DISCRETENESS CAUSES WAVES

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) = ei(kx−ωt).