Facta universitatis - series: Physics, Chemistry and Technology 2016 Volume 14, Issue 3, Pages: 143-196
https://doi.org/10.2298/FUPCT1603143A
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Discreteness causes waves
Anashin Vladimir S. (Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Moscow, Russia)
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).
Keywords: matter waves, finite discrete causal systems, binary bit sequences