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Universal Finite Resolution: A Unified Causal Foundation for Time, Entropy, and Quantum Gravity

Alexei A. Rivera

Published Jan 16, 2026• 0 citations
Publisher

Abstract

What if physical reality, from an electron to the universe itself, cannot perceivethe Present, but only an approximation of the Present? We propose the hypothesisof Universal Finite Resolution, which challenges the assumption of continuoustime fundamental to standard Quantum Mechanics and General Relativity. Drawingupon the modern concept of a ”Bandwidth-Limited System,” we posit that all physicalinteraction is bounded by a non-zero integration time τmin. Modeling our universe as aself-organized critical system analogous to a ”Sand Pile” cellular automaton, we derivethat this temporal lower bound necessitates a breakdown of unitarity at the Planckscale. This introduces an intrinsic, irreducible decoherence term to the Von Neumannequation, offering a unified causal mechanism for: (1) the Arrow of Time, (2) theorigin of Entropy, (3) objective Wave Function Collapse, and (4) a natural ultravioletcutoff for singularities. Unlike String Theory or Loop Quantum Gravity, which modifyspacetime geometry or particle content, UFR adjusts the processing rate of the vacuumitself, governed by a Twistor-formulated mass-scaled Lindblad Master Equation. Thisframework is experimentally testable across independent physical systems at vastlydifferent energy scales and offers immediate retroductive solutions to a wide range ofexisting anomalies.

DOI
10.5281/zenodo.18262817

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What if physical reality, from an electron to the universe itself, cannot perceivethe Present, but only an approximation of the Present? We propose the hypothesisof Universal Finite Resolution, which challenges the assumption of continuoustime fundamental to standard Quantum Mechanics and General Relativity. Drawingupon the modern concept of a ”Bandwidth-Limited System,” we posit that all physicalinteraction is bounded by a non-zero integration time τmin. Modeling our universe as aself-organized critical system analogous to a ”Sand Pile” cellular automaton, we derivethat this temporal lower bound necessitates a breakdown of unitarity at the Planckscale. This introduces an intrinsic, irreducible decoherence term to the Von Neumannequation, offering a unified causal mechanism for: (1) the Arrow of Time, (2) theorigin of Entropy, (3) objective Wave Function Collapse, and (4) a natural ultravioletcutoff for singularities. Unlike String Theory or Loop Quantum Gravity, which modifyspacetime geometry or particle content, UFR adjusts the processing rate of the vacuumitself, governed by a Twistor-formulated mass-scaled Lindblad Master Equation. Thisframework is experimentally testable across independent physical systems at vastlydifferent energy scales and offers immediate retroductive solutions to a wide range ofexisting anomalies.
Contact Jonathan.duchesne@hotmail.com 418-953-0596 This thesis presents Time–Decoherence Gravity (TDG), a unified theoretical framework in which spacetime geometry, gravitation, and the physical flow of time arise from fundamental quantum decoherence. Rather than treating decoherence as an environmental or effective process, TDG builds on a covariant extension of the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation, where four directional Lindblad operators encode intrinsic, irreversible information loss. These operators define a “decoherence tensor,” which acts both as a memory of quantum irreversibility and as the generator of emergent spacetime geometry through a nonlinear constitutive relation. The theory provides a coherent gravitational collapse mechanism based on the incompatibility of decoherence patterns across quantum branches. This leads to an intrinsic “decoherence energy,” whose magnitude determines the collapse timescale, extending and generalizing the well-known Penrose–Diósi models. TDG predicts a smooth transition from persistent microscopic coherence to rapid macroscopic collapse. At cosmological scales, a homogeneous decoherence tensor naturally generates modified Friedmann dynamics, early-universe stiff-fluid behavior, and late-time acceleration without requiring a fine-tuned cosmological constant. Black-hole entropy emerges as a saturation of decoherence memory at the horizon, while Hawking radiation appears as the dissipative relaxation of this saturation. The theory also predicts short-range deviations from Newtonian gravity and a universal spectrum of fundamental gravitational noise. Finally, TDG offers several experimentally testable signatures involving optical clocks, mesoscopic interferometry, short-range force measurements, and correlated phase noise in global timing networks. The framework is internally consistent, falsifiable, and provides a novel and unified approach to the relationship between quantum mechanics, gravity, and the arrow of time.
This work proposes the Collapse Clock Hypothesis, a framework in which physical time is defined by the rate of irreversible wavefunction collapse, interpreted as a process of information pruning constrained by finite informational capacity. Within this framework, spatial variations in collapse rate give rise to differential progression of proper time, providing a potential mechanism for gravitational time dilation and related phenomena. The approach integrates concepts from quantum information theory, thermodynamics, and emergent spacetime, drawing connections to prior work on entanglement entropy, holographic bounds, and thermodynamic derivations of gravitational dynamics. A computational implementation using a Score-Driven Kinetic Ising Model (SDKIM) is presented to explore whether the proposed causal chain—mass → interactions → entanglement → collapse suppression → slower time—can arise dynamically in a simplified lattice system. The simulations demonstrate robust qualitative behavior consistent with collapse-rate suppression in highly entangled regions, while also highlighting important limitations, including the use of mean-field approximations and the absence of a direct quantitative mapping to known gravitational field equations. This work is intended as a speculative but testable framework rather than a complete theory. Several falsifiable predictions are outlined, including potential signatures in precision timekeeping, quantum-coherent systems, gravitational wave phase evolution, and cosmological observables. These predictions are presented at an order-of-magnitude level and require further development for direct comparison with experimental data. The goal of this work is to explore whether irreversible information dynamics may provide a unifying underlying mechanism for time, gravity, and cosmological evolution, and to motivate further investigation into collapse-based approaches to fundamental physics.
Modern physics faces a constellation of foundational puzzles: the Big Bang singularity, time's arrow, dark matter and dark energy, the cosmological constant problem, fine-tuning, quantum measurement, and quantum gravity unification. This Perspective proposes a unified resolution grounded in complexity-driven selection from diverse quantum paths. Prior to the Big Bang, reality comprises a pre-temporal quantum substrate (lacking classical time coordinate but governed by unitary quantum evolution), evolving reversibly across multiple trajectories—including opposing time arrows. The Big Bang marks an emergence threshold (λ) where decoherence locks spacetime parameters, yielding our classical universe as a "survivor" of local emergence rather than a closed totality. Dark matter and dark energy represent unevolved quantum paths—residuals exerting gravitational influence without full manifestation. This framework reframes cosmology as the study of layered emergence, dissolving "why" questions into "when/how" selection dynamics, with testable predictions in CMB perturbations, quantum decoherence experiments, and gravitational wave observations. By shifting from reductionism to emergentism, it suggests a universal pattern: threshold-gated emergence from diverse substrates, applicable from the cosmos to consciousness.
This centennial paper revisits the foundational Einstein–Bohr debate on the quantum measurement problem and wave-function collapse - an unresolved tension that has persisted since the birth of quantum mechanics. Drawing upon the Theory of Entropicity (ToE), the paper presents a novel framework in which entropy is not merely a statistical quantity but a fundamental, causal field shaping physical interactions, information flow, and the structure of reality. At the heart of this approach is the reinterpretation of quantum collapse as an irreversible, entropy-constrained transition, governed by the Vuli-Ndlela Integral—an entropic variant of the Feynman path integral. Rather than invoking observer-induced discontinuities or metaphysical many-worlds, ToE frames collapse as a natural consequence of entropic thresholds being crossed. Time irreversibility, measurement outcomes, and system observability are shown to be emergent properties of the entropic field. The scope of the paper extends beyond quantum mechanics. By rooting wave-function collapse in entropy dynamics, the work provides a bridge to gravity, thermodynamics, black hole physics, and even artificial intelligence. The theory offers fresh insights into entanglement formation time, the arrow of time, and the emergence of consciousness—suggesting that all observable structure arises from entropic modulation. The paper concludes by proposing entropy as the universal constraint that governs what can exist, be measured, and evolve. It invites physicists, philosophers, and AI researchers alike to reimagine physical law as emerging not from geometry or probability, but from the entropic fabric of reality itself.
Title: Envelopment over Unification: Recovering Einstein’s Dream via a Generativity-First Framework Subtitle: The Sampling Paradox of State-Based Quantum Gravity and the Return to It from Wave Abstract: This paper identifies the fundamental cause of the century-long impasse in unifying quantum mechanics (QM) and general relativity (GR) as a "Sampling Paradox." Modern physics is epistemically constrained to perceive reality as a collection of static "states"—discrete snapshots sampled from a continuous generative flow. At the Planck scale, the instability of the carrier (spacetime geometry) makes the reconstruction of the generative source from these samples logically impossible. The Envelopment Framework: Departing from traditional state-based programs, we propose a "Generativity-First" ontology called Envelopment. This framework adopts a three-layer hierarchy: Primary Layer (Wave): The continuous, non-linear phase flow of the universe ("It from Wave"). Secondary Layer (Geometry): Spacetime as a stabilized, self-organizing attractor. Tertiary Layer (State): Matter and information as discrete, resolution-dependent projections. Mathematical and Information-Theoretic Foundations: We characterize the primary generative law using a non-linear evolution equation analogous to the Complex Ginzburg-Landau Equation (CGLE). In this model, spacetime geometry emerges as a steady-state attractor, while quantum states manifest as localized interference patterns. We re-derive the Energy-Time Uncertainty Relation as a rigorous consequence of finite temporal sampling windows (delta-t). Here, "uncertainty" is not an inherent fuzziness of nature but an informational limit imposed by the "shutter speed" of observation. Key Contributions: Planckian Aliasing: Redefines quantum vacuum noise as "folded" generative rhythms. The theory predicts non-random, phase-locked structures detectable through homodyne detection in quantum optics or advanced spectral analysis of LIGO data. Envelopment of Existing Theories: Repositions prominent programs—such as AdS/CFT (as shadow-to-object projections), Loop Quantum Gravity (as descriptions of discrete sampling units), and String Theory (as organizations of state-excitations)—as high-precision descriptions of specific projected regimes. The Observer as Co-creator: Positions the observer at the interface of sampling resolution, where the choice of the observational window determines which aspect of the generative wave is rendered as a physical "state." Significance: By shifting the ontological priority from "States" (nouns) to "Generativity" (verbs), this research offers a consistent bridge between continuous flow and discrete observation. It provides a roadmap for future numerical simulations based on non-linear dynamical systems and offers testable predictions for the deterministic structure of quantum noise. Keywords: Quantum Gravity, General Relativity, It from Wave, Sampling Paradox, Envelopment Framework, Complex Ginzburg-Landau Equation, Non-linear Dynamics, Vacuum Noise Aliasing, Observer as Co-creator, Information Physics. Note on Related Research: This manuscript represents a significant generalization of the author’s preceding work on "Shutter Speed Theory" and "Informational Crystallization" (Ohumi, 2025). It expands the sampling-theoretic reinterpretation of quantum uncertainty into a comprehensive framework for quantum gravity. For details, please refer to the attached PDF. This work introduces the “Envelopment over Unification” logic (Wave → Geometry → State). It is complemented by applied works translating this framework into (i) ethics of technological civilization (Envelopment Ethics, DOI: 10.5281/zenodo.18256968) and (ii) governance critique of quantified policy targets (Civilization KPI Trap, DOI: 10.5281/zenodo.18264106). References: Shannon (1948), Einstein (1916), Wheeler (1990), Ohumi (2025).
This work proposes the Collapse Clock Hypothesis, a framework in which physical time is defined by the rate of irreversible wavefunction collapse, interpreted as a process of information pruning constrained by finite informational capacity. Within this framework, spatial variations in collapse rate give rise to differential progression of proper time, providing a potential mechanism for gravitational time dilation and related phenomena.The approach integrates concepts from quantum information theory, thermodynamics, and emergent spacetime, drawing connections to prior work on entanglement entropy, holographic bounds, and thermodynamic derivations of gravitational dynamics. A computational implementation using a Score-Driven Kinetic Ising Model (SDKIM) is presented to explore whether the proposed causal chain—mass → interactions → entanglement → collapse suppression → slower time—can arise dynamically in a simplified lattice system.The simulations demonstrate robust qualitative behavior consistent with collapse-rate suppression in highly entangled regions, while also highlighting important limitations, including the use of mean-field approximations and the absence of a direct quantitative mapping to known gravitational field equations.This work is intended as a speculative but testable framework rather than a complete theory. Several falsifiable predictions are outlined, including potential signatures in precision timekeeping, quantum-coherent systems, gravitational wave phase evolution, and cosmological observables. These predictions are presented at an order-of-magnitude level and require further development for direct comparison with experimental data.The goal of this work is to explore whether irreversible information dynamics may provide a unifying underlying mechanism for time, gravity, and cosmological evolution, and to motivate further investigation into collapse-based approaches to fundamental physics.