AI 中文总结
本文提出时空是由量子信息网络纠缠结构产生的分形几何，发展相关框架，通过信息理论距离定义几何，得出随机测地线等，引力源于纠缠度规时间依赖性，该框架预测了维度约化等，为量子理论和引力提供统一信息起源。
AI 中文摘要
在本文中，我们提出时空是由潜在量子信息网络的纠缠结构产生的一种涌现分形几何。确实，我们发展了一个框架，其中时空、量子力学和引力从一个通用量子态的纠缠结构中涌现。几何由纠缠图上的信息理论距离\(d_{ij}=-\ell_0\log(I_{ij}/I_0)\)定义，产生一个依赖尺度的分形时空，其有效维度在普朗克尺度附近流向\(D\to 2\)。在这种分形几何中，不可微轨迹导致随机测地线和复协变导数，从中薛定谔方程作为涌现动力学定律出现。引力源于纠缠诱导度规的时间依赖性，在宏观极限下产生爱因斯坦引力，并在广义场方程\(G_{\mu\nu}=8\pi G(T_{\mu\nu}+\alpha E_{\mu\nu}+\beta F_{\mu\nu})\)中编码分形修正。由此产生的“分形纠缠量子引力”（FEQG）框架预测了维度约化、修正的引力势以及在超短尺度上与标准量子力学可能的偏差，为量子理论和引力提供了统一的信息起源。
英文摘要
In this paper we propose that spacetime is an emergent fractal geometry generated by the entanglement structure of an underlying quantum information network. Indeed, it is developed a framework in which spacetime, quantum mechanics, and gravity emerge from the entanglement structure of a universal quantum state. Geometry is defined by an information-theoretic distance $d_{ij}=-\ell_0\log(I_{ij}/I_0)$ on an entanglement graph, producing a scale-dependent, fractal spacetime whose effective dimension flows toward $D\to 2$ near the Planck scale. In this fractal geometry, nondifferentiable trajectories lead to stochastic geodesics and a complex covariant derivative, from which the Schrödinger equation follows as an emergent dynamical law. Gravity arises from the time dependence of the entanglement-induced metric, yielding Einstein gravity in the macroscopic limit and fractal corrections encoded in a generalized field equation $G_{μν}=8πG(T_{μν}+αE_{μν}+βF_{μν})$. The resulting \emph{Fractal Entanglement Quantum Gravity} (FEQG) framework predicts dimensional reduction, modified gravitational potentials, and possible deviations from standard quantum mechanics at ultrashort scales, offering a unified informational origin for quantum theory and gravitation.
Comments28 pages
