Velocities of the same body in two frames of reference (see text).

Advance of Mercury's perihelion

The major axes of the elliptical trajectories of the planets about the Sun turn slowly within their planes because of the interactions of the planets with each other, but it was discovered in the 19th century that interplanetary perturbations could not account fully for the turning rate of Mercury's orbit, leaving unexplained about 43 seconds of arc per century. The general theory of relativity, however, accounts exactly for this discrepancy. In 1967 Dicke--and more recently Henry Allen Hill, also of the United States--suggested that a small part of Mercury's perihelion advance may be caused by the slight flattening of the Sun at its poles, thus opening the way for possible modification of general relativity. On the other hand, support for Einstein's original version of the theory has come from a comprehensive evaluation of solar system data by the American investigator Ronald W. Hellings and from investigations of the binary pulsar system PSR 1913+16 by the American astronomer Joseph H. Taylor.

Gravitationalredshift

General relativity predicts that the wavelength of light emanating from sources within a gravitational field will increase (shift toward the red end of the spectrum) by an amount proportional to the gravitational potential at the site of the source. This effect was found first in astronomical objects, particularly in stars called white dwarfs, on whose surfaces the gravitational potential is large. The best quantitative confirmation of gravitational redshift was obtained in laboratory experiments in Great Britain and the United States in the 1960s; an accuracy of one part in 100 was achieved in measuring the minute difference in gravitational potential between two sites differing in altitude by a few metres.

Optical effects of gravitation

General relativity predicts that the curvature of space-time results in the apparent bending of light rays passing through gravitational fields and in an apparent reduction of their speeds of propagation. The bending was first observed, within a couple of years of Einstein's publication of the new theory, during a total eclipse, when stellar images near the occulted disk of the Sun appeared displaced by fractions of 1 of arc from their usual locations in the sky. The associated delay in travel time was observed in the late 1960s, when ultraintense radar pulses were reflected off Mercury and Venus just as these planets were passing behind the Sun. These experiments are difficult to perform and their accuracy is difficult to evaluate, but it seems conservative to conclude that they confirm the relativistic effect within a few parts in 100. Finally, extended massive objects such as galaxies may act as "gravitational lenses," providing more than one optical path for light emanating from a source far behind the lens and thus producing multiple images. Such multiple images, typically of quasars, had been discovered by the early 1980s.

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Contents:

Introduction
    The special theory of relativity
       Historical background
       Relativity of space and time
       Consequences
          The limiting character of the speed of light
          Variable mass
          Invariant intervals
          The "twin paradox"
          Four-dimensional space-time
    The general theory of relativity
       Physical origins
       The principle of equivalence
       Curved space-time
          The principles
          The mathematical expression
       Confirmation of the theory
          Advance of Mercury's perihelion
          Gravitational redshift
          Optical effects of gravitation
          Gravitational waves
          Future astrophysical tests
       Conceptual implications of general relativity
       Schwarzschild's solution of the field equations
    Applications of relativistic principles
       Particle accelerators
       Relativistic particle physics
       Relativistic cosmology
    Modifications of general relativity
    Bibliography