May I begin by expressing my gratitude to the Master of Trinity and his Council for their trust in assigning to me the privilege of giving the Centenary Lectures in memory of one of the most distinguished members of the College and of the University. I knew Eddington as a member of the Fellowship of Trinity during the early and the middle thirties when, besides Eddington, it included J. J. Thomson, Ernest Rutherford, George Trevelyan, Douglas Adrian, Donald Robertson, G. H. Hardy, J. E. Littlewood, and a host of others. It is hardly necessary for me to say how much it means to me to have been a member of that society during those years and to be asked now, almost fifty years later, to give these lectures in honour of one whose personal friendship I was fortunate to enjoy.

When Eddington died in November 1944 at the age of sixtytwo, Henry Norris Russell, his great contemporary across the Atlantic, wrote: ‘The death of Sir Arthur Eddington deprives astrophysics of its most distinguished representative.’ I have taken my cue from Russell for the substance of this, the first of my two lectures.

Before I turn to an assessment of Eddington's contributions to astronomy and to astrophysics, I should like to start with a few biographical notes which may give some impression of the manner of man he was.

It is almost impossible to predict what forms living organisms will take (assuming they can survive) in such time scales as we have been discussing. In an attempt to survive various extremely cold conditions, life may take forms which would be considered weird by our standards. However, the possibility of survival of life and civilization in any form depends on the availability of a source of energy, and one can discuss the latter. In this chapter I shall examine the sources of energy available, if any, during each of the stages of the universe described in the previous chapters. At each of these stages there will be enormous technical ingenuity required for civilization to survive. I will assume in the following that such technical ingenuity will be forthcoming. Very often civilization or society will have to face acute social problems. It might very well be that civilization may not survive some such problems, for example, a completely destructive nuclear war. I shall assume in the following that civilization will be able to achieve the maturity and wisdom to avoid such social catastrophies.

There will be adequate energy available as long as the Sun radiates sufficiently, which will be a few billion years.

In the last chapter we saw that after a billion billion billion (1027) years or so the universe will have two classes of black holes. Firstly there will be the very massive ones, namely galactic and supergalactic black holes. Another class of black holes will be the singly wandering stellar-size black holes (up to a few times the mass of the Sun) which were ejected from galaxies during the stage of dynamical evolution of the galaxy into a single black hole. There will, of course, also be the cold white dwarfs, neutron stars and other smaller pieces of matter (which were thrown out of galaxies) wandering in the intergalactic space. According to the laws of classical physics, all these black holes, white dwarfs, neutron stars etc. will last forever in the same form with very little further change. Perhaps we should explain here what we mean by ‘classical’ physics. ‘Classical’ here does not refer to classical Greece, but to a more modern period. Modern physics in one sense could be said to have started from the work of the Italian mathematician, astronomer and physicist Galileo Galilei (1564–1642) and of Newton. Nearly all the physical phenomena encountered in chemistry, physics and astronomy until about the end of the nineteenth century could be explained in accordance with the mechanistic principles propounded by Galileo and Newton. However, in the twentieth century it was realized that microscopic phenomena and also phenomena involving high velocities and strong gravitational fields could not be explained in terms of the laws of mechanics of Galileo and Newton.

From the last two chapters it is evident that all stars in a typical galaxy will eventually be reduced to white dwarfs, neutron stars or black holes. There will be formation of new stars from the interstellar gas but eventually most of this gas will be used up in making stars which will eventually die. The remaining gas will be too thinly dispersed and cold to make new stars. The remnants of supernova explosions could also lead to the formation of new stars but finally these remnants would become too rich in heavy elements for the normal process of star formation to take place. Thus given sufficient time, the galaxy will simply consist of cold white dwarfs, neutron stars, black holes and other forms of cold interstellar matter such as planets, asteroids, meteors, rocks, dust, etc. From the energy content of a typical galaxy, it can be shown that this stage will be reached in not much more than a thousand billion (1012) years or so. All galaxies will be losing energy by radiation to intergalactic space. The intergalactic space can be considered as a vast receptacle into which all the energy of the galaxies can be poured without raising its temperature. This is both because the empty space between galaxies increases as the universe expands and because the radiation given off by galaxies gets red shifted and becomes weaker.

In the previous chapters we have been concerned with the future of the universe if it is open, that is, if it will expand forever. The ultimate fate of the universe is dramatically different if the universe is closed, that is, if it will stop expanding at some future time and start to contract. If indeed the universe is closed, what is the time scale in which it will stop expanding and start to contract? This depends on the present average density of the universe. Models of closed universes can be constructed with arbitrarily long time scales for contraction by taking the present density to be above, but close enough to, the critical density mentioned in Chapter 5. Thus, in principle, it is possible to have a closed universe to expand for 10100 years before it starts to contract, so that most of the processes mentioned in the previous chapters will take place and then many of these processes will be reversed. If the universe is closed, however, it is extremely unlikely that its life-time will be as long as 10100 years.

Suppose for the sake of argument that the present average density of the universe is twice the critical density. Recall that in the simpler (Friedmann) models the closed universe has a finite radius. The universe will then expand until its radius is about twice its present value.

In this book I have presented what can at best be a rough outline of the long-term future of the universe and its ultimate fate. A great deal more needs to be understood about this problem, as is clear from the preceding chapters. For example, what is the nature of the long-term stability of matter? If the universe is closed, what is the precise nature of the final collapse? Is it really possible for life and civilization to exist indefinitely in an open universe? Can intelligent beings survive indefinitely the social conflicts (all too familiar in our present civilization) that beset society? One of the most intriguing problems is to understand the precise nature of time, especially with regard to the big bang, the big crunch and the long-term future of an open universe. Formulating an exact definition of time is an old problem. The early Christian philosopher, Saint Augustine (354–430) gave a classic expression to this problem when he said, ‘What then is time? If no one asks me, I know: if I wish to explain it to one that asketh, I know not.’

The study of the universe as a whole is a unique enterprise. At least in one sense one is seeking to understand the totality of things. We, as thinking beings, are as much a part of the universe as are neutron stars and white dwarfs and our destiny is inextricably bound up with that of the universe.

In astronomy one uses distances and periods of time large compared to terrestrial ones. The word ‘astronomical’ has in the English language come to mean some very large quantity. When discussing the universe as a whole one uses even larger distances and periods of time than those used in ordinary astronomy. The convenient unit for measuring distances in astronomy is not the kilometer or the mile, but the light year, which is the distance traversed in a year by light moving at the speed of about 300,000 kilometers a second (km/s); a light year is approximately 9 × 1012 km or 9 million million km. To have some idea about the light year, let us consider some familiar distances and convert these to ‘light travel time’. The circumference of the Earth is about 40 000 km, so in one second light can travel round the Earth more than seven times. The distance to the Moon is 371 000 km, so it takes light between 1 and 1.5 seconds to travel from the Earth to the Moon. The mean distance of the Earth from the Sun is approximately 150 million km. This distance is covered by light in 8–8.5 minutes. The mean distance from the Sun to Pluto, the furthest planet in the solar system, is approximately 5900 million km, which distance is covered by light in about 5.5 hours.

One of the most interesting of the non-standard models of the universe is the steady state theory, which has been the source of much controversy in the past. This controversy has, I believe, been healthy for the subject of cosmology, resulting in the creation of a great deal of interest in the subject and also stimulating new research which has led to important advances in astrophysics and cosmology. The steady state theory is currently not in favour for reasons which will be explained below.

The steady state theory was put forward by H. Bondi and T. Gold and independently by F. Hoyle in the same year (1948). The approach of Bondi and Gold was different from that of Hoyle, although the end result was the same. Bondi and Gold modified one of the cosmological assumptions to arrive at their theory, whereas Hoyle modified Einstein's equations.

In Chapter 3 I mentioned the Cosmological Principle, according to which the universe appears to be homogeneous and isotropic everywhere at any given time. The Principle of course allows the universe to evolve in time; in other words the universe can appear to be different at different epochs in its history. Bondi and Gold extended this principle to what is called the Perfect Cosmological Principle, according to which the universe is not only homogeneous and isotropic everywhere at any given time, but it appears on the average, to be the same at any time.

In this chapter we shall digress and take a first look at some of the elementary particles and their properties, knowledge of which will be useful in several places in the following chapters. We shall take a more detailed look at this subject in Chapter 14, when we consider the important question of the stability of the proton. Consider first the particle associated with light or electromagnetic waves. An alternative description of radiation exists in terms of particles called photons. It was realized at the turn of the century by Planck and later by others that radiation consists of discrete chunks of energy which are called photons. This is one of the consequences of the quantum theory, about which we will learn more later. Photons have most of the attributes of particles, and they can be considered as such. An ordinary light wave consists of billions of photons travelling all together but if we were to measure the energy of the wave very precisely we would find that it is a multiple of a definite quantity, which can be considered as the energy of a single photon. The energy of a photon is usually quite small so for most practical purposes the energy of an electromagnetic wave can have any value. However, the interaction of light or electromagnetic wave with an atom or atomic nucleus takes place one photon at a time. It is important to consider the photon picture when considering these interactions.

Other galaxies

Many of the objects in Messier's catalogue have turned out to be systems outside our Galaxy. One of these is the Andromeda nebula (Fig. 3.1), visible to the naked eye on a clear night as a hazy patch in the constellation Andromeda. In ad 964 the Persian astronomer Abdurrahman Al-Sufi mentioned it in his Book of the fixed stars, calling it ‘a little cloud’. The Andromeda nebula has turned out to be a spiral galaxy somewhat like our own, and a close neighbour of our Galaxy. In the late nineteenth and early twentieth centuries there was a great controversy about the nature of the nebulae listed by Messier, the Herschels and Dreyer. There was one school of thought which held the view that some of these nebulae were extragalactic, i.e. systems outside our Galaxy. In fact the original suggestion that some nebulae might be extragalactic seems to have been made by the German philosopher Immanuel Kant (1724–1804). Taking up Wright's theory of the Milky Way, in 1755 in his Universal natural history and theory of the heavens, he suggested that some nebulae are in fact circular discs somewhat like our Galaxy, and they are faint because they are so far away.

The controversy was finally settled in the 1920s and 1930s mainly by the American astronomer Edwin Powell Hubble (1889–1953) who demonstrated beyond reasonable doubt that most of the nebulae are indeed extragalactic.

In 1977 I wrote a short technical paper entitled ‘Possible ultimate fate of the universe’ which was published in the Quarterly Journal of the Royal Astronomical Society. A number of colleagues found this paper amusing. Just then, Weinberg's excellent book The first three minutes appeared and it occurred to me that it would be interesting to have a book about the end of the universe. Soon I was requested by the astronomical magazine Sky and Telescope to write a popular version of my paper for them. This appeared in January 1979 under the title ‘The ultimate fate of the universe’. The response to this article convinced me that a popular book on the subject would not be inappropriate. The result is this present book.

I have written the book with the person who has no special scientific knowledge in mind. All the technical terms mentioned and all the physical processes described are explained in as simple language as I have been able to use. However, I have avoided oversimplification. This means that some parts of the book will require close attention by the reader who does not have any scientific background, but I hope that everyone who cares to read the book will be able to follow the main ideas without much difficulty.

I have made free use of some of the books and articles mentioned in the bibliography for the more standard parts of this book.

What will eventually happen to the universe? The question must have occurred in one form or another to speculative minds since time immemorial. The question may take the form of asking what is the ultimate fate of the Earth and of mankind. It is only in the last two or three decades that enough progress has been achieved in astronomy and cosmology (the study of the universe as a whole) for one to be able to give at least plausible answers to this kind of question. In this book I shall try to provide an answer on the basis of the present state of knowledge.

To appreciate the possibilities for the long-term future of the universe it is necessary to understand something of the present structure of the universe and how the universe came to be in its present state. This will be explained in some detail in Chapter 3. In this introduction, I shall briefly outline the contents of this book to provide a ‘bird's eye view’ to the reader. All the terms and processes mentioned in this summary will be explained in more detail in the succeeding chapters.

The basic constituents of the universe, when considering its large-scale structure, can be taken to be galaxies (Fig. 1.1), which are ‘islands’ of stars with the ‘sea’ of emptiness in between, a typical galaxy being a congregation of about a hundred billion (1011) stars (e.g. the Sun) which are bound together by their mutual gravitational attraction.

In this chapter I shall consider one of the most important questions concerned with the long-term future of the universe and, indeed, one of the most important questions in physics. The question is whether or not the proton is stable. Until recently it had been assumed by physicists that the proton was indeed stable, that is, a proton left to itself would last forever. Recently, however, some theories of elementary particles have been put forward which imply that the proton is unstable, with a very long lifetime. In this chapter we shall try to see in what way these theories arise, and what are the consequences of proton decay. Before we can understand where the new theories fit, we shall have to know something about the theory of elementary particles, in much more detail than we considered in Chapter 4. To remind the reader I may repeat some of the points made earlier.

Every since the time of the ancient Greeks, people have wondered what is the ultimate nature of matter. They have wondered about the ultimate constituents of matter and about the manner in which these constituents affect each other or interact with one another. The Greek physical philosopher Democritus, who was born in the fifth century bc, speculated that all matter was made of atoms, which were eternal, indivisible and invisible. In the past hundred years or so and particularly in the last three or four decades a tremendous effort has gone into the investigation of this problem.

In quantum mechanics it turns out that phenomena which are forbidden in classical physics (such as particles escaping from a black hole) have a small, but real chance of happening by a mechanism called tunneling, whereby a particle crosses a ‘classical’ barrier. By a classical barrier we mean one that would be a barrier if only the laws of classical physics operated. Thus an electron which does not have sufficient energy to surmount the barrier produced by an electrical field bounces off the barrier and cannot penetrate it according to the laws of classical physics, as shown in the upper sketch in Fig. 10.1. The wavelike properties of matter in quantum mechanics, however, give the electron a small chance of getting through (see lower sketch in Fig. 10.1). This phenomenon of tunneling is important in radioactive decay of a heavy nucleus such as a uranium or a radium nucleus and also in some processes in electronics. Since quantum effects are essentially microscopic effects, it is difficult to give an example of the phenomenon of tunneling in terms of every day happenings, but presently we shall try to explain radioactivity in such terms.

We shall see that the phenomenon of quantum tunneling causes some slow and subtle changes in the remaining pieces of matter after all the black holes have gone, or even before the black holes disappear. These processes would not be possible according to classical physics, since the latter implies that the matter in the form of white dwarfs, neutron stars and other smaller pieces of matter would stay in the same form forever.

In this chapter we shall discuss briefly how stars are born and how they evolve during their life, and then we shall consider in some detail how they eventually die, that is, reach the three final states of white dwarf, neutron star and black hole. We shall also discuss the phenomenon of supernova, a phenomenon which is relevant to the final state of some stars.

The precise manner in which stars are formed is not clearly understood. The region between the stars is not empty but consists of gas clouds, consisting mostly of hydrogen, and dust grains of various kinds. The material between the stars is not uniformly distributed in space but is spread in a patchy fashion. In most places the density of gas is very low, a typical density being 10−19 kg/m3, that is about a hundred million (108) hydrogen atoms per cubic meter. Now the gravitational force between two portions of matter is inversely proportional to the square of the distance between them (for example, if the distance is doubled, the force becomes a quarter) and directly proportional to the product of the masses (if the masses of both portions are doubled, the force becomes four times as strong). Thus in a gas cloud, the higher the density of the gas, the stronger the gravitational attraction of different parts for each other.

Occasionally a cloud will become sufficiently dense and massive for gravitational attraction to draw it close together (this could conceivably happen also in the neighbourhood of a supernova explosion, as will be explained later).