The modern era of testing general relativity was ushered in largely at the impetus of
Dicke and
Schiff who laid out a framework for testing general relativity. They emphasized the importance not only of the classical tests, but of null experiments, testing for effects which in principle could occur in a theory of gravitation, but do not occur in general relativity. Other important theoretical developments included the inception of
alternative theories to general relativity, in particular,
scalar–tensor theories such as the
Brans–Dicke theory; the
parameterized post-Newtonian formalism in which deviations from general relativity can be quantified; and the framework of the
equivalence principle. Experimentally, new developments in
space exploration,
electronics and
condensed matter physics have made additional precise experiments possible, such as the Pound–Rebka experiment, laser interferometry and
lunar rangefinding.
Post-Newtonian tests of gravity Early tests of general relativity were hampered by the lack of viable competitors to the theory: it was not clear what sorts of tests would distinguish it from its competitors. General relativity was the only known relativistic theory of gravity compatible with special relativity and observations. This changed in 1960 with the introduction of
Brans–Dicke theory which provided an alternative theory also in agreement with experimental observations. Ultimately, this led to the development of the
parametrized post-Newtonian formalism by
Kenneth Nordtvedt and
Clifford Martin Will, which parametrizes, in terms of ten adjustable parameters, all the possible departures from Newton's law of universal gravitation to first order in the velocity of moving objects (
i.e. to first order in v/c, where
v is the velocity of an object and
c is the speed of light). This approximation allows the possible deviations from general relativity, for slowly moving objects in weak gravitational fields, to be systematically analyzed. Much effort has been put into constraining the post-Newtonian parameters, and deviations from general relativity are at present severely limited. The experiments testing gravitational lensing and light time delay limits the same post-Newtonian parameter, the so-called Eddington parameter γ, which is a straightforward parametrization of the amount of deflection of light by a gravitational source. It is equal to one for general relativity, and takes different values in other theories (such as Brans–Dicke theory). It is the best constrained of the ten post-Newtonian parameters, but there are other experiments designed to constrain the others. Precise observations of the perihelion shift of Mercury constrain other parameters, as do tests of the strong equivalence principle. One of the goals of the
BepiColombo mission to Mercury, is to test the general relativity theory by measuring the parameters gamma and beta of the parametrized post-Newtonian formalism with high accuracy. The experiment is part of the Mercury Orbiter Radio science Experiment (MORE). The spacecraft was launched in October 2018 and is expected to enter orbit around Mercury in November 2026.
Gravitational lensing One of the most important tests is
gravitational lensing. It has been observed in distant astrophysical sources, but these are poorly controlled and it is uncertain how they constrain general relativity. The most precise tests are analogous to Eddington's 1919 experiment: they measure the deflection of radiation from a distant source by the Sun. The sources that can be most precisely analyzed are distant
radio sources. In particular, some
quasars are very strong radio sources. The directional resolution 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-arcsecond to micro-arcsecond) was obtained by combining radio telescopes across Earth. The technique is called
very long baseline interferometry (VLBI). With this technique radio observations couple the phase information of the radio signal observed in telescopes separated over large distances. Recently, these telescopes have measured the deflection of radio waves by the Sun to extremely high precision, confirming the amount of deflection predicted by general relativity aspect to the 0.03% level. At this level of precision systematic effects have to be carefully taken into account to determine the precise location of the telescopes on Earth. Some important effects are Earth's
nutation, rotation, atmospheric refraction, tectonic displacement and tidal waves. Another important effect is refraction of the radio waves by the
solar corona. Fortunately, this effect has a characteristic
spectrum, whereas gravitational distortion is independent of wavelength. Thus, careful analysis, using measurements at several frequencies, can subtract this source of error. The entire sky is slightly distorted due to the gravitational deflection of light caused by the Sun (the anti-Sun direction excepted). This effect has been observed by the
European Space Agency astrometric satellite
Hipparcos. It measured the positions of about 105 stars. During the full mission about relative positions have been determined, each to an accuracy of typically 3 milliarcseconds (the accuracy for an 8–9 magnitude star). Since the gravitation deflection perpendicular to the Earth–Sun direction is already 4.07 milliarcseconds, corrections are needed for practically all stars. Without systematic effects, the error in an individual observation of 3 milliarcseconds, could be reduced by the square root of the number of positions, leading to a precision of 0.0016 milliarcseconds. Systematic effects, however, limit the accuracy of the determination to 0.3% (Froeschlé, 1997). Launched in 2013, the
Gaia spacecraft will conduct a census of one billion
stars in the
Milky Way and measure their positions to an accuracy of 24 microarcseconds. Thus it will also provide stringent new tests of gravitational deflection of light caused by the
Sun which was predicted by General relativity.
Light travel time delay testing Irwin I. Shapiro proposed another test, beyond the classical tests, which could be performed within the Solar System. It is sometimes called the fourth "classical" test of
general relativity. He predicted a relativistic time delay (
Shapiro delay) in the round-trip travel time for radar signals reflecting off other planets. The mere curvature of the path of a
photon passing near the Sun is too small to have an observable delaying effect (when the round-trip time is compared to the time taken if the photon had followed a straight path), but general relativity predicts a time delay that becomes progressively larger when the photon passes nearer to the Sun due to the
time dilation in the
gravitational potential of the Sun. Observing radar reflections from Mercury and Venus just before and after they are eclipsed by the Sun agrees with general relativity theory at the 5% level. More recently, the
Cassini probe has undertaken a similar experiment which gave agreement with general relativity at the 0.002% level. However, the following detailed studies revealed that the measured value of the PPN parameter gamma is affected by a
gravitomagnetic effect caused by the orbital motion of Sun around the
barycenter of the solar system. The gravitomagnetic effect in the
Cassini radioscience experiment was implicitly postulated by B. Bertotti as having a pure general relativistic origin but its theoretical value has never been tested in the experiment which effectively makes the experimental uncertainty in the measured value of gamma actually larger (by a factor of 10) than 0.002% claimed by B. Bertotti and co-authors in Nature.
Very Long Baseline Interferometry has measured velocity-dependent (gravitomagnetic) corrections to the Shapiro time delay in the field of moving Jupiter and Saturn.
Equivalence principle The equivalence principle, in its simplest form, asserts that the trajectories of falling bodies in a gravitational field should be independent of their mass and internal structure, provided they are small enough not to disturb the environment or be affected by
tidal forces. This idea has been tested to extremely high precision by
Eötvös torsion balance experiments, which look for a differential acceleration between two test masses. Constraints on this, and on the existence of a composition-dependent fifth force or gravitational
Yukawa interaction are very strong, and are discussed under
fifth force and
weak equivalence principle. A version of the equivalence principle, called the
strong equivalence principle, asserts that self-gravitation falling bodies, such as stars, planets or black holes (which are all held together by their gravitational attraction) should follow the same trajectories in a gravitational field, provided the same conditions are satisfied. This is called the
Nordtvedt effect and is most precisely tested by the
Lunar Laser Ranging Experiment. Since 1969, it has continuously measured the distance from several rangefinding stations on Earth to reflectors on the Moon to approximately centimeter accuracy. These have provided a strong constraint on several of the other post-Newtonian parameters. Another part of the strong equivalence principle is the requirement that Newton's gravitational constant be constant in time, and have the same value everywhere in the universe. There are many independent observations limiting the possible variation of Newton's
gravitational constant, but one of the best comes from lunar rangefinding which suggests that the gravitational constant does not change by more than one part in 1011 per year. The constancy of the other constants is discussed in the
Einstein equivalence principle section of the equivalence principle article.
Gravitational redshift and time dilation The first of the classical tests discussed above, the
gravitational redshift, is a simple consequence of the
Einstein equivalence principle and was predicted by Einstein in 1907. As such, it is not a test of general relativity in the same way as the post-Newtonian tests, because any theory of gravity obeying the equivalence principle should also incorporate the gravitational redshift. Nonetheless, confirming the existence of the effect was an important substantiation of relativistic gravity, since the absence of gravitational redshift would have strongly contradicted relativity. The first observation of the gravitational redshift was the measurement of the shift in the spectral lines from the
white dwarf star
Sirius B by Adams in 1925, discussed above, and follow-on measurements of other white dwarfs. Because of the difficulty of the astrophysical measurement, however, experimental verification using a known terrestrial source was preferable. Experimental verification of gravitational redshift using terrestrial sources took several decades, because it is difficult to find clocks (to measure
time dilation) or sources of electromagnetic radiation (to measure redshift) with a frequency that is known well enough that the effect can be accurately measured. It was confirmed experimentally for the first time in 1959 using measurements of the change in wavelength of gamma-ray photons generated with the
Mössbauer effect, which generates radiation with a very narrow line width. The
Pound–Rebka experiment measured the relative redshift of two sources situated at the top and bottom of Harvard University's Jefferson tower. The result was in excellent agreement with general relativity. This was one of the first precision experiments testing general relativity. The experiment was later improved to better than the 1% level by Pound and Snider. The blueshift of a falling photon can be found by assuming it has an equivalent mass based on its frequency (where
h is the
Planck constant) along with , a result of special relativity. Such simple derivations ignore the fact that in general relativity the experiment compares clock rates, rather than energies. In other words, the "higher energy" of the photon after it falls can be equivalently ascribed to the slower running of clocks deeper in the gravitational potential well. To fully validate general relativity, it is important to also show that the rate of arrival of the photons is greater than the rate at which they are emitted. A very accurate gravitational redshift experiment, which deals with this issue, was performed in 1976, where a
hydrogen maser clock on a rocket was launched to a height of 10,000 km, and its rate compared with an identical clock on the ground. It tested the gravitational redshift to 0.007%. Although the
Global Positioning System (GPS) is not designed as a test of fundamental physics, it must account for the gravitational redshift in its timing system, and physicists have analyzed timing data from the GPS to confirm other tests. When the first satellite was launched, some engineers resisted the prediction that a noticeable gravitational time dilation would occur, so the first satellite was launched without the clock adjustment that was later built into subsequent satellites. It showed the predicted shift of 38 microseconds per day. This rate of discrepancy is sufficient to substantially impair function of GPS within hours if not accounted for. An excellent account of the role played by general relativity in the design of GPS can be found in Ashby 2003. Other precision tests of general relativity, but many aspects of them remain controversial. The same effect may have been detected in the data of the
Mars Global Surveyor (MGS) spacecraft, a former probe in orbit around
Mars; also such a test raised a debate. First attempts to detect the
Sun's Lense–Thirring effect on the
perihelia of the inner
planets have been recently reported as well. Frame dragging would cause the orbital plane of stars orbiting near a
supermassive black hole to precess about the black hole spin axis. This effect should be detectable within the next few years via
astrometric monitoring of stars at the center of the
Milky Way galaxy. By comparing the rate of orbital precession of two stars on different orbits, it is possible in principle to test the
no-hair theorems of general relativity. The
Gravity Probe B satellite, launched in 2004 and operated until 2005, detected frame-dragging and the
geodetic effect. The experiment used four quartz spheres the size of ping pong balls coated with a superconductor. Data analysis continued through 2011 due to high noise levels and difficulties in modelling the noise accurately so that a useful signal could be found. Principal investigators at
Stanford University reported on May 4, 2011, that they had accurately measured the frame dragging effect relative to the distant star
IM Pegasi, and the calculations proved to be in line with the prediction of Einstein's theory. The results, published in
Physical Review Letters measured the
geodetic effect with an error of about 0.2 percent. The results reported the frame dragging effect (caused by Earth's rotation) added up to 37 milliarcseconds with an error of about 19 percent. Investigator Francis Everitt explained that a milliarcsecond "is the width of a human hair seen at the distance of 10 miles". In January 2012,
LARES satellite was launched on a
Vega rocket to measure
Lense–Thirring effect with an accuracy of about 1%, according to its proponents. This evaluation of the actual accuracy obtainable is a subject of debate.
Tests of the gravitational potential at small distances It is possible to test whether the gravitational potential continues with the inverse square law at very small distances. Tests so far have focused on a divergence from GR in the form of a
Yukawa potential V(r) = V_0\left(1 + \alpha e^{-r/\lambda}\right), but no evidence for a potential of this kind has been found. The Yukawa potential with \alpha=1 has been ruled out down to .
Mössbauer rotor experiment It was conceived as a means to measure the
time dilation effect on Earth after being motivated by Einstein's
equivalence principle that implies a rotating observer will be subject to the same transformations as an observer in a gravitational field. Mössbauer rotor experiments hence permit a precise terrestrial test of the
relativistic Doppler effect. From a radioactive source fixed at the center of a spinning disc or rod,
gamma rays travel to an absorber at the rim (in some variations of the experiment this scheme was reversed) and an unabsorbed number of them pass through depending on the rotational speed to arrive at a stationary counter (
i.e., detector of gamma quanta resting in the lab frame). In lieu with the
Clock hypothesis, Einstein's
general relativity predicts that the moving absorber's clock at the rim should retard by a specific amount due to time dilation on account of centrifugal binding alone compared to a rest frame absorber. So the transmission of gamma photons through the absorber should increase during rotation, which can be subsequently measured by the stationary counter beyond the absorber. This prediction was actually observed using the
Mössbauer effect, since the equivalence principle, as originally suggested by Einstein, implicitly allows the association of the time dilation due to rotation (calculated as a result of the change in the detector's count rate) with gravitational time dilation. Such experiments were pioneered by Hay
et al. (1960), Champeney
et al. (1965), and Kündig (1963), and all of them had declared confirmation of the prediction of Einstein's theory of relativity. Be that as it may, an early 21st Century re-examination of these endeavors called into question the validity of the past obtained results claiming to have verified time dilation as predicted by Einstein's relativity theory, whereby novel experimentations were carried out that uncovered an
extra energy shift between emitted and absorbed radiation next to the classical relativistic dilation of time. This discovery was first explained as discrediting
general relativity and successfully confirming at the laboratory scale the predictions of an alternative theory of gravity developed by T. Yarman and his colleagues. Against this development, a contentious attempt was made to explain the disclosed extra energy shift as arising from a so-far unknown and allegedly missed
clock synchronization effect, which was unusually awarded a prize in 2018 by the
Gravity Research Foundation for having secured
a new proof of general relativity. However, at the same time period, it was revealed that said author committed several mathematical errors in his calculations, and the supposed contribution of the so-called clock synchronization to the measured time dilation is in fact practically null. As a consequence, a general relativistic explanation for the outcomes of Mössbauer rotor experiments remains open. == Strong field tests ==