Possibility of causal loops without superluminal signalling - a general framework
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Date
2021-09-24Type
- Working Paper
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yes
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Abstract
Causality is fundamental to science, but it appears in several different forms. One is relativistic causality, which is tied to a space-time structure and forbids signalling outside the future. On the other hand, causality can be defined operationally using causal models by considering the flow of information within a network of physical systems and interventions on them. From both a foundational and practical viewpoint, it is useful to establish the class of causal models that can coexist with relativistic principles such as no superluminal signalling, noting that causation and signalling are not equivalent. We develop such a general framework that allows these different notions of causality to be independently defined and for connections between them to be established. The framework first provides an operational way to model causation in the presence of cyclic, fine-tuned and non-classical causal influences. We then consider how a causal model can be embedded in a space-time structure and propose a mathematical condition (compatibility) for ensuring that the embedded causal model does not allow signalling outside the space-time future. We identify several distinct classes of causal loops that can arise in our framework, showing that compatibility with a space-time can rule out only some of them. We then demonstrate the mathematical possibility of operationally detectable causal loops embedded in Minkowski space-time that do not lead to superluminal signalling. Our framework provides conditions for preventing superluminal signalling within arbitrary (possibly cyclic) causal models and also allows us to model causation in post-quantum theories admitting jamming correlations. Finally, this work introduces a new causal modelling concept of ``higher-order affects relations'' and several related technical results, which have applications for causal discovery in fined-tuned causal models. Show more
Publication status
publishedExternal links
Journal / series
arXivPages / Article No.
Publisher
Cornell UniversityOrganisational unit
03781 - Renner, Renato / Renner, Renato
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ETH Bibliography
yes
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