{
  "id": "oai:papers.qnfo.org:the-speed-of-light-as-the-tracing-capacity-of-a-distributed-estimation-vacuum-ca",
  "slug": "the-speed-of-light-as-the-tracing-capacity-of-a-distributed-estimation-vacuum-ca",
  "title": "The Speed of Light as the Tracing Capacity of a Distributed-Estimation Vacuum: Causal Bandwidth, Stability Thresholds, and Divergence Times",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The speed of light c = 2.998× 10⁸ m/s is measured, codified in the SI, and used daily, yet no established framework explains why the causal speed is finite or what physical function finiteness performs beyond kinematics. This paper develops a control-theoretic answer: the vacuum is modeled as a distributed estimation network whose nodes track unstable field dynamics through nearest-neighbor communication on a lattice of spacing a, so that c is the network's tracing capacity — the fastest instability the network can track without its self-estimation error diverging. From the lattice dispersion ω(k) = (2v/a) |sin(ka/2)| we derive the exact causal bound |v_g| ≤ v; from the per-update error recursion we derive the stability threshold λ_crit = -ln(1-g) c/a on the trackable instability rate at correction gain g. Under the Planck-spacing assumption a = ℓ_P = 1.616× 10^-35 m and $g = 1/2$, the threshold is λ_crit = 1.286× 10⁴3 mathrms^-1. An instability running at $1.5$ times this threshold overruns a 10⁶-fold error tolerance within 2.15× 10^-42 s, about $40$ update intervals. The model reproduces the causal bandwidth B = 5.905× 10⁴2 Hz, the congestion delay 3.336× 10^-12 s/m at ρ/ρ_c = 10^-3, and a device-scale cutoff 4.772× 10¹0 Hz for millimetre geometry, and satisfies its own Nyquist consistency check with margin 1/π. The result converts a kinematic axiom into a falsifiable stability condition and specifies the analogue lattice simulation that would confirm or refute it.",
  "abstract_markdown": "The speed of light $c = 2.998\\times 10^{8}\\ \\mathrm{m/s}$ is measured, codified in the SI, and used daily, yet no established framework explains why the causal speed is finite or what physical function finiteness performs beyond kinematics. This paper develops a control-theoretic answer: the vacuum is modeled as a distributed estimation network whose nodes track unstable field dynamics through nearest-neighbor communication on a lattice of spacing $a$, so that $c$ is the network's tracing capacity — the fastest instability the network can track without its self-estimation error diverging. From the lattice dispersion $\\omega(k) = (2v/a)\\,|\\sin(ka/2)|$ we derive the exact causal bound $|v_g| \\le v$; from the per-update error recursion we derive the stability threshold $\\lambda_{\\mathrm{crit}} = -\\ln(1-g)\\,c/a$ on the trackable instability rate at correction gain $g$. Under the Planck-spacing assumption $a = \\ell_P = 1.616\\times 10^{-35}\\ \\mathrm{m}$ and $g = 1/2$, the threshold is $\\lambda_{\\mathrm{crit}} = 1.286\\times 10^{43}\\ \\mathrm{s^{-1}}$. An instability running at $1.5$ times this threshold overruns a $10^{6}$-fold error tolerance within $2.15\\times 10^{-42}\\ \\mathrm{s}$, about $40$ update intervals. The model reproduces the causal bandwidth $B = 5.905\\times 10^{42}\\ \\mathrm{Hz}$, the congestion delay $3.336\\times 10^{-12}\\ \\mathrm{s/m}$ at $\\rho/\\rho_c = 10^{-3}$, and a device-scale cutoff $4.772\\times 10^{10}\\ \\mathrm{Hz}$ for millimetre geometry, and satisfies its own Nyquist consistency check with margin $1/\\pi$. The result converts a kinematic axiom into a falsifiable stability condition and specifies the analogue lattice simulation that would confirm or refute it.",
  "date": "2026-11-02",
  "first_published": "2026-11-02",
  "last_revised": "2026-11-02T00:00:00Z",
  "modified": "2026-11-02T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/the-speed-of-light-as-the-tracing-capacity-of-a-distributed-estimation-vacuum-ca",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
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        "title": "The Speed of Light as the Tracing Capacity of a Distributed-Estimation Vacuum: Causal Bandwidth, Stability Thresholds, and Divergence Times"
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        "description": "The speed of light c = 2.998× 10⁸ m/s is measured, codified in the SI, and used daily, yet no established framework explains why the causal speed is finite or what physical function finiteness performs beyond kinematics. This paper develops a control-theoretic answer: the vacuum is modeled as a distributed estimation network whose nodes track unstable field dynamics through nearest-neighbor communication on a lattice of spacing a, so that c is the network's tracing capacity — the fastest instability the network can track without its self-estimation error diverging. From the lattice dispersion ω(k) = (2v/a) |sin(ka/2)| we derive the exact causal bound |v_g| ≤ v; from the per-update error recursion we derive the stability threshold λ_crit = -ln(1-g) c/a on the trackable instability rate at correction gain g. Under the Planck-spacing assumption a = ℓ_P = 1.616× 10^-35 m and $g = 1/2$, the threshold is λ_crit = 1.286× 10⁴3 mathrms^-1. An instability running at $1.5$ times this threshold overruns a 10⁶-fold error tolerance within 2.15× 10^-42 s, about $40$ update intervals. The model reproduces the causal bandwidth B = 5.905× 10⁴2 Hz, the congestion delay 3.336× 10^-12 s/m at ρ/ρ_c = 10^-3, and a device-scale cutoff 4.772× 10¹0 Hz for millimetre geometry, and satisfies its own Nyquist consistency check with margin 1/π. The result converts a kinematic axiom into a falsifiable stability condition and specifies the analogue lattice simulation that would confirm or refute it.",
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