Collapse of the Wave Function as a Topological Restructuring

Pavel Trojan

Published Oct 14, 2026• 0 citations

Abstract

Attention: This version is preliminary and contains errors that will be corrected in subsequent publications. A mechanism is proposed for the collapse of the wave function as a topological restructuring of the holographic barrier—the surface separating realized (classical) and unrealized (superpositional) configurations. Collapse occurs when the information load of the superposition exceeds a threshold determined by the geometry of the barrier. The geometry is described by a series of information dimensions derived from the energy balance of the Universe: the smooth screen D_0 = 2; the information dimension of the barrier D_1 = 2 + Ω_b ≈ 2.049; the matter dimension D_m = 2 + Ω_m ≈ 2.31; the total dimension of rendered space D_3 = 2 + Ω_tot = 3. The dimensional balance formula 2 + Ω_b + Ω_c + Ω_Λ = 3 links the flatness of the Universe (Ω_tot = 1) to the integrality of the dimension of observed space. The theory yields two independent falsifiable predictions with no free parameters: the scalar spectral index n_s = 0.9754 ± 0.0010 (theoretical uncertainty) and the superlinear scaling of the decoherence rate of GHZ states Γ ∝ N^(1+α_1), α_1 ≡ Ω_b = 0.0493 ± 0.0020, accessible to testing on existing quantum processors. The work is positioned within the information-gravitational program (Jacobson 1995; Dorau–Much 2026) and reproduces the latter's result as the limiting case α_1 → 0. Recent experimental evidence for the exponential law of collapse (RCE 2026; non-local gravity 2025; XENONnT 2026) is shown to be consistent with the mechanism. The dynamical foundation of the mechanism (Lagrangian, topological transition weight) is given in the companion work. Keywords: measurement problem, collapse of the wave function, holographic principle, fractal dimension, spectral index, decoherence, GHZ states.

DOI: 10.5281/zenodo.23370828

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