Causal theory is an attempt to describe physics at the fundamental scale by means of binary relations on sets. Such relations, called causal relations, are generalizations of partial orders. In causal theory, the concept of causality is fundamental, while the concept of spacetime is derivative. The apparent continuum properties of spacetime are hypothesized to be macroscopic manifestations of microscopic causal structure. The principal philosophical difference between classical causal theory and relativity is that causal structure is taken to determine geometry, rather than vice versa. The proposal that all metric properties, such as distance and time, arise from causal structure is called the causal metric hypothesis.
Causal theory has a wide range of applications. While its primary purpose is to describe fundamental physics, the same methods also apply to other fields such as information theory and computer science. In general, causal structures are neither continuous nor discrete. Causal relations need not be transitive, interval finite, or even acyclic. Even at the classical level, the algebraic objects involved are generally noncommutative. These features do not represent vacuous generality, but rather reflect crucial physical considerations that demand serious study. Some of these features play pivotal roles in macroscopic applications in fields such as computer science in ways that make their relevance to the general theory obvious.
Quantum causal theory combines the classical theory, which replaces relativity, with quantum theory. A particularly fruitful approach is the natural generalization of Feynman’s sum over histories method, which is central to both nonrelativistic quantum theory and quantum field theory. The sum over histories method invokes causal configuration spaces whose elements are universes and which themselves possess an induced causal structure. This transition to the quantum paradigm by simply iterating the same type of structure is one of the most striking aspects of the theory. Quantum causal theory has immediate applications in the field of quantum computing.