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Stochastic Rupture as a Bekenstein-Bounded Mechanism for Objective Wave-Function Collapse: Emergent Proper Time, Entropic Gravity, and Informational Constraints on Quantum Histories

GUILHERME ZAMBUZI

Published Apr 6, 2026• 0 citations
Publisher

Abstract

We propose a model in which proper time emerges from a finite local information samplingcapacity and wave-function collapse occurs when the informational content of a quantumbranch approaches the Bekenstein bound. Combining insights from entropic gravity, holographic entropy limits, and objective collapse models, we suggest that collapse correspondsto stochastic pruning of branches approaching saturation of local information capacity. Themodel predicts anomalous decoherence in massive spatial superpositions and provides experimentally testable thresholds relevant to next-generation interferometers. This frameworkoffers a unified perspective relating emergent time, collapse dynamics, and gravitationalinformation bounds.

DOI
10.5281/zenodo.19434251

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We propose a model in which proper time emerges from a finite local information samplingcapacity and wave-function collapse occurs when the informational content of a quantumbranch approaches the Bekenstein bound. Combining insights from entropic gravity, holographic entropy limits, and objective collapse models, we suggest that collapse correspondsto stochastic pruning of branches approaching saturation of local information capacity. Themodel predicts anomalous decoherence in massive spatial superpositions and provides experimentally testable thresholds relevant to next-generation interferometers. This frameworkoffers a unified perspective relating emergent time, collapse dynamics, and gravitationalinformation bounds.
We propose a model in which proper time emerges from a finite local informationsampling capacity and wave-function collapse occurs when the informational content ofa quantum branch approaches the Bekenstein bound. Combining insights from entropicgravity, holographic entropy limits, and objective collapse models, we suggest that collapsecorresponds to stochastic pruning of branches approaching saturation of local informationcapacity. The collapse rate is derived from the gravitational self-energy of spatially separated branches, yielding a dimensionally consistent scaling relation with quadratic massdependence consistent with the Diósi–Penrose framework. The model predicts anomalousdecoherence in massive spatial superpositions and provides experimentally testable thresholds relevant to next-generation interferometers. This framework offers a unified perspectiverelating emergent time, collapse dynamics, and gravitational information boundsNote: Bekenstein bound proposed as suggestion of pruning trigger, not definitive mechanism. Other informational thresholds possible.
We propose a model in which proper time emerges from a finite local information sampling rate and wavefunction collapse occurs when the informational contentof a quantum branch approaches the Bekenstein bound. Combining insights from entropic gravity, holographic entropy limits, and objective collapse models, we suggestthat collapse corresponds to stochastic pruning of branches approaching saturationof local information capacity. The model predicts anomalous decoherence in massivespatial superpositions and provides experimentally testable thresholds relevant to nextgeneration interferometers. This framework offers a unified perspective relating emergent time, collapse dynamics, and gravitational information bounds.
We propose a falsifiable model where proper time emerges from a finite local sampling rate N(x) = Ilocal/IPlanck, and wavefunction collapse occurs when a branch’sinformation exceeds the Bekenstein bound. The model recovers General Relativity inthe low-entropy limit and predicts anomalous decoherence for massive superpositionswith SvN ≳ 0.1 · IBek. A concrete experimental test is proposed using next-generationmatter-wave interferometers, along with a near-term laboratory suggestion using optomechanical platforms.
Stochastic Rupture (SR) proposes that objective wavefunction collapse is triggered when local von Neumann entropy saturates a fraction eta of the holographic Bousso bound on causal-diamond surfaces. The SR network is concretely realized as a simple cubic lattice — square holographic sheets stacked at Planck-scale intervals — whose exact Laplacian spectrum derives the dimensional flow d s: 2 ( UV, holographic ) to 3 ( stacking ) to 4 ( Lorentzian, open ) without free parameters. The framework has two logically independent sectors. The collapse sector is self-contained and makes parameter-free falsifiable predictions. The general SR decoherence rate Gamma SR = Gm squared /(4 h bar sigma x squared ) produces a sigma x to the minus 2 scaling that discriminates SR from CSL (sigma x to the minus 3) and Diósi–Penrose (flat), independently of any free parameters; the definitive test is at MAQRO (10 to the 9–10 to the 10 amu). For GHZ/Bell states on NISQ hardware, the SR-native prediction is tau Bell / tau GHZ is similar to N squared, with a finite-size correction: reliable collapse onset at N stable is approximately equal to 1.25/(1 minus eta ) rather than the theoretical threshold 1/(1 minus eta ). The geometric sector — Newton's law, Einstein equations, spin-2 graviton — is conditional on the IR limit d s to 4 and is presented explicitly as such. Two new structural results reduce the number of free parameters. The bond-percolation threshold of the simple cubic lattice, p c = 0.2488, matches the cosmological structure-suppression parameter e 0 = 0.249 plus or minus 0.035 to within 0.1 %, linking the connectivity transition of the SR network to the S8 tension without a free fit. The restoration rate lambda q, previously unconstrained, is shown to satisfy lambda q/ gamma 0 is approximately equal to 1/ the square root of pi through a three-step geometric argument: vibrating holographic sheets drive saturation fluctuations to the 2D square interface critical point p c=1/2; Bernoulli variance at criticality gives sigma = the square root of 3 /2; three independent propagation channels in 3D then fix lambda q/ gamma 0 = C/ the square root of pi with C is approximately equal to 0.995. The remaining open step — showing the SR interface dynamics belongs to the Model A universality class with additive noise — reduces to a single one-loop RG calculation. The framework makes fourteen falsifiable predictions spanning NISQ processors, MAQRO, LISA, and Euclid, explicitly distinguishing derived results from calibrated parameters and open problems.
Objective collapse models, such as the Diósi–Penrose (DP) model, propose that gravityinduces the loss of coherence in spatial superpositions. In an earlier Bekenstein-thresholdrealization of the Stochastic Rupture framework (Zambuzi, 2026), collapse is triggered whenthe von Neumann entropy reaches a fraction η of an effective maximum informational limitImax of the system. Although the Bekenstein bound provides a natural theoretical ceilingfor this limit, the true effective informational capacity of nature that may trigger collapse,here denoted Inature, remains an open empirical question. In this paper, we show that thefunctional dependence of the collapse time on the wavepacket width, τ ∝ σ2x , provides adistinctive experimental signature of that earlier realization. We propose an optomechanicalinterferometry experiment that uses controlled variation of σx not only to distinguish thisσx-dependent law from the asymptotic DP prediction, but also to constrain the effectivecombination ηInature. In this way, the interferometer becomes a macroscopic probe of theinformational threshold entering the collapse dynamics.
We propose a model of objective wave-function collapse in which reduction is triggered not by a fixed rate or by gravitational self-energy alone, but by the approach of the reduced von Neu- mann entropy SvN toward a fraction η of the Bekenstein bound IBek applicable to the system. Dynamics are governed by a Lindblad master equation with a position-based collapse operator in- herited from Continuous Spontaneous Localization (CSL), supplemented by a feedback function F(SvN /ηIBek) = (1 − SvN /ηIBek) −1 that diverges as the system approaches informational satura- tion. The model recovers the Di´osi Penrose (DP) timescale in the limit SvN ≪ ηIBek, resolves a divergence present in the predecessor “Stochastic Rupture” model for d ≫ σx, and makes a qualita- tively new prediction absent from both DP and CSL: systems with high entanglement entropy but no spatial superposition should undergo collapse on timescales of order τ ∼ γ −1 0 (1 − η), potentially as short as 10−8 s for macroscopic entangled systems. We identify explicitly every postulate and every regime of approximation.