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1 Experimental Tests of General Relativity: Introcluction Perhaps more than in any other area of physics, progress in gravitation physics has been dominated by theoretical work; experi- mental tests of general relativity have lagged far behind theoretical ideas and predictions. In part this unbalance is due to the extreme difficulty of doing laboratory experiments at interesting levels of accuracy, but it is also true that the elegance and richness of gravitation theory has captured the interest of some of the best theorists of this century. Fortunately for the field, the last two decades have seen dramatic advances in our ability to test gravitation theories. Most of this upsurge in experimental activity was brought about by technolog- ical advances in radio and radar astronomy and by the development of precision tracking capabilities for solar-system spacecraft. The theory of general relativity, devised nearly 70 years ago by Einstein, is still the most successful description of gravitation. Progress in the field has been characterized by the invention of plausible alternatives (such as the scalar-tensor theory) that predict different effects or magnitudes than those predicted by general relativity. Experimental work then decides. Currently, there is no reason to think that general relativity needs modification in the classical domain. As we shall see below, some basic tenets of general relativity have been well tested (parts in 10~), some predicted effects have been measured with good agreement (parts in 103), but some major predictions (''magnetic" effects) have not been tested at all. 11
12 GRAVITATION General relativity makes two distinct statements about the nature of gravitation. First, the metric hypothesis states that gravitation can be described as a Riemannian curvature of space-time, with the laws of physics for all nongravitational interactions having the same form in the local Lorentz frames of curved space-time as in the flat space-time of special relativity. Second, the curvature of space-time is deter- mined, through the Einstein field equation, by the energy, momentum, and stress of all matter and nongravitational fields contained in space-time. Gravitation in this view is an intrinsically nonlinear phe- nomenon; the field equation alone allows the equation of motion for particles to be deduced from it. This characteristic stands in sharp contrast to Newtonian theory in which the field equation and the equations of motion are separate postulates. Other metric theories of gravitation incorporate the metric hypothesis but differ from general relativity by the manner in which space-time curvature is generated. Experimental tests of general relativity can correspondingly be sepa- rated into two categories: tests of the metric hypothesis, such as facets of the principle of equivalence, and tests of the properties of space-time curvature, such as the orbits of light rays and test particles. The structure of metric theories of gravitation can be clarified by analogy with electromagnetic theory. Gravitation is described by a four-dimensional metric of space-time and electromagnetism by a four-dimensional tensor for the electromagnetic field. However, one often gains insight and computational power by decomposing the four-dimensional quantities into separate spatial and temporal compo- nents. In such a decomposition, the electromagnetic field splits into electric and magnetic parts. Similarly, the gravitational field, or metric tensor, separates into three parts: a gravitoelectric field, a gravitomag- netic field, and a part that represents the curvature of space. In the Newtonian limit of any metric theory of gravitation, the gravitomagnetic field and space curvature vanish; the much stronger gravitoelectric field reduces to the Newtonian gravitational accelera- tion. In the post-Newtonian regime, a rich variety of new phenomena appear, such as the gravitomagnetic dragging of inertial frames, the gravitoelectric and space-curvature-induced gravitational deflection of light, and the perihelion advance of planetary orbits. To express clearly the consequences of these different post-Newtonian phenomena and the differences between the predictions for each from different metric theories, one can use the parameterized-post-Newtonian (PPN) formal- ism. With it, all metric theories can be expressed in a common framework in a special coordinate system. In this special coordinate system, the three basic fields gravitoelectric, gravitomagnetic, and
EXPERIMENTAL TESTS OF GENERAL RELATIVITY: INTRODUCTION 1 3 space curvature are expressed in terms of potentials whose coupling strengths are given by ten dimensionless parameters whose values generally vary from one metric theory to another. Thus, each theory can be characterized, at this level, by the nu- merical values of its PPN parameters; and each experiment can be characterized by a predicted result, dependent on one or more of these parameters. Currently the best tested parameters are ~ and P; these describe, respectively, the amount of spatial curvature generated by a unit rest mass and the amount of nonlinearity in the superposition of Newtonian gravitational potentials (gravitoelectric fieldsJ. There is also one parameter that describes the amount of any preferred-location effect, three that describe the amount and kind of preferred-frame effects, and five (four distinct from those already listed) that describe the amount and nature of violations of global conservation laws for total energy-momentum. An eleventh parameter, G/G, introduced to describe any fractional time rate of change of the constant of gravita- tion, depends more on cosmology than on a metric theory of gravita- tion. For general relativity, ~ and ~ are unity and all other parameters vanish. Although the PEN formalism has its limitations, it has served admirably as a framework to incorporate a large number of theories of gravitation and to stimulate the invention of new experiments. As we shall see, the best measurements of ~ and ~ have come from experiments using solar-system gravitational fields. The solar system has three special properties in this regard: (a) its gravity is everywhere very weak; the dimensionless ratio of the gravitational potential to the square of the speed of light is 2 x 10-6 on the Sun's surface; (b) the square of the ratio of the speed of each source of significant gravity to that of light is under 10-7; and (c) the ratios of the internal stress energies of all bodies to their respective rest energies are less than 10-s. These three conditions guarantee that Newton's theory of gravitation will provide the same predictions as general relativity to within about 1 part in IOs for the structure of the Sun and to within I part in 106 for experiments confined to the exterior of the Sun. Thus7 the goals of most experiments have been to measure deviations from Newtonian theory, i.e., post-Newtonian effects of gravitation whose fractional magnitudes are about 10-6 or somewhat less. Of course, higher-order relativistic deviations from Newtonian theory are also predicted to exist in the solar system. These post-post-Newtonian effects are not discernible in present experiments, but they may be reached by the next generation of space experiments. The discovery of neutron stars and perhaps black holes in our galaxy brings hope that experimental gravitation might escape the realm of tiny effects. Mul-
14 GRAVITATION tiple systems of these compact objects approach the ideal gravitational laboratory of massive pointlike bodies having negligible nongravita- tional interactions. One such systemthe binary pulsar has already yielded spectacular results, but the intrinsic advantages of such sys- tems have not yet been fully realized. This remains as a bright hope for the next decade.
