On the Absence of Homogeneous Scalar Unitary Cellular Automata

Failure to find homogeneous scalar unitary cellular automata (CA) in one dimension led to consideration of only “approximately unitary” CA—which motivated our recent proof of a No-go Lemma in one dimension. In this note we extend the one dimensional result to prove the absence of nontrivial homogeneous scalar unitary CA on Euclidean lattices in any dimension. PACS numbers: 05.30.-d, 89.80.+h, 03.65.Fd, 11.30.-j.