Impossibility of superluminal signalling in Minkowski space-time does not rule out causal loops

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. A second is an operational notion of causation that considers the flow of information between physical systems and interventions on them. In [Vilasini and Colbeck, Phys. Rev. A. 106, 032204 (2022)], we propose a framework for characterising when a causal model can coexist with relativistic principles such as no superluminal signalling, while allowing for cyclic and non-classical causal influences and the possibility of causation without signalling. In a theory without superluminal causation, both superluminal signalling and causal loops are not possible in Minkowski space-time. Here we demonstrate that if we only forbid superluminal signalling, superluminal causation remains possible and show the mathematical possibility of causal loops that can be embedded in a Minkowski space-time without leading to superluminal signalling. The existence of such loops in the given space-time could in principle be operationally verified using interventions. This establishes that the physical principle of no superluminal signalling is not by itself sufficient to rule out causal loops between Minkowski space-time events. Interestingly, the conditions required to rule out causal loops in a space-time depend on the dimension. Whether such loops are possible in three spatial dimensions remains an important open question.

4+4 pages. This work is based on the framework of arXiv:2109.12128, which is an update of the relevant parts of VV's PhD thesis arXiv:2102.02393

References in corpus (12)

• Closed timelike curves via post-selection: theory and experimental demonstration
• Theory-independent limits on correlations from generalised Bayesian networks
• Quantum Graphical Models and Belief Propagation
• Inferring causal structure: a quantum advantage
• Quantum Dynamics as an analog of Conditional Probability
• Cyclic Quantum Causal Models
• On Deducing Conditional Independence from d-Separation in Causal Graphs with Feedback (Research Note)
• Markov Properties for Graphical Models with Cycles and Latent Variables
• Unscrambling the omelette of causation and inference: The framework of causal-inferential theories
• Variable Bias Coin Tossing
• A general framework for cyclic and fine-tuned causal models and their compatibility with space-time
• Quantum Causal Networks

Cited by in corpus (9)

• A general framework for cyclic and fine-tuned causal models and their compatibility with space-time
• Embedding cyclic information-theoretic structures in acyclic spacetimes: no-go results for indefinite causality
• Fundamental limits for realising quantum processes in spacetime
• Weak versus deterministic macroscopic realism, and Einstein-Podolsky-Rosen's elements of reality
• A general quantum circuit framework for Extended Wigner's Friend Scenarios: logically and causally consistent reasoning without absolute measurement events
• Mapping indefinite causal order processes to composable quantum protocols in a spacetime
• Forward-backward stochastic simulations: Q-based model for measurement and Bell-nonlocality consistent with weak local realistic premises
• The standard no-signalling constraints in Bell scenarios are neither sufficient nor necessary for preventing superluminal signalling with general interventions
• Monogamy relations for relativistically causal correlations