{
  "abstract": "Recent orthodoxy, which we call Curvature Fundamentalism, posits that the field strength $F$ on spacetime exhausts the physically significant content of electromagnetism, at least on prosaic (contractible) spacetimes. We argue that it is gauge invariance that constrains physical significance. As a result, there are physically significant quantities that $F$ does not capture, even on contractible spacetimes. We show that this result is robust: in the presence of charged matter fields, there are interference experiments whose outcome cannot be predicted by $F$ or any other point-local gauge invariant quantities on the basis of initial Cauchy data. We prove this using the example of relative phase of a Klein-Gordon-Maxwell field, and use it to identify a context in which the widely-claimed equivalence between the Maxwell-Faraday formulation $EM_1$ and the gauge formulation $EM_2$ of electromagnetism is untenable, and that new strategies may be needed for the reductionist project.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13017",
  "author_total": 2,
  "authors": [
    {
      "name": "Henrique Gomes"
    },
    {
      "name": "Bryan W Roberts"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/49f8yp1s0bk6z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13017",
  "fulltext_url": null,
  "id": "49f8yp1s0bk6z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13017",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "physics.hist-ph"
    ],
    [
      "openalex",
      "3107|Quantum and Classical Electrodynamics"
    ]
  ],
  "openalex": "W7212772131",
  "pdf_url": "https://arxiv.org/pdf/2609.13017",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/49f8yp1s0bk6z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:07Z",
      "native_id": "2609.13017",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13017"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Gauge Matters More Than Curvature",
  "title_text": "Gauge Matters More Than Curvature",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/49f8yp1s0bk6z",
  "venue": "arXiv",
  "versions": []
}