  We show that the dynamics of an elastic solid embedded in a Minkowski space
consist of a set of coupled equations describing a spin-1/2 field, $\Psi$,
obeying Dirac's equation, a vector potential, $A_\mu$, obeying Maxwell's
equations and a metric, $g_{\mu\nu}$, which satisfies the Einstein field
equations. The combined set of Dirac's, Maxwell's and the Einstein field
equations all emerge from a simple elastic model in which the field variables
$\Psi$, $A_\mu$ and $g_{\mu\nu}$ are each identified as derived quantities from
the field displacements of ordinary elasticity theory. By quantizing the
elastic field displacements, a quantization of all of the derived fields are
obtained even though they do not explicitly appear in the Lagrangian. We
demonstrate the approach in a three dimensional setting where explicit
solutions of the Dirac field in terms of fractional derivatives are obtained. A
higher dimensional version of the theory would provide an alternate approach to
theories of quantum gravity.
