{
  "id": "oai:papers.qnfo.org:zitterbewegung-as-an-archimedean-2-adic-adelic-mixing-signature-spectral-gap-for",
  "slug": "zitterbewegung-as-an-archimedean-2-adic-adelic-mixing-signature-spectral-gap-for",
  "title": "Zitterbewegung as an Archimedean–2-adic Adelic Mixing Signature: Spectral-Gap Formalization, Numerical Anchors, and a Falsifiable Simulation Program",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Zitterbewegung (ZBW) — the trembling motion of a Dirac wave packet at angular frequency ω = 2mc²/ℏ — is conventionally treated as an interference artifact of the Dirac Hamiltonian, with no independent physical content. A gap remains: no existing framework makes precise, in a falsifiable way, what it would mean for ZBW to carry structure beyond that interference. We propose and partially formalize a stronger claim: ZBW is the observable trace of mixing between the Archimedean place R (denoted ∞) and the 2-adic place Q₂ of the rationals, in the framework of adelic quantum mechanics. We (i) prove a spectral-gap proposition showing that any operator coupling an ∞-localized sector to a p-adic sector forces an oscillation at Δ E/ℏ, with the exact two-level frequency Ω = √(Δ E)² + 4|g|²/ℏ; (ii) derive the electron ZBW frequency ω_ZBW = 1.55268 × 10²1 mathrmrad s^-1 and reduced Compton wavelength 3.8616 × 10^-13 m with full arithmetic; (iii) argue that the prime 2 is structurally distinguished because the Bruhat–Tits tree of Q₂ is 3-regular, the smallest degree any prime admits; and (iv) specify a trapped-ion Dirac simulation test, labeled throughout as a projection, in which the oscillation amplitude is regressed against a 2-adic delocalization measure μ₂(2^nZ₂) = 2^-n, yielding a projected factor-of-$4$ suppression per confinement step. We report no new experimental data; every quantitative result is computed here from stated constants or explicitly flagged as a projection with stated assumptions. If the projection holds, ZBW amplitude becomes a number-theoretic diagnostic; if it fails, the adelic interpretation is eliminated.",
  "abstract_markdown": "Zitterbewegung (ZBW) — the trembling motion of a Dirac wave packet at angular frequency $\\omega = 2mc^{2}/\\hbar$ — is conventionally treated as an interference artifact of the Dirac Hamiltonian, with no independent physical content. A gap remains: no existing framework makes precise, in a falsifiable way, what it would mean for ZBW to carry structure beyond that interference. We propose and partially formalize a stronger claim: ZBW is the observable trace of mixing between the Archimedean place $\\mathbb{R}$ (denoted $\\infty$) and the 2-adic place $\\mathbb{Q}_2$ of the rationals, in the framework of adelic quantum mechanics. We (i) prove a spectral-gap proposition showing that any operator coupling an $\\infty$-localized sector to a $p$-adic sector forces an oscillation at $\\Delta E/\\hbar$, with the exact two-level frequency $\\Omega = \\sqrt{(\\Delta E)^2 + 4|g|^2}/\\hbar$; (ii) derive the electron ZBW frequency $\\omega_{\\mathrm{ZBW}} = 1.55268 \\times 10^{21}\\,\\mathrm{rad\\,s^{-1}}$ and reduced Compton wavelength $3.8616 \\times 10^{-13}\\,\\mathrm{m}$ with full arithmetic; (iii) argue that the prime 2 is structurally distinguished because the Bruhat–Tits tree of $\\mathbb{Q}_2$ is 3-regular, the smallest degree any prime admits; and (iv) specify a trapped-ion Dirac simulation test, labeled throughout as a projection, in which the oscillation amplitude is regressed against a 2-adic delocalization measure $\\mu_2(2^n\\mathbb{Z}_2) = 2^{-n}$, yielding a projected factor-of-$4$ suppression per confinement step. We report no new experimental data; every quantitative result is computed here from stated constants or explicitly flagged as a projection with stated assumptions. If the projection holds, ZBW amplitude becomes a number-theoretic diagnostic; if it fails, the adelic interpretation is eliminated.",
  "date": "2026-10-11",
  "first_published": "2026-10-11",
  "last_revised": "2026-10-27T08:11:10Z",
  "modified": "2026-10-27T08:11:10Z",
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  "peer_review_status": "Not independently peer-reviewed",
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  "doi": null,
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  "url": "https://papers.qnfo.org/papers/zitterbewegung-as-an-archimedean-2-adic-adelic-mixing-signature-spectral-gap-for",
  "license_url": "https://legal.qnfo.org/",
  "license_spdx": null,
  "sha256": "0b3548406cc94d6db33bf61d8e762acf6b6f3e1abb42bd6bf8f5fcbd0a60d7ac",
  "version_url": "https://papers.qnfo.org/papers/zitterbewegung-as-an-archimedean-2-adic-adelic-mixing-signature-spectral-gap-for/v/2.0.0",
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    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Zitterbewegung as an Archimedean–2-adic Adelic Mixing Signature: Spectral-Gap Formalization, Numerical Anchors, and a Falsifiable Simulation Program"
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    "publicationYear": "2026",
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        "date": "2026-10-11",
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        "date": "2026-10-27",
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        "description": "Zitterbewegung (ZBW) — the trembling motion of a Dirac wave packet at angular frequency ω = 2mc²/ℏ — is conventionally treated as an interference artifact of the Dirac Hamiltonian, with no independent physical content. A gap remains: no existing framework makes precise, in a falsifiable way, what it would mean for ZBW to carry structure beyond that interference. We propose and partially formalize a stronger claim: ZBW is the observable trace of mixing between the Archimedean place R (denoted ∞) and the 2-adic place Q₂ of the rationals, in the framework of adelic quantum mechanics. We (i) prove a spectral-gap proposition showing that any operator coupling an ∞-localized sector to a p-adic sector forces an oscillation at Δ E/ℏ, with the exact two-level frequency Ω = √(Δ E)² + 4|g|²/ℏ; (ii) derive the electron ZBW frequency ω_ZBW = 1.55268 × 10²1 mathrmrad s^-1 and reduced Compton wavelength 3.8616 × 10^-13 m with full arithmetic; (iii) argue that the prime 2 is structurally distinguished because the Bruhat–Tits tree of Q₂ is 3-regular, the smallest degree any prime admits; and (iv) specify a trapped-ion Dirac simulation test, labeled throughout as a projection, in which the oscillation amplitude is regressed against a 2-adic delocalization measure μ₂(2^nZ₂) = 2^-n, yielding a projected factor-of-$4$ suppression per confinement step. We report no new experimental data; every quantitative result is computed here from stated constants or explicitly flagged as a projection with stated assumptions. If the projection holds, ZBW amplitude becomes a number-theoretic diagnostic; if it fails, the adelic interpretation is eliminated.",
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