Relativity
Albert Einstein's theory of relativity has caused major revolutions in physics and astronomy during the 20th century. It introduced to science the concept of "relativity"--the notion that there is no absolute motion in the universe, only relative motion--thus superseding the 200-year-old theory of mechanics of Isaac Newton. Einstein showed that we reside not in the flat, Euclidean space and uniform, absolute time of everyday experience, but in another environment: curved space-time. The theory played a role in advances in physics that led to the nuclear era, with its potential for benefit as well as for destruction, and that made possible an understanding of the microworld of elementary particles and their interactions. It has also revolutionized our view of COSMOLOGY, with its predictions of apparently bizarre astronomical phenomena such as the big bang, NEUTRON STARS, BLACK HOLES, and GRAVITATIONAL WAVES.
SCOPE OF RELATIVITY
The theory of relativity is a single, all-encompassing theory of space-time, gravitation, and mechanics. It is popularly viewed, however, as having two separate, independent theoretical parts--special relativity and general relativity. One reason for this division is that Einstein presented special relativity in 1905, while general relativity was not published in its final form until 1916. Another reason is the very different realms of applicability of the two parts of the theory: special relativity in the world of microscopic physics, general relativity in the world of astrophysics and cosmology.
A third reason is that physicists accepted and understood special relativity by the early 1920s. It quickly became a working tool for theorists and experimentalists in the then-burgeoning fields of atomic and nuclear physics and quantum mechanics. This rapid acceptance was not, however, the case for general relativity. The theory did not appear to have as much direct connection with experiment as the special theory; most of its applications were on astronomical scales, and it was apparently limited to adding minuscule corrections to the predictions of Newtonian gravitation theory; its cosmological impact would not be felt for another decade. In addition, the mathematics of the theory were thought to be extraordinarily difficult to comprehend. The British astronomer Sir Arthur Eddington, one of the first to fully understand the theory in detail, was once asked if it were true that only three people in the world understood general relativity. He is said to have replied, "Who is the third?"
This situation persisted for almost 40 years. General relativity was considered a respectable subject not for physicists, but for pure mathematicians and philosophers. Around 1960, however, a remarkable resurgence of interest in general relativity began that has made it an important and serious branch of physics and astronomy. (By 1977, Eddington's remark was recalled at a conference on general relativity attended by more than 800 researchers in the subject.) This growth has its roots, first, beginning around 1960, in the application of new mathematical techniques to the study of general relativity that significantly streamlined calculations and that allowed the physically significant concepts to be isolated from the mathematical complexity, and second, in the discovery of exotic astronomical phenomena in which general relativity could play an important role, including quasars (1963), the 3-kelvin microwave background radiation (1965), pulsars (1967), and the possible discovery of black holes (1971). In addition, the rapid technological advances of the 1960s and '70s gave experimenters new high-precision tools to test whether general relativity was the correct theory of gravitation.
The distinction between special relativity and the curved space-time of general relativity is largely a matter of degree. Special relativity is actually an approximation to curved space-time that is valid in sufficiently small regions of space-time, much as the overall surface of an apple is curved even though a small region of the surface is approximately flat. Special relativity thus may be used whenever the scale of the phenomena being studied is small compared to the scale on which space-time curvature (gravitation) begins to be noticed. For most applications in atomic or nuclear physics, this approximation is so accurate that relativity can be assumed to be exact; in other words, gravity is assumed to be completely absent. From this point of view, special relativity and all its consequences may be "derived" from a single simple postulate. In the presence of gravity, however, the approximate nature of special relativity may manifest itself, so the principle of equivalence is invoked to determine how matter responds to curved space-time. Finally, to learn the extent that space-time is curved by the presence of matter, general relativity is applied.
SPECIAL RELATIVITY
The two basic concepts of special relativity are the inertial frame and the principle of relativity. An inertial frame of reference is any region, such as a freely falling laboratory, in which all objects move in straight lines with uniform velocity. This region is free from gravitation and is called a Galilean system. The principle of relativity postulates that the result of any physical experiment performed inside a laboratory in an inertial frame is independent of the uniform velocity of the frame. In other words, the laws of physics must have the same form in every inertial frame. A corollary is that the speed of light must be the same in any inertial frame (because a speed-of-light measurement is a physical experiment) regardless of the speed of its source or that of the observer. Essentially all the laws and consequences of special relativity can be derived from these concepts.
The first important consequence is the relativity of simultaneity. Because any operational definition of simultaneous events at different locations involves the sending of light signals between them, then two events that are simultaneous in one inertial frame may not be simultaneous when viewed from a frame moving relative to the first. This conclusion helped abolish the Newtonian concept of an absolute, universal time. In some ways the most important consequences and confirmations of special relativity arise when it is merged with quantum mechanics, leading to many predictions in agreement with experiments, such as elementary particle spin, atomic fine structure, antimatter, and so on.
The mathematical foundations of special relativity were explored in 1908 by the German mathematician Hermann Minkowski, who developed the concept of a "four-dimensional space-time continuum," in which time is treated the same as the three spatial dimensions--the fourth dimension of Minkowski space-time.
THE PRINCIPLE OF EQUIVALENCE AND SPACE-TIME CURVATURE
The exact Minkowski space-time of special relativity is incompatible with the existence of gravity. A frame chosen to be inertial for a particle far from the Earth where the gravitational field is negligible will not be inertial for a particle near the Earth. An approximate compatibility between the two, however, can be achieved through a remarkable property of gravitation called the weak equivalence principle (WEP): all modest-sized bodies fall in a given external gravitational field with the same acceleration regardless of their mass, composition, or structure. The principle's validity has been checked experimentally by Galileo, Newton, and Friedrich Bessel, and in the early 20th century by Baron Roland von Eotvos (after whom such experiments are named). If an observer were to ride in an elevator falling freely in a gravitational field, then all bodies inside the elevator, because they are falling at the same rate, would consequently move uniformly in straight lines as if gravity had vanished. Conversely, in an accelerated elevator in free space, bodies would fall with the same acceleration (because of their inertia), just as if there were a gravitational field.
Einstein's great insight was to postulate that this "vanishing" of gravity in free-fall applied not only to mechanical motion but 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 red shift, 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/c(2) 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 red shift 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 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 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. 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.
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. For a number of years the big bang theory was contested by an alternative known as the steady state theory, based on the concept of the continuous creation of matter throughout the universe. Later knowledge gained about the universe, however, has strongly supported the big bang theory as against its competitors. Such findings either were predicted by or did not conflict with relativity theory, thus also further supporting the theory. Perhaps the most critical piece of evidence was the discovery, in 1965, of what is called BACKGROUND RADIATION. This "sea" of electromagnetic radiation fills the universe at a temperature of about 2.7K (2.7 degrees C above absolute zero). Background radiation had been proposed by general relativity as the remaining trace of an early, hot phase of the universe following the big bang. The observed cosmic abundance of helium (20 to 30 percent by weight) is also a required result of the big-bang conditions predicted by relativity theory.
In addition, general relativity has suggested various kinds of celestial phenomena that could exist, including neutron stars, black holes, gravitational lenses, and gravitational waves. According to relativistic theory, neutron stars would be small but extremely dense stellar bodies. A neutron star with a mass equal to that of the Sun, for example, would have a radius of only 10 km (6 mi). Stars of this nature have been so compressed by gravitational forces that their density is comparable to densities within the nuclei of atoms, and they are composed primarily of neutrons. Such stars are thought to occur as a by-product of violent celestial events such as supernovae and other gravitational implosions of stars. Since neutron stars were first proposed in the 1930s, numerous celestial objects that exhibit characteristics of this sort have been identified. In 1967 the first of many objects now called pulsars was also detected. These stars, which emit rapid regular pulses of radiation, are now taken to be rapidly spinning neutron stars, with the pulse period represent the period of rotation.
Black holes are among the most exotic of the predictions of general relativity, although the concept itself dates from long before the 20th century. These theorized objects are celestial bodies with so strong a gravitational field that no particles or radiation can escape from them, not even light--hence the name. Black holes most likely would be produced by the implosions of extremely massive stars, and they could continue to grow as other material entered their field of attraction. Some theorists have speculated that supermassive black holes may exist at the centers of some clusters of stars and of some galaxies, including our own. While the existence of such black holes has not been proven beyond all doubt, evidence for their presence at a number of known sites is very strong.
In theory, even a relatively small mass could become a black hole. The mass would have to be compressed to higher and higher densities until it diminished to a certain critical radius, the so-called "event horizon," named the SCHWARZSCHILD RADIUS because it was first calculated in 1916 by German astronomer Karl Schwarzschild. (His calculations apply to a nonrotating object. The figures for a rotating object were developed in 1963 by New Zealand mathematician Roy Kerr.) For an object having the mass of the Sun the event horizon would be approximately 3 km (2 mi). Scientists such as the English theoretical physicist Stephen HAWKING have speculated that tiny black holes may indeed exist.
The concept of gravitational lenses is based on the already discussed and proven relativistic prediction that when light from a celestial object passes near a massive body such as a star, its path is deflected. The amount of deflection depends on the massiveness of the intervening body. From this came the notion that very massive celestial objects such as galaxies could act as the equivalent of crude optical lenses for light coming from still more distant objects beyond them. An actual gravitational lens was first identified in 1979.
One phenomenon predicted by general relativity has not yet been substantially verified, however: the existence of gravitational waves. Gravitational waves would be produced by changes in gravitational fields. They would travel at the speed of light, transport energy, and induce relative motion between pairs of particles in their path (or produce strains in more massive objects). Astrophysicists think that gravitational waves should be emitted by dynamic sources such as supernovae, massive binary (or multiple-star) systems, and black holes or collisions between black holes. Various attempts, unsuccessful thus far, have been made to observe such waves.
A more fundamental matter confronting general relativity is that of the attempt being made by physicists to unite gravitation with QUANTUM MECHANICS, the other paradigm of modern physics. This search for some UNIFIED FIELD THEORY is the major task of workers in QUANTUM COSMOLOGY.