Constraining torsion with Gravity Probe B

It is well-entrenched folklore that all 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, and consider nonstandard torsion theories in which torsion can be generated by macroscopic rotating objects. In the spirit of action=reaction, if a rotating mass like a planet can generate torsion, then a gyroscope would be expected to feel torsion. An experiment with a gyroscope (without nuclear spin) such as Gravity Probe B (GPB) can test theories where this is the case. Using symmetry arguments, we show that to lowest order, any torsion field around a uniformly rotating spherical mass is determined by seven dimensionless parameters. These parameters effectively generalize the parametrized post-Newtonian formalism and provide a concrete framework for further testing Einstein's general theory of relativity (GR). We construct a parametrized Lagrangian that includes both standard torsion-free GR and Hayashi-Shirafuji 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 is an ideal experiment for further constraining nonstandard torsion theories, and work out the most general torsion-induced precession of its gyroscope in terms of our torsion parameters