of a Yukawa
potential, 
) of a few hundred meters.
This proposal dovetailed with earlier hints of a deviation from the
inverse-square law of Newtonian gravitation derived from measurements of
the gravity profile down deep mines in Australia,
and with ideas from particle physics suggesting the possible
presence of very low-mass particles with gravitational-strength couplings.
During the next four years
numerous experiments looked for evidence of the fifth force by searching
for composition-dependent differences in acceleration, with variants of
the Eötvös experiment or with free-fall Galileo-type experiments.
Although two early experiments reported positive evidence, the others
all yielded null results. Over the range between one and 
meters,
the null experiments produced upper limits on the strength of a postulated
fifth force between 
and 
of the strength of gravity.
Interpreted as tests of WEP (corresponding to the limit of
infinite-range forces), the results of two representative experiments from
this period, the free-fall Galileo experiment
and the early Eöt-Wash experiment, are shown in
Figure 1. At the same time, tests of the inverse-square
law of gravity were carried out by comparing variations in gravity
measurements up tall towers or down mines or boreholes with gravity
variations predicted using the inverse square law together with Earth
models and surface gravity data mathematically ``continued'' up
the tower or down the hole. Despite early reports of anomalies,
independent tower, borehole and seawater measurements now show no evidence of a
deviation. Analyses of orbital data from planetary range
measurements, lunar laser ranging, and laser tracking of the LAGEOS
satellite verified the inverse-square law to parts in 
over
scales of 
to 
km, and to parts in 
over planetary
scales of several astronomical units [122
].
The consensus at present is that there is no
credible experimental evidence for a fifth force of nature.
For reviews and bibliographies,
see [61, 63, 64, 2, 143].
Nevertheless, theoretical evidence continues to mount that EEP is likely to be violated at some level, whether by quantum gravity effects, by effects arising from string theory, or by hitherto undetected interactions, albeit at levels well below those that motivated the fifth-force searches. Roughly speaking, in addition to the pure Einsteinian gravitational interaction, which respects EEP, theories such as string theory predict other interactions which do not. In string theory, for example, the existence of such EEP-violating fields is assured, but the theory is not yet mature enough to enable calculation of their strength (relative to gravity), or their range (whether they are long range, like gravity, or short range, like the nuclear and weak interactions, and thus too short-range to be detectable).
In one simple example, one can write the Lagrangian for the low-energy limit of string theory in the so-called ``Einstein frame'', in which the gravitational Lagrangian is purely general relativistic:
where 
is the non-physical metric,
is the Ricci tensor derived from
it,
is a
dilaton field, and 
, U and 
are functions of
. The Lagrangian includes that for the electromagnetic field
, and that for
particles, written in terms of Dirac spinors 
. This is
not a metric representation because of the coupling of to
matter via 
and 
.
A conformal transformation 
, 
,
puts the Lagrangian in the form (``Jordan'' frame)
One may choose 
so that the particle Lagrangian takes the
metric form (no explicit
coupling to ), but the electromagnetic Lagrangian
will still couple non-metrically to . The gravitational
Lagrangian here takes the form of a scalar-tensor theory (Sec. 3.3.2). But the non-metric electromagnetic term will, in
general, produce violations of EEP. For examples of specific models,
see [125, 50].
Thus, EEP and related tests are now viewed as ways to discover or place constraints on new physical interactions, or as a branch of ``non-accelerator particle physics'', searching for the possible imprints of high-energy particle effects in the low-energy realm of gravity. Whether current or proposed experiments can actually probe these phenomena meaningfully is an open question at the moment, largely because of a dearth of firm theoretical predictions. Despite this uncertainty, a number of experimental possibilities are being explored.
Concepts for an equivalence principle experiment in space have been developed.
The project MICROSCOPE, designed to test WEP to 
has been
approved by the French space agency CNES for a possible 2004 launch.
Another, known as
Satellite Test of the Equivalence Principle (STEP),
is under consideration as a possible
joint effort of NASA and the European Space Agency (ESA), with the
goal of a 
test.
The gravitational redshift could be improved to the 
level
using atomic clocks on board
a spacecraft which would travel to
within four solar radii of the Sun.
Laboratory tests of the gravitational inverse square law at
sub-millimeter scales are being developed as ways to search for new
short-range interactions or for the existence of large extra dimensions;
the challenge of these experiments is to
distinguish gravitation-like interactions from electromagnetic and
quantum mechanical (Casimir) effects [88].
|
The Confrontation between General Relativity and Experiment Clifford M. Will http://www.livingreviews.org/lrr-2001-4 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |
