Discrete models of physical phenomena are an attractive alternative to
continuous models such as partial differential equations. In discrete models,
such as cellular automata, space is treated as having finitely many locations
per unit volume and time is discrete, whereas continuous models (e.g. Schroedinger's
equation, and most field theories) specify detail down to infinitesimal spatial
and time scales. But all existing discrete models depend critically on a
regular (crystalline) lattice, as well as the global synchronization of all
sites. We should ask, on the grounds of minimalism, whether the global synchronization
and regular lattice are inherent in any discrete formulation. Is it possible
to do without these conditions and still have a useful physical model?
Or are they somehow fundamental?
