Impossibility of Superluminal Signaling in Minkowski Spacetime Does Not Rule Out Causal Loops

Area of Science:

• Theoretical Physics
• Quantum Information Theory
• Spacetime Physics

Background:

• Causality is a fundamental concept in science, with relativistic causality forbidding signaling outside the future.
• Operational causality considers information flow and interventions on physical systems.
• Previous work explored cyclic causal models compatible with spacetime principles.

Purpose of the Study:

• To investigate the coexistence of causal models with relativistic principles, specifically focusing on superluminal signaling and causal loops.
• To determine if forbidding superluminal signaling is sufficient to prevent causal loops in Minkowski spacetime.
• To explore the possibility of cyclic causal influences and causation without signaling.

Main Methods:

• Developed a general framework for characterizing causal models and their compatibility with spacetime.
• Analyzed the implications of forbidding only superluminal signaling, not superluminal causation.
• Investigated the mathematical possibility of embedding causal loops within Minkowski spacetime.

Main Results:

• Demonstrated that superluminal causation remains possible even when superluminal signaling is forbidden.
• Showed the mathematical possibility of causal loops in Minkowski spacetime that do not involve superluminal signaling.
• Established that the principle of no superluminal signaling alone is insufficient to rule out causal loops.

Conclusions:

• The absence of superluminal signaling does not inherently prevent causal loops in Minkowski spacetime.
• The possibility of causal loops is dependent on spacetime dimensionality, with three spatial dimensions presenting an open question.
• Operational verification of causal loops using interventions is theoretically possible.