{
  "id": "oai:papers.qnfo.org:quantized-ringdown-echoes-from-a-discrete-clockwork-spacetime-substrate",
  "slug": "quantized-ringdown-echoes-from-a-discrete-clockwork-spacetime-substrate",
  "title": "Quantized Ringdown Echoes from a Discrete Clockwork Spacetime Substrate",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Gravitational‑wave observations of binary‑black‑hole mergers provide direct access to the post‑merger ringdown, a regime traditionally modeled by a smooth superposition of quasi‑normal modes (QNMs). A discrete computational substrate for spacetime predicts that the ringdown should contain a comb‑like series of equally spaced spectral lines—“quantized echoes”—instead of a continuous chirp. Existing analyses assume equal‑interval echoes or ignore discreteness altogether, leaving a gap in tests of the clockwork hypothesis. We model the substrate as an Abelian clockwork chain with N + 1 sites, integer gear ratio q>1, and explicit‑breaking parameter ε. Using the hierarchy q^-N to set the fundamental time step, we derive a line‑spacing formula Δ f_rm eff= f_rm QNM q^-N and an amplitude suppression factor A_rm echo= ε^N. For a representative merger with f_rm QNM=250 Hz, q=3, N=10, and ε=0.1, we obtain Δ f_rm eff≈4.2×10^-3 Hz and A_rm echo≈10^-10 relative to the dominant QNM. These numbers place the predicted comb well below current detector noise but within reach of next‑generation facilities. The result offers a falsifiable discriminator between continuous general relativity and a discrete clockwork spacetime.",
  "abstract_markdown": "Gravitational‑wave observations of binary‑black‑hole mergers provide direct access to the post‑merger ringdown, a regime traditionally modeled by a smooth superposition of quasi‑normal modes (QNMs). A discrete computational substrate for spacetime predicts that the ringdown should contain a comb‑like series of equally spaced spectral lines—“quantized echoes”—instead of a continuous chirp. Existing analyses assume equal‑interval echoes or ignore discreteness altogether, leaving a gap in tests of the clockwork hypothesis. We model the substrate as an Abelian clockwork chain with \\(N\\!+\\!1\\) sites, integer gear ratio \\(q>1\\), and explicit‑breaking parameter \\(\\epsilon\\). Using the hierarchy \\(q^{-N}\\) to set the fundamental time step, we derive a line‑spacing formula \\(\\Delta f_{\\rm eff}= f_{\\rm QNM}\\,q^{-N}\\) and an amplitude suppression factor \\(\\mathcal{A}_{\\rm echo}= \\epsilon^{N}\\). For a representative merger with \\(f_{\\rm QNM}=250\\;\\mathrm{Hz}\\), \\(q=3\\), \\(N=10\\), and \\(\\epsilon=0.1\\), we obtain \\(\\Delta f_{\\rm eff}\\approx4.2\\times10^{-3}\\;\\mathrm{Hz}\\) and \\(\\mathcal{A}_{\\rm echo}\\approx10^{-10}\\) relative to the dominant QNM. These numbers place the predicted comb well below current detector noise but within reach of next‑generation facilities. The result offers a falsifiable discriminator between continuous general relativity and a discrete clockwork spacetime.",
  "date": "2026-10-21",
  "first_published": "2026-10-21",
  "last_revised": "2026-10-21T00:00:00Z",
  "modified": "2026-10-21T00:00:00Z",
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  "peer_review_status": "Not independently peer-reviewed",
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  "doi": null,
  "doi_url": null,
  "url": "https://papers.qnfo.org/papers/quantized-ringdown-echoes-from-a-discrete-clockwork-spacetime-substrate",
  "license_url": "https://legal.qnfo.org/",
  "license_spdx": null,
  "sha256": "46ee201c1097641e694096ade152fabe3b167ec46e16992e2c4647bd2cdb0d3f",
  "version_url": "https://papers.qnfo.org/papers/quantized-ringdown-echoes-from-a-discrete-clockwork-spacetime-substrate/v/1.0.0",
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    "creators": [
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Quantized Ringdown Echoes from a Discrete Clockwork Spacetime Substrate"
      }
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    "publisher": "QNFO",
    "publicationYear": "2026",
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    "dates": [
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        "date": "2026-10-21",
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        "description": "Gravitational‑wave observations of binary‑black‑hole mergers provide direct access to the post‑merger ringdown, a regime traditionally modeled by a smooth superposition of quasi‑normal modes (QNMs). A discrete computational substrate for spacetime predicts that the ringdown should contain a comb‑like series of equally spaced spectral lines—“quantized echoes”—instead of a continuous chirp. Existing analyses assume equal‑interval echoes or ignore discreteness altogether, leaving a gap in tests of the clockwork hypothesis. We model the substrate as an Abelian clockwork chain with N + 1 sites, integer gear ratio q>1, and explicit‑breaking parameter ε. Using the hierarchy q^-N to set the fundamental time step, we derive a line‑spacing formula Δ f_rm eff= f_rm QNM q^-N and an amplitude suppression factor A_rm echo= ε^N. For a representative merger with f_rm QNM=250 Hz, q=3, N=10, and ε=0.1, we obtain Δ f_rm eff≈4.2×10^-3 Hz and A_rm echo≈10^-10 relative to the dominant QNM. These numbers place the predicted comb well below current detector noise but within reach of next‑generation facilities. The result offers a falsifiable discriminator between continuous general relativity and a discrete clockwork spacetime.",
        "descriptionType": "Abstract"
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