The Möbius Ring Topology of Dimensional Space: A Topological Resolution of the Black Hole Information Paradox
Abstract
Abstract The black hole information paradox stands as the longest-standing unresolved conflict between general relativity and quantum mechanics. Here we propose a resolution rooted in the Möbius-ring topology of dimensional space, derived from an axiomatic field framework grounded in Einstein's relativistic postulates. The dimension parameter α obeys the master equation α = ln 2 + (1 − ln 2)[Q(t) − C(t)], with Q(t) and C(t) the quantum and classical (entropy) response fields. Three critical constants—α₀ = ln 2, β₁ = 1 − ln 2, and Rc = (2 ln 2 − 1)/(ln 2)² ≈ 0.804—are derived analytically from hyperbolic geometry and Lorentz-invariant dissipative systems via five exact theorems, establishing a deductive bridge from cosmic-scale physics to topological order parameters. The bridge mapping Φ(r) establishes an exact correspondence with Feigenbaum's universal bifurcation structure: r = 3.0 ↔ α = 1 − ln 2 (P₁), r = 1 + √6 ≈ 3.44949 ↔ α = ln 2 (P₂), and r = r_∞ ≈ 3.569946 ↔ α = Rc (P₃). This correspondence is not fortuitous; it reflects a deep isomorphism between relativistic constraint satisfaction and chaotic universality. The topology contains four critical nodes derived as exact theorems: P₀ (α = 0 ≡ 1, bonding point), P₁ (α = 1 − ln 2 ≈ 0.307, Cosmic Dam), P₂ (α = ln 2 ≈ 0.693, Life Singularity), and P₃ (α = Rc ≈ 0.80402, Reflux Gate). The event horizon is identified as a local realization of P₃. Matter crossing the horizon enters the quantum reflux zone (0.80402 ≤ α
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