On how the (1+1)-dimensional Dirac equation arises in classical physics

We demonstrate how the (1+1)-dimensional Dirac equation can be derived from the equation for the probability distribution governing a stochastic process when particles are permitted to propagate both backwards and forwards in time. This derivation uses a real transfer matrix and does not require a formal analytic continuation from classical physics. The physical significance of the quantity we interpret as being the wave function is discussed.