Tests of general relativity: Encyclopedia II - Tests of general relativity - Classical tests

Tests of general relativity - Classical tests

In his 1916 paper, Einstein proposed three famous tests of general relativity, now called the classical tests:

1. the gravitational redshift of light
2. the deflection of light by the Sun
3. the precession of the perihelion of Mercury

In Newtonian physics, a lone object orbiting a spherical mass would trace out an ellipse with the spherical mass at a focus. The point of closest approach, called the perihelion in the solar system, is fixed. There are a number of solar system effects that cause the perihelion of a planet to precess, or rotate around the sun. These are mainly because of solar oblateness and the presence of other planets, which perturb orbits. The precession of the perihelion of Mercury was a longstanding problem in celestial mechanics. Careful observations of Mercury showed that the actual value of the precession disagreed with that calculated from Newton's theory by 43 seconds of arc per century, which was much larger than the experimental error at the time. A number of ad hoc and ultimately unsuccessful solutions had been proposed, but they tended to introduce more problems. In general relativity, this orbit will precess, or change orientation within its plane, due to gravitation being mediated by the curvature of spacetime. Since the orientation of an orbit is usually given by the position of its periapsis, this change of orientation is described as being a precession in the periapsis of an object. However, the problem was resolved by Einstein's theory (Einstein, 1916), which predicted exactly the observed amount of perihelion shift. This was a powerful factor motivating the adoption of Einstein's theory.

The total observed precession of Mercury is 5600 arc-seconds per century with respect to the position of the Vernal Equinox of the Sun. This precession is due the following causes (the numbers quoted are the modern values):

Thus, the predictions of general relativity perfectly account for the missing precession (the remaining discrepancy is within observational error). All other planets experience perihelion shifts as well, but, since they are further away from the Sun and have lower speeds, their shifts are lower and harder to observe. For example, the perihelion shift of Earth's orbit due to general relativity effects is about 5 seconds of arc per century.

The first observation of light deflection was performed by noting the change in position of stars as they passed near the Sun on the celestial sphere. The observations were performed by Sir Arthur Eddington (Dyson, 1920) and his collaborators during a total solar eclipse, so that the stars near the sun could be observed. Observations were made simultaneously in the city of Sobral, Ceará, Brazil and in the west coast of Africa. The result was considered spectacular news and made the front page of most major newspapers. It made Einstein and his theory of general relativity world famous.

The early accuracy, however, was poor. Dyson et al. quoted an optimistically low uncertainty in their measurement, which is thought to be plagued by systematic error. Considerable uncertainty remained in these measurements for almost fifty years, until observations started being made at radio frequencies. In 1801 J. Soldner pointed out that Newtonian gravity also predicts that starlight will bend around a massive object, but the predicted effect is only half the value predicted by general relativity (which gives a bending effect much closer to the observed value), which is the same as the value calculated by Einstein in his 1911 paper. The results of Soldner were revived by the anti-Semite Philipp Lenard (1921) in an attempt to discredit Einstein. It was not until the late 1960s that it was definitively shown that the amount of deflection was the full value predicted by general relativity, and not half that number.

The gravitational redshift of light, was predicted by Einstein from the equivalence principle in 1907. However, despite effort, it is very difficult to measure astrophysically. It was not conclusively tested until the Pound-Rebka experiment in 1959 measured the relative redshift of two sources situated at the top and bottom of Harvard University's Jefferson tower. This was one of the first precision experiments testing general relativity.

Adapted from the Wikipedia article "Classical tests", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki