Frame-dependent causal structures compatible with independent settings and no-retrocausality

Determine whether empirically adequate frame-indexed causal models of the Bell scenario can satisfy Independent Settings and No-Retrocausality while allowing arbitrary frame dependence of the causal structure.

Background

The main no-go theorems exclude empirically adequate frame-indexed causal models under particular invariance assumptions on causal structure, namely Causal Lorentz Invariance or Lorentz Invariance of Causal Connections. Appendix C considers the remaining possibility in which causal structures may vary arbitrarily between reference frames and no invariance assumption is imposed. The appendix subsequently shows that adding Independent Explanation and Cross-Frame Measurement Independence forces determinism and recovers Gisin’s original obstruction, but the broader possibility is explicitly identified as one left open by the main part of the paper.