Introduction

Experimental tests of general relativity are difficult. Physicists were well aware that pregnant new conceptual insights came mostly from young minds. Now, experimentalists must be cut from that mold, previously the exclusive preserve of theorists. Why? The time elapsed between a good idea for an experimental test and its execution is fast approaching the normal human lifetime. Experimenters must now start young-very young-to live to see the fruits of their ideas realized.

I divide the remainder of this paper into two parts, corresponding, respectively, to the past light cone and the future light cone. Under the former rubric, I discuss, in order, tests of the principle of equivalence, light deflection, signal retardation, perihelia advances, geodetic precession, and the constancy of the gravitational “constant.” Under the latter, I mention improved reincarnations of some of these tests, as well as proposed redshift and frame-dragging experiments.

With the proper reference frame established, I move on to the review of recent results and present plans. Because of space and time constraints, much of the treatment is perforce superficial, but, in keeping with the Fourth of July spirit, I shall be democratic and treat all experiments with (almost) equal superficiality.

Past light cone

Principle of equivalence

Space tests of the principle of equivalence have been primarily concerned with measuring the equivalence between gravitational and inertial mass in regard to the contribution to each of gravitational self-energy.

Studies of the ˜ 3K cosmic microwave background or “relict” radiation, discovered 25 years ago, have substantially improved our understanding of cosmology and of the formation of large-scale structure in the universe. Here, I look at the implications of these studies for gravity theory.

I will begin by reviewing the observations, particularly the spectrum and the large-scale isotropy of the radiation. Measurements of the spectrum, when combined with other astrophysical data like the abundance of light nuclei, establish the temperature and expansion rate of the universe at early times. These values in turn may be used to tell us whether unmodified general relativity adequately describes the dynamics of the early universe. Upper limits on any large-scale anisotropy sharply restrict the range of possible anisotropic cosmological models, and provide supporting evidence for a period of “inflationary” expansion early in the universe. The preceding paper by Dr. Panek explores some of these consequences further.

Introduction

It is an honor to have been invited to review the cosmic microwave background radiation (CBR) for this audience. As an observer and experimentalist, I feel particularly privileged since general relativity is sometimes viewed as the province of theoreticians, not those of us with hands dirtied in the laboratory or at thy telescope.

As is well known, the CBR was discovered 25 years ago by Penzias and Wilson (1965).

The upper limit set by gravity on the rotation of neutron stars is sensitive to the equation of state of matter at high density. No uniformly rotating equilibrium can have angular velocity greater than that of a particle in circular orbit at its equator, and, for a given baryon mass, the configuration with maximum angular velocity rotates at this Keplerian frequency. The limiting frequency decreases with increasing stiffness in the equation of state, because (for a given mass) models of neutron stars constructed from equations of state that are stiff above nuclear density have substantially larger radii and moments of inertia than models based on the softer equations of state. While for cold neutron stars the Keplerian frequency is the gravitational limit on angular velocity, for hotter stars (T > 10 K), viscosity is apparently low enough that gravitational instability to nonaxisymmetric perturbations sets in slightly earlier. The corresponding constraint on the equation of state is more stringent; and if the 1968 Hz frequency seen in optical emission from SN 1987A is the angular velocity of a newly formed pulsar, neutron star matter must be unexpectedly soft above nuclear density. Too soft an equation of state, however, cannot support a spherical neutron star with mass as large as the observed 1.44 solar mass member of the binary pulsar 1913+16. A rather narrow range of equations of state survives the two observational constraints.

Quark stars and stars with pion or kaon condensates are possible alternatives.

The study of exact solutions and exact properties of Einstein's equations is a rather broad mathematical subfield of general relativity. Of the roughly 80 abstracts submitted to the symposium devoted to this topic, time limitations permitted only a small fraction to be presented orally. Table 1 lists the papers given at the two sessions of this symposium. The 16 presented papers fall roughly within the categories of “exact solutions,” “gravitational energy,” “mathematical results” and “symmetry properties of Einstein's equations” and are briefly discussed under those headings in the following. Since most of the oral presentations described extremely recent research results, they did not, for the most part, include references to published papers concerning these results. For this reason the attached reference list is extremely sketchy.

Exact solutions

Virtually all of the known exact solutions of Einstein's equations involve some significant element of idealization. One usually imposes a stringent geometrical symmetry upon the solutions to be considered and, in the non-vacuum case, simplifying assumptions upon the matter sources to be included. Goenner and Sippel discussed several classes of exact solutions which, though highly idealized in the geometrical sense (being in fact pp waves), were nevertheless more realistic in their material content. The sources included both Maxwell fields and a viscous, heat-conducting plasma subject to certain natural energy and entropy inequalities. Several classes of solutions were discussed which represented the generation of a gravitational wave by an electromagnetic wave and a temperature wave propagating in the viscous gas.

We note with sadness that GR-12 was the last important conference for two of the significant figures in physics in the last half of the twentieth century: William M. Fairbank and Eduardo Amaldi. Ironically, they were raised in traditions far removed from general relativity but both had made important experimental contributions to the field during the past twenty years. Fairbank, with Schiff, Cannon, and Everitt, started the investigation that we now call the Stanford Relativity Gyroscope experiment and helped bring it to the point that it will be put into orbit as NASA's Gravity Probe B. He then, with Hamilton, started the cryogenic gravity wave detection project at Stanford to further advance the pioneering experiments of Weber. Amaldi joined with Pizzella to build tuned gravity wave detectors in Italy. When the Italian bureaucracy became too difficult he helped move the experimental laboratory to CERN where it has become the world's strongest program.

In the evening of the next to last day of GR-12 both Fairbank and Amaldi attended a small informal meeting of experimentalists representing all of the major tuned bar groups. The focus of the meeting was to establish times when all of the experiments would be operated in coincidence and to establish protocols for exchanging the data that would be generated by these coincidence experiments. They both expressed great confidence that such a coordinated effort would lead us to the discovery of gravitational waves and the development of gravitational wave astronomy.

Introduction

During the last two years a burst of results has come from radio and optical surveys of “galaxy lenses” (where the main deflector is a galaxy). Even if this kind of work were better known and had already been reviewed for this assembly a few years ago, I cannot pass up the main results which have presently emerged. This will be the first part of the presentation.

On the other hand, in September 1985 we pointed out a very strange blue ring-like structure on a Charge-Coupled Device (CCD) image of the cluster of galaxies Abell 370 (Soucail et al. (1987a)). After ups and downs and a persistent observational quest, this turned out to be the Einstein arcs discovery (Soucail et al. (1988); Lynds and Petrosian (1989)), an important observational step in this particular field since the first observation of the double Quasi-Stellar Object (QSO) 0957 + 561 in 1979 (Walsh et al. (1979)).

Following this discovery, new observational results have shown that many rich clusters of galaxies can produce numerous arclets: tangen-tially distorted images of an extremely faint galaxy population probably located at redshift larger than 1 (Fort et al. (1989); Tyson (1989)). This new class of gravitational lenses proves to be an important observational topic (Mellier (1989a); Fort (1989a)). This story will be the second part of this presentation.

The classification between galaxy lenses and cluster lenses is somewhat arbitrary.

Introductory survey

The implementation of a new computer algebra system is time consuming: designers of general purpose algebra systems usually say it takes about 50 man-years to create a mature and fully functional system. Hence the range of available systems and their capabilities changes little between one GR meeting and the next, despite which there have been significant changes in the period since the last report.

I do not believe there is a single “best” system (though like everybody else I am biased towards the systems I actually use), and in particular one should be extremely cautious about any claims about comparative efficiency of systems. These introductory remarks therefore aim to give a very brief survey of capabilities of the principal available systems and highlight one or two trends. The most recent full survey of computer algebra in relativity (as far as I know) is in Ref. 2, while very full descriptions of the Maple, REDUCE and SHEEP applications will appear in a forthcoming lecture notes volume.

The oldest of the still current general purpose systems are REDUCE and Macsyma. REDUCE is a highly portable system available on a very wide range of machines and is sufficiently cheap to have become widespread in most parts of the world. Its main disadvantage until recently has been the rather small range of auxiliary packages for applied mathematics, but this is improving rapidly with the availability of contributed programs through electronic mail (to reduce-netlib@rand.org: an initial mail should contain the one line ‘send index’).

The aims of quantum cosmology

Our observations of the world give us specific facts. Here, there is a galaxy; there, there is none. Today, there is a supernova explosion; yesterday, there was a star. Here, there are fission fragments; before, there was a uranium nucleus. The task of physics is to bring order to this great mass of facts which constitutes our experience. In the language of complexity theory, the task is to compress the message which describes these facts into a shorter form — to compress it, in particular, to a form where the message consists of just a few observed facts together with simple universal laws of nature from which the rest can be deduced.

In the past, physics, for the most part, has concentrated on finding dynamical laws which correlate facts at different times. Such laws predict later evolution given observed initial conditions. However, there is no logical reason why we could not look for laws which correlate facts at the same time. Such laws would be, in effect, laws of initial conditions.

I believe it was the limited nature of our observations which led to our focus on dynamical laws. Now, however, in cosmology, in the observations of the early universe and even on familiar scales, it is possible to discern regularities of the world which may find a compressed expression in a simple, testable, theory of the initial conditions of the universe as a whole.

Introduction

At the Padova GRG conference, a new avenue to non-perturbative, canonical quantum gravity was suggested (Newman (1984)). By the time the Stockholm conference was held, these preliminary ideas had blossomed into a broad program aimed at analysing the structure of classical and quantum general relativity from a somewhat unusual standpoint (Ashtekar (1986), (1987)). By now, over two dozen individuals have contributed to this program. The purpose of this chapter is to present a brief status report of this body of ideas. Although I will try to be objective, it is inevitable that not everyone who is working in this field will agree with all the views expressed here. Also, since my space is limited, I will have to leave out several interesting results; I apologize in advance for these omissions.

The key idea underlying this program is to shift the emphasis from geometrodynamics to connection dynamics. In the classical theory, the new viewpoint merely complements the traditional one in which the metric, rather than a connection, is taken as the fundamental variable. We do obtain a fresh perspective that simplifies certain issues and suggests new ways of tackling unresolved problems. However, as far as the basic features of the theory are concerned, nothing is really altered conceptually. It is in the quantum regime that the shift of emphasis plays a major role. More precisely, there are indications that connection dynamics is indeed a better tool to analyze the micro-structure of space-time in a non-perturbative way.

Recent suggestions of a “fifth force” have stimulated many experiments to search for new macroscopic interactions arising from the exchange of ultra-low mass fundamental bosons. The experiments fall into two categories: searches for violation of the inverse square law, or of the universality of free fall. The principles of both classes of experiments are described and their results are summarized. Because some groups claim positive effects considerably larger than the upper limits established by others, subtle systematic errors that could masquerade as a “fifth force” are briefly discussed. I conclude that there is, at present, no credible evidence for new macroscopic interactions.

Introduction

One feature common to essentially all extensions of the standard model is the prediction of additional fundamental scalar or vector bosons. While these particles are ordinarily expected to be very massive (mbc2 > 1015 eV), the possibility that some have them have such a low mass, mbc2 < 10−3 eV, that they produce macroscopic forces between unpolarized test bodies, has been considered in a variety of contexts. For example, such speculations have been inspired by Kaluza-Klein theories, quantum gravity ideas, scale invariance, CP-violating pseudo-Goldstone bosons, etc. Some of these would have profound astrophysical consequences: ultra-low mass bosons have been invoked to explain the “vanishing” of the cosmological constant, the anomalous rotation curves of galaxies, and the observed “cumpiness” of the universe.

The workshop on mathematical cosmology was devoted to four topics of current interest. This report contains a brief discussion of the historical background of each topic and a concise summary of the content of each talk.

The observational cosmology program

The standard approach for analyzing cosmological observations is to assume that space-time is isotropic and spatially homogeneous (i.e. that the cosmological principle holds). It then follows that the universe can be described by a Friedmann-Lemaitre-Robertson-Walker (FLRW) model, and the aim is to use the observations to determine the free parameters that characterize such models. A fundamental question, however, is whether ideal cosmological observations on our past null cone can be used to actually determine the geometry of the cosmological space-time, without introducing a priori assumptions about the geometry. This question provides the rationale for the observational cosmology program, as described by Ellis et al. (1985). In this paper it was shown that ideal observations alone do not determine the geometry of spacetime. For example, even if all observations are isotropic about our position, it does not follow that the spacetime is spherically symmetric about our position. However, if the Einstein field equations (EFEs) are assumed to hold, then ideal observations do determine the spacetime geometry off our past null cone.

In the workshop, W. R. Stoeger reported on work in progress with S. D. Nel and G. F. R. Ellis concerning the observational cosmology program.

Inflationary supercomputing

There are many problems in numerical relativity. From a view point of asymptotic behavior of space-times they are divided into three categories as:

On the other hand from a view point of dimension of the problem they are divided into another three categories as:

ID: A problem in which all the physical quantities depend on one spatial coordinate x1 and the time t;

2D: A problem in which all the physical quantities depend on two spatial coordinates x1 and x2 and the time t;

3D: A problem in which all the physical quantities depend on three spatial coordinates x1, x2 and x3 and the time t.

Every problem can be characterized according to these two classifications. For example, the two black hole collision calculated by Smarr belongs to V-2D. There are also many numerical methods for each problem. They include the characteristic method, Regge calculus, finite element method, finite difference method, spectral method, particle method and so on. Moreover the choice of coordinate conditions is not usually unique for each method. Therefore there are a tremendous variety of possibilities for each author's problem. In reality there are up to 30 papers on numerical relativity in this conference which are reviewed by Centrella in this volume.

One of the main factors, however, which determines progress in numerical relativity is the power of available computers.

Introduction

After 20 years of careful and innovative experimenting most of the researchers in the field of gravitational wave detection believe that success is on the horizon. Theoretical predictions of source strengths and source types have been steadily evolving and it is now clear that we should be aiming to build gravitational wave detectors which have strain sensitivities of ∼ 10-22 over kilohertz bandwidths. Such sensitivity should allow the detection of signals from, for example, supernova events at distances out to the Virgo cluster, coalescing compact binary systems and continuous and stochastic background sources.

One of the most promising ways of achieving the required sensitivity and bandwidth is to use laser interferometry between freely suspended test masses placed several kilometers apart, and the majority of contributions to the workshop on laser interferometer gravitational wave detectors were related to the large laser interferometer projects currently well advanced in planning. These instruments rely on searching for changes in the relative length of two paths, usually at right angles to each other, and formed between the test masses suspended as pendulums.

As will be mentioned again later, a number of interferometers are required around the world to obtain useful astrophysical information from the strength, polarization and timing of signals detected, and currently the belief is that at least three separate detector systems at different sites are necessary.

The present status of the new variables program for canonical quantum gravity is discussed. A summary is given of the papers which were presented at the New Variables Workshop at GR-12, and particular attention is given to those issues which are crucial at the present stage of development of this program. Chief among these issues is whether a theory can be quantized nonperturbatively in the absence of any information about the physical observables algebra of the corresponding classical theory. Finally, a wild speculation about the relationship between nonperturbative quantum general relativity and perturbative string theory is made.

Introduction

Abhay Ashtekar introduced his new variables in the Fall of 1985. In the intervening four years this new formalism has been developed and applied to both classical and quantum general relativity. On both sides significant new results have been achieved, and these developments are being actively pursued by a growing number of people. It was thus appropriate to have a workshop at GR-12 dedicated to this subject. In this, a summary of that workshop, I will try to describe briefly several of the directions that this work has taken, with an emphasis on the present status and open problems. In doing so I will touch on each of the six presentations that were given in the workshop, but I will not strictly follow the format of the workshop itself.

The hot big-bang cosmology is based upon the Friedmann-Robertson-Walker (FRW) solution of general relativity. It is a remarkably successful model, providing a reliable and tested accounting of the history of the universe from about 10-2 sec after the bang until today, some 15 Gyr later. It is so successful that it is known as the standard model of cosmology. It accommodates—and in some instances explains—most of the salient features of the observed universe, including the Hubble expansion, the 2.74 K cosmic microwave background radiation (CMBR), the abundance of the light elements D, 3He, 4He, and 7Li, and the existence of structures likes galaxies, clusters of galaxies, etc. In the splendor of its success, it has elevated our thinking about the evolution of the universe, and we have been able to ask a new set of even more profound questions about the universe. These questions include: What is the origin of the baryon number of the universe? What is the origin of the primeval inhomogeneities that gave rise to the structure we see today? Why is the part of the universe we can see (our present Hubble volume) so isotropic and homogeneous—as evidenced by the uniformity of the CMBR temperature—and spatially flat? What is the structure of the universe beyond our Hubble volume? What is the nature of the ubiquitious dark matter? Are there other significant cosmological relics to be discovered? Why is the cosmological constant (equivalently the present vacuum energy density) so small compared to its natural scale: ∧ ≲ 10-122G-1?