Quantum Geometry Wave Theory (QGW)

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)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)

Canadian Journal of Marketing ResearchMay 13, 20260 citations

Quantum geometry and quantum force: Wave and geodesic equations

E. R. Caianiello, GAETANO SCARPETTA, Giuseppe Marmo

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoApr 1, 19838 citations

Title: Non-Linear Geometry via Wave Function Collapse

Jincheng Zhang

This paper explores the potential of non-linear geometry, leveraging the concept of wave function collapse, to generate complex geometries from simple perturbations. The core claim is to extend this established theory beyond conventional geometric applications, demonstrating the emergence of intricate structures through the manipulation of wave function dynamics. We propose a modified collapse theory that allows for the formation of non-linear geometric properties, opening new avenues for understanding and potentially creating novel geometries. This work builds upon established quantum mechanics principles, aiming to provide a fundamentally different approach to geometric analysis.This paper explores the potential of non-linear geometry, leveraging the concept of wave function collapse, to generate complex geometries from simple perturbations. The core claim is to extend this established theory beyond conventional geometric applications, demonstrating the emergence of intricate structures through the manipulation of wave function dynamics. We propose a modified collapse theory that allows for the formation of non-linear geometric properties, opening new avenues for understanding and potentially creating novel geometries. This work builds upon established quantum mechanics principles, aiming to provide a fundamentally different approach to geometric analysis.

Aug 31, 20260 citations

The Wave Theory of Quantum Mechanics

College PhysicsSep 16, 20260 citations

Geometry of quantum active subspaces and of effective Hamiltonians

David Viennot

We propose a geometric formulation of the theory of effective Hamiltonians associated with active spaces. We analyze particularly the case of the time-dependent wave operator theory. This formulation is related to the geometry of the manifold of the active spaces, particularly to its Kählerian structure. We introduce the concept of quantum distance between active spaces. We show that the time-dependent wave operator theory is, in fact, a gauge theory, and we analyze its relationship with the geometric phase concept.We propose a geometric formulation of the theory of effective Hamiltonians associated with active spaces. We analyze particularly the case of the time-dependent wave operator theory. This formulation is related to the geometry of the manifold of the active spaces, particularly to its Kählerian structure. We introduce the concept of quantum distance between active spaces. We show that the time-dependent wave operator theory is, in fact, a gauge theory, and we analyze its relationship with the geometric phase concept.

Journal of Mathematical PhysicsMay 1, 20076 citations

Geometric Quantum Theory

James Thomas Wheeler

Jan 1, 19900 citations

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)