RELATIVITY

in physics, the problem of whether and how physical laws and measurements change when considered by observers in various states of motion. Specifically the term appears in the work of the German physicist Albert Einstein, whose special theory of relativity (1905) and general theory of relativity (1916) are major milestones in the history of modern physics. The classic illustration of relativity uses the example of a railway train in motion. Suppose a train is traveling in a straight line at 100 km per hour, relative to a fixed point on the ground, and that a passenger is walking forward through the train at 3 km per hour, relative to the train. What is the passenger's speed relative to a point on the ground? The obvious, almost intuitive, answer is 103 km per hour. In classical mechanics, quantities such as speed and distance may be transformed from one frame of reference to another, provided that the frames are in uniform motion with respect to one another, by very simple operations known as Galilean transformations. In electrodynamics, such is not the case. If the passenger is replaced by a ray of light traveling through the train, the speed of the light ray with respect to a point on the ground is not simply the sum of its speed with respect to the train and the train's speed with respect to the ground; in fact, it is the same with respect to both frames of reference. The first empirical demonstration of this fact was made by A.A. Michelson and Edward Williams Morley in a famous set of experiments in 1887 that showed that the speed of light is the same in all directions and the same with respect to any frame of reference regardless of its state of motion. This startling fact has several important implications. Just as in Galilean transformations, there is no true or preferred frame of reference (frame of absolute rest). But in order for the speed of light in empty space to be the same for all unaccelerated observers, rather more complex operations are required to transform measures in one unaccelerated frame of reference to another frame; these operations, which involve explicit references to the speed of light, are called Lorentz transformations. They imply that clocks moving relative to an observer appear to be running more slowly than they do to an observer with respect to whom they are at rest. The dimensions of a moving object appear foreshortened in the direction of motion if the length is, for instance, determined by the time elapsed between the passages of two marks on the object past one point at rest relative to the observer. These last effects are vanishingly small when speeds of everyday objects or even of most astronomical bodies are being considered, but they become significantand have been confirmedin the realm of subatomic particles. Such particles also exhibit another relativistic effect: as they are accelerated to an appreciable fraction of the speed of light, their mass increases. This effect derives from the limiting character of the speed of light, and it implies the most familiar conclusion of special relativity, the equivalence of matter and energy, expressed in the well-known formula E = mc2, where the energy equivalent of a mass is equal to the mass times the speed of light squared. Another implication of special relativity is that the universe must be thought of as a continuum with both spatial and temporal dimensions. In other words, in the space-time continuum, the notion of a purely spatial separation between events is ambiguous; any such distance will be measured differently by observers in different states of motion. Similarly, the time elapsed between two events will depend on the observer's motion and will not be a fixed datum. A measure of separation called interval, involving both spatial and temporal terms, will however, be invariant (i.e., will be calculated to be the same by all observers regardless of motion). These basic notions essentially comprise the special theory of relativity, which provides a framework for translating physical events and laws into forms appropriate for any frame of reference in uniform motion, or, as they are also called, inertial frames of reference. When the speeds involved are very small compared with the speed of light, the Lorentz transformations simplify to the Galilean formulas, and the laws of classical Newtonian mechanics hold sway. The general theory of relativity addresses the problem of gravity and that of nonuniform, or accelerated, motion. In one of his famous thought-experiments, Einstein showed that it is not possible to distinguish between an inertial frame of reference in a gravitational field and an accelerated frame of reference. That is, an observer in a closed space capsule who found himself pressing down on his seat could not tell whether he and the capsule were at rest in a gravitational field, or whether he and the capsule were undergoing acceleration. From this principle of equivalence, Einstein moved to a geometric interpretation of gravitation. The presence of mass or concentrated energy causes a local curvature in the space-time continuum. This curvature is such that the inertial paths of bodies are no longer straight lines but some form of curved (orbital) path, and this acceleration is what is called gravitation. Einstein was able to construct a single field equation capable of describing the curvature of space at and the energy or mass of any point in space-time. With each such point he associated a set of 10 functionsthe metric tensorthat characterize the geometrical properties of space, including curvature, at the point, and a second set of 10the energy-stress tensorthat specify the material contents of space at the point. This equation, together with the rule that freely falling bodies follow geodesic paths (essentially, the shortest distance between two points, which, where space-time is curved, is not a straight line), constitutes the general theory. With suitable simplifying assumptions, Einstein's field equation reduces to Newton's law of gravitation, which can be considered a special case for relatively slow speeds and weak fields. The general theory has been confirmed experimentally in a number of ways. One of its predictions, that a ray of light passing near a very massive object such as the Sun will be bent, was confirmed as early as 1919, during a solar eclipse. It also succeeded in accounting for an anomaly in the motion of the planet Mercury that had defied explanation by Newtonian theory. Other predictions of the general theory that await complete confirmation include the existence of gravity waves and of black holes formed by the collapse of massive stars into extremely small, dense objects whose gravitational fields are so intense that not even light can escape. in physics, the problem of how physical laws and measurements change when considered by observers in various states of motion. Thus, relativity is concerned with measurements made by different observers moving relative to one another. In classical physics it was assumed that all observers anywhere in the universe, whether moving or not, obtained identical measurements of space and time intervals. According to relativity theory, this is not so, but their results depend on their relative motions. There are actually two distinct theories of relativity known in physics, one called the special theory of relativity, the other the general theory of relativity. Albert Einstein proposed the first in 1905, the second in 1916. Whereas the special theory of relativity is concerned primarily with electric and magnetic phenomena and with their propagation in space and time, the general theory of relativity was developed primarily in order to deal with gravitation. Both theories centre on new approaches to space and time, approaches that differ profoundly from those useful in everyday life; but relativistic notions of space and time are inextricably woven into any contemporary interpretation of physical phenomena ranging from the atom to the universe as a whole. This article will set forth the principal ideas comprising both special and general relativity. It will also deal with some implications and applications of these theories. For treatment of the motion of relativistic bodies, see the article relativistic mechanics. Additional reading Among expositions for general readers are Albert Einstein, Relativity: The Special and General Theory: A Popular Exposition, 17th ed. (1961; originally published in German, 1917), a popularization for the lay reader of a classic work written by one of the greatest scientists of all time; Bertrand Russell, The ABC of Relativity, 4th rev. ed. edited by Felix Pirani (1985); Albert Einstein and Leopold Infeld, The Evolution of Physics (1938, reissued 1961); Leopold Infeld, Albert Einstein: His Work and Its Influence on Our World (1950), two books that cover the whole of physics, with special emphasis on relativity (Infeld was one of Einstein's chief collaborators in the 1930s); Hermann Bondi, Relativity and Common Sense: A New Approach to Einstein (1964, reissued 1980); Robert Geroch, General Relativity from A to B (1978), a beautiful book explaining general relativity in an exciting and insightful manner to an audience of humanists; Peter G. Bergmann, The Riddle of Gravitation, rev. and updated ed. (1987, reissued 1992), a work that emphasizes the general theory of relativity and includes a discussion of research; Sam Lilley, Discovering Relativity for Yourself (1981), a work that covers both theories; George F.R. Ellis and Ruth M. Williams, Flat and Curved Space-times (1988); Eric Chaisson, Relatively Speaking: Relativity, Black Holes, and the Fate of the Universe (1988); and Clifford M. Will, Was Einstein Right?: Putting General Relativity to the Test, 2nd ed. (1993), the last two works stressing the astronomical aspect of relativity. Presentations for readers with technical training include H.A. Lorentz et al., The Principle of Relativity (1923, reissued 1952), a collection of fundamental research papers, all in English; Albert Einstein, The Meaning of Relativity, 5th ed., trans. from German (1955, reprinted 1988), based on lectures by Einstein delivered in 1921, with two appendixes containing Einstein's views on cosmology through 1945, and his work on the nonsymmetric unified field theory to the time of his death in 1955; Abraham Pais, Subtle Is the Lord: The Science and the Life of Albert Einstein (1982), containing a wealth of material on relativity, its history, and its relationship to the whole of physics; David Bohm, The Special Theory of Relativity (1965, reprinted 1989), a thoroughgoing treatment of the special theory combined with a discussion of the philosophical foundations of physics; A.P. French, Special Relativity (1968, reissued 1984), an introduction at the undergraduate level; Hermann Bondi, Cosmology, 2nd ed. (1961), a survey of cosmology at a technical level, including observational data through the late 1950s; Peter G. Bergmann, Introduction to the Theory of Relativity (1942, reissued 1976); C. Mller, The Theory of Relativity, 2nd ed. (1972); J.L. Synge, Relativity: The Special Theory, 2nd ed. (1964, reissued 1972), and Relativity: The General Theory (1960, reissued 1971); Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler, Gravitation (1973), technical texts, on the graduate level, that represent distinct approaches to the subject by active research workers; Steven Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (1972), by a Nobel laureate; J.L. Martin, General Relativity: A Guide to Its Consequences for Gravity and Cosmology (1988), a text on the general theory; S.W. Hawking and G.F.R. Ellis, The Large Scale Structure of Space-Time (1973), a work principally concerned with the geometric aspects of general relativity on a global scale; Robert M. Wald, General Relativity (1984), and Space, Time, and Gravity, 2nd ed. (1992), written by one of the experts and an active contributor in the field; Roberto Torretti, Relativity and Geometry (1983), an exposition of the general and special theories from a geometric perspective, for the advanced reader; and Wolfgang Rindler, Introduction to Special Relativity, 2nd ed. (1991). Two historical works are Don Howard and John Stachel (eds.), Einstein and the History of General Relativity (1989); and Jean Eisenstaedt and A.J. Kox (eds.), Studies in the History of General Relativity (1992). Peter G. Bergmann The Editors of the Encyclopdia Britannica