Tests of general relativity

Tests of general relativity are used to verify the standard model for the description of gravity, general relativity theory (ART) Albert Einstein performed.

At the time of its introduction in 1915, the ART had no solid empirical basis. She was originally rather philosophical reasons very satisfactory, since they filled the equivalence principle and Newton's law of gravitation and the theory of special relativity included as limiting cases. From the experimental point of view it was only known that they can explain " anomalous " perihelion of Mercury which, and in 1919 it was shown that light is deflected in a gravitational field according to the ART. However, it took until 1959 that it was to test the predictions of ART in the region of weak gravitational fields possible, making possible deviations from the theory could be accurately determined. Only in 1974 could be researched with the study of Binärpulsaren much stronger gravitational fields than there are them in the Solar System. Finally, the study of strong gravitational fields was also associated with black holes and quasars. Observations here are of course very difficult, although the results agree with the predictions of ART previously agreed.

According to the equivalence principle must be locally valid in the special theory of relativity Lorentz invariance must be fulfilled ( " Local Lorentz invariance "). For the corresponding experiments see tests of special relativity.

2.1 Post- Newtonian gravitational tests
2.2 Gravitational Lensing
2.3 Tests for delaying the time of flight
2.4 The principle of equivalence
2.5 Gravitational redshift
Lense- Thirring effect 2.6
2.8 gravitational waves
2.9 Cosmological Tests

3.1 Secondary sources
3.2 Primary Sources

Classical tests

Einstein suggested three tests in 1916 the ART, which later became known as "the classical tests of the ART ":

Perihelion of Mercury

In Newtonian physics, describe objects in a two- body system, ie two orbiting celestial bodies, an ellipse, with the center of gravity as its focus. The point of closest approach, the perihelion is immovable,. In our solar system, however, cause a range of effects that the perihelion of the planets around the sun rotates. The main reason for this is the presence of other planets, disrupt their orbits each other. Another very much smaller effect, the flattening of the sun. Originally, the measurements of the planetary orbits were carried out by conventional telescopes, but are now carried much more accurate measurements with radar.

According to the Newtonian theory of gravitation, a perihelion of about 531 arc seconds would be expected. Urbain Le Verrier in 1859 recognized that the perihelion of Mercury from that which follows from the Newtonian effects differs. His analysis of the transit of Mercury across the solar disk from 1697 to 1848 showed a deviation from Newton's theory of about 38 " arc seconds per tropical century (later it was at 43 " changed). A number of ad hoc hypotheses and ultimately false solutions have been proposed. In ART, however, is the remaining rotation, or the change in the orientation of the orbital ellipse in its orbital plane, caused by the curvature of space. Einstein was able to show that the ART is very close in accordance with the observed amount of about 43 " of Perihelverschiebung, which was of considerable weight for the acceptance of ART.

The other planets are also subject Periheldrehungen, but they have lower orbital speeds and less eccentric orbits, so are their shifts to find smaller and heavier. For example, the perihelion of the Earth's orbit is about 5 arc seconds per century due to ART. The Perihelverschiebungen of binary pulsar systems have also been measured, it is for example in PSR 1913 16 approximately 4.2 ° per year. These observations are consistent with the ART.

Deflection of light from the sun

Henry Cavendish ( 1784 in an unpublished manuscript ) and Johann Georg von Soldner (1801 ) pointed out that the Newtonian theory of gravitation predicts a deflection of starlight at celestial bodies, if light is regarded as a mass -affected particles. Approximately the same value as von Soldner was derived from Einstein on the assumption of the equivalence principle alone. In 1915, he remarked, however, also taking into account the curvature of space in the ART that this represents only half of the correct value.

The first observation of the deflection of light was made in observing the change in position of stars when they are on the celestial sphere very close to the Sun. The observations were carried out in 1919 by Arthur Stanley Eddington and Frank Dyson during a total solar eclipse. The result was seen as a spectacular message and found himself on the front pages of many major newspapers again. It made Einstein and his theory of world-famous. When he was asked about his reaction if the ART had not been confirmed by Eddington, Einstein said jestingly: "That would have been sorry for the dear God - the theory is correct."

The original accuracy was not particularly high, but was a modern re-analysis of the data show that Eddington's analysis was essentially correct. The measurement was repeated by a team from the Lick Observatory in 1922, and also in 1973 by a team from the University of Texas at Austin, with results that were consistent with those of 1919. However, a truly great precision had only the measurements with the aid of radio astronomy, beginning in the 1960s, who could dispel the last doubts on the validity of the ART values.

In addition to the deflection by the sun Einstein rings are an example of the deflection of light.

Gravitational redshift of light

Einstein predicted the gravitational redshift of light as a consequence of the equivalence principle as early as 1907, however, the measurement of which proved to be very difficult. Although it was measured approximately by Walter Sydney Adams in 1925, was a clear measurement only by the pound- Rebka experiment ( 1959). There was the relative redshift of two sources who were at the top and bottom of the Jefferson Tower of Harvard University, measured by use of the Mössbauer effect. The result was in excellent agreement with the ART and one of the first precision measurements of their predictions.

Modern tests

The modern era of the tests of general relativity was additionally driven by Robert Henry thickness and Leonard ship that developed a scheme for testing the ART. They stressed the importance of not only the classic tests but also of zero results, ie the search for the true effects can in principle occur in a gravitational theory, but not in the ART. Other important theoretical developments relating to the consideration of alternatives to ART, particularly scalar - tensor theories such as the Brans Dicke theory. or the parameterized post -Newtonian formalism, a test theory of the deviations can be quantified by the ART and effects associated with the equivalence principle.

Post- Newtonian gravitational tests

Due to the lack of useful alternative theories, the range for tests of ART was initially restricted, because it was not clear what kind of tests they differ from other theories. At that time, the ART was the only relativistic theory of gravitation, which was consistent with the special theory of relativity ( in its scope) and the observations. That changed with the introduction of the Brans Dicke theory in 1960., This theory can be described in a manner as simple as it contains no dimensionful constants, and compatible with the Mach 's principle and Paul Dirac's Large Number Hypothesis, ie two philosophical ideas which have been found in the history of ART as influential. This eventually led to the development of the parameterized post -Newtonian formalism ( PPN) by Kenneth Nordtvedt and Clifford Will, who describe all possible deviations from Newton's law of gravitation for sizes first order ( where v is the velocity of the object and c is the speed of light). This approximation allows us to analyze the possible deviations from the ART for slowly moving objects systematically in weak gravitational fields. A great deal of experimental effort has been made to limit the post -Newtonian parameters - with the result that deviations from the ART only within very narrow limits are possible.

The experiments to check the gravitational lensing and light delays limits the same post -Newtonian parameters, the so-called Eddington parameter, a, which is a direct parameterization of the size of the deflection of light by a gravitational source. It is equal to 1 for ART, and takes different values in other theories. He is the most certain of the ten post -Newtonian parameters, but also exist for the localization of the other parameter tests. These include the perihelion of Mercury or the tests of the strong equivalence principle.

Gravitational lensing

The gravitational lens effect was observed in distant astrophysical sources, but it is difficult experimentally to control the conditions and it is uncertain how the results are to be classified in the context of ART. The most accurate tests correspond to Eddington's 1919 experiment: measure the deflection of the radiation from a distant source by the sun. The sources, which can be most accurately analyzed are distant radio sources, particularly quasars. The directional accuracy of all telescopes is fundamentally limited by diffraction, and for radio telescopes, this is the practical limit. An important improvement to obtain positional data of high accuracy ( in the range of milli -to micro- arcseconds ) was the combination of radio telescopes all over the world reached ( VLBI ). With this technique, the phase information of the measured with telescopes radio signals over long distances are joined together by radio observations. 2009 such telescopes have the distractions of radio waves measured by the sun with extremely high accuracy, with the amount of the following from the ART deflection was measured to be 0.03 % accurate. At this level, systematic effects must be carefully considered to determine the exact position of ground telescopes. Some important effects are the nutation, rotation, atmospheric refraction, tectonic shift and tidal waves. Another effect is the refraction of radio waves through the solar corona. Helps to distinguish that this effect has a characteristic spectrum as gravitational distractions are independent of the wavelength. Consequently, a careful analysis of measurements at different frequencies reduce this source of error.

The entire sky is the gravitational deflection of light ( caused by the sun ) slightly distorted (except in the opposite direction of the sun). This effect was observed by Hipparcos, an astrometric satellite of the European Space Agency. He measured the position of stars around. Throughout the mission relative positions were determined, each with an average accuracy of 3 milliarcseconds ( the accuracy for a star the size 8-9). Since the gravitational deflection of Earth-Sun direction is perpendicular already 4.07 milliarcseconds, corrections are necessary for virtually all stars. Of error of 3 milliarcseconds a single observation on the square roots of the number of positions can be reduced without systematic effects, which leads to a precision of 0.0016 milliarcseconds. Systematic effects limit the accuracy of determining the size of the entire effect to 0.3%.

Tests for delaying the time of flight

Irwin I. Shapiro proposed a test before, which can be carried out within the solar system, and is sometimes referred to as the fourth " classical" test of ART. He calculated a relativistic time delay ( Shapiro delay) for the Zweiwegzeit ( round trip ) of radar signals that are reflected from other planets. The simple curvature of the path of a photon, which passes close to the sun is too small to an observable delay effect of producing (when the two-way time is compared with the time required for a straight moving photon), but the means predicts a delay which is larger due to the gravitational time dilation continuously when the photon passes close to the Sun. The observation of radar reflections from Mercury and Venus immediately before and after they were darkened by the sun, shows a match to ART with a maximum deviation of 5 %. It has recently been carried out with the Cassini satellite, a similar experiment, the maximum deviation from the ART was even only 0.002%. With the VLBI velocity-dependent ( gravitomagnetic ) corrections to the Shapiro delay in the moving Jupiter and Saturn were measured field beyond.

The principle of equivalence

The equivalence principle states in its simplest form, that the trajectories of a falling body in a gravitational field should be independent of its mass and internal structure, provided they are small enough not to be affected by the environment or by tidal forces. This principle was confirmed with great precision by the Eötvös experiment with a torsion balance, was where to look for different accelerations of different masses. Limits to this effect and the existence of a composition -dependent fifth force or a gravitational Yukawa interaction are already very narrow.

The strong equivalence principle states among other things that falling bodies, which are held together by their gravitational forces, such as stars, planets and black holes, the same trajectories are subjected to a gravitational field, provided that the same conditions are met. This is called the Nordtvedt effect, and was most accurately confirmed by Lunar Laser Ranging. 1969 so that the removal of some stations is measured on the ground relative to the moon, with a centimeter precision. Thus, a strong confinement of various post- Newtonian parameters was achieved.

Another part of the high equivalence principle is the condition that the Newtonian gravitational constant in time is fixed, and has the same value everywhere in the universe. There are many independent measurements, which limit a possible deviation from it, but one of the best based on lunar laser ranging. These measurements showed that the gravitational constant can not change by more than a year.

Gravitational redshift

The first of the above-discussed classical tests, the gravitational redshift, is a simple consequence of the equivalence principle, and was predicted by Einstein in 1907. In and of itself it is not a test in the form of post -Newtonian tests, as any theory which involves the equivalence principle, this effect must also predict. Nevertheless, the evidence of this effect is an important support for the relativistic gravitational considers that the absence of the gravitational redshift of the theory of relativity would have clearly contradicted. The first observation of this effect was to measure the spectral shift of the white dwarf star Sirius B by Adams ( 1925). Although these and subsequent measurements of the spectral shift of other white dwarf stars were consistent with the predictions of GR could be argued that the shift may have different causes, so an experimental verification would be preferable using terrestrial sources.

The experimental confirmation of the gravitational redshift using underground sources lasted for several decades, since the effect is much smaller and therefore accurate frequency measurements are needed very much. He was first demonstrated experimentally in 1960 using the Mössbauer effect. By these photons can be generated by gamma radiation with a very narrow line width. The process performed by Robert Pound and Glen Rebka experiment that was later improved by Pound and Snyder is referred to as pound- Rebka experiment. The frequency shift could be measured with an accuracy of 1%. The blue shift of the falling photon can be calculated by assuming that they are an equivalent mass according to their frequency E = hf ( where h is the Planck constant is ) and have E = mc ² - a result of special relativity. However, such simple derivations ignore the fact that in the ART rather watch transition rates are compared as energy. In other words, the "higher power " of the photon after it has fallen, and the slow rate of the clocks can be attributed in deeper areas of the gravitational potential. To confirm the kind, totally, it is important to show that the rate of arrival of the photons is greater than the emission rate. A very accurate Rotverschiebungsexperiment was carried out in 1976, a hydrogen maser clock was brought to a height of 10,000 km in a rocket, and its rate was compared with an identical clock on Earth's surface. The gravitational redshift was thus measured up to 0.007 % accurate.

Although GPS was not designed as a test of fundamental physics, the gravitational redshift has to be considered, where physicists have analyzed the time data to verify statements of various theories. When the first satellite was launched, ignoring some engineers to predict a noticeable gravitational time dilation, so that the satellite was launched without proper clock setting. The watches showed the expected shift in accordance with the theory of relativity of 38 microseconds per day. The variation rate is sufficient to substantially impair the functions of the GPS in hours, when it is not taken into account.

Other precision tests in this context have been carried out for example with the satellite Gravity Probe A ( 1976), which has been shown that gravitational and velocity effects, the ability to synchronize the transition rates of clocks in orbit influence. In the Hafele - Keating experiment ( 1971) as well as the Maryland experiment atomic clocks were used in aircraft, whereby the relativistic gravitational and velocity effects were also confirmed.

Through the use of optical clocks, the accuracy could now be increased such that the gravitational time dilation could be measured even at distances of less than one meter. Chou et al. (2010) use this Al ions as watches. During an ion was at rest, the other was raised by 33 cm. The measured redshift corresponds to a height difference of 37 ± 15 cm, which is in very good agreement.

Lense- Thirring effect

Tests of the Lense- Thirring effect, according to which small precessions of the orbits of a test particle yield, which moves around a central, rotating mass such as a planet or a star, were performed with the LAGEOS satellites, but remained some aspects of these tests controversial. The effect could have been measured with the Mars Global Surveyor, but even this was not without controversy.

The Gravity Probe B satellite, which was launched in 2004 and by 2005 was in function, this effect was finally able to prove without doubt for the first time. In this experiment, four quartz spheres of the size of table-tennis balls coated with a superconductor used. The data analysis took account of the high levels of disturbance and difficulties in the correct modeling of the disturbances until 2011, until a meaningful signal could be found. Researchers at Stanford University have on 4 May 2011 to announce that they have the Lense- Thirring effect measured relative to distant star IM Pegasi. The geodetic effect was able to be detected down to 0.2 % accurate (measured value: -6601.8 ± 18.3 milliarcseconds / year, ART- Value: -6606.1 mas / year) and the Lense- Thirring effect was to to 37 milliarcseconds measured with an error margin of 19 % (measured value: -37.2 ± 7.2 mas / year, ART- value: -39.2 mas / year). In comparison, a milliarcsecond corresponds to the width of a human hair from a distance of 16 km.

Attempts to detect the Lense- Thirring effect of the sun on the Periheldrehungen of the inner planets are also performed. Another consequence of the effect would be that the orbital plane of the stars that orbit close to a supermassive black hole, would be brought to a precession around the axis of rotation of the black hole. This effect should be detectable in the next few years, through astrometric observation of the stars in the center of the Milky Way. And by comparing the rate of orbital precession of two stars on different orbits, it should in principle be possible, the "no -hair theorem" of ART to confirm in the context of black holes.

Pulsars are rapidly rotating neutron stars that emit radio pulses constant while rotating. Therefore, they can also be regarded as watches, which allows very accurate tests of their orbital motions. Observations of pulsars that are in orbit around other stars have all demonstrated Periheldrehungen that can not be explained by classical means, but only with the ART. For example, the Hulse -Taylor binary pulsar PSR 1913 16 ( a neutron star pair, one of which is a pulsar ) an observed precession of about 4 ° per year. This precession was used to calculate the mass of the components.

Analogous to the emission of electromagnetic radiation by atoms and molecules, a mass distribution with a quadrupole moment or a higher kind of vibration, or if it is asymmetric and in rotation, emit gravitational waves. This should propagate at the speed of light. For example, losing planets in orbit around the sun energy via gravitational radiation, but this effect is so small that it is unlikely that it can be observed in the near term ( the gravitational radiation from the Earth is approximately 200 watts). Through the Hulse -Taylor pulsar, this radiation could be detected indirectly. Precise time measurements of pulsars showed that their orbits only approximately correspond to Kepler's laws, because over time they move in a spiral toward each other, thereby showing a loss of energy, which is in close agreement with the predicted energy output by gravitational waves. Thus, although the waves were not measured directly, the consideration of their impact is necessary in order to explain the orbits. For this work, Hulse and Taylor were awarded the Nobel Prize.

The double pulsar PSR J0737 - 2003 discovered 3039 has a perihelion of 16.90 ° per year; In contrast to the Hulse -Taylor pulsar is at two stars around pulsars, which allows precision measurements of both parts of the system. Due to the fact that the system can be almost directly observed " on the edge " (inclination 90 °), and the very low transverse velocity of the system from the earth point of view, is J0737 - 3039 so far by far the best for testing strong gravitational fields of ART. Several different effects were observed, including the decrease of the orbit as Hulse Taylor system. After the system was observed 2 ½ years, four independent tests of ART were possible, the most accurate ( the Shapiro delay ) confirmed the predictions of ART within 0.05 %.

Experiments for the detection of black holes are indirect. They relate to the effects of their extremely strong gravitational fields on any nearby stars, the formation of accretion disks, the deflection of light rays, the gravitational time dilation and redshift, and other effects. See for more details: observation of black holes.

Gravitational waves

A number of gravitational wave detectors were built for the direct detection of gravitational waves emitted from astronomical objects, such as the merger of two neutron stars. Currently, the most accurate detector Laser Interferometer Gravitational - is the wave Observatory ( LIGO ), which has been operating since 2002. So far, not a single direct detection of gravitational waves is successful. Future detectors with significantly improved precision are developed or are being planned, such as the Advanced LIGO detector and the task planned Laser Interferometer Space Antenna ( LISA ). It is expected that the Advanced LIGO gravitational wave events may be seen almost every day.

In contrast, the indirect detection of gravitational waves is already successful, see the previous section.

Cosmological tests

Tests of ART to the fullest, cosmological scale are not nearly as compelling as, for example, solar system tests. The first of these tests was the prediction and discovery of the expansion of the universe. 1922 was Alexander Alexandrovich Friedmann that the equations of ART non-stationary solutions include ( even in the presence of a cosmological constant). Georges Lemaître in 1927 showed that static solutions of the equations of ART as the original solution of Einstein, which should occur in the presence of a cosmological constant, are unstable and therefore do not exist, ie the universe must either expand or contract. Lemaître made this explicit prediction that the universe is expanding. He derived a relationship between redshift and distance, which became known as Hubble's law. The fact of Edwin Hubble (1929 ) discovered red shift and related to the expansion of the universe, was seen by many ( still ) considered as a confirmation of the predictions of ART. This meant that even Einstein in 1931 coincided with the solutions of Friedmann and Lemaître. In the 1930s, mainly through the work of Edward Arthur Milne, but was recognized that the linear relationship between the redshift and the distance derived from the more general assumption of uniformity and isotropy as specifically from the ART. Nevertheless, the dramatic at the time prediction of a non-static universe was by no means trivial and mainly motivated by the ART.

Some other cosmological tests are the search for gravitational waves generated during cosmic inflation, which could be observed in the polarization of the cosmic background radiation or with the planned space-based Gravitationswelleninterfermoter "Big Bang Observer" ( BBO ). Other tests at high redshift are aimed at restricting the possibility of alternative theories of gravity and to check the variation of the gravitational constant since the Primordial nucleosynthesis.

766741