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Experimental Tests of General Relativity: Highlights This chapter summarizes the current status of tests of general relativity, with emphasis on more recent achievements. For reference while reading this chapter, we list in Table 2.1 the most accurate test results as of mid-1984. EQUIVALENCE PRINCIPLE, EOTVOS TO LUNAR LASER RANGING In his approach to the theory of gravitation, Einstein did not seek to explain the equivalence of gravitational and inertial mass but instead elevated it to the status of a principle and proposed a generalization stating that, locally, gravitation and acceleration are indistinguishable. The most accurate experimental tests of this principle are of the Eotvos type to determine whether the ratio of inertial to (passive) gravitational mass is the same for all bodies, independent of size or composition. Modern experiments have found no difference in this ratio to a few parts in 10' i for several substances. Thus, Eotvos experiments show with high accuracy that nuclear, electromagnetic, and weak interac- tions contribute equally to gravitational and inertial mass. But does gravitational energy contribute by the same amount? The gravitational binding energy, important theoretically because it invokes the nonlinear character of gravitation, is too small to measure in laboratory-sized objects. Astronomical bodies must be used, and 15

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EXPERIMENTAL TESTS OF GENERAL RELA TI VI TY: HIGHLIGHTS 17 three or more are required. Our first manned mission to another astronomical body enabled an accurate test to be performed with the Earth-Moon-Sun system. Emplacement on the lunar surface of optical corner reflectors by the Apollo astronauts has allowed us to distinguish whether the Moon and the Earth fall toward the Sun with equal accelerations. Any anomalous difference in these two accelerations would manifest itself in a corresponding monthly variation in the Earth-Moon distance, now determined from laser measurements to within 10 cm. The measurements set stringent limits on any anomalous behavior and establish that at least 98.5 percent of the gravitational binding energy of the Moon contributes to both its gravitational mass and its inertial mass. To this accuracy, therefore, it has been verified that all ordinary mass-energy, including that due to gravitational self-energy, gravitates in the same manner. This result constrains a combination of PEN parameters; for the special case of fully conserv- ative metric theories without preferred frame or location effects, it implies that the linear combination 4F - ~ - 3 vanishes to within +0.015. Some metric theories predict a violation of the principle of equivalence for massive bodies because, in these theories, only part of the mass due to gravitational self-energy gravitates, although the principle is obeyed for the contributions to mass from all other forms of energy. The class of such theories has thus been sharply curtailed by this result from the lunar laser-ranging experiment. Space techniques may provide an opportunity for improving the classical Eotvos experiment. An apparatus is being developed where two masses (of different composition) in the form of concentric cyl- inders are free to move along their common axis on magnetic bearings. In orbit around the Earth the difference in their free-fall accelerations would be measured. The geometry minimizes the effect of gravity gradients, which are large for a torsion balance experiment. It is anticipated that ground-based tests with this apparatus should reach an accuracy of 10-'', and in space the experiment may reach an accuracy of -5, depending on the levels of mechanical and gravity gradient disturbances. GRAVITATIONAL REDSHIFT, MOSSBAUER TO ROCKETBORNE MASER One of the most celebrated predictions of general relativity concerns the effect of gravitational potential on the rates of clocks and on the frequency of an electromagnetic signal. A given clock appears to run more slowly than an identical clock located in a region of lower

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8 GRA VITATION GRAVITATIONAL REDSHIFT EXPERIMENT ALTITUDE 40,060 KH .4 - tutus REDSHANK ~ xt040 ~ ~ (. SECOND IN 400 YEA - ) TNER~L SH~SPIN AXIS THEE OF FLIGHT, ~ ~S~ , / 1 ~ TRACK. - / me' TRANSPONDER AND / ~ CLOCK 51GNA I 1~ I TWITTER tow ~ rS - CE - AFT l ~ / 1 WITH CLOCK MEL EARTH STATION WITH ATOMIC ~ r CLOCKS ~ , H - BASER REDSHIFT ~magnified;\ ANTES~ 51( `` T O AY SIGNAL TRACKING SIGNALS E ARTH STATION 2 t DOPPLER MAGNETIC SHIELDS SOLENOID STORAGE BULB CAVITY R ESONATOR 4420 ~Hz ' ~ E:= ,~- rraans| | H-~4SER| ~ APACE SIGNAL OUTPUT STATE - SELECTOR MAGNET ATOMIC HYDROGEN BEAR ATo~lc HYDROGEN OISSOCIATOR H2 INLET DOPPLER CANCELATION SYSTEM 2 t DOPPLER HOWLER ~ H I t DOPPLER ~ _ ~ FIGURE 2.1 A suborbital clock has measured the gravitational redshift eject; the result agrees with theory to within the experimental accuracy of I part in 104. Keys to the success of the experiment were the special hydrogen maser and the two-way communi- cations link that allowed subtraction of a huge Doppler effect. gravitational potential. The most precise laboratory verification of the gravitational redshift effect was obtained a decade and a half ago using the Mossbauer effect to obtain extremely narrow spectral lines. By velocity compensation of the change in frequency of the gamma rays over a vertical distance of 25 m, it was possible to verify the prediction of general relativity to about 1 percent. By far the most accurate experiment to test the effect of gravitation on the rate of a clock was performed by the placement of a hydrogen- maser frequency standard on a rocket that traveled on an orbital arc with a lO,000-km maximum altitude. In this experiment, diagramed in Figure 2. 1, a sophisticated radio communication link was employed to circumvent ionospheric propagation effects and to cancel the large Doppler shift. Thus, the rate of the hydrogen-maser clock in orbit is accurately compared with similar masers on the ground. The measured redshift agreed with the prediction to within the experimental uncer- tainty of about 1 part in 104the most accurate relativity experiment yet performed with space techniques.

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EXPERIMENTA L TESTS OF GENERAL RELA TI VI TY: HIGHLIGHTS 19 LIGHT DEFLECTION, ECLIPSES TO RADIO INTERFEROMETRY Electromagnetic radiation is predicted by general relativity to be deflected by massive bodies, in part from the action of the gravitoelec- tric component of the gravitational field (a direct consequence of the principle of equivalence) and in equal part as a consequence of space curvature. The deflection of light by the Sun was dramatically verified by an eclipse expedition team in 1919, catapulting Einstein to world fame. But Earth-based observations of total eclipses have not achieved the level of reliability needed for accurate verification of the predicted deflection. In the late 1960s optical eclipse observations were largely supplanted by radio-interferometric techniques. Simultaneous mea- surements at two radio-frequency bands enable the refractive effects of the solar corona to be reduced to a benign level. As a result, the uncertainty of the verification of the predicted 1.75-arcsec deflection for rays grazing the solar limb was decreased by a factor of 1O, now implying that ~ is unity to within about 2 percent. SIGNAL RETARDATION, NEWEST AND MOST ACCURATE TEST General relativity also predicts that the transit times of electromag- netic signals traveling between two points will be increased if a massive body is placed near the path of these signals. Thus, a measurement of the round-trip time of signals propagating between two points will be greater the nearer a massive body lies to the path of propagation, owing in part to the principle of equivalence and in equal part to space curvature, as for light deflection. The development of radar and of space techniques made this test possible, and as a latecomer it is sometimes called the "Fourth Test," the classical three being Mer- cury's perihelion precession, light deflection, and the gravitational redshift. Signal retardation measurements currently provide our best test of the important space-curvature effects in general relativity. The increase of the round-trip times for light or radio signals propagating between planets, owing to the direct effect of solar gravitation, is predicted by general relativity to reach a maximum of about 250 As for ray paths that graze the limb of the Sun. This prediction was verified first through measurement of echo times of radar signals bounced from the surfaces of the inner planets.

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20 GRA VITA TION ~ 300 ~ 1100 C) o 900 By a: 700 0.2 a) - 0./ Z 1 - ~ 6 tr-O.4 _ X 0.2 1 1 1 ~ 1 1 1 1 1 , 1 , a s 0 N Dl J F M a M J J a s VIKING RELATIVITY EXP ER I MENT - - , , , , 1l , , , , , , ,\ .: x 4 o.o ~ ' ' s fit ~ divvy+ ~ $;, ~ v V it, o 1' X^ {+ ~ ~ ~~ * ~ O ~ ~ 3 ~ ~ "x I ~ g ~ of Q ~ ~ xs ! x .$ ! X 4976 1 4977 DAT E FIGURE 2.2 Ranging to the Viking Landers. Shown here are the residuals after fitting measured round-trip times to the range model. Measurement uncertainties are omitted to avoid cluttering the figure. Mars was on the other side of the Sun on November 25, 1976. VL1 and VL2 denote Viking Landers I and 2, and 14, 43. and 61 and 63 denote, respectively, Deep Space Network tracking stations in Goldstone, California; Canberra, Australia; and Madrid, Spain (26- and 64-m antennas). More recently a 50-fold improvement in this test was realized by using the Viking Lander spacecraft on the surface of Mars. The round-trip travel times of radio signals were measured with uncertainty as small as 10 ns, about 10-~ of the total travel time. The measure- ments were then fit to an elaborate range model including many solar-system parameters, the relativistic delay, and positions for the spacecraft and tracking stations. The residuals of the measurements from the model are shown in Figure 2.2. The final uncertainty in measuring the relativistic delay arises from possible systematic errors and parameter correlations in the model fitting. The Viking experiment reduced the uncertainty in the measurement of the relativistic delay from 5 percent (obtained with radar) to 0.1 percent. The measured delay agrees with the prediction of general relativity twhich is propor-

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EXPERIMENTALTESTSOFGENERA~RELATIVITY: HIGHLIGHTS 21 tional to (1 + y)/2], showing that ~ = 1 + 0.002 an order of magnitude higher accuracy than yet achieved for the light deflection test. PERIHELION ADVANCE, EINSTEIN'S ONLY HANDLE The anomalous advance of the perihelion of the orbit of the planet Mercury, noted in the mid-nineteenth century, provided the first hint that Newtonian theory was not adequate as a description of the dynamics of the solar system. This advance, subsequently determined to be 43 arcsec per century, was an elegant confirmation of Einstein's theory. Because this effect increases secularly, the improvement from use of modern radar observations of Mercury over the results obtained from several hundred years of optical observations has not been so dramatic. At present, radar observations of Mercury yield an uncer- tainty of 0.5 percent in the determination of the anomalous perihelion advance, a twofold improvement over the results from optical obser- vations. The relativistic contribution to the perihelion advance depends not only on space curvature but also on the nonlinearity of the superposition law for the gravitational potential and on preferred-frame and location effects. If one assumes that the contributions of the solar quadrupole moment and of possible preferred-frame and location effects are negligible, the measurements demonstrate that for fully conservative theories the combination (2 + 2y - Q)/3 of PPN param- eters is unity to within 0.5 percent. Relativistic perihelion advances have also been detected for Mars and for the asteroid Icarus. The results agree, to within the 20 percent experimental uncertainties, with the values predicted by general relativity. CHANGING GRAVITATIONAL CONSTANT, SOLAR-SYSTEM TIME VERSUS ATOMIC TIME A deep question of physics concerns possible variations with time of certain constants of nature. General relativity assumes that the con- stant of gravitation G is a universal constant, independent of both spatial location and time. The possibility that this constant varies with time is based in part on the so-called large numbers hypothesis. This hypothesis stems from the fact that the ratio of the electrostatic to the gravitational force between an electron and a proton, about 1039, iS approximately equal to the age of the universe expressed in atomic units. Is this near equality a mere coincidence confined to the present epoch? If one assumes instead that it is of fundamental significance, independent of epoch, then some physical constant must vary with

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22 GRA VITA TION time. It has been proposed that the gravitational interaction, as measured against the electromagnetic, may be weakening with time. Any such effect should be detectable by comparing time kept by an atomic clock with the time kept by a gravitational clock. In practice, precise ranges to solar system bodies are measured as a function of time, as kept by atomic clocks. The ranges are fitted to an elaborate solar-system model that includes general relativity and a possible eject due to a changing value of G. Recent results from ranges to Mars (using the Viking Lander and Mariner 9), radar ranges to Mercury and Venus, lunar laser ranges, and optical positions of the Sun and planets have set a limit at about ~G/G~ < 10-"/year. Accuracy is limited more by incompleteness of the solar-system model than by experimental errors; currently the limit is imposed by uncertainty in the gravitational perturbation of Mars by the asteroids. LABORATORY TESTING OF GRAVITATION, SEARCHING FOR THE UNEXPECTED We must not allow these impressive advances afforded by space techniques to overshadow completely the important contributions of laboratory gravitation experiments. Many of these experiments achieve great accuracy by using null techniques, as in the celebrated Eotvos experiments. The methodology is to propose plausible anom- alies to the standard theory or its assumptions. Null experiments are then devised such that the proposed anomaly leads to a nonzero result. Because of the characteristic high precision of null experiments, the results often yield deeper and broader insights than originally intended. Many basic aspects of Newtonian gravitation are taken for granted in spite of a lack of experimental verification. Recently, the validity of the R-2 dependence of gravitation for laboratory distance scales has been questioned and tested. (From 104 km to planetary distance scales the exponent is known to be -2 with an accuracy of a few parts in 108.) Torsion balance experiments give an exponent of -2~1 + 0.1 percent) on distance scales from a few centimeters to a meter, while surface and satellite measurements of the Earth s gravitational field give -2~1 + 1 percent) on a 1-km scale. Although the results are not surprising, they do put gravitation on a better footing. An unexpected bonus of the short-range experiments is that the results place constraints on prop- erties of possible new particles (e.g., anions) that might lead to short-ranged exchange forces in ordinary matter. When we write down Newton s second law for a planet orbiting the Sun we generally do not notice that the three masses in that equation

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EXPERIMENTAL TES TS OF GENERA ~ RELA TI VI TY: HIGHLIGHTS 23 are playing distinctively different roles. The active (attractor) mass, passive (attracted) mass, and inertial mass are assumed to have the same ratios, independent of composition. This is a fundamental as- sumption of general relativity and is well tested for passive and inertial masses where large solar-system bodies can be used as the active third mass. Unfortunately, experiments to compare active mass with inertial or passive masses necessarily use laboratory-scale masses. One tech- nique uses a Cavendish-type experiment except that the large movable (active) mass floats beneath a fluid of exactly the same (passive) density. As the mass moves back and forth, the torque on a torsion pendulum is proportional to the difference in the ratios of active to passive masses for the solid mass versus the displaced fluid material. A composition dependence in (active mass)/(passive mass) would result in a nonzero torque. The ratio has been found to be the same for fluorine and bromine to an accuracy of a part in 104. Laboratory experiments to look for effects of local anisotropy of space have achieved high precision. These so-called Hughes-Drever experiments search for tiny frequency shifts in atomic and nuclear resonance lines that might be correlated with the orientation in space of a polarized nucleus, rotated once a day by the Earth. Exceedingly small shifts (compared to nuclear binding energy) are detectable, leading to one of the most accurate null results in physics: inertial mass is locally isotropic to better than 10-2. Though more than two decades old, we mention these important results because new techniques in atomic physics have brought renewed interest in the experiments. Only a few experimenters choose to do laboratory gravitation. The work is characterized by clever techniques, compulsion with systematic er- rors, long integration times, and great experimental ingenuity.