{
  "annotation_id": "cb2d90bb-8e38-460b-9a08-e38b5211b9a0",
  "date_created": "2026-03-02T18:02:23.777000Z",
  "date_modified": "2026-03-02T18:02:23.777000Z",
  "file_hash": "e6357bbb587a899072d3844b77ba0174f1254c359c695ace90ac6cd14dd91230",
  "private": false,
  "record": {
    "abstract": "Starting from relativistic mass-less Madelung fluid, we shall develop a class\nof typical wave functions by imposing it to maximize Shannon entropy given its\nfinite average quantum potential. We show that there is a class of solutions in\nwhich the wave function is spatiotemporally localized with finite spacetime\nsupport, uniformly moving hence stationary. It turns out that the quantum\namplitude satisfies Klein-Gordon equation with emergent mass term proportional\nto the square root of average quantum potential. We show that there is physical\ntime uncertainty which decreases as the mass increases. We also rederive the\nclassical energy-momentum relation provided the de Broglie-Einstein relation\nholds. In this case, the time uncertainty is proportional to the inverse of\nclassical energy.",
    "arxiv_id": "quant-ph/0512235",
    "authors": [
      "Agung Budiyono"
    ],
    "categories": [
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Spatiotemporally-localized-stationary typical wave function satisfying   Klein-Gordon equation with emergent mass",
    "url": "https://arxiv.org/abs/quant-ph/0512235"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "371fad24-951e-4118-af6a-9322eb86fcec",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}