简单计算模型的因果集
Causal sets from simple models of computation
摘要：
事件之间的因果关系被广泛认为是时空的最基本结构，因果集在量子引力理论中被提出作为后者的离散模型，特别是在因果集计划中。在相当不同的背景下，什么可能被称为“计算宇宙计划”-一个将物理现象的复杂性与诸如元胞自动机等模型的涌现特征相关联的计划-一个选择问题出现在各种形式系统中，由于其计算的普遍性，（图灵完备性），有资格作为一个计算的，统一的物理理论同样好的候选人。本文提出了因果集作为唯一的物理意义和相关性的对象下考虑的“计算宇宙”的角度来看，并作为适当的抽象屏蔽许多不同的计算通用的候选模型的不必要的细节。与此同时，我们提出了一个完全确定性的，激进的替代概率技术目前考虑的因果集计划不断增长的离散时空。我们研究了一些计算模型，将它们分为两大类，基于它们操作的支持;在一种情况下，这是线性的，像磁带或符号串;在另一种情况下，它是一个二维网格或平面图。对于每个模型，我们确定计算事件之间的因果关系，实现它，并进行可能详尽的探索相关的因果集空间，同时检查定量和定性的功能，如维数，曲率，平面性，伪随机性的出现，因果集子结构和粒子。
英文摘要：
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.
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