From Objective Collapse to Emergent Mass A Stochastic Rupture Proposal: Inertia, Gravity, and the Equivalence Principle from Branch Pruning Working document conceptual proposal, with derivations
Within the Stochastic Rupture (SR) framework an objective-collapse proposal in which physical facts are produced by the local, irreversible pruning of quantum branches we ask what mass is. We argue that mass is not a substance but a dual manifestation of pruning: gravitationally, as the curvature sourced by the information that pruning records; inertially, as the cost of reorganizing the underlying sheet pattern when a localized excitation is displaced. We derive Newton's second law F = ma from a Lagrangian for that reorganization cost, with inertial mass min = Rf′2 du, and show by a soliton boost that the inertial and gravitational masses are exactly equal, min = mgrav = E0/c2 , so that the equivalence principle becomes a consequence rather than a postulate. We then confront the central diculty: the SR master equation is a reactiondiusion law and carries a preferred frame, so Lorentz invariance cannot be assumed. We develop a candidate route in which the vacuum is a polycrystalline, coordination-three eggbox lattice: each ordered domain supplies a local Dirac cone (giving an emergent light speed), while disordered domain orientations restore spatial isotropy by averaging, the two eects living at separate scales. This route makes a falsiable prediction a residual anisotropy scaling as (D/L) 3/2 with a discriminating exponent and it identies, rather than hides, serious open problems (that pruning must produce the ordered lattice it does not freely generate, the grainsize mechanism, the veried Dirac touching, and the full 3 + 1 gluing). The genuinely novel claim is conceptual: the bridge from objective collapse to emergent spacetime. We restrict the present article to the static stage the spatial vacuum structure and defer the temporal (boost) sector to companion work, with physical justication. The document is oered as a proposal, to invite examination and independent review.
Within the Stochastic Rupture (SR) framework an objective-collapse proposal in which physical facts are produced by the local, irreversible pruning of quantum branches we ask what mass is. We argue that mass is not a substance but a dual manifestation of pruning: gravitationally, as the curvature sourced by the information that pruning records; inertially, as the cost of reorganizing the underlying sheet pattern when a localized excitation is displaced. We derive Newton's second law F = ma from a Lagrangian for that reorganization cost, with inertial mass min = Rf′2 du, and show by a soliton boost that the inertial and gravitational masses are exactly equal, min = mgrav = E0/c2 , so that the equivalence principle becomes a consequence rather than a postulate. We then confront the central diculty: the SR master equation is a reactiondiusion law and carries a preferred frame, so Lorentz invariance cannot be assumed. We develop a candidate route in which the vacuum is a polycrystalline, coordination-three eggbox lattice: each ordered domain supplies a local Dirac cone (giving an emergent light speed), while disordered domain orientations restore spatial isotropy by averaging, the two eects living at separate scales. This route makes a falsiable prediction a residual anisotropy scaling as (D/L) 3/2 with a discriminating exponent and it identies, rather than hides, serious open problems (that pruning must produce the ordered lattice it does not freely generate, the grainsize mechanism, the veried Dirac touching, and the full 3 + 1 gluing). The genuinely novel claim is conceptual: the bridge from objective collapse to emergent spacetime. We restrict the present article to the static stage the spatial vacuum structure and defer the temporal (boost) sector to companion work, with physical justication. The document is oered as a proposal, to invite examination and independent review.
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.
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.
This companion collects results of the Stochastic Rupture (SR) framework that are absent from the main paper. Its organising claim is that a single geometric object—the Fisher–Rao metric, unique by Chentsov’s theorem—supplies the pruning rate, the noise, and the barrier of the collapse sector, leaving that sector with no free choice of its own. We derive rather than posit. The barrier V = γ0/(1−χ) is the Fisher transport of the Casini relative entropy, which fixes the inverse-square exponent as the product of a logarithmic divergence and the Chentsov metric; the noise temperature is Teff = ℏγ0/kB, saturating the Feller condition as an identity. We construct the flash map, identifying pruning events with Wright–Fisher fixations: a martingale argument gives P(k) = |ak|², supplying the branch→effect map that Busch’s theorem requires, so that Born becomes a theorem conditional on one hypothesis-and Born exactness becomes equivalent to neutrality of the race, hence falsifiable. That hypothesis, that the quantum phase is the tangent orientation, is promoted to an elimination theorem: of the four compact angular variables the substrate possesses, Wallstrom’s condition leaves exactly one, with Poincar´e–Hopf supplying the integer winding. On the field-theoretic side we concede that friction is a relevant operator and show its coefficient is nevertheless fixed: multiplicative noise vanishes in vacuum, leaving Γ0 = Λ, so the wave regime (z = 1) holds for all observable physics and diffusive scaling is confined to super-Hubble scales. Transverse traceless gravitons preserve areas at linear order and do not inherit the friction; we accordingly retract an earlier gravitational-wave damping estimate and replace it with a polarisation-selective prediction. The MSRJD action, having no free choices, selects Itˆo by covariance and causality; its quantum lift is the Drude–Lorentz bath, satisfying KMS with analyticity strip 1/γ0 and saturating both the Planckian dissipation and Maldacena-Shenker-Stanford chaos bounds. Throughout, the epistemic status of each claim-derived, assumed, or open-is stated in the text. Two founding premises remain declared rather than derived: the master equation itself, and relational parsimony. Results here are internally verified, symbolically or numerically; they have not been subjected to independent review, which we invite.
Paper I derived gravitational geometry and Schrödinger dynamics from finite accessibility in stationary configurations. This work extends the same operational constraints to nonstationary situations, completing the derivation of classical and relativistic dynamics. The action gap ℏ* forces the minimal certifiable state to be (x, ẋ), yielding second-order dynamics as a structural necessity rather than an empirical postulate. Fisher additivity forces the linear response F = ma, and the equivalence principle emerges as a consequence: inertial and gravitational mass are identical because both are projections of the same local QFI density. The Lagrangian and action principle are not assumed; they arise as the unique intersubjectively stable summary of nonstationary coordination demand. In the relativistic regime, geodesic motion follows from the same certification budget that produced the Schwarzschild exterior: a trajectory that deviates from a geodesic demands excess coordination overhead, and the unique certification-cost minimizer is the geodesic. Multi-body dynamics inherit linearity from Fisher additivity, and the field limit is the unique admissible extension consistent with local accessibility and shell composition. Finite update bandwidth ω* introduces inference inertia in wave propagation, producing a distinctive ω^(+2) dispersion signature in gravitational waves — higher frequencies arrive later. The dispersion relation is ω_k² = q²(1 + q²/ω*²) This distinguishes the framework from massive graviton theories (ω^(−2)) and Lorentz violation (ω^(+1)). The connection to frame dissolution (Paper IV) closes the derivation chain: the certification ceiling ω* is the same parameter that governs frame coherence and dispersion. **This paper is part of the Finite Accessibility series, which reconstructs gravitational geometry, quantum dynamics, gauge structure, cosmological perturbation theory, and the dark sector from a single operational primitive: a finite certification ceiling ω* governing the maximum rate at which physical relations can be maintained across extended domains.** **Introductory papers** - Geometric Limits to Coherent Timekeeping in Extended Reference Frames — https://doi.org/10.5281/zenodo.18824556 - Accessibility Selection Law (ASL) — https://doi.org/10.5281/zenodo.18824649 - Phase Boundary Gravity — https://doi.org/10.5281/zenodo.18824707 **Pillars (numbered I–IV)** - Paper I: Deriving Gravitational Geometry and Schrödinger Dynamics from Finite Accessibility — https://doi.org/10.5281/zenodo.18601600 - Paper II: Deriving Inertia, Motion, and Wave Propagation from Finite Accessibility — https://doi.org/10.5281/zenodo.18625174 - Paper III: Accessible State Spaces, Record Stability, and the Emergence of Quantum Statistics — https://doi.org/10.5281/zenodo.18625192 - Paper IV: Frame Dissolution, the Certification Ceiling, and Observable Deformations — https://doi.org/10.5281/zenodo.18654458 **Extension papers** - Dark Matter from Finite Accessibility — https://doi.org/10.5281/zenodo.18654433 - Dark Energy from Finite Accessibility — https://doi.org/10.5281/zenodo.18654523 - No-Go Theorems and the Admissibility Corridor — https://doi.org/10.5281/zenodo.18654493 - Gauge Structure from Finite Accessibility — https://doi.org/10.5281/zenodo.18928152 - Perturbation Theory from Finite Accessibility — https://doi.org/10.5281/zenodo.18928213 **Experimental paper** - Experimental Probes of Finite Accessibility: GW Dispersion and Vacuum Path Independence — https://doi.org/10.5281/zenodo.18931126 **Keywords:** inertia derivation, equations of motion, finite accessibility, action gap, Fisher additivity, equivalence principle, geodesic motion, second-order dynamics, Lagrangian emergence, wave propagation, gravitational wave dispersion, omega plus two dispersion, certification ceiling, operational axioms, quantum Fisher information, Lorentz violation
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.
Modern theoretical physics rests on two highly successful but conceptually distinct frameworks: quantum mechanics and general relativity. While both theories are experimentally confirmed to high precision within their respective domains, they rely on fundamentally different starting points. General relativity takes spacetime as a primitive geometric structure, whereas quantum mechanics is formulated in terms of abstract state spaces without intrinsic spacetime meaning. Most approaches to quantum gravity attempt to reconcile this tension by modifying, quantizing, or discretizing spacetime itself. Even in approaches where spacetime is said to be “emergent,” it typically remains the primary conceptual backdrop on which physical processes are defined. Despite extensive efforts, there is no consensus on whether spacetime should be regarded as fundamental or derivative. In this work, a more radical starting point is explored. Rather than modifying spacetime or its geometry, we ask whether spacetime can be excluded entirely from the fundamental layer of the theory and recovered only at a later, operational stage. The central question is not how spacetime behaves, but whether the notion of “what lies between physical objects” must be spatial or temporal at the most fundamental level. We propose a framework—referred to here as Super Relativity (SR)—based on a single pre-geometric postulate: the existence of a monotonically expanding set of possible quantum configurations, referred to as the flux. Formally, this flux is represented as a monotone, σ-finite family of capacity measures on a common configuration space (introduced in Section 2). This postulate deliberately refrains from assuming spacetime, time ordering, metric structure, causality, or dynamics. Within this pre-geometric core, two derived, dimensionless notions are introduced: utilization, describing the realization of configurations, and saturation, defined as the ratio between utilized and available configurations. A central structural element of SR is the strict separation between a core layer and an interface layer. In the core layer, all quantities are pre-geometric and dimensionless, and no reference is made to space, time, motion, energy, or interaction. Only at the interface layer are operational notions introduced, including clocks, rulers, and signal propagation. Spacetime, in this construction, is not a dynamical entity but an effective bookkeeping structure that encodes relative rates of change once a calibration to physical units is performed. Within this framework, gravitational phenomena do not originate from spacetime curvature taken as fundamental. Instead, they arise from variations in saturation that, at the interface level, manifest as uniform rescalings of physical processes. When expressed in geometric language, these rescalings reproduce the standard predictions of general relativity, including gravitational time dilation and the equivalence between gravitation and acceleration. The invariant local speed of light is not postulated but follows as a derived consequence, since both clock rates and signal propagation are affected identically by the same underlying saturation mechanism. The aim of this paper is not to introduce new empirical predictions beyond those of general relativity, nor to present a complete theory of quantum gravity. Rather, the objective is foundational: to demonstrate that the mathematical structure of general relativity can be reconstructed from a single pre-geometric postulate without assuming spacetime as part of the fundamental ontology. In this sense, SR should be understood as a reconstruction and reinterpretation of known physics, rather than as a competing dynamical theory. An extended and fully explicit formulation of the framework, including all intermediate steps, is available in a companion preprint (version V12) deposited on Zenodo. The present paper restricts itself to the minimal conceptual and mathematical structure required to establish logical consistency and to demonstrate the emergence of general-relativistic behavior at the interface level.