{
  "abstract": "We propose a geometric formulation of quantum indeterminacy based on polar duality between convex bodies representing position and momentum data. A pair (X,P) of centrally symmetric convex bodies is said to satisfy the indeterminacy condition when the h-polar of X is included in P. We show that this condition naturally arises from the geometry of quantum blobs and is closely related to Hardy's uncertainty principle and the Donoho--Stark inequalities. Using symplectic capacities and John ellipsoids, we associate a canonical covariance ellipsoid with every quantum polar pair and prove that it satisfies the quantum condition. The Robertson--Schrödinger inequalities follow as a consequence. This provides a non-statistical formulation of quantum indeterminacy from which the usual uncertainty relations emerge. which the usual uncertainty relations emerge.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.01103",
  "author_total": 1,
  "authors": [
    {
      "name": "Maurice de Gosson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7n9rjd3k26rgd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.01103",
  "fulltext_url": null,
  "id": "7n9rjd3k26rgd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.01103",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
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  "openalex": "W7160324370",
  "pdf_url": "https://arxiv.org/pdf/2605.01103",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7n9rjd3k26rgd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2605.01103",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.01103"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "On Quantum Indeterminacy and the Uncertainty Principle",
  "title_text": "On Quantum Indeterminacy and the Uncertainty Principle",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/7n9rjd3k26rgd",
  "venue": "arXiv",
  "versions": []
}