## The General Theory of Relativity

The special theory of relativity applies only to observers moving with uniform velocity in relation to each other. Einstein expanded this theory into a general theory that also applies to observers with nonuni-form, or accelerated, relative motion. The general theory of relativity has strongly influenced developments in advanced physics, geometry, and astronomy. The theory is of particular importance in cosmology.

As an essential part of the theory, Einstein developed a theory of gravitation fundamentally different from that developed by Newton. The concept of gravitation in the general theory of relativity is largely based on the principle of equivalence. According to this principle, it is not possible by experiment to distinguish between the effects caused by the acceleration of a system and those caused by gravitation—the effects are equivalent to each other.

For example, a person in an elevator that accelerates upward will sense that the floor is pushing up against him. This effect results from the tendency of the person's body to resist acceleration. However, the same effect would be produced if the elevator were stationary and the pull of gravity increasing—there is no way to distinguish between the two effects.

Einstein saw that this equivalence could be explained by relating gravitation to the geometrical properties of the space-time continuum. According to the general theory of relativity, space-time is distorted by the presence of matter: specifically, gravitating bodies bend the space-time continuum. As an object moves through the space-time continuum, it follows the curvature of space-time. The resulting motion of the object is interpreted in classical physics as gravitational attraction.

Einstein developed a set of equations to describe the manner in which space-time is distorted by matter. These equations make use of a geometry developed by the 19th-century German mathematician Georg F. B. Riemann. In Riemannian geometry there are no straight lines but only curves. Therefore, the space described by the general theory of relativity is a curved space without straight lines.

Einstein proposed three relativistic effects that could be measured to test the general theory. These effects were the bending of light by a gravitational field, the shifting of the planet Mercury's orbit around the sun, and the gravitational redshift of light (the change in the wavelength of light as it enters or leaves a gravitational field).

Measurements of each of these effects supported the general theory. The most famous test was conducted during the total eclipse of the sun in 1919. One of the most conclusive tests involves an effect called time delay—a slight delay in the passage of radio signals through a gravitational field. This delay was very accurately measured in the late 1970's by determining the time it took radio signals from spacecraft on Mars to reach the earth when Mars was on the opposite side of the sun.

During the time since the publication of the general theory of relativity, various new theories of gravitation have been proposed that also incorporate the principle of equivalence. These theories make use of a curved space-time, but they differ from Einstein's theory in the amount of curvature they predict. Various experiments conducted since the 1960's to measure the effects of the curvature of space-time have tended to support Einstein's theory over the others.

The general theory of relativity is used in studying the overall structure of the universe. With the theory, scientists have predicted the existence of a variety of exotic celestial objects and phenomena, including black holes and gravitational lenses.

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