THE DYNAMICAL ORIGIN OF THE MASSIVE GRAVITON AND DECOUPLING OF TORSION

When a direction vector is attached to a space-time point, we may really express it as a spin.opposite orientations of the vector produce opposite helicities, which indicate states of spin up and down.Discreteness embedded in the space-time manifold 4 M gives rise to a lattice where Lorentz symmetry is broken due to the noncommutativity of space-time coordinates, resulting in an anisotropic space.But when the noncommutativity parameter falls to the usual symplectic matrix, space-time and torsion are no longer connected, and general relativity realizes gravity with two additional degrees of freedom: a scalar field and a heavy graviton.The condition is similar to spin-charge separation of Yang-Mills gauge fields in the low energy domain.