Primitive causality

Primitive causality is a dynamical completeness condition: the state restricted to a suitable initial spacetime region determines its expectations throughout that region's domain of dependence. Algebraically one requires the later domain-of-dependence observable algebra to be contained in the initial algebra, under the identifications supplied by the dynamics. A local time-slice axiom gives this property for a neighbourhood of a Cauchy slice. Knowledge of the full restricted state, including correlations, is required; knowing only mean initial fields is insufficient.