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Canadian Journal of Marketing Research

《量子引力扳手理论:一种自然实现面积律与全息原理的新框架》《Quantum Gravity Wrench Theory: A Novel Framework Naturally Realizing Area Law and Holographic Principle》

Jiang C

Published May 13, 2026• 0 citations
Publisher

Abstract

This dataset contains the numerical validation and supplementary materials for the paper **"Quantum Gravity Wrench Theory: A Natural Holographic Framework"**. ## Content Overview- **Area Law Verification Data**: Raw numerical results confirming the area-law scaling of entanglement entropy ($S \sim A^{1/2}$) with high precision across varying coupling constants ($\lambda = 1.0, 2.0, 5.0$).- **Scaling Analysis**: Data files documenting the extraction of scaling dimensions and critical exponents supporting the holographic principle.- **Theory Summary**: Consolidated reports detailing the geometric "wrench" operator formalism and its application to black hole thermodynamics. ## Key FindingsThe data robustly supports that the Quantum Gravity Wrench (QGW) framework naturally realizes:1. **Holographic Area Law**: Entanglement entropy scales with the boundary area, not the volume.2. **Dimensional Reduction**: Effective spatial dimension flows to $d=2$ in the infrared regime.3. **Black Hole Entropy**: A microscopic explanation for the Bekenstein-Hawking entropy formula. Usage Notes- **Formats**: Primary data is provided in plain text (.txt) for machine readability.- **Relation**: This dataset is the companion to the preprint available on arXiv.- **License**: Creative Commons Attribution 4.0 International (CC BY 4.0) 本数据集为论文《量子引力扳手理论:一种自然实现面积律与全息原理的新框架》的数值验证与补充材料。 ## 内容概述- **面积律验证数据**:不同耦合常数($\lambda = 1.0, 2.0, 5.0$)下精确验证纠缠熵满足面积律标度($S \sim A^{1/2}$)的原始数值结果。- **标度分析**:提取标度维度和临界指数以支持全息原理的数据文件。- **理论总结**:详细阐述几何“扳手”算子形式及其在黑洞热力学中应用的报告。 ## 核心结论数据强有力地支持量子引力扳手(QGW)框架自然实现了:1. **全息面积律**:纠缠熵随边界面积而非体积标度。2. **维度约化**:红外区域有效空间维度流向 $d=2$。3. **黑洞熵**:为Bekenstein-Hawking熵公式提供了微观解释。 使用说明- **格式**:主要数据以纯文本(.txt)格式提供,便于机器读取。- **关联**:本数据集是arXiv预印本论文的配套数据。- **许可**:知识共享署名 4.0 国际许可协议 (CC BY 4.0)

DOI
10.5281/zenodo.20150861

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This dataset contains the numerical validation and supplementary materials for the paper "Quantum Gravity Wrench Theory: A Natural Holographic Framework". ## Content Overview- Area Law Verification Data: Raw numerical results confirming the area-law scaling of entanglement entropy (S∼A1/2S \sim A^{1/2}S∼A1/2) with high precision across varying coupling constants (λ=1.0,2.0,5.0\lambda = 1.0, 2.0, 5.0λ=1.0,2.0,5.0).- Scaling Analysis: Data files documenting the extraction of scaling dimensions and critical exponents supporting the holographic principle.- Theory Summary: Consolidated reports detailing the geometric "wrench" operator formalism and its application to black hole thermodynamics. ## Key FindingsThe data robustly supports that the Quantum Gravity Wrench (QGW) framework naturally realizes:1. Holographic Area Law: Entanglement entropy scales with the boundary area, not the volume.2. Dimensional Reduction: Effective spatial dimension flows to d=2d=2d=2 in the infrared regime.3. Black Hole Entropy: A microscopic explanation for the Bekenstein-Hawking entropy formula. Usage Notes- Formats: Primary data is provided in plain text (.txt) for machine readability.- Relation: This dataset is the companion to the preprint available on arXiv.- License: Creative Commons Attribution 4.0 International (CC BY 4.0) 本数据集为论文《量子引力扳手理论:一种自然实现面积律与全息原理的新框架》的数值验证与补充材料。 ## 内容概述- 面积律验证数据:不同耦合常数(λ=1.0,2.0,5.0\lambda = 1.0, 2.0, 5.0λ=1.0,2.0,5.0)下精确验证纠缠熵满足面积律标度(S∼A1/2S \sim A^{1/2}S∼A1/2)的原始数值结果。- 标度分析:提取标度维度和临界指数以支持全息原理的数据文件。- 理论总结:详细阐述几何“扳手”算子形式及其在黑洞热力学中应用的报告。 ## 核心结论数据强有力地支持量子引力扳手(QGW)框架自然实现了:1. 全息面积律:纠缠熵随边界面积而非体积标度。2. 维度约化:红外区域有效空间维度流向 d=2d=2d=2。3. 黑洞熵:为Bekenstein-Hawking熵公式提供了微观解释。 使用说明- 格式:主要数据以纯文本(.txt)格式提供,便于机器读取。- 关联:本数据集是arXiv预印本论文的配套数据。- 许可:知识共享署名 4.0 国际许可协议 (CC BY 4.0)
It was found, by studying black holes, that the compatibility of the theory of gravity and the laws of quantum mechanics demands that the universe must act like a hologram. That is, all the information inside a region of the universe should be encoded on a so-called holographic screen of one-lesser dimension. This is termed the holographic principle. In a generic spacetime, such as an expanding universe, holographic screens depend on the choice of an observer, which is consistent with the notion that the observer is part of the system in cosmology. In the first part of this dissertation, we study the observer-dependence of holographic screens. This will help us understand how the fundamental description of the universe depends on the choice of the observer. Furthermore, we study the dynamics of the holographic screens and their geometry in the first part of this dissertation.An example where the holographic principle is manifest is the AdS-CFT correspondence. This correspondence connects quantum information quantities, like entanglement and complexity, to geometric quantities, like area and volume, respectively. In the second and the third part of this dissertation, we use the AdS-CFT correspondence as a tool to calculate the entanglement entropy and the computational complexity of a quenched CFT state. Studying the time evolution of the entanglement entropy following a quantum quench teaches us how a CFT state thermalizes. On the other hand, studying the time evolution of the computational complexity allows us to check the validity of various recent conjectures involving black holes and complexity.
Black holes are windows into the deepest structures of reality, where quantum mechanics, thermodynamics, and geometry converge. In this pedagogical preprint we explore how quantum entanglement entropy provides a microscopic foundation for black hole thermodynamics. Starting from rst principles of quantum information theory, we introduce entanglement entropy, the area law, and Hawking radiation, then proceed to modern results: the Ryu-Takayanagi formula, quantum extremal surfaces, the Page curve, replica wormholes, and the island formula. Throughout, the emphasis is on physical intuition. No prior knowledge of string theory or loop quantum gravity is assumed.
A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gauge-gravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement entropy, whereas a full understanding of a quantum state requires Rényi entropies. Here we show that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes. This geometric prescription is a one-parameter generalization of the minimal surface prescription for entanglement entropy. Applying this we provide the first holographic calculation of mutual Rényi information between two disks of arbitrary dimension. Our results provide a framework for efficiently studying Rényi entropies and understanding entanglement structures in strongly coupled systems and quantum gravity.
The non-factorizing nature of the Hilbert space in Loop Quantum Gravity (LQG) due to gauge invariance requires a generalized definition of entanglement entropy. This work employs the framework of von Neumann algebras to investigate the entanglement entropy in LQG. On a graph, the holonomy and flux operators within a region and on the boundary generate a non-factor type I von Neumann algebra, which is used to define the entanglement entropy for LQG states. This algebraic formalism is applied to ``fixed-area states''--superpositions of spin networks associated with a surface with a definite macroscopic area given by the LQG area spectrum. By maximizing the entropy, we derive a geometrical area law where the entanglement entropy is proportional to the area. In addition, we show that bulk entanglement can renormalize the area-law coefficient and produce logarithmic corrections. The results in this paper closely relate to LQG black hole entropy.
Abstract Black hole entropy is one of the few windows into the quantum aspects of gravitation, and its study over the years has highlighted the holographic nature of gravity. At the non-perturbative level in quantum gravity, promising explanations are being explored in terms of the entanglement entropy between regions of space. In the context of loop quantum gravity, this translates into an analysis of the correlations between the regions of the spin network states defining the quantum state of the geometry of space. In this paper, we explore a class of states, motivated by results in condensed matter physics, satisfying an area law for entanglement entropy and having non-trivial correlations. We highlight that entanglement comes from holonomy operators acting on loops crossing the boundary of the region.
In this paper, we discover the topological quantization and phase transition mechanisms of holographic extremal surfaces in discrete tensor networks, providing a rigorous discrete dynamical benchmark for the proposition that "gravity is entanglement". Using a one-dimensional spin network with a fixed truncated hopping step k, we derive a rigorous analytical solution for the peak position of entanglement entropy, demonstrating that it is solely determined by the underlying connectivity step k. The perturbative phase diagram further reveals that this quantized gravity ladder is strongly protected by the topological gap below a critical perturbation V_c, exhibiting unique critical scaling behavior at the transition point. The fitted critical exponent beta approx 0.07 is significantly lower than the mean-field exponent of conventional phase transitions, revealing a unique "critical rigidity" characteristic of finite-size long-range topological networks. This model not only provides a rigorous graph-theoretical benchmark for a discrete analogue of the Ryu-Takayanagi area law but also, through the "geometric decoupling" mechanism, constructs an analytically solvable microscopic dynamical sandbox for the highly debated entanglement wedge disconnection in the black hole island formula.