GENERAL RELATIVITYThe principle of equivalence and its experimental confirmation reveal that space-time is curved by the
presence of matter, but they do not indicate how much space-time curvature matter actually produces. To determine this curvature requires a specific metric theory of gravity, such as general
relativity, which provides a set of
equations that allow computation of the space-time curvature from a given distribution of matter. These are called field equations. Einstein's aim was to find the simplest field equations that could be constructed in terms of the space-time curvature and that would have the matter distribution as source. The result was a set of 10 equations. This is not, however, the only possible metric theory. In 1960, C. H. Brans and Robert Dicke developed a metric theory (see gravitation) that proposed, in addition to field equations for curvature, equations for an additional gravitational field whose role was to mediate and augment the way in which matter generated curvature. Between 1960 and 1976 it became a serious competitor to general relativity. Many other metric theories have also been invented since 1916.An important issue, therefore, is whether general relativity is indeed the correct theory of gravity. The only way to answer this question is by means of experiment. In the past scientists customarily spoke of the three classical tests proposed by Einstein: gravitational red shift, light deflection, and the perihelion shift of Mercury. The red shift, however, is a test of the equivalence principle, not of general relativity itself, and two new important tests have been discovered since Einstein's time: the time-delay by I. I. Shapiro in 1964, and the Nordtvedt effect by K. Nordtvedt, Jr., in 1968.The confirmation of the deflection of starlight by the Sun by the solar eclipse expedition of 1919 was one of the triumphant moments for general relativity and brought Einstein worldwide fame. According to the theory, a ray of light propagating through the curved space-time near the Sun should be deflected in direction by 1.75 seconds of arc if it grazes the solar surface. Unfortunately, measurements of the deflection of optical starlight are difficult (in part because of need for a solar eclipse to obscure the light of the Sun), and repeated measurements between 1919 and 1973 yielded inaccurate results. This method has been supplanted by measurements of the deflection of radio waves from distant quasars using radio-telescope interferometers, which can operate in broad daylight. Between 1969 and 1975, 12 such measurements ultimately yielded agreement, to 1 percent, with the predicted deflection of general relativity.The time-delay effect is a small delay in the return of a light signal sent through the curved space-time near the Sun to a planet or spacecraft on the far side of the Sun and back to Earth. For a ray that grazes the solar surface, the delay amounts to 200 millionths of a second. Since 1964, a systematic program of radar ranging to the planets Mercury and Venus, to the spacecraft Mariners 6, 7, and 9, and to the Viking orbiters and landers on Mars has been able to confirm this prediction to better than half of 1 percent.Another of the early successes of general relativity was its ability to account for the puzzle of Mercury's orbit. After the perturbing effects of the other planets on Mercury's orbit were taken into account, an unexplained shift remained in the direction of its perihelion (point of closest approach to the Sun) of 43 seconds of arc per century; the shift had confounded astronomers of the late 19th century. General relativity explained it as a natural effect of the motion of Mercury in the curved space-time around the Sun. Recent radar measurements of Mercury's motion have confirmed this agreement to about half of 1 percent.The Nordtvedt effect is one that does not occur in general relativity but is predicted by many alternative metric theories of gravity, including rans-Dicke theory. It is a possible violation of the equality of acceleration of massive bodies that are bound by gravitation, such as planets or stars. The existence of such an effect would not violate the weak equivalence principle that was used as a foundation for curved space-time, as that principle applies only to modest-sized objects whose internal gravitational binding is negligible. One of the remarkable properties of general relativity is that it satisfies EEP for all types of bodies. If the Nordtvedt effect were to occur, then the Earth and Moon would be attracted by the Sun with slightly different accelerations, resulting in a small perturbation in the lunar orbit that could be detected by lunar laser ranging, a technique of measuring the distance to the Moon using laser pulses reflected from arrays of mirrors deposited there by Apollo astronauts. In data taken between 1969 and 1976, no such perturbation was detected, down to a precision of 30 cm (1 ft), in complete agreement with the zero prediction of general relativity and in disagreement with the prediction of the Brans-Dicke theory.A number of secondary tests of more subtle gravitational effects have also been performed during the last decade. General relativity has passed every one, while many of its competitors have failed. Tests of gravitational radiation and inertial frame-dragging are now being devised. One experiment would involve placing spinning objects in Earth orbit and measuring expected relativistic effects.