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.

INTRODUCTION

Those of us who had the privilege of being Dennis Sciama's students during what Hajicek has described as ‘the Golden Age of General Relativity’ can trace many of the current concerns of the subject back to the ideas which he fostered, either directly or indirectly, within his research group in Cambridge. This was the environment in which major contributions to most of the foundational ideas about singularities: from the controversies about the steady state and big bang theories; through the critique of the early Lifshitz-Khalatnikov arguments which at first suggested that the big bang singularity was not generic, leading to definitions of just what constituted a singularity; to the Hawking-Penrose singularity theorems themselves. The issue of cosmic censorship stemmed naturally from this work, and illustrates well the combination of rigorous mathematics with a firm hold on physical relevance which he established at that time. In this talk I shall try to give an outline of the historical work on cosmic censorship, focussing at the end on my own recent work on shell crossing singularities. I shall not be concerned with what George Ellis, in this meeting, has termed the position of the goal posts — the details of exactly what the target is; rather, I shall be arguing that we should in fact be playing a different game.

A fully covariant approach to transfer phenomena by using flux-limiters is presented. Explicit formulas for the radiation flux and radiation stress tensor are given for a wide class of physical situations.

INTRODUCTION

In several areas of cosmology and astrophysics the transfer of radiation through high-speed moving media plays a crucial role (accretion flow into black holes, X-ray bursts on a neutron star, supernova collapse, jets in radio sources, galaxy formation, phase transition in the early universe). If one wants to take into account all the effects associated with these transport processes, the full relativistic transport equation must be used.

Early discussion of radiative viscosity was performed by several authors in a non covariant formulation (Jeans 1925, Rosseland 1926, Vogt 1928, Milne 1929), but the appropriate transfer equation for the case of special relativity was given in a classical paper by Thomas (1930). A manifestly covariant form of the transfer equation was obtained by Hazelhurst and Sargent (1959), by using a geometrical formalism. Finally Lindquist (1966) performed the extension to the general relativistic situation and Mihalas (1983) analyzed in depth the order of magnitude of the various terms which appear in the transport equation.

From a mathematical point of view, the transport equation is an integro—differential equation and the task to solve it is in general very hard.

From the time that Newton first proposed that there was a universal force of gravity inversely proportional to the square of the distance between two point masses, there have been recurrent investigations of how far that rule was correct, and many different alternative forms have been suggested. The other assumption that Newton made, that the force of gravity did not depend on the chemical composition of bodies, has also been questioned from time to time; Newton himself carried out the first experimental test of what has become known as the weak principle of equivalence. It has often been suggested that some apparently anomalous behaviour in celestial mechanics should be ascribed to a failure of the inverse square law; indeed Clairaut developed the first analytical theory of the motion of the Moon because of discrepancies between Newton's theory and observation that might have been due to an inverse-cube component of the force. As with all subsequent studies before general relativity, careful analysis showed that the effects were consistent with the inverse square law. General relativity predicts a small deviation from the inverse square law close to very massive bodies, a deviation that has been confirmed by careful observation.

The motions of celestial bodies about each other are, with very minor exceptions, unable to reveal any departure from the weak principle of equivalence; if such departures are to be detected, they must be sought in laboratory experiments or geophysical observations.

Three hundred years after Newton published Philosophiae Naturalis Principia Mathematica the subject of gravitation is as lively a subject for theoretical and experimental study as ever it has been (Hawking & Israel, 1987). Theorists endeavour to relate gravity to quantum mechanics and to develop theories that will unify the description of gravity with that of all other physical forces. Experimenters have looked for gravitational radiation, for anomalies in the motion of the Moon that would correspond to a failure of the gravitational weak principle of equivalence, for deviations from the inverse square law and for various other effects that would be inconsistent with general relativity. The cosmological implications of general relativity continue to be elaborated and various ways of using space vehicles to test notions of gravitation have been proposed. In particular, the last three decades have seen a considerable effort devoted to applying modern techniques of measurement and detection of small forces to experiments on gravitation that can be done within an ordinary physics laboratory, and it is those that are the subject of this book.

Our scope is indeed quite restricted. It is concerned with experiments where the conditions are under the experimenter's control, in contrast to observation, where they are not. It is concerned with experiments that can be done within a more or less ordinary-sized room, that is to say, the distances between attracting body and attracted body do not usually exceed a few metres and may often be much less, while the masses of gravitating bodies are of the order of kilograms or much less.

Introduction

Thermal noise is unavoidable and sets the fundamental limit to the detectability of the response of an oscillator to any gravitational effect, but it is not the only disturbance to which an oscillator may be subject. Other forces may act on the mass of a torsion pendulum if it is subject to electric or magnetic or extraneous gravitational fields. The point of support of a torsion pendulum or other mechanical oscillator may be disturbed by ground motion. Ground motion is predominantly translational and so might be thought not to affect a torsion pendulum to a first approximation. However, all practical oscillators have parasitic modes of oscillation besides the dominant one, and although in linear theory normal modes are independent, in real non-linear systems modes are coupled. Thus, even if in theory seismic ground motion had no component of rotation about a vertical axis, none the less there would be some coupling between the primary rotational mode of a torsion pendulum and its oscillations in a vertical plane. In practice, therefore, any disturbance of a mechanical oscillator may masquerade as a response to a gravitational signal.

External sources of noise can be avoided with proper design of experiments. In this chapter we shall discuss both the sources of external disturbance and also the ways in which oscillators of different design respond.

Ground disturbance

Sources of ground noise

We begin with a discussion of seismic motions that move the point of support of a pendulum.

Introduction

The essence of the principle of equivalence goes back to Galileo and Newton who asserted that the weight of a body, the force acting on it in a gravitational field, was proportional to its mass, the quantity of matter in it, irrespective of its constitution. This is usually known as the weak principle of equivalence and is the cornerstone of Newtonian gravitational theory and the necessary condition for many other theories of gravitation including the theory of general relativity. In recent times, however, it was found that the weak principle of equivalence was not sufficient to support all theories and the principle has been extended as (1) Einstein's principle of equivalence and (2) the strong principle of equivalence.

Following a brief discussion of the principle of equivalence, this chapter is devoted to an account of the principal experimental studies of the weak principle of equivalence.

Einstein's principle of equivalence

Gravitation is one of the three fundamental interactions in nature and a question at the heart of the understanding of gravitation is whether or how other fundamental physical forces change in the presence of a gravitational force.

Einstein answered this fundamental question with the assertion that in a non-spinning laboratory falling freely in a gravitational field, the non-gravitational laws of physics do not change. That means that the other two fundamental interactions of physics – the electro-weak force and the strong force between nucleons – all couple in the same way with a gravitational interaction, namely: in a freely falling laboratory, the non-gravitational laws of physics are Lorentz invariant as in the theory of special relativity.