The Impedance of Spacetime
DOI:
https://doi.org/10.65649/ys645s16Keywords:
Ze system, vacuum impedance, permittivity, permeability, causal counters, Ze impedance, fixed-point attractor, Maxwell equations, proper time, binary event streamAbstract
The vacuum impedance Z₀ = √(μ₀/ε₀) ≈ 376.73 Ω and the speed of light c = 1/√(μ₀ε₀) are two complementary invariants derived from the same pair of electromagnetic constants {μ₀, ε₀}: one encodes dynamics, the other kinematics. This paper shows that an identical structural duality arises within the Ze framework (Tkemaladze, 2026a), where a binary event stream is partitioned into N_T T-events and N_S S-events. We define Ze permittivity ε_Ze = N_T/T = 1 − v (temporal accumulation, analogous to ε₀) and Ze permeability μ_Ze = N_S/T = v (spatial flow, analogous to μ₀). Two invariants follow: Ze impedance Z_Ze = √(μ_Ze/ε_Ze) = √(v/(1−v)) and Ze speed c_Ze = τ/T = √(1−v²). We show that Z_Ze is universal: it is independent of stream type (i.i.d. Bernoulli, Markov, deterministic) when v is held fixed. The Ze generation map v₁ → v₂ = 2(1−v₁)/(2−v₁)² (Tkemaladze, 2026b) translates into an impedance map Z₁ → Z₂, with a unique stable fixed point Z* = 0.9161 (corresponding to v* = 0.4563). The matching condition Z_Ze = 1 (v = 0.5) coincides exactly with the Nash equilibrium of Ze competition (Tkemaladze, 2026c): the maximum-entropy state. The paper proposes five falsifiable predictions connecting Ze impedance to measurable properties of causal event streams.
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