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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 ( $\ell_p = \sqrt{\hbar G/c^3} = 1.6 \times 10^{-35}$ 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.


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