A Geometric Resolution of the Quantum Measurement Problem: Derivations and Predictions from the 4-Simplex Framework

Sadik Basha

Published Jul 24, 2026• 0 citations

Abstract

The quantum measurement problem asks: why and when does unitary Schrödingerevolution stop and irreversible collapse begin? We derive a quantitative resolution from the 4-Simplex Framework, which proposes that every physical systemoccupies a position in a four-dimensional simplex parameterised by a single access function A. Systems near the apex (A ≈ 1) evolve unitarily in the Reality layer where ∆τ =0. Systems near the base (A ≈ 0) behave classically in the Causality layer.Measurement is the coupling of a quantum system to an apparatus with ma ≫mth, which forces the joint access function to zero and irreversibly projects thesystem into the Causality layer. From these two ingredients alone we derive:(i) a finite collapse timescale tcol = (mth/ma) · (τc/ε); (ii) the preferred-basisrule — outcomes always appear in the energy eigenbasis of the apparatus; (iii) aquantitative resolution of Wigner’s Friend in which collapse is observer-relative,exactly as simultaneity is in special relativity; (iv) partial collapse for nearthreshold detectors (ma ∼ mth); (v) a decoherence rate formula Γd = (ma/mth)·γ0 that reduces to the standard Lindblad form in the limit ma ≫ mth. Allpredictions are parameter-free except mth, which is itself derived from ℏ, c, andG. The framework makes predictions distinguishable from standard quantummechanics and from the GRW and Penrose–Diósi collapse models, providing clearexperimental targets for attosecond-scale and nano-mechanical experiments.

DOI: 10.5281/zenodo.21538418

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