Causal Sets from Simple Models of Computation
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. We address this problem by proposing Causal Sets to be the only objects of physical significance under the computational universe perspective. At the same time, we propose a fully deterministic, radical alternative to the probabilistic techniques considered in the Causal Set Programme for growing discrete spacetime instances.We investigate a number of computation models, all operating on a one-dimensional support like a tape or a string of symbols, we identify the causality relation among their 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 and particles.
Keywords: Causal set, cellular automata, dimension estimator, discrete spacetime, emergent particle, network mobile automata.