The internal description of a causal set: What the universe looks like from the inside

Details The internal description of a causal set: What the universe looks like from the inside The internal description of a causal set: What the universe looks like from the inside

1998-11-17

arxiv.org/abs/gr-qc/9811053v2

Commun.Math.Phys. 211 (2000) 559-583

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Version to appear in Comm.Math.Phys. (minor modifications). 37 pages, several eps figures

Scientific paper

10.1007/s002200050826

We describe an algebraic way to code the causal information of a discrete spacetime. The causal set C is transformed to a description in terms of the causal pasts of the events in C. This is done by an evolving set, a functor which to each event of C assigns its causal past. Evolving sets obey a Heyting algebra which is characterised by a non-standard notion of complement. Conclusions about the causal structure of the causal set can be drawn by calculating the complement of the evolving set. A causal quantum theory can be based on the quantum version of evolving sets, which we briefly discuss.

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