  Starting from a model of an elastic medium, we derive equations of motion
that are identical in form to Dirac's equation for a spin 1/2 particle with
mass, coupled to electromagnetic and gravitational interactions. The mass and
electromagnetic terms are not added by hand but emerge naturally from the
formalism. A two dimensional version of this equation is derived by starting
with a model in three dimensions and deriving equations for the dynamics of the
lowest Fourier modes assuming one dimension to be periodic. Generalizations to
higher dimensions are discussed.
