{
  "annotation_id": "0b8ce1c2-8ef7-4775-9b76-88665fa03527",
  "date_created": "2026-03-02T18:02:45.249000Z",
  "date_modified": "2026-03-02T18:02:45.249000Z",
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  "record": {
    "abstract": "We shall argue in this paper that a central piece of modern physics does not\nreally belong to physics at all but to elementary probability theory. Given a\njoint probability distribution J on a set of random variables containing x and\ny, define a link between x and y to be the condition x=y on J. Define the {\\it\nstate} D of a link x=y as the joint probability distribution matrix on x and y\nwithout the link. The two core laws of quantum mechanics are the Born\nprobability rule, and the unitary dynamical law whose best known form is the\nSchrodinger\u0027s equation. Von Neumann formulated these two laws in the language\nof Hilbert space as prob(P) = trace(PD) and D\u0027T = TD respectively, where P is a\nprojection, D and D\u0027 are (von Neumann) density matrices, and T is a unitary\ntransformation. We\u0027ll see that if we regard link states as density matrices,\nthe algebraic forms of these two core laws occur as completely general theorems\nabout links. When we extend probability theory by allowing cases to count\nnegatively, we find that the Hilbert space framework of quantum mechanics\nproper emerges from the assumption that all D\u0027s are symmetrical in rows and\ncolumns. On the other hand, Markovian systems emerge when we assume that one of\nevery linked variable pair has a uniform probability distribution. By\nrepresenting quantum and Markovian structure in this way, we see clearly both\nhow they differ, and also how they can coexist in natural harmony with each\nother, as they must in quantum measurement, which we\u0027ll examine in some detail.\nLooking beyond quantum mechanics, we see how both structures have their special\nplaces in a much larger continuum of formal systems that we have yet to look\nfor in nature.",
    "arxiv_id": "quant-ph/9808011",
    "authors": [
      "H. Pierre Noyes",
      "Tom Etter"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.4006/1.3028803",
    "journal_ref": "Phys.Essays 12 (1999) 733-765",
    "title": "Process, System, Causality, and Quantum Mechanics, A Psychoanalysis of   Animal Faith",
    "url": "https://arxiv.org/abs/quant-ph/9808011"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "76620aa9-1478-41b8-906d-b76d17b2906a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}