.. to all the laws of physics, such as electromagnetism. In any freely falling frame, therefore, the laws of physics should (at least locally) take on their special relativistic forms. This postulate is called the Einstein equivalence principle (EEP). One consequence is the gravitational redshift, a shift in frequency f for a light ray that climbs through a height h in a gravitational field, given by (delta f)/f = gh/cc where g is the gravitational acceleration. (If the light ray descends, it is blueshifted.) Equivalently, this effect can be viewed as a relative shift in the rates of identical clocks at two heights.
A second consequence of EEP is that space-time must be curved. Although this is a highly technical issue, consider the example of two frames falling freely, but on opposite sides of the Earth. According to EEP, Minkowski space-time is valid locally in each frame; however, because the frames are accelerating toward each other, the two Minkowski space-times cannot be extended until they meet in an attempt to mesh them into one. In the presence of gravity, space-time is flat only locally but must be curved globally. Any theory of gravity that fulfills EEP is called a “metric” theory (from the geometrical, curved-space-time view of gravity).
Because the equivalence principle is a crucial foundation for this view, it has been well tested. Versions of the Eotvos experiment performed in Princeton in 1964 and in Moscow in 1971 verified EEP to 1 part in 10(12). Gravitational redshift measurements using gamma rays climbing a tower on the Harvard University campus (1965), using light emitted from the surface of the Sun (1965), and using atomic clocks flown in aircraft and rockets (1976) have verified that effect to precisions of better than 1 percent. General Relativity The 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 redshift, light deflection, and the perihelion shift of Mercury. The redshift, 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 the Brans-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. Continuing to test general relativity is important, in order to strengthen confidence in its use as a tool for analyzing many of the newly discovered phenomena in astronomy and astrophysics.
Cosmology One of the first astronomical applications of general relativity was in the area of cosmology. The theory predicts that the universe could be expanding from an initially condensed state, a process known as the big bang. Despite many challenges (including the popularity during the 1950s of the steady-state theory), the big bang is now accepted as the standard model of the universe. Three important pieces of evidence, accumulated mainly since 1960, support this conclusion: (1) more precise measurements of the universe’s expansion rate, first measured by Edwin Hubble in 1929, indicating that the big bang occurred between 10 and 20 billion years ago; (2) the discovery in 1965 of the 3K (3 degrees above absolute zero) microwave background radiation, a uniform “sea” of electromagnetic radiation left over from the earlier hot phase of the universe (700,000 years after the big bang); and (3) the realization that the observed cosmic abundance of helium (20 to 30 percent by weight) is necessarily produced in the conditions of the big bang. One aspect of the model that is still uncertain is whether the universe will continue to expand indefinitely or whether it will slow down and eventually recollapse to a “big crunch.” Astronomical observations may yield an answer. Another important application of general relativity is to the theory of neutron stars, bodies that have been so compressed by gravitational forces that their density is comparable to that within the atomic nucleus, and their composition is primarily neutrons.
(A neutron star whose mass equals that of the Sun has a radius of only 10 km/6 mi.) They are thought to occur as a by-product of such violent events as supernovae and other gravitational implosions of stars. Pulsars, first discovered in 1967, are generally believed to be rapidly spinning neutron stars. Pulsars are objects that emit pulses of radio waves at regular intervals, ranging from about 30 milliseconds to 3 seconds; as of 1979, 200 have been discovered. According to one model, the neutron star acts as a lighthouse, emitting a narrow beam from its surface that sweeps by an observer’s telescope once each rotation period. One of the most exotic predictions of general relativity is the black hole. Implosions of extremely massive stars can proceed beyond the neutron star configuration.
As the matter continues to implode, it crosses an imaginary spherical surface known as the event horizon, located at a radius given by 2MG/cc, where M is the mass that has imploded and G is Newton’s constant of gravitation; for one solar mass, this radius is about 3 km (1.9 mi). Once inside the event horizon, nothing–not even light–can escape. The exterior space-time geometry of the black hole is described by the Schwarzschild solution of the field equations if it has no rotation, and by the Kerr solution if it rotates (solutions discovered respectively in 1916 by Karl Schwarzschild and in 1963 by R. Kerr). Rather strong evidence now exists that the companion of the star denoted HDE 226868 in the constellation Cygnus is a black hole.
According to the most favored model, gas from the atmosphere of HDE 226868 is stripped off by the gravitational field of the hole, heats up as it falls toward the hole, and emits copious amounts of X rays just before plunging across the event horizon. The X rays from this source, called Cygnus X-1, were detected in 1971 by a telescope on a satellite called Uhuru. Some theorists have speculated that supermassive black holes may exist at the centers of some clusters of stars (with masses of 1 thousand solar masses) and of some galaxies (with masses of 1 million to 1 billion solar masses), including perhaps our own. One prediction of general relativity has not yet been verified: gravitational radiation, a wave of gravitational force that travels at the speed of light, transports energy, and induces relative motion between pairs of particles in its path or produces strains in bulk objects. Astrophysicists believe that it should be emitted by dynamic sources such as supernovae, double-star systems, and black-hole formations and collisions. Although experiments around 1970 using 1.5-ton aluminum cylinders fitted with strain gauges were thought to have detected it, subsequent experiments by other groups did not confirm the detection.
A worldwide effort is now in progress to build gravitational radiation antennas, not only to detect this phenomenon but also, ultimately, to make use of it as a new window on the universe. Recently, indirect evidence for the existence of gravitational radiation has been discovered in a system known as a binary pulsar, a pulsar in orbit around a companion star. Careful measurements, by radio telescopes, of the motion of the pulsar have shown that the orbit is losing energy and is decaying at just the rate to be expected from the loss of energy by means of emission of gravitational waves by the system. CLIFFORD M. WILL Bibliography Barnett, Lincoln, The Universe and Dr. Einstein, rev.
ed. (1968) Born,Max, Einstein’s Theory of Relativity, rev. ed. (1962) Einstein, Albert, The Meaning of Relativity, 5th ed. (1956) Gardner, Martin, Relativity for the Millions (1962) Reichenbach, Hans, The Philosophy of Space and Time, trans.
by Maria Reichenbach (1958) Russell, Bertrand, The A B C of Relativity, 3d ed. (1969) Struble, Mitch, The Web of Space-Time: A Step by Step Exploration of Relativity (1973) Taylor, E. F., and Wheeler, J. A., Spacetime Physics (1966) Weinberg, Steven, The First Three Minutes (1977). See also – CLOCK PARADOX; SPACE-TIME CONTINUUM; WORLD LINE. .