According to newtonian theory, gravitational effects propagate

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According to newtonian theory, gravitational effects propagate from place toplace instantaneously. With the advent of Einstein's special theory ofrelativity in 1905, a theory uniting the concepts of space and time into thatof four dimensional flat space-time (named Minkowski space-time after themathematician Hermann Minkowski), a problem became discernible withnewtonian theory. According to special relativity, which is the currentguideline 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: Therecan be no instantaneous propagation. After a decade of search for newconcepts to make gravitational theory compatible with the spirit of specialrelativity, Einstein came up with the theory of general relativity (1915), theprototype of all modern gravitational theories. Its crucial ingredient,involving a colossal intellectual jump, is the concept of gravitation, not as aforce, but as a manifestation of the curvature of space-time, an idea firstmentioned in rudimentary form by the mathematician Ceorg BernhardRiemann in 1854. In Einstein's hands gravitation theory was thustransformed from a theory of forces into the first dynamical theory ofgeometry, the geometry of four dimensional curved space-time.Why talk of curvature? One of Einstein's first predictions was thegravitational redshift: As any wave, such as light, propagates away from agravitating mass, all frequencies in it are reduced by an amount proportionalto the change in gravitational potential experienced by the wave. Thisredshift has been measured in the laboratory, in solar observations, and bymeans of high precision clocks flown in airplanes. However, imagine for amoment that general relativity had not yet been invented, but the redshift hasalready been measured. According to a simple argument owing to AlfredSchild, wave propagation under stationary circumstances can display aredshift only if the usual geometric relations implicit in Minkowski space-time are violated: The space-time must be curved. The observations of theredshift 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 10independent components describing the geometry of space-time) to thematerial energy momentum tensor (also composed of 10 components, one ofwhich corresponds to our previous). These Einstein field equations, inwhich both of the previously mentioned constantsGandcfigure asparameters, 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 gravitationtheorist John Archibald Wheeler has encapsulated general relativity in theaphorism "curvature tells matter how to move, and matter tells space-timehow to curve." The Eotvos-Dicke-Braginsky experiments demonstrate withhigh precision that free test particles all travel along the same trajectories in
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