{
  "abstract": "This paper algebraically derives the core equations of special and general relativity without postulating time as a fourth geometric coordinate axis or introducing Riemannian geometric curvature of 3-dimensional space. The study departs from two physical premises. First, time is not an independent geometric dimension, but the accumulation of internal state-update periods (tc) within 3-dimensional space, and the total state-update speed capacity permitted per unit time is finite at c0. Second, the 3-dimensional vacuum possesses measurable electromagnetic properties—permittivity (epsilon0) and permeability (mu0)—and the maximum propagation speed of electromagnetic waves (light) is governed by c0 equals 1 over the square root of epsilon0 times mu0. From these two premises, the following results are deduced. First, through the orthogonal allocation (c0 squared equals v squared plus u squared) of the update capacity (c0)—which is used entirely for internal state maintenance at rest—into spatial coordinate transition speed (v) and internal state-update speed (u) during motion, the Lorentz factor (gamma), the relativistic energy-momentum equation (E squared equals the square of p times c0 plus the square of m0 times c squared), and Lorentz length contraction (L equals L0 over gamma) due to information overlapping are derived. Second, from the local state-update delay rate (Gamma sub delay of r equals the inverse square root of 1 minus 2GM over r times c0 squared) arising as the rest binding energy of a body relaxes near a mass M, gravitational time dilation, gravitational redshift, and the integrated proper-time equation for satellites (GPS) are derived. Third, by showing that vacuum permittivity and permeability near a mass M increase in proportion to the square of the local state-update delay rate (epsilon sub eff equals epsilon0 times the square of Gamma sub delay, mu sub eff equals mu0 times the square of Gamma sub delay) under the condition of wave impedance (Z0) invariance, it is established that the local propagation speed of light in a gravitational field decelerates in inverse proportion to the square of the update delay rate (c sub local equals c0 over the square of Gamma sub delay). From this, the formulas for Shapiro time delay, gravitational lensing deflection angle (Delta theta equals 4GM over b times c0 squared), and planetary perihelion precession (Delta phi equals 6 pi GM over a times 1 minus e squared times c0 squared) are identically derived without assuming spacetime curvature. Fourth, by extending the vacuum state-update structure to a 10-degree-of-freedom symmetric tensor network (1 scalar delay plus 3 rotational drag vector components plus 6 anisotropic tensor components), the frame-dragging Sagnac time delay (Delta t sub FD equals minus 8 pi GJ over c0 to the 4th power times r), the Lense-Thirring precession rate (vector Omega sub LT equals one-half times the curl of vector v sub drag) around a rotating mass, and the spin-2 (pi rotational symmetry, R of 2 theta) matrix transformation of gravitational waves are mathematically derived from pure continuum and tensor algebra.",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Kiman Jung",
      "orcid": "0009-0007-7283-2083"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1rwqytj42r9z2.bib",
  "cited_by": 6,
  "doi": "10.5281/zenodo.23498327",
  "fulltext_url": null,
  "id": "1rwqytj42r9z2",
  "issns": [],
  "landing_url": "https://doi.org/10.5281/zenodo.23498327",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3103|Relativity and Gravitational Theory"
    ]
  ],
  "openalex": "W7223103498",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/1rwqytj42r9z2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:26:43Z",
      "native_id": "W7223103498",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.23498327"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "openalex:3103|Relativity and Gravitational Theory",
      "subfield": "general"
    }
  ],
  "title": "Algebraic Derivation of Relativity based on Finite State-Update Capacity and Vacuum Permittivity-Permeability Modulation",
  "title_text": "Algebraic Derivation of Relativity based on Finite State-Update Capacity and Vacuum Permittivity-Permeability Modulation",
  "type": "preprint",
  "updated_at": "2026-11-03T13:20:27Z",
  "url": "https://research.draconitic.com/paper/1rwqytj42r9z2",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}