Cellular automata provide interesting models of physics: Google Scholar gives more than 25,000 results when searching for "cellular automata" physics.
Google Scholar still gives more than 2,000 results when searching for "quantum cellular automata".
But it gives only 1 (one!) result when searching for "relativistic cellular automata", i.e. cellular automata with a (discrete) Minkoswki space-time instead of an Euclidean one.
How can this be understood?
Why does the concept of QCA seem more
promising than that of RCA?Are there conceptual or technical barriers for a thorough treatment of RCA?
Best Answer
One of the reasons that it may be difficult to model Minkowski space based on cellular automata is that there are no "non-trivial" finite sub-groups of $O(3,1)$, where non-trivial means that it doesn't just reduce to just a finite sub group of $O(3)$ via conjugation. So while cellular automata can be manifestly be homogeneous and isotropic (so admits a discrete $O(3)$ symmetry), it becomes conceptually difficult to imagine some cellular automata capturing Lorentz symmetry.