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Probing the Informational Limit of Nature: An Interferometric Proposal Based on the σx Dependence of Stochastic Rupture

GUILHERME ZAMBUZI

Published Apr 10, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.19498299

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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.
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 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.
Three independent frameworks propose that wavefunction collapse is a physical process rather than a postulate: the DiósiPenrose (DP) model, the Stochastic Rupture (SR) model, and the emergent-time theory of Lee (2025). We argue that these are not simply alternative theories but occupy distinct levels of a natural hierarchy. Lee establishes the geometric mechanism by which time and collapse emerge from stochastic relaxation of dieomorphism- constraint violations in full general relativity, but provides no local criterion specifying when a particular system collapses. SR supplies exactly this missing criterion: collapse occurs when the local von Neumann entropy approaches the Bousso-bounded informational capacity, SvN → η IBousso. DiósiPenrose appears as the low-saturation operational limit of SR, valid when SvN ≪ η IBousso and gravitational self-energy dominates. The proposed hierarchy is Lee semiclassical limit −−−−−−−−−−−→ SR SvN ≪ ηIBousso −−−−−−−−−−→ DP. We derive the experimental discriminators that distinguish all three models, identify the conjectural steps in the hierarchy that remain to be derived, and discuss how the SR frame- work resolves the Schrödinger cat problem by providing the local informational criterion absent in both Lee and DP.