INTRODUCTION

There has been a tremendous growth in the understanding of General Relativity and of its relation to experiment in the past 30 years, resulting in its transformation from a subject in the doldrums on the periphery of theoretical physics, to a subject with a considerable experimental wing and and many recognised major theoretical achievements to its credit. The main areas of development have been,

1. * solar system tests of gravitational theories,

2. * gravitational radiation theory and detectors,

3. * black holes and gravitational collapse,

4. * cosmology and the dynamics of the early universe.

On the theoretical side, this development is based on understanding exact and inexact solutions of the Field Equations (the latter has three different meanings I will discuss later). In this brief review of theoretical developments, there is not space to give full references to all the original papers. Detailed references can be found in previous surveys, in particular ‘HE’ is Hawking and Ellis (1973), ‘TCE’ is Tipler Clarke and Ellis (1980), ‘HI’ is Hawking and Israel (1987), and ‘GR13’ is the proceedings of the 13th International meeting on General Relativity and Gravitation held in Cordoba, Argentina in 1992. Many of the issues raised here are considered at greater length elsewhere in this book, e.g. in the articles by MacCallum and Tod.

It is a great pleasure to speak at this meeting since it gives me a chance to acknowledge the great influence Dennis Sciama has had on my life. It was Dennis who first introduced me to relativity as an undergraduate at Cambridge in 1968 and it was through a popular lecture he gave to the Cambridge University Astronomical Society in that year that I first learnt about the microwave background radiation. I well recall his remark that he was “wearing sackcloth and ashes” as a result of his previous endorsement of the Steady State theory. This made a great impression on me and was an important factor in my later choosing to do research in Big Bang cosmology. When I was accepted as a PhD student by Stephen Hawking, I was therefore delighted to become Dennis' academic grandson. (Incidentally since Stephen has related how he had originally wanted to do his PhD under Fred Hoyle, having never heard of Dennis, I must confess - with some embarrassment - that, when I applied for a PhD, I had never heard of Stephen!) The subject of my PhD thesis was primordial black holes, so it seems appropriate that I should talk on this topic at this meeting, especially as Dennis was my PhD examiner.

Although I am one of the very few people represented here who was never technically a student of Dennis Sciama's (or a student's student or a student's student's student), I was, on the other hand, very much a student of his in a less formalized sense. He was a close personal friend when I was at Cambridge as a research student, and then a little later as a Research Fellow. Although my Ph.D. topic was in pure mathematics, Dennis took me under his wing, and taught me physics. I recall attending superb lecture courses by Bondi and by Dirac, when I started at Cambridge, which in their different ways were inspirations to me, but it was Dennis Sciama who influenced my development as a physicist far more than any other single individual. Not only did he teach me a great deal of actual physics, but he kept me abreast with everything that was going on and, more importantly, provided the depth of insight and excitement - indeed, passion - that made physics and cosmology into such profoundly worthwhile and thrilling pursuits.

I first encountered Dennis at the Kingswood Restaurant, in Cambridge, somewhat before I went up there as a research student, where I was introduced to him by my brother Oliver.

INTRODUCTION

I started as a research student with Dennis Sciama in 1971 at the beginning of his time at Oxford, after he had transferred there from Cambridge, and was subsequently a post-doc with his groups in Oxford and Trieste. It is a great pleasure to have the opportunity of contributing to this book.

In the renaissance of general relativity and cosmology, which is our subject here, one of the central themes has been the study of relativistic gravitational collapse, black holes and neutron stars. At the beginning of my research work, Dennis emphasized to me the role which was going to be played in this by numerical computing and he pointed me in that direction despite some initial reluctance on my part. Applying general relativity to real problems in the real world is a complicated business but gradually it has entered the mainstream of astrophysics to the extent that it now no longer seems to be an exotic curiosity but has come of age as an equal member of the collection of physical theories which are brought into service in attempting to explain how things work. Computing has played a key role in this, making it possible to move beyond theoretical models which have been simplified to the point where analytical techniques are sufficient for studying them, to the development of more detailed models which probe more deeply into the consequences of the theory and come closer to contact with possible observations.

We review the properties of the cluttered Minkowski vacuum. In particular we discuss the example of a uniformly accelerated quantum oscillator in the Minkowski vacuum showing that it does not radiate. Equivalently, the presence of the oscillator does not lead to decoherence (i.e. the emergence of classical probabilities). Mach's Principle was related originally by Einstein to the non-existence of (classical) vacuum cosmological models. We speculate that Mach's Principle may acquire a quantum role as a condition for decoherence of the universe.

INTRODUCTION

Following Hawking's announcement (Hawking 1974,1975) of his result that black holes radiate a thermal flux, Davies (1975) applied an analogous technique to the spacetime of a uniformly accelerated observer in the Minkowski vacuum in the presence of a reflecting wall. He interpreted the result as a flux of radiation from the wall at a temperature ha/4π2ck, where a is the acceleration of the observer. Unruh (1976) independently showed that the Minkowski vacuum appears as a thermal state to any uniformly accelerated detector, the normal modes of which were defined with respect to its own proper time. There is no flux from the horizon but the detector is raised to an excited state with its levels populated according to a Boltzmann distribution at a temperature ha/4π2ck as it would be in an inertial radiation bath at this temperature.

This is mainly a review of the properties of gravitational galaxy distribution functions. It discusses their theoretical derivation, comparison with N-body simulations, and — perhaps most importantly — their observed features. The observed distribution functions place strong constraints on any theory of galaxy clustering.

INTRODUCTION

The galaxy distribution function f(N, v) is the probability of finding N galaxies in a given size volume of space (or in a projected area of the sky) with velocities between v and v + dv. It is the direct analog of the distribution function in the kinetic theory of gases. For perfect gases, the spatial distribution is provided by a Poisson distribution at low densities and a Gaussian distribution at high densities, along with a Maxwell-Boltzmann distribution for the velocities. It is only in the last few years that we have discovered the comparable distribution for galaxies interacting gravitationally in the expanding universe. There are still many aspects of this problem which need to be understood.

Distribution functions had their origin in the observations and speculations of William Herschel two hundred years ago. In his catalog of nebulae he noticed that their distribution was irregular over the sky. Although we now know that some of these nebulae were galaxies and others resulted from stars, HII regions and planetary nebulae, and that some of the irregularities are intrinsic while others are due to local obscuration by the interstellar matter in our Milky Way, Herschel tended to view them all as a single class of objects.

Quasars offer important clues to the process of galaxy formation and the epoch when it occurred. Although they almost certainly involve relativistic processes close to a collapsed object, quasars have unfortunately not yet given us any real tests of strong-field gravity.

INTRODUCTION

In December 1963, the first Texas Conference on Relativistic Astrophysics was held in Dallas. Quasars had just been discovered, and were already being interpreted as gravitationally-collapsed massive objects. In his after-dinner speech, Thomas Gold said that relativists were “not only magnificent cultural ornaments, but might actually be useful to science …. What a shame it would be if we had to dismiss [them all] again”. We haven't had to do so — on the contrary, ‘relativistic astrophysics’ is a subject with ever-widening scope. It burgeoned with the detection of the microwave background in 1965, of neutron stars in 1967, and of the first stellar-mass black hole candidates in 1971. Dennis Sciama's research group was at the centre of all the key debates throughout that exciting period. I was myself fortunate to begin research in 1964, when these developments were just gaining momentum. It was my great good fortune to have been assigned as one of Dennis' students, and he has been a valued mentor and advisor ever since.

The past 30 years have seen a great revival of General Relativity and Cosmology, and major developments in astrophysics. On the theoretical side this has been centred on the rise of the Hot Big Bang model of cosmology and on our developing understanding of the properties of black holes. On the observational side it has been based on astonishing improvement of detectors and measuring instruments in astronomy and experimental relativity, in particular enabling measurement of the microwave background radiation and extension of astronomical observations to the whole electromagnetic spectrum.

Dennis Sciama has played an important role in these developments, particularly through the research schools he has run at Cambridge, Oxford, and Trieste, supervising and inspiring many research students who have worked on these topics, and challenging his colleagues with penetrating questions about the physics and mathematics involved. The extent of his influence will become apparent on studying the Family Tree of students, and the list of books that have been the product of those who have taken part in these research groups (see below).

Dennis' 65th Birthday was on November 18, 1991. To mark this event, a meeting was held at SISSA, Trieste (Italy) from 13th to 15th April, 1992, under the title The Renaissance of General Relativity and Cosmology: A survey meeting to celebrate the 65th birthday of Dennis Sciama.

INTRODUCTION

Since my first interaction with the Kerr metric, early in 1967, when Dennis Sciama suggested to me that I work on it, I was fascinated by the magic of that solution to reduce whatever mathematical expression to simple terms, and by the richness of the information it provided. After nearly 25 years of intense investigation of the Kerr metric carried out by almost all the relativists around the world, new properties continue to be discussed and perhaps deep information about the very nature of gravity is still to be brought to light.

There are basic questions about gravity which, in my opinion, still need to be answered. Some (and perhaps the most obvious ones) are:

1. i) - Why do the properties of a physical system, like energy and momentum, bend the background geometry?

2. ii) - How are energy and momentum actually transferred to the background geometry, leading to a non zero curvature?

3. iii) - To what extent does energy and momentum of the background geometry contribute to these same properties of a physical system?

Answering these types of question is what I mean by going to the roots of gravity. Evidently, central to this issue is the concept of energy in general, for which we require, at the classical level at least, the fulfillment of the energy conditions.

The clustering of galaxies on scales < 5h-1Mpc1 shows some remarkable scaling properties which somehow arise out of nonlinear gravitational self-organisation. This scaling is characteristic of structures that are referred to as multifractals. There are several ways of looking at these structures each providing their own special insights into the nature of the clustering. Multifractal scaling can be shown to be closely associated with the fact that galaxy counts-in-cells are approximately Lognormally distributed and with hierarchical fragmentation processes. Moreover, the statistical moments of the galaxy distribution scale in a way that is reminiscent of the renormalization group. This may throw light on the nature of the underlying dynamics of the nonlinear gravitational clustering process.

INTRODUCTION

When Dennis Sciama published his book “The Unity of the Universe” in 1959, the great debate was which theory of the Universe was the correct one: the “Big Bang” or the “Steady State”? Dennis had been a member of a group of Steady-State enthusiasts at Cambridge in the early 1950's.

INTRODUCTION

I first met Dennis Sciama in 1974 whilst I was still an undergraduate. At our first meeting he told me about the challenge of explaining the large scale regularity of the Universe, along with other of its unusual features, like the existence of galaxies and its proximity to a state of “zero binding energy” that we now tend to call “flatness”, without making special assumptions about initial conditions. Many of these issues remain a continuing focus of attention in cosmology. Here, my intention is to review a number of cosmological ‘principles’ and their interaction with a variety of cosmological developments that have taken place over the period during which Dennis has worked on cosmology. The talk on which this article is based formed a small part of these Proceedings which celebrate the huge contribution that Dennis has made and continues to make to general relativity, cosmology and astrophysics. Besides Dennis' personal contributions and those of his students, that of so many of his former students (and their students) exhibits the non-linear amplification in their effectiveness that was always created by the collaborations and contacts between them that have been catalysed by their shared associations with Dennis.

THE PERFECT COSMOLOGICAL PRINCIPLE

In 1948 Bondi, Gold and Hoyle (Bondi and Gold, 1948; Hoyle 1948) proposed a powerful cosmological symmetry principle which they called the ‘Perfect Cosmological Principle’.

INTRODUCTION

The organisers have asked us to review the progress of some aspect of general relativity and cosmology in which they have a particular interest and to introduce their remarks by describing its relation to their interaction with Dennis Sciama. It is a great pleasure for me to do so and also to pay tribute to the inspiration that he, and his style of doing physics, has been to me over the years. In particular I have tried to follow his example by asking simple physical questions and trying to answer them with the simplest appropriate tools available. For that reason in what follows I shall not give extensive mathematical details but refer the reader to the references. Moreover because of the personal nature of the review I have made no attempt to include in those references every paper on the subject, especially where the story is widely known and can be read up in standard textbooks. For the same reason I have perhaps erred in including too many papers of my own.

I became a Research student of Dennis Sciama in October 1969 after being enthralled by his marvelously lucid and exciting Part III lectures on General Relativity. When Dennis left for Oxford a year later I transferred to Stephen Hawking, himself a former student of Dennis.

INTRODUCTION

In this talk I will discuss the hypothesis (Sciama 1990a) that most of the dark matter in the Milky Way consists of tau neutrinos whose decay into photons is mainly responsible for the widespread ionisation of hydrogen in the interstellar medium (outside HII regions). I introduced this hypothesis because there are several difficulties with the conventional explanation of the observed ionisation. This explanation involves photons emitted by O and B stars, supernovae etc. The two most important difficulties involve the large opacity of the interstellar medium to ionising photons and the large scale—height of the free electron density. The opacity arises mainly from the widespread distribution of atomic hydrogen in the interstellar medium, which makes it difficult for the ionising photons emitted by widely separated sources to reach the regions where the ionisation is observed. The scale—height of the electron density (as derived from pulsar dispersion measure data by Reynolds (1991)) is about 1 kpc, whereas the scale height of the conventional sources is only about one tenth of this.

Both of these problems would be immediately solved by my neutrino hypothesis since the neutrinos would be smoothly distributed throughout the interstellar medium and their scale—height would be expected to exceed 1 kpc.

Although Kibble's original toy cosmic string model is characterised by longitudinal Lorentz invariance, it is argued that the tacit assumption that this feature would be preserved in a realistic treatment is rather naive. Strict longitudinal Lorentz invariance is incompatible with equilibrium, but its violation allows closed string loops to survive in centrifugally supported states instead of radiating all their energy away. Following the explicit suggestion by Witten of a superconductivity mechanism whereby such a violation would be achieved, it was pointed out by Davis and Shellard that although the ensuing distribution of centrifugally supported string loops would be cosmologically admissible in a “lightweight” (electroweak transition) string scenario, it would imply a highly excessive cosmological mass density ratio, Ω ≫ 1 in a “heavyweight” (G.U.T. transition) string scenario of the kind postulated to account for galaxy formation. In order to salvage such scenarios, it might be hoped that Witten type superconductivity does not occur, except perhaps as an ephemeral phenomenon subject to decay by quantum tunnelling. However such optimism overlooks the point that the Witten mechanism is just one particularly simple example, and that even if it fails to apply, experience shows that there are many other ways by which Lorentz symmetry breaking in extended material systems is usually achieved.

Galaxies are the building blocks of the Universe, and most of what we know about them has been discovered since Dennis Sciama became a research student. In the space available to me it is not possible to cover even in outline all significant developments during this period. So I have tried to concentrate on what seem to me to be the most important themes. My choice must surely be heavily influenced by personal taste and experience; I hope only that my prejudices are not too glaringly evident.

THE STRUCTURE OF THE MILKY WAY

Galactic astronomy in the 1950s was dominated by the discovery (Ewen & Purcell, 1951) of the 21 cm line predicted by H. C. van der Hulst in 1944. This made it possible for the first time to study the large-scale kinematics of the Milky Way. For the most part the 21 cm observations confirmed the picture of a disk in differential rotation developed by Oort more than twenty years before. However, there were surprises — most notably the discovery that the disk is warped rather than being perfectly flat (Burke, 1957; Kerr, 1957).

Extinction of stars by dust had first betrayed the existence of the interstellar medium (Trumpler 1930).

In this contribution, I review the work of Dennis Sciama and his collaborators on Mach's Principle, saying both what Mach's Principle is, and more generally what we should expect a ‘Principle’ to be and to do. Then I review the notion of an isotropic singularity, and the evidence for a connection between isotropic singularities and Mach's Principle. I suggest that a reasonable formulation of the cosmological part of Mach's Principle is that the initial singularity of space-time is an isotropic singularity, and that Mach's Principle may become a ‘theorem’ of quantum gravity.

WHAT IS MACH'S PRINCIPLE?

Mach's Principle is the name usually given to a loose constellation of ideas according to which “the inertia of a body is due to the presence of all the other matter in the universe” (Milne 1952) and “the local inertial frame is determined by some average of the motion of the distant astronomical objects” (Bondi 1952). In Wheeler's aphorism “matter there governs inertia here” (Misner et al. 1973). The aim of Mach's Principle is to explain, without recourse to Absolute Space, the origin of inertia, inertial frames and the standard of non-rotation in Newtonian Mechanics, where the existence of these things is a basic assumption.

I had the privilege of collaborating with Dennis Sciama for a few years here in Trieste in building up the Astrophysical Sector of SISSA; and I am glad to tell him today that it has been for me an enjoyable and wonderful experience.

Now, first of all, I feel in some sense obliged to justify the subject of my contribution by saying that, at an age over eighty, it becomes much easier making some philosophical reflections about science than bringing some significant scientific consideration; that is why, in order to take part actively to this conference, intended to convey to Dennis all our wishes for further important scientific achievements, I have found myself confined to presenting only some epistemological puzzles. I was told by the organizers that this could be considered as tolerable; so that I have now only to ask for kindly forgiving me such a deviation from the main line of this meeting.

The second thing to do is to clarify what I mean in the title by “reality”. If scientists and philosophers are quite aware of the almost endless meanings that can be given to this word, at different levels of philosophical depth, this is not so for plain people, who generally stick to our immediate feeling that reality is what we perceive through our senses in our surroundings.