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  "slug": "quantization-as-hydrodynamic-relaxation-eigenstates-as-attractor-basins-in-a-dis",
  "title": "Quantization as Hydrodynamic Relaxation: Eigenstates as Attractor Basins in a Dissipative Madelung Fluid",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Quantum measurement is presently modeled as an instantaneous stochastic collapse, a postulate that conflicts with the continuous unitary dynamics of the Schrödinger equation and hampers the error budgets of quantum hardware. A deterministic alternative is proposed: by adding a minimal linear drag term to the Madelung hydrodynamic formulation, Hamiltonian eigenstate densities become exact fixed points of a contractive flow, and “quantum jumps’’ emerge as continuous relaxation events. The damped Madelung equations are derived, linearized about the harmonic‑oscillator ground state, and closed‑form level‑to‑level relaxation times t_n→ n-1=(ln bigl[(n+1/2)/(n-1/2)bigr])/(2γ) are obtained. For a representative damping γ=10⁹ mathrms^-1 the ground‑state perturbations decay with universal rate γ/2, the per‑period phase‑space contraction factor is 0.881911 at γ/ω=0.01, and a phenomenological diffusion‑versus‑relaxation hierarchy yields t_D≈2.2×10^-13 s≪τ_E=1.0×10^-9 s. The Born rule is retained as an explicit ensemble assumption rather than derived. The program yields testable structural predictions—accelerating relaxation with excitation and deterministic continuous trajectories—while remaining analytically tractable. If validated, the approach re‑grounds quantum statistics in classical measure theory and replaces wavefunction collapse with a computable relaxation process.",
  "abstract_markdown": "Quantum measurement is presently modeled as an instantaneous stochastic collapse, a postulate that conflicts with the continuous unitary dynamics of the Schrödinger equation and hampers the error budgets of quantum hardware. A deterministic alternative is proposed: by adding a minimal linear drag term to the Madelung hydrodynamic formulation, Hamiltonian eigenstate densities become exact fixed points of a contractive flow, and “quantum jumps’’ emerge as continuous relaxation events. The damped Madelung equations are derived, linearized about the harmonic‑oscillator ground state, and closed‑form level‑to‑level relaxation times  \n\\[\nt_{n\\to n-1}=\\frac{\\ln\\!\\bigl[(n+\\tfrac12)/(n-\\tfrac12)\\bigr]}{2\\gamma}\n\\]  \nare obtained. For a representative damping \\(\\gamma=10^{9}\\,\\mathrm{s^{-1}}\\) the ground‑state perturbations decay with universal rate \\(\\gamma/2\\), the per‑period phase‑space contraction factor is \\(0.881911\\) at \\(\\gamma/\\omega=0.01\\), and a phenomenological diffusion‑versus‑relaxation hierarchy yields \\(t_{D}\\approx2.2\\times10^{-13}\\,\\mathrm{s}\\ll\\tau_{E}=1.0\\times10^{-9}\\,\\mathrm{s}\\). The Born rule is retained as an explicit ensemble assumption rather than derived. The program yields testable structural predictions—accelerating relaxation with excitation and deterministic continuous trajectories—while remaining analytically tractable. If validated, the approach re‑grounds quantum statistics in classical measure theory and replaces wavefunction collapse with a computable relaxation process.",
  "date": "2026-10-12",
  "first_published": "2026-10-12",
  "last_revised": "2026-10-20T21:51:09Z",
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  "url": "https://papers.qnfo.org/papers/quantization-as-hydrodynamic-relaxation-eigenstates-as-attractor-basins-in-a-dis",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Quantization as Hydrodynamic Relaxation: Eigenstates as Attractor Basins in a Dissipative Madelung Fluid"
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        "description": "Quantum measurement is presently modeled as an instantaneous stochastic collapse, a postulate that conflicts with the continuous unitary dynamics of the Schrödinger equation and hampers the error budgets of quantum hardware. A deterministic alternative is proposed: by adding a minimal linear drag term to the Madelung hydrodynamic formulation, Hamiltonian eigenstate densities become exact fixed points of a contractive flow, and “quantum jumps’’ emerge as continuous relaxation events. The damped Madelung equations are derived, linearized about the harmonic‑oscillator ground state, and closed‑form level‑to‑level relaxation times t_n→ n-1=(ln bigl[(n+1/2)/(n-1/2)bigr])/(2γ) are obtained. For a representative damping γ=10⁹ mathrms^-1 the ground‑state perturbations decay with universal rate γ/2, the per‑period phase‑space contraction factor is 0.881911 at γ/ω=0.01, and a phenomenological diffusion‑versus‑relaxation hierarchy yields t_D≈2.2×10^-13 s≪τ_E=1.0×10^-9 s. The Born rule is retained as an explicit ensemble assumption rather than derived. The program yields testable structural predictions—accelerating relaxation with excitation and deterministic continuous trajectories—while remaining analytically tractable. If validated, the approach re‑grounds quantum statistics in classical measure theory and replaces wavefunction collapse with a computable relaxation process.",
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