The logic of causally closed spacetime subsets

被引：16

作者：

Casini, H ^{[1
]}

机构：

[1] CNRS, Ctr Phys Theor, F-13288 Marseille, France

来源：

CLASSICAL AND QUANTUM GRAVITY | 2002年 / 19卷 / 24期

关键词：

D O I：

10.1088/0264-9381/19/24/308

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

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.

引用

页码：6389 / 6404

页数：16

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