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OCR for page 15
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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OCR for page 17
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
OCR for page 18
8 GRA VITATION
GRAVITATIONAL REDSHIFT
EXPERIMENT
ALTITUDE 40,060 KH
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(. SECOND IN 400 YEA - ) TNER~L SH~SPIN AXIS
THEE OF FLIGHT, ~ ~S~ ,
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CLOCKS ~ ,
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~ _ ~
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 104—the most accurate relativity experiment
yet performed with space techniques.
OCR for page 19
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.
OCR for page 20
20 GRA VITA TION
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VIKING RELATIVITY
EXP ER I MENT
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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-
OCR for page 21
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
OCR for page 22
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
OCR for page 23
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.
Representative terms from entire chapter:
inertial mass
