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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

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.

DOI
10.5281/zenodo.19435895

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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

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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.
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.
The Stochastic Rupture (SR) framework for objective wave-function collapse is reformulated as a non-equilibrium statistical field theory using the Martin–Siggia–Rose–Janssen–De Domini- cis (MSRJD) path-integral formalism. The SR Langevin equation for the holographic saturation field χ admits an exact mapping to an MSRJD action with a cubic nonlinearity. Dimensional analysis yields an upper critical dimension dc = 4 and a dynamic exponent z = 2. In d = 3 a one-loop renormalization group (RG) analysis reveals a non-trivial infrared-stable fixed point at dimensionless coupling g ∗ = π (exact, of geometric origin). At this fixed point the satu- ration parameter η—previously phenomenological in SR v14–v15 with the empirical window 3 × 10−2 ≲ η ≲ 1—emerges as the expectation value ⟨χ⟩|g ∗ , not a free input. A specific prediction, contingent on the explicit evaluation of the source-renormalization diagram coefficient cS, is η = 2/3 (verified to machine precision under the stated condition). All assumptions are stated explicitly and open theoretical problems are listed
The Stochastic Rupture (SR) framework for objective wave-function collapse is reformulated as a non-equilibrium statistical field theory using the Martin–Siggia–Rose–Janssen–De Domini- cis (MSRJD) path-integral formalism. The SR Langevin equation for the holographic saturation field χ admits an exact mapping to an MSRJD action with a cubic nonlinearity. Dimensional analysis yields an upper critical dimension dc = 4 and a dynamic exponent z = 2. In d = 3 a one-loop renormalization group (RG) analysis reveals a non-trivial infrared-stable fixed point at dimensionless coupling g ∗ = π (exact, of geometric origin). At this fixed point the saturation parameter η—previously phenomenological in SR v14–v15 with the empirical window 3 × 10−2 ≲ η ≲ 1—emerges as the expectation value ⟨χ⟩|g ∗ , not a free input. A specific prediction, contingent on the explicit evaluation of the source-renormalization diagram coefficient cS, is η = 2/3 (verified to machine precision under the stated condition). All assumptions are stated explicitly and open theoretical problems are listed.
We present numerical evidence for the structural predictions of the Stochastic Rupture (SR) framework [1], focusing on three independent simulation programs. First, direct computation of modular variance Var(Jz) confirms the GHZ/Bell scaling theorem: ISR[GHZN ] = N2/4 and ISR[BellN/2] = N/2, giving τBell/τGHZ ∼ N/2 for systems of equal total mass. Second, percolation simulations on entanglement networks reveal a universal scaling law for the Erd˝os– R´enyi topology: pc ·N = 1+√η, confirmed numerically for N = 50 to N = 1000 and converging to the theoretical value 1+√η as N → ∞. Third, these results are shown to depend on network topology in a structured way—reflecting the bond percolation critical exponents of each graph class—and are robust to random site defects up to 50%, with the universal form surviving after replacing N with Neff. Connections to the superfluid 4He λ-transition and to measurementinduced phase transitions in random quantum circuits are identified as consistency anchors, providing plausibility support without constituting independent tests of SR. The simulations suggest that η is experimentally calibrable from the entanglement percolation threshold of a physical platform, provided the underlying network topology is known.
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.
The quantum Zeno effect (QZE) predicts that frequent measurement of an unstable quantum system suppresses its decay by repeatedly collapsing the wavefunction back to the undecayed state. However, experimentally confirmed results show that the QZE is fundamentally unattainable for radioactive or radiative decay, because the measurement rates required would destroy the system. We identify a distinct but phenomenologically analogous mechanism within the Stochastic Rupture (SR) framework: informational isolation. In SR, collapse occurs when the local von Neumann entropy approaches the Bousso-bounded informational capacity, SvN → η IBousso. A system that is informationally isolated from its environment — such as a single atom in vacuum, or a system inside a Casimir cavity with suppressed vacuum modes — has a reduced local saturation fraction I, and therefore a suppressed collapse rate. This is decay suppression without measurement, without observer, and without the destructive back-action that kills the standard QZE for radioactive systems. Unlike CSL and Diósi–Penrose, which predict measurable heating of diffuse cosmological matter at rates incompatible with Lyman-α forest and CMB temperature constraints, the SR mechanism is structurally silent in low-saturation environments: the collapse rate vanishes identically when I ≪ 1, independently of particle number or system mass. Informational isolation is thus not merely an analogue of the quantum Zeno effect — it is the same threshold geometry that resolves the cosmological heating problem of competing collapse models, and constitutes a necessary condition for any objective collapse theory to survive cosmological scrutiny. We derive the SR prediction for the suppression factor as a function of environmental mode density and identify two distinct regimes. In the low-saturation regime (I ≪ 1) accessible to current cavity QED, SR reduces exactly to Purcell physics and is not experimentally distinguishable from standard quantum optics. The genuinely SR-specific signature emerges only in the high-saturation regime (I → η), where the runaway factor (1 − I/η)−1 amplifies environmental modulation nonlinearly. This regime is accessible only at macroscopic mass scales (~109 –1010 amu, the MAQRO regime), where the SR discriminator combines with the σ x −2 scaling signature distinguishing SR from CSL and DP. The Casimir-cavity proposal is therefore reframed as a conceptual benchmark rather than a near-term experiment.