Reversible dynamics with closed time-like curves and freedom of choice

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.

arXiv commentProcess function search code at github.com/gtobarSU/Classical-Process-Matrix-Search-Code.git. Counter-examples to the characterization theorem in arxiv.org/abs/1703.00779 (upon which ours is based) were reported in arXiv:2512.23599. These counter-examples affect the stated characterisation theorem (eventual errata) but not the validity of the process matrices found by the code

References in corpus (52)

• Quantum correlations with no causal order
• The warp drive: hyper-fast travel within general relativity
• Quantum causal modelling
• Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure
• Witnessing causal nonseparability
• Closed timelike curves via post-selection: theory and experimental demonstration
• Causal and causally separable processes
• Hyperfast Interstellar Travel in General Relativity
• Quantum superposition of the order of parties as a communication resource
• Is a time symmetric interpretation of quantum theory possible without retrocausality?
• Bell's Theorem for Temporal Order
• A Superluminal Subway: The Krasnikov Tube
• The quantum mechanics of time travel through post-selected teleportation
• The simplest causal inequalities and their violation
• A new time-machine model with compact vacuum core
• Does Time-Symmetry Imply Retrocausality? How the Quantum World Says "Maybe"
• Disentangling the Quantum World
• Quantum Computational Complexity in the Presence of Closed Timelike Curves
• Maximal incompatibility of locally classical behavior and global causal order in multi-party scenarios
• Formation of closed timelike curves in a composite vacuum/dust asymptotically-flat spacetime
• A purification postulate for quantum mechanics with indefinite causal order
• Multipartite Causal Correlations: Polytopes and Inequalities
• The space of logically consistent classical processes without causal order
• Updating the Born rule
• Path Integrals, Density Matrices, and Information Flow with Closed Timelike Curves
• A New Class of Retrocausal Models
• Effective Quantum Time Travel
• Quantum States as Ordinary Information
• New Slant on the EPR-Bell Experiment
• Information Flow of quantum states interacting with closed timelike curves
• Relativistic quantum information and time machines
• Glimmers of a pre-geometric perspective
• Open timelike curves violate Heisenberg's uncertainty principle
• Causation does not explain contextuality
• Closed Timelike Curves and "Effective" Superluminal Travel with Naked Line Singularities
• Causal order as a resource for quantum communication
• Semi-device-independent certification of indefinite causal order
• Indefinite causal structures for continuous-variable systems
• Treating Time Travel Quantum Mechanically
• Device-independent test of causal order and relations to fixed-points
• Reversible time travel with freedom of choice
• Replicating the benefits of closed timelike curves without breaking causality
• Accommodating Retrocausality with Free Will
• Genuinely Multipartite Noncausality
• Nonlocality without nonlocality
• How Retrocausality Helps
• Quantum fields on closed time-like curves
• A time machine for free fall into the past
• Revisiting consistency conditions for quantum states of systems on closed timelike curves: an epistemic perspective
• Quantum from principles without assuming definite causal structure
• Appearance of causality in process matrices when performing fixed-basis measurements for two parties
• Time travel without paradoxes: Ring resonator as a universal paradigm for looped quantum evolutions

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• Cyclic Quantum Causal Models
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• Reassessing thermodynamic advantage from indefinite causal order
• Embedding cyclic information-theoretic structures in acyclic spacetimes: no-go results for indefinite causality
• Admissible Causal Structures and Correlations
• Equivalence of Grandfather and Information Antinomy Under Intervention
• A no-go theorem for superpositions of causal orders
• Time-travelling billiard-ball clocks: a quantum model
• Life on a closed timelike curve
• The Multi-round Process Matrix
• Analogue time machine in a photonic system
• Billiard-ball paradox for a quantum wave packet
• Shadow geometry of Kerr MOG naked singularity and analysis of accretion disk luminosity
• On the role of closed timelike curves and confinement structure around Kerr-Newman singularity
• Looping back to the past through free fall in a controlled warp drive spacetime