Definition
A causal set (or causet) is a set with a partial order relation that is
- Reflexive: For all, we have .
- Antisymmetric: For all, we have .
- Transitive: For all, we have implies .
- Locally finite: For all, we have card.
Here card denotes the cardinality of a set . We'll write if and .
The set represents the set of spacetime events and the order relation represents the causal relationship between events (see causal structure for the analogous idea in a Lorentzian manifold).
Although this definition uses the reflexive convention we could have chosen the irreflexive convention in which the order relation is irreflexive. The causal relation of a Lorentzian manifold (without closed causal curves) satisfies the first three conditions. It is the local finiteness condition that introduces spacetime discreteness.
Read more about this topic: Causal Sets
Famous quotes containing the word definition:
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)