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 .
|The Confrontation between General Relativity and
Clifford M. Will
© Max-Planck-Gesellschaft. ISSN 1433-8351
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