Doctoral thesis

Causal loops : logically consistent correlations, time travel, and computation


181 p

Thèse de doctorat: Università della Svizzera italiana, 2017

English Causal loops are loops in cause-effect chains: An effect can be the cause of that effect's cause. We show that causal loops can be unproblematic, and explore them from different points of view. This thesis is motivated by quantum theory, general relativity, and quantum gravity. By accepting all of quantum theory one can ask whether the possibility to take superpositions extends to causal structures. Then again, quantum theory comes with conceptual problems: Can we overcome these problems by dropping causality? General relativity is consistent with space-time geometries that allow for time-travel: What happens to systems traveling along closed time-like curves, are there reasons to rule out the existence of closed time-like curves in nature? Finally, a candidate for a theory of quantum gravity is quantum theory with a different, relaxed space-time geometry. Motivated by these questions, we explore the classical world of the non-causal. This world is non-empty; and what can happen in such a world is sometimes weird, but not too crazy. What is weird is that in these worlds, a party (or event) can be in the future and in the past of some other party (time travel). What is not too crazy is that this theoretical possibility does not lead to any contradiction. Moreover, one can identify logical consistency with the existence of a unique fixed point in a cause-effect chain. This can be understood as follows: No fixed point is the same as having a contradiction (too stiff), multiple fixed points, then again, is the same as having an unspecified system (too loose). This leads to a series of results in that field: Characterization of classical non-causal correlations, closed time- like curves that do not restrict the actions of experimenters, and a self-referential model of computation. We study the computational power of this model and use it to upper bound the computational power of closed time-like curves. Time travel has ever since been term weird, what we show here, however, is that time travel is not too crazy: It is not possible to solve hard problems by traveling through time. Finally, we apply our results on causal loops to other fields: an analysis with Kolmogorov complexity, local and classical simulation of PR-box correlations with closed time-like curves, and a short note on self-referentiality in language.
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Computer science and technology
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