David Deutsch (1991), Physical Review D 44(10), 3197–3217 — DOI-10.1103/PhysRevD.44.3197
Key takeaways
Filed, not read. Known here by what it is standardly cited for, and by how A161 uses it.
- A quantum system that interacts with a copy of itself on a closed timelike curve is required to be self-consistent as a density matrix: the state on the loop is a fixed point of the map the interaction induces on it.
- Such a fixed point always exists, so the grandfather paradox has no quantum counterpart in this model. Its classical shadow is the negation loop: x = ¬x has no solution in {0,1}, but p ↦ 1 − p has the fixed point p = ½. A161 gives exactly this: “A distributional fixed point exists even though no deterministic fixed point exists.”
Standing in the record
Registered on 2026-10-10 to ground CLAIM-141, which contrasts causal-loop consistency with sheaf contextuality: passing to distributions creates a fixed point for the first and gives no global distribution for the second. See the curation entry of that day.
Deferred because it is not read. Two things a reading should check:
- whether the paper states existence for every finite-dimensional system and every interaction, as the record assumes from the Brouwer-type argument, and what it says about uniqueness, which is the open issue;
- how it relates its condition to the classical consistency condition of Friedman et al. 1990 (doi:10.1103/PhysRevD.42.1915, not held), which A161 cites beside it.
Lloyd et al.’s post-selected closed timelike curves (arXiv:1005.2219, not held) are a rival model that treats the grandfather paradox differently. The record does not take Deutsch’s model to be the physics of closed timelike curves; it uses only its fixed-point condition, as a contrast.