Counterfactual Local Friendliness: An epsilon-Bounded Interaction-Free Paradox and a Disturbance-Robust Three-Box Inequality

• URL: http://arxiv.org/abs/2509.01290v1
• Date: Mon, 01 Sep 2025 09:19:34 GMT
• Title: Counterfactual Local Friendliness: An epsilon-Bounded Interaction-Free Paradox and a Disturbance-Robust Three-Box Inequality
• Authors: Maximilian Ralph Peter von Liechtenstein,
• Abstract summary: We show a Wigner's-friend-type logical collision in which every decisive inference is obtained by interaction-free flags.<n>Under (Q) universal unitarity for outside observers, (S) single-outcome facts, (C) cross-agent consistency, and (IF-$epsilon$) $epsilon$-counterfactuality of the friends' internal modules.<n>We also derive an $epsilon$-IF three-box noncontextual bound: any single-world, noncontextual model satisfying exclusivity must obey $P(A) + P(B)
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a new paradox, which we call Counterfactual Local Friendliness (CLF): a Wigner's-friend-type logical collision in which every decisive inference is obtained by interaction-free flags whose disturbance on the probed object is bounded by a tunable parameter $\epsilon$. Under (Q) universal unitarity for outside observers, (S) single-outcome facts, (C) cross-agent consistency, and (IF-$\epsilon$) $\epsilon$-counterfactuality of the friends' internal modules, quantum theory predicts a nonzero post-selected event that forces mutually incompatible certainties about a single upstream variable -- without appealing to absorptive or projective in-lab measurements. We also derive an $\epsilon$-IF three-box noncontextual bound: any single-world, noncontextual model satisfying exclusivity and epsilon-stability must obey $P(A) + P(B) \le 1 + K_\epsilon$, while quantum theory yields $P(A) = P(B) = 1$, violating the bound for arbitrarily small $\epsilon$. Together these results isolate what is paradoxical about counterfactual phenomena: not energy exchange with the probed system, but the incompatibility of agent-level facts in single-world narratives.

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