Signature of Einstein-Cartan theory

Abstract

We study the effects of torsion as predicted by the Einstein-Cartan theory in the test-particle non-relativist approximation. We derive the corresponding 2-spinor Hamiltonian. Then, we solve an idealized reflection and transmission problem for a beam travelling across a spin-polarized target. We identify deviations in the spin polarizations on the reflected and transmitted beams that can distinguish Einstein-Cartan from general relativity. These deviations would constitute compelling evidence for a non-trivial spacetime torsion if measured.