The Universe as an RLC Network: Analogue Gravity and Quantum Coherence via Impedance-Matched Transmission Lines — The Dipolar Strings Model

The Universe as an RLC Network: Analogue Gravity and Quantum Coherence via Impedance-Matched Transmission Lines — The Dipolar Strings Model This working document presents an exploratory phenomenological model in which the physical vacuum is treated as a gas of massless dipolar cells (Dipolar Quantum Doubles, DQD) modeled as impedance-matched bifilar transmission lines. Gravity is described as vacuum refraction driven by an impedance field Z(x); electric charge and mass are attributed to the topology of dipolar strings. The framework yields several parameter-free structural results (electron characteristic impedance Z_e ≈ 0.73 Z₀ ≈ 275 Ω; universal geometric ratio D/r = 2cosh(π)), a scalar gravitational sector indistinguishable from General Relativity at first post-Newtonian order (γ = β = 1), and a stable branch of horizonless compact objects ("substrate stars") with critical mass M_crit ≈ 1.6×10⁶ M☉ ∝ ℓ₁². The deposit includes a registered, time-stamped prediction: in electron-scattering-corrected mass calibrations, ~80% of substrate-star candidates should accumulate in the half-decade below log M = 6.21, followed by a cutoff — a discriminant testable against forthcoming JWST Little Red Dot samples (cf. Rusakov et al., Nature 649, 574, 2026). The statistical criteria of this test are frozen as stated in the manuscript. Status. Speculative working document by an independent researcher; not peer reviewed. Developed with extensive AI assistance (Claude, Anthropic) — the division of contributions and the model's open problems are disclosed in full in the manuscript's Acknowledgments and Appendix A. Codes, figure scripts, and symbolic verifications are included and maintained at: https://github.com/rstpier/DipolarString