ar X iv : g r - qc / 0 60 81 21 v 2 2 9 A ug 2 00 6 Constraining Torsion with Gravity Probe

It is well-entrenched folklore that torsion gravity theories predict observationally negligible torsion in the solar system, since torsion (if it exists) couples only to the intrinsic spin of elementary particles, not to rotational angular momentum. We argue that this assumption has a logical loophole which can and should be tested experimentally. We give an explicit counterexample where a rotating body generates a torsion field in Weitzenböck spacetime with a Hayashi-Shirafuji Lagrangian. More generally, in the spirit of action=reaction, if a rotating mass like a planet can generate torsion, then a gyroscope should also feel torsion. Using symmetry arguments, we show that to lowest order, the torsion field around a uniformly rotating spherical mass is determined by seven dimensionless parameters. These parameters effectively generalize the PPN formalism and provide a concrete framework for further testing GR. We construct a parametrized Lagrangian that includes both standard torsion-free GR and HayashiShirafuji maximal torsion gravity as special cases. We demonstrate that classic solar system tests rule out the latter and constrain two observable parameters. We show that Gravity Probe B (GPB) is an ideal experiment for further constraining torsion theories, and work out the most general torsion-induced precession of its gyroscope in terms of our torsion parameters.