Abstract
The theory of general relativity predicts the existence of closed time-like curves (CTCs), which theoretically would allow an observer to travel back in time and interact with their past self. This raises the question of whether this could create a grandfather paradox, in which the observer interacts in such a way to prevent their own time travel. Previous research has proposed a framework for deterministic, reversible, dynamics compatible with non-trivial time travel, where observers in distinct regions of spacetime can perform arbitrary local operations with no contradiction arising. However, only scenarios with up to three regions have been fully characterised, revealing only one type of process where the observers can verify to both be in the past and future of each other. Here we extend this characterisation to an arbitrary number of regions and find that there exist several inequivalent processes that can only arise due to non-trivial time travel. This supports the view that complex dynamics is possible in the presence of CTCs, compatible with free choice of local operations and free of inconsistencies.
Highlights
The dominant paradigm in physics relies on the idea that systems evolve through time according to dynamical laws, with the state at a given time determining the entire history of the system.General relativity challenges this view
We have developed a characterisation of deterministic processes in the presence of closed time-like curves (CTCs) for an arbitrary number of localised regions
The most significant result of our work is our discovery of distinct non-trivial quadripartite process functions which are compatible with the presence of CTCs
Summary
The dominant paradigm in physics relies on the idea that systems evolve through time according to dynamical laws, with the state at a given time determining the entire history of the system. A different approach is the so called “process matrix formalism”, which takes as a starting point the local validity of the ordinary laws of physics and asks what type of global processes are compatible with this assumption [59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74] This framework enforces that all operations that would normally be possible in ordinary spacetime should still be available in local regions. Our results show that CTCs are compatible with determinism and with the local “free choice” of operations, and with a rich and diverse range of scenarios and dynamical processes
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