Tests of general relativity: Encyclopedia II - Tests of general relativity - Modern tests

Tests of general relativity - Modern tests

The modern era of testing general relativity was ushered in largely at the impetus of Dicke (1959, 1962) and Schiff (1960) 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. Another important theoretical development were the new alternatives to general relativity theory – such as Brans-Dicke theory and other scalar-tensor theories – by the parameterized post-Newtonian formalism in which deviations from general relativity can be quantified; and by the framework of the equivalence principle.

Experimentally, new developments in space exploration, electronics and condensed matter physics have made precise experiments, such as the Pound-Rebka experiment, laser interferometry and lunar rangefinding possible.

Tests of general relativity - 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 relativitistic theory of gravity compatible with special relativity and observations. Moreover, it is an extremely simple and elegant theory. This changed with the introduction of Brans-Dicke theory in 1960. This theory is arguably simpler, as it contains no dimensionful constants, and is compatible with a version of Mach's principle and Dirac's large numbers hypothesis, two philosophical ideas which have been influential in the history of relativity. Ultimately, this led to the development of the parameterized post-Newtonian formalism by Nordtvedt and Will, which parameterizes, 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.

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, 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 the 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 this aspect of Einstein's theory to the 0.04% 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 the 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 3.5 × 10⁶ 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 mas, 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 mas. Systematic effects, however, limit the accuracy of the determination to 0.3% (Froeschlé, 1997).

Shapiro (not the same Shapiro cited above) 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 (Shapiro, 1964). He predicted a relativistic time delay in the round-trip travel time for radar signals reflecting off other planets (Shapiro, 1964). 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 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 it will be eclipsed by the Sun gives agreement with general relativity theory at the 5% level (Shapiro, 1971). More recently, the Cassini probe has undertaken a similar experiment which gives perfect agreement with general relativity at the 0.002% level.

These experiments all test the same post-Newtonian parameter, the so-called Eddington parameter γ, which is a straightforward parameterization 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.

Tests of general relativity - The 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 incredible 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 attaction) should follow the same trajectories in a gravitational field, provided the same conditions are satisfied. This is called the Nordtvedt effect (Nordvedt, 1968) and is most precisely tested by the Lunar Laser Ranging Experiment. It has continuously, since 1969, measured the distance from several rangefinding stations on Earth to reflectors on the Moon to approximately centimeter accuracy (Williams, 2004). 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 constant be constant in time, and not varying cosmologically. There are many independent constraints on the variation of Newton's constant (Uzan, 2003), but one of the best comes from lunar rangefinding which suggests that the gravitational constant is changing by no more than one part in 10^-11 per year. The constancy of the other constants is discussed in the Einstein equivalence principle section of the equivalence principle article.

The first of the classical tests discussed above, the gravitational redshift, is a simple consequence of the Einstein equivalence principle and was discovered 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. Experimental verification of this principle 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 1960 using measurements of the change in wavelength of gamma-ray photons generated with the Mössbauer effect, which generates radiation with a very narrow linewidth. The experiment, performed by Pound and Rebka and later improved by Pound and Snyder, is called the Pound-Rebka experiment. The accuracy of the gamma-ray measurements was typically 1%. The blueshift of a falling photon can be found by assuming it has an equivalent mass based on its frequency E = hf (where h is Planck's constant) along with E = mc², a result of special relativity. Such simple derivations ignore the fact that in general relativity the experiment compares clock rates, rather than 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 (Vessot, 1980). 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 neither designed nor operated as a test of fundamental physics, it must account for the gravitational redshift in its timing system. 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 built into subsequent satellites. It showed the predicted shift of 38 microseconds per day. If general relativity suddenly stopped working tomorrow, the GPS control center in Colorado would know within hours; the relativistic correction to the timing is large enough to make GPS useless if it is not allowed for. Also, while it is true that GPS is not operated by the Defense Department as a test of general relativity, physicists have analyzed timing data from the GPS to confirm other tests. An excellent account of the role played by general relativity in the design of GPS and be found in Ashby 2003.

Other precision tests of general relativity, not discussed here, are the Gravity Probe A satellite, launched in 1976, which showed gravity and velocity affect the ability to synchronize the rates of clocks orbiting a central mass; the Gravity Probe B satellite, launched in 2004, is currently attempting to detect frame dragging (Lense-Thirring effect); the Haefele-Keating experiment, which used atomic clocks in circumnavigating aircraft to test general relativity and special relativity together; and the forthcoming Satellite Test of the Equivalence Principle.

Adapted from the Wikipedia article "Modern tests", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki