Propagation equations for test bodies with spin and rotation in theories of gravity with torsion

We generalize the Papapetrou equations by deriving propagation equations for the energy-momentum and angular momentum of a test body which has both elementary-particle spin and macroscopic rotation and which is moving in background metric and torsion fields. Our results show that the torsion couples to spin but not to rotation. Thus a rotating test body with no net spin will ignore the torsion and move according to the usual Papapetrou equations. Hence the standard tests of gravity are insensitive to a torsion field. We propose experiments (although still infeasible) to compare the motion of a spin-polarized body with the motion of a rotating body. If the spin and rotation precess differently, the theory of gravity cannot be a metric theory but may be a torsion theory.