Do Spinors Frame-Drag?

Abstract

We investigate the effect of the intrinsic spin of a fundamental spinor field on the surrounding spacetime geometry. We show that despite the lack of a rotating stress-energy source (and despite claims to the contrary) the intrinsic spin of a spin-half fermion gives rise to a frame-dragging effect analogous to that of orbital angular momentum, even in Einstein-Hilbert gravity where torsion is constrained to be zero. This resolves a paradox regarding the counter-force needed to restore Newton's third law in the well known spin-orbit interaction. In addition, the frame-dragging effect gives rise to a {\it long-range} gravitationally mediated spin-spin dipole interaction coupling the {\it internal} spins of two sources. We argue that despite the weakness of the interaction, the spin-spin interaction will dominate over the ordinary inverse square Newtonian interaction in any process of sufficiently high-energy for quantum field theoretical effects to be non-negligible.