What makes a causal loop consistent?
Abstract
Causal loops escape paradoxes if they generate valid probabilities under arbitrary independent local interventions. We show that a deterministic classical process is logically consistent if and only if it contains no signaling loops: cyclic signaling is forbidden but cyclic causation is not, allowing indefinite causal order. Logical consistency is then found to hold exactly when the list of events of a process is pairwise exclusive and complete, providing the first event-based, intervention-free, non-recursive characterization of consistent causal loops. Our results repair a previously introduced intervention-free criterion that misses global loops and reveal that what makes deterministic classical communications without causal order consistent is a multipartite form of Specker's principle: if any two of several questions can be answered jointly, so can all of them.
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BibTeX
@misc{dourdent2026what,
title = {{What makes a causal loop consistent?}},
author = {Hippolyte Dourdent and Andreas Leitherer and Emanuel-Cristian Boghiu and Kyrylo Simonov and Ravi Kunjwal and Antonio Acín},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39735},
eprint = {2609.39735},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05791416v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - What makes a causal loop consistent?
AU - Hippolyte Dourdent
AU - Andreas Leitherer
AU - Emanuel-Cristian Boghiu
AU - Kyrylo Simonov
AU - Ravi Kunjwal
AU - Antonio Acín
PY - 2026
DA - 2026/09/30
PB - HAL
DO - 10.48550/arxiv.2609.39735
UR - https://hal.science/hal-05791416v1
AB - Causal loops escape paradoxes if they generate valid probabilities under arbitrary independent local interventions. We show that a deterministic classical process is logically consistent if and only if it contains no signaling loops: cyclic signaling is forbidden but cyclic causation is not, allowing indefinite causal order. Logical consistency is then found to hold exactly when the list of events of a process is pairwise exclusive and complete, providing the first event-based, intervention-free, non-recursive characterization of consistent causal loops. Our results repair a previously introduced intervention-free criterion that misses global loops and reveal that what makes deterministic classical communications without causal order consistent is a multipartite form of Specker's principle: if any two of several questions can be answered jointly, so can all of them.
ER -