# relativity, general theory

## relativity, general theory

(rel-ă-**tiv**-ă-tee) The theory put forward by Albert Einstein in 1915. It describes how the relationship between space and time, as developed in the special theory of relativity, is affected by the gravitational effects of matter. The basic conclusion is that gravitational fields change the geometry of spacetime, causing it to become curved. It is this curvature of spacetime that controls the natural motions of bodies. Thus matter tells spacetime how to curve and spacetime tells matter how to move. General relativity (GR) may therefore be considered as a theory of gravitation, the differences between it and Newtonian gravitation appearing only when the gravitational fields become very strong, as with black holes, neutron stars, and white dwarfs, or when very accurate measurements can be made. GR also reduces to the special theory when gravitational effects are negligible.

The basic postulate from which GR was developed is the principle of equivalence between gravitational and inertial forces: in two laboratories, one in a uniform gravitational field and the other suitably accelerated, the same laws of nature apply and thus the same phenomena, including optical ones, will be observed. Einstein was able to show that the natural motion of a body was in a ‘straight line’, i.e. along the shortest path between two points (a geodesic), in the geometry required to describe the physical world (compare Newton's laws of motion). Three-dimensional Euclidean geometry could not be used for this purpose. The requisite geometry had to be more flexible: this was the geometry of spacetime. The presence of gravitational fields leads to the curvature of spacetime. The curvature produced by a particular gravitational field can be calculated from Einstein's *field equations*, advanced as part of GR. It is then possible to calculate the geodesics followed by particles in this curved spacetime.

Experimental tests of GR require either very strong gravitational fields or very accurate measurements. These tests must verify the predictions of GR where they deviate from the predictions of Newtonian gravitation and also where they deviate from the predictions of other relativistic theories of gravitation (including the Brans–Dicke theory) that have been developed since 1915. The main tests involve four predicted effects.

One effect is the bending of light or other electromagnetic radiation in a gravitational field. Measurements of the positions of stars when close to the Sun's limb (i.e. during total solar eclipses) and when some distance from the Sun have been shown to differ: the Sun's gravitational field changes the path of a photon of radiation from a straight line to a path bent toward the Sun. The angle by which the photon's path is deflected is called the *deflection of light*. The measured deflection for stars on the solar limb is near Einstein's predicted value, which is 1.75 arc secs. Closer agreement (within 1%) has been found when the bending of radiation from radio sources such as quasars is determined (see also gravitational lens). A related effect is the time delay in radio signals from spacecraft when they are close to the Sun. The measured delays from the Viking probes and other craft agree with Einstein's prediction within 0.1%.

The predicted gravitational redshift in the spectral lines of radiation emitted from a massive body has also been successfully demonstrated using both the Sun's and also the Earth's gravitational fields. A related prediction is that clocks run more slowly in a strong gravitational field than in a weaker one. An atomic clock flown at an altitude of 10 km has been shown to run faster than at sea level by a value within 0.02% of the predicted amount (47 × 10^{–9} seconds).

The effects of curved spacetime on the motions of orbiting bodies were shown convincingly when the advance of the perihelion of Mercury was found to be accounted for by GR. Recent measurements of the very much larger periastron shift of the binary pulsar 1913+16 provided much stronger evidence, being in very close agreement with prediction.

The fourth test of GR concerns the predicted existence of gravitational waves. The emission of such waves causes a loss of energy from a system and in a binary system alters the orbital period. Recent measurements of the speed-up in the period of the binary pulsar 1913+16 are in almost precise agreement with the predicted value of GR. Many alternative theories of gravitation predict much higher values.

Other predictions of GR are the existence of singularities in the structure of spacetime leading to black holes, and the constancy of the gravitational constant. There is no direct evidence as yet for (or against) these, although indirect evidence of black holes is accumulating.

It cannot be said that GR has been conclusively proved. The experimental evidence does, however, seem to be mounting in its favor.