{
  "annotation_id": "524add26-0b28-4049-8562-f84efce77b1a",
  "date_created": "2026-03-02T18:02:06.807000Z",
  "date_modified": "2026-03-02T18:02:06.807000Z",
  "file_hash": "3ac600804003ad8f61f635881d503a64c667849a0e86c568d05b8e8100c7a16d",
  "private": false,
  "record": {
    "abstract": "A not-too-technical version of the paper: \"A Granular Permutation-based\nRepresentation of Complex Numbers and Quaternions: Elements of a Realistic\nQuantum Theory\" - Proc. Roy. Soc.A (2004) 460, 1039-1055. The phrase\n\"meteorological butterfly effect\" is introduced to illustrate, not the familiar\nloss of predictability in low-dimensional chaos, but the much less familiar and\nmuch more radical paradigm of the finite-time predictability horizon,\nassociated with upscale transfer of uncertainty in certain multi-scale systems.\nThis motivates a novel reinterpretation of unit complex numbers (and\nquaternions) in terms of a family of self-similar permutation operators. A\nrealistic deterministic kinematic reformulation of the foundations of quantum\ntheory is given using this reinterpretation of complex numbers. Using a\nproperty of the cosine function not normally encountered in physics, that it is\nirrational for all dyadic rational angles between 0 and pi/2, this\nreformulation is shown to have the emergent property of counterfactual\nindefiniteness and is therefore not non-locally causal.",
    "arxiv_id": "quant-ph/0404041",
    "authors": [
      "T. N. Palmer"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1175/BAMS-86-4-519",
    "title": "Quantum Reality, Complex Numbers and the Meteorological Butterfly Effect",
    "url": "https://arxiv.org/abs/quant-ph/0404041"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "35049556-a1b3-4761-9119-fcd44c5407b5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}