Аннотация:In the paper, we show that matter waves can be derived from discreteness
and causality. Namely we show that matter waves can naturally be ascribed to finite
discrete causal systems, the Mealy automata having binary input/output which are
bit sequences. If assign real numerical values (‘measured quantities’) to bit sequences,
the waves arise as a correspondence between the numerical values of input sequences
(‘impacts’) and output sequences (‘system-evoked responses’). We show that among
all discrete causal systems with arbitrary (not necessarily binary) inputs/outputs, only
the ones with binary input/output can be ascribed to matter waves ψ(x, t) = e^{i(kx−ωt)}.