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

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.