Tests of general relativity

At its introduction in 1915, the general theory of relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Newton's law of universal gravitation with special relativity. That light appeared to bend in gravitational fields in line with the predictions of general relativity was found in 1919 but it was not until a program of precision tests was started in 1959 that the various predictions of general relativity were tested to any further degree of accuracy in the weak gravitational field limit, severely limiting possible deviations from the theory. Beginning in 1974, Hulse, Taylor and others have studied the behaviour of binary pulsars experiencing much stronger gravitational fields than found in our solar system. Both in the weak field limit (as in our solar system) and with the stronger fields present in systems of binary pulsars the predictions of general relativity have been extremely well tested locally.

The very strong gravitational fields that must be present close to black holes, especially those supermassive black holes which are thought to power active galactic nuclei and the more active quasars, belong to a field of intense active research. Observations of these quasars and active galactic nuclei are difficult, and interpretation of the observations is heavily dependent upon astrophysical models other than general relativity or competing fundamental theories of gravitation, but they are qualitatively consistent with the black hole concept as modelled in general relativity.

As a consequence of the equivalence principle, Lorentz invariance holds locally in freely falling reference frames. Experiments related to Lorentz invariance and thus special relativity (i.e., when gravitational effects can be neglected) are described in Tests of special relativity.

Classical tests

Albert Einstein proposed three tests of general relativity, subsequently called the classical tests of general relativity, in 1916:[1]

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

In the letter to the London Times on November 28, 1919, he described the theory of relativity and thanked his English colleagues for their understanding and testing of his work. He also mentioned three classical tests with comments:[2]

"The chief attraction of the theory lies in its logical completeness. If a single one of the conclusions drawn from it proves wrong, it must be given up; to modify it without destroying the whole structure seems to be impossible."

Perihelion precession of Mercury

Transit of Mercury on November 8, 2006 with sunspots #921, 922, and 923

Under Newtonian physics, a two-body system consisting of 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 periapsis (or, as the central body in our Solar System is the sun, perihelion), is fixed. A number of effects in our solar system cause the perihelia of planets to precess (rotate) around the sun. The principal cause is the presence of other planets which perturb each other's orbit. Another (much less significant) 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" (arc seconds) per tropical century (later re-estimated at 43").[3] A number of ad hoc and ultimately unsuccessful solutions were proposed, but they tended to introduce more problems. 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[1] 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 574.10±0.65 arc-seconds per century[4] relative to the inertial ICFR. This precession can be attributed to the following causes:

Sources of the precession of perihelion for Mercury
Amount (arcsec/Julian century) Cause
531.63 ±0.69[4] Gravitational tugs of the other planets
0.0254 Oblateness of the Sun (quadrupole moment)
42.98 ±0.04[5] General relativity
574.64±0.69 Total
574.10±0.65[4] Observed

The correction by 42.98" is 3/2 multiple of classical prediction with PPN parameters ${\displaystyle \gamma =\beta =0}$.[6]

Thus the effect can be fully explained by general relativity. More recent calculations based on more precise measurements have not materially changed the situation.

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 of 3.84 seconds of arc per century, and Venus's is 8.62". Both values are in good agreement with observation.[7] The periapsis shift of binary pulsar systems have been measured, with PSR 1913+16 amounting to 4.2º per year.[8] These observations are consistent with general relativity.[9] 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 - so a few systems such as DI Herculis have been considered as problematic cases for general relativity.

Deflection of light by the Sun

One of Eddington's photographs of the 1919 solar eclipse experiment, presented in his 1920 paper announcing its success

Henry Cavendish in 1784 (in an unpublished manuscript) and Johann Georg von Soldner in 1801 (published in 1804) had pointed out that Newtonian gravity predicts that starlight will bend around a massive object.[10] 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 (and thus Soldner's) 1911-result is only half of the correct value. Einstein became the first to calculate the correct value for light bending.[11]

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 in May 1919 by Arthur Eddington and his collaborators during a total solar eclipse,[12] so that 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.[13] 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." [14]

References

Notes

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3. U. Le Verrier (1859), (in French), "Lettre de M. Le Verrier à M. Faye sur la théorie de Mercure et sur le mouvement du périhélie de cette planète", Comptes rendus hebdomadaires des séances de l'Académie des sciences (Paris), vol. 49 (1859), pp.379–383.
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5. Myles Standish, Jet Propulsion Laboratory (1998) http://classroom.sdmesa.edu/ssiegel/Physics%20197/labs/Mercury%20Precession.pdf
6. http://www.tat.physik.uni-tuebingen.de/~kokkotas/Teaching/Experimental_Gravity_files/Hajime_PPN.pdf - Perihelion shift of Mercury, page 11
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14. Rosenthal-Schneider, Ilse: Reality and Scientific Truth. Detroit: Wayne State University Press, 1980. p 74. See also Calaprice, Alice: The New Quotable Einstein. Princeton: Princeton University Press, 2005. p 227.)
15. Harry Collins and Trevor Pinch, The Golem, ISBN 0-521-47736-0
16. Template:Cite arXiv
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18. D. Kennefick, "Testing relativity from the 1919 eclipse- a question of bias", Physics Today, March 2009, pp. 37–42.
19. van Biesbroeck, G.: The relativity shift at the 1952 February 25 eclipse of the Sun., Astronomical Journal, vol. 58, page 87, 1953.
20. Texas Mauritanian Eclipse Team: Gravitational deflection of-light: solar eclipse of 30 June 1973 I. Description of procedures and final results., Astronomical Journal, vol. 81, page 452, 1976.
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27. Fact Sheet-BepiColombo
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29. Gaia overview
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41. Gravitational Physics with Optical Clocks in Space - http://www.exphy.uni-duesseldorf.de/Opt_clocks_workshop/Talks_Workshop/Presentations%20Thursday%20morning/Presentation%20Schiller%20Gravitational%20Physics%20with%20Optical%20Clocks.pdf
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62. In general relativity, a perfectly spherical star (in vacuum) that expands or contracts while remaining perfectly spherical cannot emit any gravitational waves (similar to the lack of e/m radiation from a pulsating charge), as Birkhoff's theorem says that the geometry remains the same exterior to the star. More generally, a rotating system will only emit gravitational waves if it lacks the axial symmetry with respect to the axis of rotation.
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75. Rudnicki, 1991, p. 28. The Hubble Law was viewed by many as an observational confirmation of General Relativity in the early years
76. W.Pauli, 1958, pp.219–220
77. Kragh, 2003, p. 152
78. Kragh, 2003, p. 153
79. Rudnicki, 1991, p. 28
80. Chandrasekhar, 1980, p. 37

Other research papers

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• A. Einstein, "Über das Relativitätsprinzip und die aus demselben gezogene Folgerungen", Jahrbuch der Radioaktivitaet und Elektronik 4 (1907); translated "On the relativity principle and the conclusions drawn from it", in The collected papers of Albert Einstein. Vol. 2 : The Swiss years: writings, 1900–1909 (Princeton University Press, Princeton, New Jersey, 1989), Anna Beck translator. Einstein proposes the gravitational redshift of light in this paper, discussed online at The Genesis of General Relativity.
• A. Einstein, "Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes", Annalen der Physik 35 (1911); translated "On the Influence of Gravitation on the Propagation of Light" in The collected papers of Albert Einstein. Vol. 3 : The Swiss years: writings, 1909–1911 (Princeton University Press, Princeton, New Jersey, 1994), Anna Beck translator, and in The Principle of Relativity, (Dover, 1924), pp 99–108, W. Perrett and G. B. Jeffery translators, ISBN 0-486-60081-5. The deflection of light by the sun is predicted from the principle of equivalence. Einstein's result is half the full value found using the general theory of relativity.
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Textbooks

• S. M. Carroll, Spacetime and Geometry: an Introduction to General Relativity, Addison-Wesley, 2003. An introductory general relativity textbook.
• A. S. Eddington, Space, Time and Gravitation, Cambridge University Press, reprint of 1920 ed.
• A. Gefter, "Putting Einstein to the Test", Sky and Telescope July 2005, p. 38. A popular discussion of tests of general relativity.
• H. Ohanian and R. Ruffini, Gravitation and Spacetime, 2nd Edition Norton, New York, 1994, ISBN 0-393-96501-5. A general relativity textbook.
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• C. M. Will, Theory and Experiment in Gravitational Physics, Cambridge University Press, Cambridge (1993). A standard technical reference.
• C. M. Will, Was Einstein Right?: Putting General Relativity to the Test, Basic Books (1993). This is a popular account of tests of general relativity.
• L. Iorio, The Measurement of Gravitomagnetism: A Challenging Enterprise, NOVA Science, Hauppauge (2007). It describes various theoretical and experimental/observational aspects of frame-dragging.