3 Tests of Post-Newtonian Gravity2 Tests of the Foundations 2.2 Theoretical Frameworks for Analyzing

2.3 EEP, particle physics, and the search for new interactions 

In 1986, as a result of a detailed reanalysis of Eötvös' original data, Fischbach et al. [62] suggested the existence of a fifth force of nature, with a strength of about a percent that of gravity, but with a range (as defined by the range tex2html_wrap_inline4183 of a Yukawa potential, tex2html_wrap_inline4185) 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 tex2html_wrap_inline4187 meters, the null experiments produced upper limits on the strength of a postulated fifth force between tex2html_wrap_inline4189 and tex2html_wrap_inline4191 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 tex2html_wrap_inline4193 over scales of tex2html_wrap_inline4195 to tex2html_wrap_inline4197 km, and to parts in tex2html_wrap_inline4199 over planetary scales of several astronomical units [122Jump To The Next Citation Point In The Article]. 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 tex2html_wrap_inline4201 is the non-physical metric, tex2html_wrap_inline4203 is the Ricci tensor derived from it, tex2html_wrap_inline4205 is a dilaton field, and tex2html_wrap_inline4207, U and tex2html_wrap_inline4211 are functions of tex2html_wrap_inline4205 . The Lagrangian includes that for the electromagnetic field tex2html_wrap_inline4215, and that for particles, written in terms of Dirac spinors tex2html_wrap_inline4217 . This is not a metric representation because of the coupling of tex2html_wrap_inline4205 to matter via tex2html_wrap_inline4221 and tex2html_wrap_inline4223 . A conformal transformation tex2html_wrap_inline4225, tex2html_wrap_inline4227, puts the Lagrangian in the form (``Jordan'' frame)


One may choose tex2html_wrap_inline4229 so that the particle Lagrangian takes the metric form (no explicit coupling to tex2html_wrap_inline4205), but the electromagnetic Lagrangian will still couple non-metrically to tex2html_wrap_inline4223 . 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 tex2html_wrap_inline4235 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 tex2html_wrap_inline4237 test. The gravitational redshift could be improved to the tex2html_wrap_inline4239 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].

3 Tests of Post-Newtonian Gravity2 Tests of the Foundations 2.2 Theoretical Frameworks for Analyzing

image The Confrontation between General Relativity and Experiment
Clifford M. Will
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