A Derivation of the Classical Einstein-Dirac-Maxwell Equations From a   Model of an Elastic Medium
  Starting from a model of an elastic medium, partial differential equations with the form of the coupled Einstein-Dirac-Maxwell equations are derived. The form of these equations describes particles with mass and spin coupled to electromagnetic and gravitational type of interactions. A two dimensional version of these equations is obtained 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. 
John M. Baker