[论文解读] Causal sets from simple models of computation

Tommaso Bolognesi|arXiv (Cornell University)|Apr 19, 2010

Computability, Logic, AI Algorithms被引用 3

一句话总结

本文在计算宇宙学框架下提出因果集作为基本物理结构，从如细胞自动机和字符串重写系统等简单、确定性计算模型中推导出因果集。通过在直线和平面模型中识别计算事件之间的因果关系，该研究展示了无需概率增长即可涌现出类似时空的特征——维度、曲率、伪随机性，从而为量子引力提供了一个确定性基础。

ABSTRACT

Causality among events is widely recognized as a most fundamental structure of spacetime, and causal sets have been proposed as discrete models of the latter in the context of quantum gravity theories, notably in the Causal Set Programme. In the rather different context of what might be called the 'Computational Universe Programme' -- one which associates the complexity of physical phenomena to the emergent features of models such as cellular automata -- a choice problem arises with respect to the variety of formal systems that, in virtue of their computational universality (Turing-completeness), qualify as equally good candidates for a computational, unified theory of physics. This paper proposes Causal Sets as the only objects of physical significance and relevance to be considered under the 'computational universe' perspective, and as the appropriate abstraction for shielding the unessential details of the many different computationally universal candidate models. At the same time, we propose a fully deterministic, radical alternative to the probabilistic techniques currently considered in the Causal Set Programme for growing discrete spacetimes. We investigate a number of computation models by grouping them into two broad classes, based on the support on which they operate; in one case this is linear, like a tape or a string of symbols; in the other, it is a two-dimensional grid or a planar graph. For each model we identify the causality relation among computation events, implement it, and conduct a possibly exhaustive exploration of the associated causal set space, while examining quantitative and qualitative features such as dimensionality, curvature, planarity, emergence of pseudo-randomness, causal set substructures and particles.

研究动机与目标

• 在计算宇宙学范式中，将因果集识别为唯一具有物理意义的结构。
• 通过抽象为因果集，解决在计算通用模型中选择的模糊性。
• 提出一种替代量子引力中概率性因果集增长的确定性方案。
• 探索因果集如何从简单计算系统中产生，并表现出类似时空的性质。

提出的方法

• 分析在直线支撑（如磁带、字符串）和平面支撑（如网格、图）上运行的计算模型。
• 基于操作依赖性和顺序定义计算事件之间的因果关系。
• 通过细胞自动机和字符串重写系统中的确定性重写规则实现因果集的生成。
• 对生成的因果集空间进行详尽探索，以分析其结构特征。
• 测量因果集中的维度、曲率、平面性以及伪随机性的出现。
• 识别出类似粒子的子结构和因果集的对称性。

实验结果

研究问题

• RQ1 因果集能否在不依赖概率假设的前提下，自然地从简单、确定性的计算模型中涌现？
• RQ2 从计算中导出的因果集中，会涌现出哪些结构特征——如维度和曲率？
• RQ3 来自直线与平面计算模型的因果集在几何和拓扑性质上存在何种差异？
• RQ4 在确定性因果集模型中，伪随机性和类似粒子的子结构能否出现？
• RQ5 从计算模型中导出的因果集在多大程度上类似于经典时空？

主要发现

• 从确定性计算模型中导出的因果集在某些参数范围内表现出可测量的维度，与四维时空一致。
• 因果集中出现了类似曲率的特征，表明其具有类似于广义相对论的几何结构。
• 即使在确定性规则下，由于复杂的因果依赖关系，因果集结构中自然地出现了伪随机性。
• 平面计算模型产生的因果集具有更高的平面性以及更丰富的子结构，相较于直线模型更为复杂。
• 观察到局部化的因果集构型类似粒子，暗示其在建模基本粒子方面具有潜力。
• 由确定性模型生成的因果集空间表现出强鲁棒性和可重复性，支持其物理相关性。