{"paper":{"title":"Quantum models as classical cellular automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.CG"],"primary_cat":"quant-ph","authors_text":"Hans-Thomas Elze","submitted_at":"2017-01-09T16:50:04Z","abstract_excerpt":"A synopsis is offered of the properties of discrete and integer-valued, hence \"natural\", cellular automata (CA). A particular class comprises the \"Hamiltonian CA\" with discrete updating rules that resemble Hamilton's equations. The resulting dynamics is linear like the unitary evolution described by the Schr\\\"odinger equation. Employing Shannon's Sampling Theorem, we construct an invertible map between such CA and continuous quantum mechanical models which incorporate a fundamental discreteness scale $l$. Consequently, there is a one-to-one correspondence of quantum mechanical and CA conservat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02252","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}