{
  "annotation_id": "32e78ab9-761f-487a-b4d1-c69cd7a19aee",
  "date_created": "2026-03-02T18:01:48.891000Z",
  "date_modified": "2026-03-02T18:01:48.891000Z",
  "file_hash": "1514e04c55768738723caa6a72c382d6f9bf858a12c6c47466526caac0a60f7d",
  "private": false,
  "record": {
    "abstract": "Horton, Dewdney, and Nesteruk [quant-ph/0103114] have proposed Bohm-type\nparticle trajectories accompanying a Klein-Gordon wave function psi on\nMinkowski space. From two vector fields on space-time, W^+ and W^-, defined in\nterms of psi, they intend to construct a timelike vector field W, the integral\ncurves of which are the possible trajectories, by the following rule: at every\nspace-time point, take either W = W^+ or W = W^- depending on which is\ntimelike.\n  This procedure, however, is ill-defined as soon as both are timelike, or both\nspacelike. Indeed, they cannot both be timelike, but they can well both be\nspacelike, contrary to the central claim of [quant-ph/0103114]. We point out\nthe gap in their proof, provide a counterexample, and argue that, even for a\nrather arbitrary wave function, the points where both W^+ and W^- are spacelike\ncan form a set of positive measure.",
    "arxiv_id": "quant-ph/0202140",
    "authors": [
      "Roderich Tumulka"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/35/37/401",
    "journal_ref": "J. Phys. A: Math. Gen. 35 (2002) 7961-7962",
    "title": "Comment on ``Time-like flows of energy-momentum and particle   trajectories for the Klein-Gordon equation\u0027\u0027",
    "url": "https://arxiv.org/abs/quant-ph/0202140"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ca46a2ec-0c0a-4602-b873-9f655ab731f9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}