31.3 Causal sets
Causal sets are models which describe sets of events (regarded as fundamental),
some of which are related to others by an ‘influenced by’ or ‘informed by’ relation.
This relation can be regarded as that of some primitive causation. Following
Bombelli et al. (1987) and subsequent work, we
assume that those relations are non-circular and transitive. That allows us to partially
order all the events, making up a ‘causal set’ of all events in a network structure
defined by causal relations.
Physicists then want to recover a uniform space-time with the invariance properties
of Galileo and/or Lorentz, so they proceed to assume a ‘uniform sprinkling’ of events
over all space and time such that the events have ‘unit density’ in some natural
units usually taken to be that of the very small Planck length (
metres). Further, Knuth and Bahrenyi (2010) show
how to use counts of links to define pair intervals, from which a scalar measure
can be found that could be an invariant metric under Lorentz transformations. This
can be thought of as leading to (or even deriving) Einstein’s special relativity.