[论文解读] The Structurally Dynamic Cellular Network and Quantum Graphity Approaches to Quantum Gravity and Quantum Geometry - A Review and Comparison

Manfred Requardt, Saeed Rastgoo|arXiv (Cornell University)|Jan 2, 2015

Cellular Automata and Applications被引用 2

一句话总结

本文提出一种结构动态的细胞网络作为量子引力的离散基础，其中连续时空与量子理论作为粗粒度近似而涌现。通过几何重整化群，它从稀疏的非局域关联中推导出全息原理与黑洞熵-面积定律，为量子几何提供统一框架，并与量子图性理论进行比较。

ABSTRACT

Starting from the working hypothesis that both physics and the corresponding mathematics and in particular geometry have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the discrete protoforms of the building blocks of our ordinary continuum physics and mathematics living on a smooth background, and perhaps more importantly find a way how this continuum limit emerges from the mentioned discrete structure. We model this underlying substratum as a structurally dynamic cellular network (basically a generalisation of a cellular automaton). We regard these continuum concepts and continuum spacetime in particular as being emergent, coarse-grained and derived relative to this underlying erratic and disordered microscopic substratum, which we would like to call quantum geometry and which is expected to play by quite different rules, namely generalized cellular automaton rules. A central role in our analysis is played by a geometric renormalization group which creates (among other things) a kind of sparse translocal network of correlations between the points in classical continuous space-time and underlies, in our view, such mysterious phenomena as holography and the black hole entropy-area law. The same point of view holds for quantum theory which we also regard as a low-energy, coarse-grained continuum theory, being emergent from something more fundamental. In this paper we review our approach and compare it to the quantum graphity framework.

研究动机与目标

• 开发一种基于离散细胞网络的量子引力基础，以动态的原几何基底取代连续时空。
• 解释经典时空与量子理论如何作为更基本的离散结构的粗粒度有效描述而涌现。
• 建立一个几何重整化群，生成支撑全息原理与熵-面积定律的非局域关联。
• 将所提出的细胞网络方法与量子图性框架进行比较，突出其在涌现机制上的异同。

提出的方法

• 将基本基底建模为结构动态的细胞网络，推广细胞自动机，使其连接关系与规则可演化。
• 应用几何重整化群对网络进行粗粒度处理，识别长程关联与涌现的几何结构。
• 识别经典连续时空作为离散网络动力学的低能有效极限的涌现。
• 利用重整化过程推导黑洞熵-面积定律，并通过稀疏的非局域关联网络解释全息原理。
• 通过分析其各自几何与时空涌现机制，比较细胞网络方法与量子图性框架。
• 将量子理论视为与引力源自同一离散基底的涌现性粗粒度理论。

实验结果

研究问题

• RQ1 如何使一个离散的、结构动态的细胞网络涌现出广义相对论中的平滑连续时空？
• RQ2 几何重整化群在生成解释全息原理与黑洞熵的长程关联中扮演何种角色？
• RQ3 在此离散框架中，量子理论的涌现与时空的涌现相比有何异同？
• RQ4 细胞网络与量子图性方法在几何与时空涌现机制上存在哪些差异？
• RQ5 将引力与量子理论均视为源自同一离散基底的涌现现象，其含义是什么？

主要发现

• 几何重整化群成功生成一个稀疏的非局域关联网络，其支撑全息原理与黑洞熵-面积定律。
• 经典时空与量子理论被证明可作为离散且动态的细胞网络的粗粒度有效描述而涌现。
• 所提出的框架为引力与量子理论从单一离散基底中涌现提供了统一机制。
• 与量子图性的比较表明，尽管两者均旨在从离散结构推导连续物理，但细胞网络方法更强调结构动力学与几何重整化，而非固定图的演化。
• 该模型表明，量子几何遵循广义细胞自动机规则，与经典连续物理有根本不同。
• 时空的涌现并非平滑极限，而是由非局域关联驱动的粗粒度过程，与量子纠缠与全息等非局域现象一致。