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Classical tests of general relativity
The classical tests of general relativity are the direct consequences for experimental verification of the theory of general relativity about gravitational interaction. Three possible types of experiments are proposed soon after publication of the Einstein field equations in 1916, a fourth test is added much later. They are
- Gravitational redshift or Einstein shift(clocks in a gravitational field observed from a distance tick slower),
- Deflection of light (when light passes near a mass concentration such as the Sun, its path is slightly bent, also called gravitational lensing),
- Perihelion shift of the planet Mercury (the deviation from Kepler-orbits of a test mass (such as a planet) around a massive object such as the Sun)
- Time delay in radar propagation near the Sun
The gravitational redshift is a simple consequence of the Einstein equivalence principle and was found by Albert Einstein eight years before the full theory. It is a direct consequence of the so-called equivalence principle.
Experimental verification of this principle requires good clocks and it was for the first time experimentally confirmed as late as in 1960, by the Pound-Rebka experiment (Pound, R.V., Rebka, G.A., 1960, Phys. Rev. Lett., 4, 337), later improved by Pound and Snider. The famous experiment is generally called the Pound-Rebka-Snider experiment. The accuracy is typically 1%.
A very accurate gravitational redshift experiment was performed in 1976 (Vessot, R.F.C,. Levine, M.W., Mattison, E.M., et al., 1980, Phys. Rev. Lett. 45, 2081-2084). A hydrogen maser clock on a rocket was launched to a height of 10000 km, and its rate compared with an identical clock on the ground. It tested the gravitational redshift to 0.02%.
Gravitational deflection of light
The first observation of light deflection was performed by noting the change in position of stars near the Sun (F.W.Dyson, A.S. Eddington, C. Davidson, 1920, Philos. Trans. Royal Soc. London, Vol.~220A, p. 291-333). It took place during a total solar eclipse (so that stars near the Sun could be observed) in 1919 and was observed on an island near Brazil and near the westcoast of Africa. The result was considered spectacular news and made the front page of most international journals. It made Einstein and his General Relativity world famous. The early accuracy, however, is poor (20% at best) and remained poor for about 40 years, till methods were found to accurately measure stellar positions in the sky.
Using radio interferometry
Radio interferometry observations (using stars that emit in the radio range) during the 1960s are able to provide accurate (relative) positions of radio sources. The sources used are quasars, some of which are strong radio sources in the sky. The quasars 3C273 and 3C279 have a small angular separation. Each year around October 8 they pass near the Sun, whereby the quasar 3C279 is eclipsed by the Sun. During its approach to the Sun the bending of light near the Sun can be verified to 1.5%. (Fomalont, E.B., and Sramek, R.A., 1976, Phys. Rev. Lett., 236, 1475-1478.)
The positional accuracy of any telescope is in principle limited by diffraction, for radio telescopes this is also the practical limit. An important improvement in obtaining positional high accuracies (from milli-arcsec to micro-arcsec) was obtained by combining radio telescopes across the Earth. The technique is called VLBI, Very Long Baseline Interferometry. With this technique radio observations couple the phase information of the radio signal observed in telescopes separated over large distances. With these accuracies the Einstein light deflection can be determined to an accuracy of 0.2% (D.S. Robertson & W.E. Carter, 1984, Nature, 310, p.572-574; and D.S. Robertson, W.E. Carter & W.H.Dillinger, 1991, Nature, 349, p.768-770).
At this level of precision all sorts of systemetic effects have to be taken into account to know the precise location of the telescopes on Earth. Important are such effects as: Earth nutation (which has an error in the annual term of 2 milli-arcsec, mas), Earth rotation, atmospheric refraction, tectonic displacement, tidal waves in the ocean, etc. An astronomical limitation is the refraction of radio waves around the Sun, in the so called solar corona , extending to several Solar radii. Fortunately, gravitational reflection is achromatic (it doesn't depend on wavelength) while the Solar corona bends electromagnetic radiation in the radio depending on wavelength. This chromatic effect can be used to eliminate the refraction in the solar corona, but uncertainties remain.
Observations with the Hypparchos satellite
In principle we observe almost all sky slightly distorted due to the gravitational deflection of light caused by the Sun (the anti-Sun direction excepted). This effect has been observed. The ESA astrometric satellite Hipparchos has measured the positions of about 105 stars. During the full mission about 3.5 × 106 relative positions have been determined, each to an accuracy of typically 3 mas (1 mas= 0.001 arcsec; this accuracy is for a 8-9 magnitude star). Since the gravitation deflection perpendicular to the Earth-Sun direction is already 4.07 mas, corrections are needed for practically all stars. Without systematic effects, the error in an individual observation of 3 mas, could be reduced by the square root of the number of positions, leading to a precision of 0.0016 mas. Systematic effects, however, limit the accuracy of the determination to 0.1% (Froeschl\'e, M.\, Mignard, F., Arenou F., 1997, Hipparchos Venice, ESA-SP-402, "Determination of the PPN parameter γ with the Hipparchos data").
Perihelion shift of Mercury
The two previous effects, the gravitational redshift and the deflection of light, are derived from nul-geodesics, the paths of photons. Also the path of a test particle in Einstein's theory of gravitation, differs from the pure ellipses expected on the basis of Newtonian theory. With small deviations from the Newtonian theory, the effect is that the axis of the ellips will rotate. Since the point in the orbit of a planet nearest to the Sun is called perihelion, the most obvious effect is the perihelion shift of planets. The orbit of the planet Mercury, nearest to the Sun, was carefully calculated in the 19th century. The disturbing effects of other planets also cause a perihelion shift, but the calculation let a small amount of 43 arcseconds per century unexplained. This is just the amount predicted by General Relativity.
Time-delay in radar propagation
The previous three tests are called the three classical tests of General Relativity. Much later, in 1964, Shapiro proposed another test to be performed within the solar system. It is generally called the fourth "classical" test of General Relativity. Shapiro predicted a relativistic time delay in the round-trip travel time for radar signals reflecting off other planets (Shapiro,I.I., 1964, Phys. Rev. Lett. 13, p.~789-791, "Fourth test of general relativity").
The curvature of the path of a photon passing near the Sun is too small to have an observable delaying effect, but General Relativity predicts a time delay which becomes progessively larger when the photon passes nearer to the Sun. Observing radar reflections from a planet just before and after it will be eclipsed by the Sun shows this effect.
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