The problem of obtaining a realistic, relativistic description of a quantum system is discussed in the context of a simple (light-cone) lattice field theory. A natural stochastic model is proposed which, although non-local, is relativistic (in the appropriate lattice sense), and which is operationally indistinguishable from the standard quantum theory. The generalization to a broad class of lattice theories is briefly described.

Correction to second-last paragraph of section 6; footnote added in section 5; section 9 trimmed; other minor changes. PlainTex 19pp. 4 eps figs.