The problem of obtaining a realistic relativistic description of a qua
ntum system is discussed in the context of a simple (light-cone) latti
ce field theory. A natural stochastic model is proposed which, althoug
h nonlocal, is relativistic (in the appropriate lattice sense), and wh
ich is operationally indistinguishable from the standard quantum theor
y. The generalization to a broad class of lattice theories is briefly
described.