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OCR for page 11
1
Experimental Tests of
General Relativity:
Introcluction
Perhaps more than in any other area of physics, progress in
gravitation physics has been dominated by theoretical work; experi-
mental tests of general relativity have lagged far behind theoretical
ideas and predictions. In part this unbalance is due to the extreme
difficulty of doing laboratory experiments at interesting levels of
accuracy, but it is also true that the elegance and richness of gravitation
theory has captured the interest of some of the best theorists of this
century. Fortunately for the field, the last two decades have seen
dramatic advances in our ability to test gravitation theories. Most of
this upsurge in experimental activity was brought about by technolog-
ical advances in radio and radar astronomy and by the development of
precision tracking capabilities for solar-system spacecraft.
The theory of general relativity, devised nearly 70 years ago by
Einstein, is still the most successful description of gravitation. Progress
in the field has been characterized by the invention of plausible
alternatives (such as the scalar-tensor theory) that predict different
effects or magnitudes than those predicted by general relativity.
Experimental work then decides. Currently, there is no reason to think
that general relativity needs modification in the classical domain. As
we shall see below, some basic tenets of general relativity have been
well tested (parts in 10~), some predicted effects have been measured
with good agreement (parts in 103), but some major predictions
(''magnetic" effects) have not been tested at all.
11
OCR for page 12
12 GRAVITATION
General relativity makes two distinct statements about the nature of
gravitation. First, the metric hypothesis states that gravitation can be
described as a Riemannian curvature of space-time, with the laws of
physics for all nongravitational interactions having the same form in
the local Lorentz frames of curved space-time as in the flat space-time
of special relativity. Second, the curvature of space-time is deter-
mined, through the Einstein field equation, by the energy, momentum,
and stress of all matter and nongravitational fields contained in
space-time. Gravitation in this view is an intrinsically nonlinear phe-
nomenon; the field equation alone allows the equation of motion for
particles to be deduced from it. This characteristic stands in sharp
contrast to Newtonian theory in which the field equation and the
equations of motion are separate postulates. Other metric theories of
gravitation incorporate the metric hypothesis but differ from general
relativity by the manner in which space-time curvature is generated.
Experimental tests of general relativity can correspondingly be sepa-
rated into two categories: tests of the metric hypothesis, such as facets
of the principle of equivalence, and tests of the properties of space-time
curvature, such as the orbits of light rays and test particles.
The structure of metric theories of gravitation can be clarified by
analogy with electromagnetic theory. Gravitation is described by a
four-dimensional metric of space-time and electromagnetism by a
four-dimensional tensor for the electromagnetic field. However, one
often gains insight and computational power by decomposing the
four-dimensional quantities into separate spatial and temporal compo-
nents. In such a decomposition, the electromagnetic field splits into
electric and magnetic parts. Similarly, the gravitational field, or metric
tensor, separates into three parts: a gravitoelectric field, a gravitomag-
netic field, and a part that represents the curvature of space.
In the Newtonian limit of any metric theory of gravitation, the
gravitomagnetic field and space curvature vanish; the much stronger
gravitoelectric field reduces to the Newtonian gravitational accelera-
tion. In the post-Newtonian regime, a rich variety of new phenomena
appear, such as the gravitomagnetic dragging of inertial frames, the
gravitoelectric and space-curvature-induced gravitational deflection of
light, and the perihelion advance of planetary orbits. To express clearly
the consequences of these different post-Newtonian phenomena and
the differences between the predictions for each from different metric
theories, one can use the parameterized-post-Newtonian (PPN) formal-
ism. With it, all metric theories can be expressed in a common
framework in a special coordinate system. In this special coordinate
system, the three basic fields gravitoelectric, gravitomagnetic, and
OCR for page 13
EXPERIMENTAL TESTS OF GENERAL RELATIVITY: INTRODUCTION 1 3
space curvature are expressed in terms of potentials whose coupling
strengths are given by ten dimensionless parameters whose values
generally vary from one metric theory to another.
Thus, each theory can be characterized, at this level, by the nu-
merical values of its PPN parameters; and each experiment can be
characterized by a predicted result, dependent on one or more of these
parameters. Currently the best tested parameters are ~ and P; these
describe, respectively, the amount of spatial curvature generated by a
unit rest mass and the amount of nonlinearity in the superposition of
Newtonian gravitational potentials (gravitoelectric fieldsJ. There is also
one parameter that describes the amount of any preferred-location
effect, three that describe the amount and kind of preferred-frame
effects, and five (four distinct from those already listed) that describe
the amount and nature of violations of global conservation laws for
total energy-momentum. An eleventh parameter, G/G, introduced to
describe any fractional time rate of change of the constant of gravita-
tion, depends more on cosmology than on a metric theory of gravita-
tion. For general relativity, ~ and ~ are unity and all other parameters
vanish. Although the PEN formalism has its limitations, it has served
admirably as a framework to incorporate a large number of theories of
gravitation and to stimulate the invention of new experiments.
As we shall see, the best measurements of ~ and ~ have come from
experiments using solar-system gravitational fields. The solar system
has three special properties in this regard: (a) its gravity is everywhere
very weak; the dimensionless ratio of the gravitational potential to the
square of the speed of light is 2 x 10-6 on the Sun's surface; (b) the
square of the ratio of the speed of each source of significant gravity to
that of light is under 10-7; and (c) the ratios of the internal stress
energies of all bodies to their respective rest energies are less than
10-s. These three conditions guarantee that Newton's theory of
gravitation will provide the same predictions as general relativity to
within about 1 part in IOs for the structure of the Sun and to within I
part in 106 for experiments confined to the exterior of the Sun. Thus7
the goals of most experiments have been to measure deviations from
Newtonian theory, i.e., post-Newtonian effects of gravitation whose
fractional magnitudes are about 10-6 or somewhat less. Of course,
higher-order relativistic deviations from Newtonian theory are also
predicted to exist in the solar system. These post-post-Newtonian
effects are not discernible in present experiments, but they may be
reached by the next generation of space experiments. The discovery of
neutron stars and perhaps black holes in our galaxy brings hope that
experimental gravitation might escape the realm of tiny effects. Mul-
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14 GRAVITATION
tiple systems of these compact objects approach the ideal gravitational
laboratory of massive pointlike bodies having negligible nongravita-
tional interactions. One such system—the binary pulsar has already
yielded spectacular results, but the intrinsic advantages of such sys-
tems have not yet been fully realized. This remains as a bright hope for
the next decade.
Representative terms from entire chapter:
metric theories
