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Quantum Collapse and Topological Entanglement: τ_collapse = 2.07 × 10⁻¹¹ s, v_entangle = c

Runbiao Fang

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Quantum Collapse and Topological Entanglement: τ_collapse = 2.07 × 10⁻¹¹ s, v_entangle = c
DOI
10.5281/zenodo.21410107

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WITHDRAWN

Arie Todd Greenleaf

Wave-function collapse is usually regarded as independent of a detector's temporal resolution.In this Rapid Communication that view is challenged.I derive the Temporal-Binding Collapse Theorem and show that coarse-grained measurements introduce a universal decoherence channel proportional to 1 ⁄ τ, where τ is the detector's temporal binding window.The theorem predicts tc(τ) = tc(E) + τ, so the measured coherence time grows linearly with detector timescale-behavior absent from standard decoherence theory and objective-collapse models.This relation is placed in a unified context with the quantum-Zeno effect, existing CSL bounds, and recent photonic experiments that employ variable-jitter superconducting detectors.Finally, a falsifiable protocol is proposed: the coherence time of entangled photons will be measured across a bank of SNSPDs spanning τ = 5-500 ps.Observation of a unit-slope tc -τ relationship would demonstrate that collapse is relational, governed by the observer's timescale; any deviation would either falsify the theorem or establish a lower bound on intrinsic collapse mechanisms.

•Jul 19, 2025•0 citations
The quantum mechanics measurement problem is reformulated following the Article XX method: 'what causes collapse' is apparently a wrongly posed question. Collapse is identified with τ-crystallization (N₂-transition Ξ₀→Ξ₁): accumulation of coherence in prefield Ξ₀ until the point of irreversibility, after which a definite Ξ₁ configuration forms. Consequences: (1) no observer needed as a separate entity — any system with sufficient τ-coupling serves as measurer; (2) decoherence is identified with the spread of constraint downward through τ-topology; (3) a potentially falsifiable distinguishing feature is proposed — the reversibility boundary in recoherence experiments.
Abstract Circuit topology—the pattern of two-qubit entangling gates—determines noise propagation paths in variational quantum circuits (VQCs). Using the normalized rank-displacement diagnostic D(ε) across 26 experiment configurations spanning five topologies and five CPTP noise types, plus 135 IBM ibm fez hardware circuits, we show that topology accounts for 48.9% of explainable D(0.05) variance under ω 2 decomposition (Cohen’s d = 2.66 between ring and star; permutation p = 7.1×10−12). The ranking hierarchy (star>grid≈linear>ring, where lower D indicates better ranking preservation) is invariant across the four nondepolarizing noise types (Kendall τ = 1.0 over four ranked lists, p = 0.017 by exact permutation test) but collapses under depolarizing noise. On IBM hardware, the qualitative ranking survives transpilation, though effect magnitude attenuates ∼ 10×. A Heisenberg-picture analytical model qualitatively predicts the τ (n, L) ranking from circuit structure alone (r = 0.645, p = 0.013; R2 = 0.35), providing a theoretical basis for topology-dependent noise sensitivity. We find that classical ML systems (MLP, XGBoost) achieve comparable D(0.05) values, showing that the τ -D functional form is consistent across classical and quantum computation, suggesting a shared noise-response structure. Practical design heuristics are provided
Wave-function collapse is usually regarded as independent of a detector's temporal resolution.In this Rapid Communication that view is challenged.I derive the Temporal-Binding Collapse Theorem and show that coarse-grained measurements introduce a universal decoherence channel proportional to 1 ⁄ τ, where τ is the detector's temporal binding window.The theorem predicts tc(τ) = tc(E) + τ, so the measured coherence time grows linearly with detector timescale-behavior absent from standard decoherence theory and objective-collapse models.This relation is placed in a unified context with the quantum-Zeno effect, existing CSL bounds, and recent photonic experiments that employ variable-jitter superconducting detectors.Finally, a falsifiable protocol is proposed: the coherence time of entangled photons will be measured across a bank of SNSPDs spanning τ = 5-500 ps.Observation of a unit-slope tc -τ relationship would demonstrate that collapse is relational, governed by the observer's timescale; any deviation would either falsify the theorem or establish a lower bound on intrinsic collapse mechanisms.