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General Relativity: The First Dynamical Theory of Geometry

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Added on  2019-09-20

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General relativity is a theory of gravitation that transformed the way we understand space-time. It replaced the newtonian law of motion with the statement that free test particles move along geodesics, the shortest curves in the space-time geometry. Einstein's theory provided 10 equations relating the metric to the material energy momentum tensor, replacing Poisson's equation. The theory predicts the gravitational redshift, the deflection of light beams passing near a gravitating body, and the precession of the periastron of a binary system. Learn more about general relativity and its predictions on Desklib.
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According to newtonian theory, gravitational effects propagate from place toplace instantaneously. With the advent of Einstein's special theory of relativity in 1905, a theory uniting the concepts of space and time into that of four dimensional flat space-time (named Minkowski space-time after the mathematician Hermann Minkowski), a problem became discernible with newtonian theory. According to special relativity, which is the current guideline to the form of all physical theory, the speed of light,c= 3 × 1010cm s-1, is the top speed allowed to physical particles or forces: There can be no instantaneous propagation. After a decade of search for new concepts to make gravitational theory compatible with the spirit of special relativity, Einstein came up with the theory of general relativity (1915), the prototype of all modern gravitational theories. Its crucial ingredient, involving a colossal intellectual jump, is the concept of gravitation, not as a force, but as a manifestation of the curvature of space-time, an idea first mentioned in rudimentary form by the mathematician Ceorg Bernhard Riemann in 1854. In Einstein's hands gravitation theory was thus transformed from a theory of forces into the first dynamical theory of geometry, the geometry of four dimensional curved space-time.Why talk of curvature? One of Einstein's first predictions was the gravitational redshift: As any wave, such as light, propagates away from a gravitating mass, all frequencies in it are reduced by an amount proportionalto the change in gravitational potential experienced by the wave. This redshift has been measured in the laboratory, in solar observations, and by means of high precision clocks flown in airplanes. However, imagine for a moment that general relativity had not yet been invented, but the redshift hasalready been measured. According to a simple argument owing to Alfred Schild, wave propagation under stationary circumstances can display a redshift only if the usual geometric relations implicit in Minkowski space-time are violated: The space-time must be curved. The observations of the redshift thus show that space-time must be curved in the vicinity of masses, regardless of the precise form of the gravitational theory.Einstein provided 10 equations relating the metric (a tensor with 10 independent components describing the geometry of space-time) to the material energy momentum tensor (also composed of 10 components, one ofwhich corresponds to our previous). These Einstein field equations, in which both of the previously mentioned constantsGandcfigure as parameters, replace Poisson's equation. Einstein also replaced the newtonianlaw of motion by the statement that free test particles move along geodesics,the shortest curves in the space-time geometry. The influential gravitation theorist John Archibald Wheeler has encapsulated general relativity in the aphorism "curvature tells matter how to move, and matter tells space-time how to curve." The Eotvos-Dicke-Braginsky experiments demonstrate with high precision that free test particles all travel along the same trajectories in
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