudden appearance.

One might imagine that early Christianity inherited the idea of creation out of nothing from Judaism, but the evidence for its presence in Jewish texts is by no means incontrovertible or unambiguous. There is no explicit statement in early Jewish writings about the creation of the Universe. It was not a doctrinal ingredient of its theology. There appears to have been little interest in the question. There was no doubt in anyone’s mind about the existence and omnipotence of Yahweh and so no motivation for proofs of His existence that appealed to the need for a Creator. Although no systematic position is explicitly worked out there is evidence that, if pressed on the issue, there was a clear defence of the concept of creation out of nothing. At the end of the first century, the influential Rabbi Gamaliel engaged in a debate10 with a philosopher on the question of whether the world was formed from pre-existent materials. The philosopher describes the work of God as that of a great artist using the materials (‘colours’) that are made available in the opening verses of Genesis. But Gamaliel counters this theory by arguing that all these ‘colours’ are explicitly described in the Bible as having been created by God. Thus he rejects an interpretation of the first two verses of Genesis as supporting the idea that the world was formed out of pre-existing material. Implicitly, he asserts creation out of nothing by declaring that anything you nominate as the raw material for creation was created by God. Here, as in other places, we seem to be seeing a theological affirmation that happens to use cosmological categories rather than the development of any explicit cosmological theory that can be used to deduce other properties of the Universe. There would have been religious views about the end of the world but they would not in any sense have been consequences of the teachings about its beginning.

The Wisdom of Solomon11 speaks of the formation of the world out of formless matter that the Almighty ‘made’. The text most frequently cited as the earliest explicit statement of the idea of creation from nothing is in the second book of Maccabees,12 which speaks of the ‘Creator of the world’ bringing about ‘the beginning of all things’. The context is a story in which a mother of seven martyrs encourages her youngest son to remain faithful by calling upon him to ‘look upon the heaven and the earth, and all that is therein, and consider that God made them of things that were not’ and be assured that ultimately he will awaken the righteous from death. But there is no philosophical purpose in the mother’s mind. She is just basing hope for resurrection upon her faith in the power of God. Other examples can be found of similar phraseology being used to express the coming of children into the world ‘out of non-being’.13 Again, there is no engagement with the sort of tricky philosophical problems for which the possibility of creation out of nothing would be a possible remedy or counter-example.

In the earliest Christian traditions there is, accordingly, no ready-made inherited position about the creation of the world out of nothing. There is considerable freedom to develop this idea gradually during the first and second centuries, for nowhere in the New Testament writings is the doctrine of creation out of nothing explicitly taught. It began to be discussed seriously by theologians in about AD 160 as a result of the challenging questions raised by Gnostic philosophies.

In Gnosticism the questions of ‘why’ and ‘how’ the world was created were of great significance, not because the Gnostics were especially interested in cosmology but because of their negative view of the world. They needed to have some explanation as to why this defective, immoral world came into being, and how it could result from the actions of the one true and perfect God. Gnostics maintained that the world was the creation of a group of more limited lesser beings (‘angels’) who either did not know the true God or were in rebellion against Him. They viewed matter and the physical Universe as something possessing only a partial reality which disturbed the true plan for the Universe. The ensuing process of salvation had as its primary goal the destruction of the defective material world. It was the complex evolution of the debate between the Gnostics and their opponents (and a whole spectrum of intermediate positions) in the early Church that led to the emergence in the early Christian Church of a clear doctrine of the creation of the Universe out of nothing in the writings of Basilides, Valentius and Irenaeus.

Basilides and his school in Antioch developed a Gnostic system unlike all others. It focused on the need to determine the nature of creation itself. Basilides proposed that in the beginning there was just pure ineffable Nothing.14 It may be that he equated Nothing with God, and on one occasion he describes God as ‘non-being’. This is probably just a rather extreme use of a form of negative theology in which one defines God in terms of the things that He is not.15 Unlike other Gnostics, Basilides rejects the idea that there is some germinating world-seed or pre-existent formless matter from which the world emerges. He regarded such devices as limitations on the power and superhuman nature of God. He rejects totally the idea that God works like a human craftsman or an artist using the materials that are at hand to fashion the Universe.

This is the earliest explicit rejection of the general idea of the formation of the world out of formless materials. From now on it became clear that divine creation must be placed on a higher plane than artistic creation.16 Basilides’ views became widely accepted and the rejection of the formation model for the origin of the world allowed the idea of creation out of nothing to become established during the second half of the second century. Quite quickly, the world-formation model came to be regarded as impossible to reconcile with the biblical concept of creation. Previously, the concept of ‘nothing’ was often defined in such a way that a formation out of pre-existent material could be accommodated within a statement of creation out of nothing, but Basilides, a non-standard Gnostic, was the first Christian theologian17 to speak unambiguously about creation out of nothing in a very inflexible sense that was designed to be exclusive.

In less than a generation, a surprising change of attitude had occurred. In the middle of the second century, the early Christian Church had no interest in any specific doctrine of the creation of the world and would have been happy to accommodate a picture of the world forming out of pre-existent material with the Genesis account. Basilides’ careful argument turned things around. Creation ex nihilo was adopted as a central doctrine and the theories of world formation out of anything other than nothing were rejected as heretical challenges to the omnipotence of God and an adherence to the heretical theories of the godless philosophers. The resulting doctrine emerges from a synthesis of three convictions: that creation occurs ‘out of nothing’, that God is the supreme Creator, and the rejection of the tempting old idea that God acts in a way that is analogous to human creative action.

It is curious that the Christian doctrine of creation out of nothing was introduced by a Gnostic, since the doctrine is by no means a Gnostic idea. Its Gnostic legacy is a reflection of the more sophisticated cosmological thinking that the Gnostics developed in order to deal with their own complicated doctrinal problems. They thought that the version of Christian truth that they taught was plainly superior to the insights coming from existing philosophy and science.

The rejection of the world-formation cosmology was first made explicit in the works of Tatian and Theophilus of Antioch (Basilides’ home town also), but there would later emerge a view that formless matter was created out of nothing and then shaped into an orderly universe. Tatian claimed that matter is made out of nothing by God and Theophilus developed a solid biblical basis for the doctrine of creation out of nothing.

From the modern perspective it is easy to wonder why early theologians seem to make such heavy weather of all this. There seem to be so few alternatives to the creation-out-of-nothing idea and it seems strange that such a complicated sequence of events was needed for the alternatives to be mapped out clearly. It is important to remember that one reason for their slowness is simply that they were not looking for such a doctrine. They were not motivated by a special interest in astronomy or natural philosophy. Parts of their doctrine were constructed occasionally when needed to defend specific theological points. It was synthesised into a fully worked-out form only when it was needed to counter the theological consequences of rival Greek views about the world being fashioned from pre-existent matter. Creation out of Nothing is one of the by-products of the early Christian Church’s disputes with the ideas of Greek philosophy.

One must also remember the confusing background of Platonic philosophical ideas which were still very influential. The Platonic view of the world was that there exists an unseen eternal realm of ideal ‘forms’ which are the perfect blueprints of the things that we see in the material world. Thus each triangular shape that we see drawn on a piece of paper is an imperfect representation of the ideal triangular form. This makes the idea of nothing a very difficult one to entertain. Even if you wish to conceive of a moment before which the material world did not exist, the eternal forms still exist. Complete Nothingness is inconceivable. Thus the world-formation cosmologies which produce order in chaotic or unformed material can be seen as in-forming the raw material with the patterns from the eternal forms – transferring ‘information’ content as we might say today. In modern approaches to these problems the Platonic worry still exists in a slightly different form. We can perhaps imagine that no material universe exists, maybe even that no laws of Nature exist, but nothing at all is unimaginable for us because it would mean no facts could exist – not even a fact like the statement that nothing exists, in fact.

PHILOSOPHICAL PROBLEMS ABOUT NOTHING AND HOW WE ESCAPED FROM IT

“Every public action, which is not customary, either is wrong, or, if it is right, is a dangerous precedent. It follows that nothing should ever be done for the first time.”

Francis Cornford18

The question of why there is a world at all was raised in a short pamphlet by the philosopher Leibniz in 1697 entitled ‘On the Ultimate Origination of Things’.19 Leibniz realised that it did not matter whether you thought the world was eternal or appeared out of nothing as maintained by orthodox Christian doctrine. All theories and beliefs still faced the problem of why there was something rather than nothing. Philosophers took little interest in this question for a long time after Leibniz. Problems like this were not part of an analytical philosophy that built up understanding of things step by step. Leibniz’s problem needed an understanding of everything all at once. It was too ambitious. In fact, it was as good a candidate as any for an intrinsically insoluble problem.20 Philosophers who considered the question, like Wittgenstein (‘Not how the world is, is the mystical, but that it is’)21 and Heidegger, had little to say in answer to it and appear more interested in wondering about why the question is one that we find so compelling.22

The only novel contribution to this problem before the twentieth century was the consideration of whether the well-defined concept of mathematical existence had any cosmological implications. The development of axiomatic mathematical systems, in which a system of self-consistent rules (‘axioms’) were laid down and consequences deduced or constructed from them, led to a ‘creation’ of mathematical truths that ‘existed’ in a rather particular sense. Any mathematical statement that was logically consistent was said to ‘exist’. Mathematicians would produce what became known as ‘existence proofs’. This is clearly a far broader concept of existence than physical existence. Not all the things that are logically possible seem to be physically possible and not all of those now seem physically to exist. However, a philosopher like Henri Bergson clearly thought that this type of weak mathematical existence was a possible avenue along which to search for a satisfying solution to Leibniz’s problem:23

“I want to know why the universe exists … Whence comes it, and how can it be understood, that anything exists? … Now, if I push these questions aside and go straight to what hides behind them, this is what I find: – Existence appears to me like a conquest over nought … If I ask myself why bodies or minds exist rather than nothing, I find no answer; but that a logical principle, such as A = A, should have the power of creating itself, triumphing over the nought throughout eternity, seems to be natural … Suppose, then, that the principle on which all things rest, and which all things manifest, possesses an existence of the same nature as that of the definition of the circle, or as that of the axiom A = A: the mystery of existence vanishes …”

Unfortunately, this approach to why we see what we see is doomed to failure. As the nature of axiomatic systems has become more fully appreciated it is clear that any statement can be ‘true’ in some mathematical system. Indeed, a statement which is true in one system might be false in another.24

As an interesting sidelight, there is an amusing dialogue reproduced in Andrew Hodges’ biography25 of Alan Turing. Turing attended Wittgenstein’s lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that Wittgenstein was pursuing which wanted to allow contradictions to exist in mathematical systems. Wittgenstein argues that he can see why people don’t like contradictions outside of mathematics but cannot see what harm they do inside mathematics. Turing is exasperated and points out that such contradictions inside mathematics will lead to disasters outside mathematics: bridges will fall down. Only if there are no applications will the consequences of contradictions be innocuous. Turing eventually gave up attending these lectures. His despair is understandable. The inclusion of just one contradiction (like 0 = 1) in an axiomatic system allows any statement about the objects in the system to be proved true (and also proved false). When Bertrand Russell26 pointed this out in a lecture he was once challenged by a heckler demanding that he show how the questioner could be proved to be the Pope if 2 + 2 = 5. Russell replied immediately that ‘if twice 2 is 5, then 4 is 5, subtract 3; then 1 = 2. But you and the Pope are 2; therefore you and the Pope are 1’! A contradictory statement is the ultimate Trojan horse.

This temptation to replace physical existence by mathematical existence can be taken to extremes. Suppose that we imagine that all possible mathematical formalisms are laid out in front of us. They each appear like a great network of all possible deductions that follow from their axioms. If the mathematical system is very simple then the deductions will also be very limited in their complexity. But if the axioms are rich enough then the sea of deductions will include extremely complex structures which possess the capability of self-awareness. It is as if we are building a computer simulation of how a system of planets might form around a star. We tell the computer all the laws of motion and gravity, and whatever other physics and chemistry that we want included in the story. The computer will produce a simulation, or artificial sequence of events, culminating in the formation, say, of a planet like the Earth. We could imagine a future in which the computational capability was such that the simulation could be continued in great detail. Biochemical replication could be followed and early life forms simulated. Eventually, the complexity of the replicators being modelled in the computer could reach a level that displayed self-awareness and an ability to communicate with other self-aware sub-processors in the simulation. They might even engage in philosophical debates about the nature of the simulation, whether it was designed for them, and whether there exists a Great Programmer behind the scenes. At root these ‘conscious’ subprogrammes would exist only in the logical structure of the computer. They would be part of the mathematical formalism being explored and elaborated by the machine.

We can ask whether the possibility of containing structures able to be self-aware is a general or a rather special property of mathematical formalisms. One day it may be possible to answer this but at present we can only make rather weak statements. There have been controversial proposals27 that the Gödel incompleteness28 properties of arithmetic may be necessary for consciousness to operate as it does in humans. If true, this would be equivalent to saying that mathematical systems need to be rich enough to contain arithmetic in order to contain structures with the complexity of human consciousness. Thus, Euclidean geometry, which is smaller than arithmetic and does not possess incompleteness, would be too simple a logical system to become self-aware. If this approach could be developed further then we might be able to isolate a collection of mathematical structures which allow the possibility of encoding conscious subprogrammes. Conscious life would ‘exist’ in the mathematical sense only in these mathematical formalisms.

Most philosophers treat such recipes with distaste. They regard real physical existence as distinct from mathematical existence. In the words of Nicholas Rescher,29

“… getting real existence from pure logic is just too much of a conjuring trick. That sort of hat cannot contain rabbits.”

Mathematical existence allows anything to ‘exist’. Some axiomatic system can always be framed in which any statement is true (and others found in which it is false). This type of existence does not, therefore, really explain anything. We want to know why so much of what we see around us can be explained as a truth of a particular system of logical rules with a single set of axioms. The fact that those axioms are not too exotic shows that the world can be described by quite simple ideas (that is, ones that are intelligible to human beings) to a very surprising degree.

CREATION OUT OF NOTHING IN MODERN COSMOLOGY

“Then God created Bohr,
And there was the principle
And the principle was quantum,
And all things were quantified,
But some things were still relative
And God saw that it was confusing.”

Tim Joseph30

The discovery of the general theory of relativity by Einstein enabled the first mathematical descriptions of entire universes to be made. Only very simple solutions of Einstein’s equations have been found completely by direct calculation, but fortunately these simple solutions are extremely good descriptions of the visible part of the Universe for a considerable time in the past. They describe expanding universes in which the distant clusters of galaxies are moving away from each other at ever-increasing speeds. Deviations from the exact symmetry of the special solutions can be introduced quite easily, so long as they are small, and this results in a good description of the real non-uniformities in the Universe.

As we try to reconstruct the past history of these cosmologies, we encounter a striking feature. If matter and radiation continue to behave as they do today, and Einstein’s theory continues to hold, then there will be a past time when the expansion must have encountered a state of infinite density and temperature. When this property was first appreciated, it sparked a number of very different reactions. Einstein31 thought that it was merely a consequence of considering expanding universes that contained matter without significant pressure. If pressure was included then he thought that it would resist the contraction of a universe down to infinite density, just as air pressure resists our attempts to squeeze an inflated balloon into a very small volume. It would ‘bounce’ back. But this intuition was completely wrong. When normal pressures were included in the universe models it made the singularity worse because in Einstein’s theory all forms of energy, including those associated with pressures, have mass and gravitate by curving space. The singular state of infinite density remained. Others objected that the singular ‘beginning’ only appeared because we were looking at descriptions of expanding universes which were spherical, with expansion at exactly the same rate in every direction. If the rate was made slightly different in different directions then, when the expansion was retraced backwards in time, the material would not all end up in the same place at the same time and the singularity would be avoided. Unfortunately, this also proved to be no defence against the singular beginning. Rotating, asymmetrical, non-uniform universes all had the same feature: an apparent beginning. If matter was present in the universe, its density was infinite there.

The next attempts to evade this conclusion looked to a more subtle possibility. Perhaps it was just the way of measuring time and mapping space in the model universe that degenerated into a singularity, just as with the coordinates on a globe of the Earth’s surface. At the Poles the meridians intersect and create a singularity in the mapping coordinates; yet nothing odd happens on the Earth’s surface. Likewise, perhaps nothing dramatic happens at the Universe’s apparent beginning; you merely change to measuring time and space in a new way and repeat this process, as required, indefinitely into the past.

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.

However, as Frank Tipler and I also showed,47 if the vacuum energy exists then everything changes – for the worse. All evolution heads inevitably for a state of uniformity characterised by the accelerating universe of de Sitter. Information processing cannot continue for ever: it must die out. There will be less and less utilisable energy available as the material Universe is driven closer and closer to a state of uniformity. If the vacuum energy exists but there is insufficient matter in the Universe to reverse its expansion into contraction before the vacuum energy gets a grip on the expansion48 and begins to accelerate it, then the Universe seems destined for a lifeless far future. Eventually, the acceleration leads to the appearance of communication barriers. We will be unable to receive signals from sufficiently remote parts of the Universe. It will be as if we are living inside a black hole. The part of the Universe that can affect us (or our descendants) and with which they may be in contact will be finite. In order to escape this claustrophobic future we would need the ubiquitous vacuum energy to decay. We think it must stay constant for ever, but maybe it is slowly, imperceptibly eroding. Maybe one day it will decay suddenly into radiation and ordinary forms of matter and the Universe will be left to pick up the pieces, and slowly use gravity to aggregate matter and process information. But the decay may not be so benign. We have seen that it could herald a slump into an even lower energy state for the Universe with a sudden change in the nature of physics accompanying it. It is even possible for the vacuum to decay into a new type of matter that is even more gravitationally repulsive than the lambda force. If its pressure is even more negative then something very dramatic can lie in the future. The expansion can run into a singularity of infinite density at a finite time in the future.49

There is one last line of speculation that must not be forgotten. In science we are used to neglecting things that have a very low probability of occurring even though they are possible in principle. For example, it is permitted by the laws of physics that my desk rise up and float in the air. All that is required is that all the molecules ‘happen’ to move upwards at the same moment in the course of their random movements. This is so unlikely to occur, even over the fifteen-billion-year history of the Universe, that we can forget about it for all practical purposes. However, when we have an infinite future to worry about all this, fantastically improbable physical occurrences will eventually have a significant chance of occurring. An energy field sitting at the bottom of its vacuum landscape will eventually take the fantastically unlikely step of jumping right back up to the top of the hill. An inflationary universe could begin all over again for us. Yet more improbably, our entire Universe will have some minutely small probability of undergoing a quantum-transition into another type of universe. Any inhabitants of universes undergoing such radical reform will not survive. Indeed, the probability of something dramatic of a quantum-transforming nature occurring to a system gets smaller as the system gets bigger. It is much more likely that objects within the Universe, like rocks, black holes or people, will undergo such a remake before it happens to the Universe as a whole. This possibility is important, not so much because we can say what might happen when there is an infinite time in which it can happen, but because we can’t. When there is an infinite time to wait then anything that can happen, eventually will happen. Worse (or better) than that, it will happen infinitely often.

Globally, the Universe may be self-reproducing but that will merely provide other expanding regions with new beginnings. Perhaps some of their inhabitants will master the techniques needed to initiate these local inflations to order and engineer their outcomes in life-enhancing ways. For us, there is a strange symmetry to existence. The Universe may once have appeared out of the quantum vacuum, retaining a little memory of its energy. Then in the far future that vacuum energy will reassert its presence and accelerate the expansion again, this time perhaps for ever. Globally, the self-reproduction may inspire new beginnings, new physics, new dimensions, but, along our world line, in our part of the Universe, there will ultimately be sameness, starless and lifeless, for ever, it seems. Perhaps it’s good that we won’t be there after all.