Tests of general relativity
Tests of general relativity serve to establish observational evidence for the theory of general relativity. The first three tests, proposed by Albert Einstein in 1915, concerned the "anomalous" precession of the perihelion of Mercury, the bending of light in gravitational fields, and the gravitational redshift. The precession of Mercury was already known; experiments showing light bending in accordance with the predictions of general relativity were performed in 1919, with increasingly precise measurements made in subsequent tests; and scientists claimed to have measured the gravitational redshift in 1925, although measurements sensitive enough to actually confirm the theory were not made until 1954. A more accurate program starting in 1959 tested general relativity in the weak gravitational field limit, severely limiting possible deviations from the theory.
In the 1970s, scientists began to make additional tests, starting with Irwin Shapiro's measurement of the relativistic time delay in radar signal travel time near the Sun. Beginning in 1974, Russell Alan Hulse, Joseph Hooton Taylor Jr. and others studied the behaviour of binary pulsars experiencing much stronger gravitational fields than those found in the Solar System. Both in the weak field limit and with the stronger fields present in systems of binary pulsars the predictions of general relativity have been extremely well tested.
In February 2016, the Advanced LIGO team announced that they had directly detected gravitational waves from a black hole merger. This discovery, along with additional detections announced in June 2016 and June 2017, tested general relativity in the very strong field limit, observing to date no deviations from theory.
Classical tests
proposed three tests of general relativity, subsequently called the "classical tests" of general relativity, in 1916:- the perihelion precession of Mercury's orbit
- the deflection of light by the Sun
- the gravitational redshift of light
Perihelion precession of Mercury
Under Newtonian physics, an object in an two-body system, consisting of the object orbiting a spherical mass, would trace out an ellipse with the center of mass of the system at a focus of the ellipse. The point of closest approach, called the periapsis, is fixed. Hence the major axis of the ellipse remains fixed in space. Both objects orbit around the center of mass of this system, so they each have their own ellipse. However, a number of effects in the Solar System cause the perihelia of planets to precess around the Sun in the plane of their orbits, or equivalently, cause the major axis to rotate about the center of mass, hence changing its orientation in space. The principal cause is the presence of other planets which perturb one another's orbit. Another effect is solar oblateness.Mercury deviates from the precession predicted from these Newtonian effects. This anomalous rate of precession of the perihelion of Mercury's orbit was first recognized in 1859 as a problem in celestial mechanics, by Urbain Le Verrier. His re-analysis of available timed observations of transits of Mercury over the Sun's disk from 1697 to 1848 showed that the actual rate of the precession disagreed from that predicted from Newton's theory by 38″ per tropical century. A number of ad hoc and ultimately unsuccessful solutions were proposed, but they tended to introduce more problems. Le Verrier suggested that another hypothetical planet might exist to account for Mercury's behavior. The previously successful search for Neptune based on its perturbations of the orbit of Uranus led astronomers to place some faith in this possible explanation, and the hypothetical planet was even named Vulcan. Finally, in 1908, W. W. Campbell, Director of the Lick Observatory, after the comprehensive photographic observations by Lick astronomer, Charles D. Perrine, at three solar eclipse expeditions, stated, "In my opinion, Dr. Perrine's work at the three eclipses of 1901, 1905, and 1908 brings the observational side of the famous intramercurial-planet problem definitely to a close." Subsequently, no evidence of Vulcan was found and Einstein's 1915 general theory accounted for Mercury's anomalous precession. Einstein wrote to Michele Besso, "Perihelion motions explained quantitatively ... you will be astonished".
In general relativity, this remaining precession, or change of orientation of the orbital ellipse within its orbital plane, is explained by gravitation being mediated by the curvature of spacetime. Einstein showed that general relativity agrees closely with the observed amount of perihelion shift. This was a powerful factor motivating the adoption of general relativity.
Although earlier measurements of planetary orbits were made using conventional telescopes, more accurate measurements are now made with radar. The total observed precession of Mercury is ″ per century relative to the inertial ICRF. This precession can be attributed to the following causes:
| Amount | Cause |
| 532.3035 | gravitational tugs of other solar bodies |
| 0.0286 | oblateness of the Sun |
| 42.9799 | gravitoelectric effects, a general relativity effect |
| −0.0020 | Lense–Thirring precession |
| 575.31 | total predicted |
| 574.10 ± 0.65 | observed |
The correction by ″/cy is the prediction of post-Newtonian theory with parameters. Thus the effect can be fully explained by general relativity. More recent calculations based on more precise measurements have not materially changed the situation.
In general relativity the perihelion shift σ, expressed in radians per revolution, is approximately given by:
where L is the semi-major axis, T is the orbital period, c is the speed of light, and e is the orbital eccentricity.
The other planets experience perihelion shifts as well, but, since they are farther from the Sun and have longer periods, their shifts are lower, and could not be observed accurately until long after Mercury's. For example, the perihelion shift of Earth's orbit due to general relativity is theoretically 3.83868″ per century and experimentally ″/cy, Venus's is 8.62473″/cy and ″/cy and Mars' is ″/cy. Both values have now been measured, with results in good agreement with theory. The periapsis shift has also now been measured for binary pulsar systems, with PSR 1913+16 amounting to 4.2° per year. These observations are consistent with general relativity. It is also possible to measure periapsis shift in binary star systems which do not contain ultra-dense stars, but it is more difficult to model the classical effects precisely – for example, the alignment of the stars' spin to their orbital plane needs to be known and is hard to measure directly. A few systems, such as DI Herculis, have been measured as test cases for general relativity.
Deflection of light by the Sun
in 1784 and Johann Georg von Soldner in 1801 had pointed out that Newtonian gravity predicts that starlight will bend around a massive object. The same value as Soldner's was calculated by Einstein in 1911 based on the equivalence principle alone. However, Einstein noted in 1915 in the process of completing general relativity, that his 1911 result is only half of the correct value. Einstein became the first to calculate the correct value for light bending: 1.75 arcseconds for light that grazes the Sun.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 Arthur Eddington and his collaborators during the total solar eclipse of May 29, 1919, when the stars near the Sun could be observed. Observations were made simultaneously in the cities of Sobral, Ceará, Brazil and in São Tomé and Príncipe on 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. When asked by his assistant what his reaction would have been if general relativity had not been confirmed by Eddington and Dyson in 1919, Einstein famously made the quip: "Then I would feel sorry for the dear Lord. The theory is correct anyway."
The early accuracy, however, was poor and there was doubt that the small number of measured star locations and instrument questions could produce a reliable result. The results were argued by some to have been plagued by systematic error and possibly confirmation bias, although modern reanalysis of the dataset suggests that Eddington's analysis was accurate. The measurement was repeated by a team from the Lick Observatory led by the Director W. W. Campbell in the 1922 eclipse as observed in remote Australian station of Wallal, with results based on hundreds of star positions that agreed with the 1919 results and has been repeated several times since, most notably in 1953 by Yerkes Observatory astronomers and in 1973 by a team from the University of Texas. Considerable uncertainty remained in these measurements for almost fifty years, until observations started being made at radio frequencies.
The deflection of starlight by the nearby white dwarf star Stein 2051 B has also been measured.
Gravitational redshift of light
Einstein predicted the gravitational redshift of light from the equivalence principle in 1907, and it was predicted that this effect might be measured in the spectral lines of a white dwarf star, which has a very high gravitational field. Initial attempts to measure the gravitational redshift of the spectrum of Sirius-B were done by Walter Sydney Adams in 1925, but the result was criticized as being unusable due to the contamination from light from the primary star, Sirius. The first accurate measurement of the gravitational redshift of a white dwarf was done by Popper in 1954, measuring a 21 km/s gravitational redshift of 40 Eridani B.The redshift of Sirius B was finally measured by Greenstein et al. in 1971, obtaining the value for the gravitational redshift of, with more accurate measurements by the Hubble Space Telescope showing.