Abstract. The causal structure of spacetime offers a natural notion of an opposite or orthogonal in the logical sense, where the opposite of a set is formed by all points non-timelike related with it. We show that for a general spacetime the algebra of subsets that arises from this negation operation is a complete orthomodular lattice, and thus has several of the properties characterizing the algebra of physical propositions in quantum mechanics. We think this lattice could be used to investigate the causal structure in an algebraic context. As a first step in this direction, we show that the causal lattice is, in addition, atomic, find its atoms, and give necessary and sufficient conditions for irreducibility.

PACS numbers: 0420G, 0210A

Print publication: Issue 24 (21 December 2002)
Received 9 May 2002, in final form 24 October 2002
Published 28 November 2002