Statistical formulation of no-retrocausality in ontological models

Develop a reasonable statistical formulation of no-retrocausality for probabilistic ontological models that captures the prohibition of influence from the future to the past without introducing the incompatibilities identified for genuinely stochastic theories.

Background

The paper examines attempts to extend Gisin’s deterministic argument to probabilistic ontological models. It argues that a naive conditional-independence formulation of probabilistic no-retrocausality is too restrictive for genuinely stochastic dynamics, while a more sophisticated formulation is too weak to derive Bell locality. The unresolved issue is therefore how to formulate no-retrocausality statistically in a way that is both physically reasonable and useful for a probabilistic generalization of Gisin’s argument.

References

The difficulty lies in the fact that it is not clear how the condition of no-retrocausality can be formulated in a reasonable way using only statistical notions.

— Gisin's Argument and the Limits of Causal Explanations in Relativistic Spacetime  (2608.18010 - Rutzinger, 18 Aug 2026) in Section III.B, Ontological Models

However, the inclusion of measurements in the SLGF description is distinctly artificial. Given that measurement devices are also physical systems, how can the outcomes O, which presumably merely reflect possible events involving the internal variables U of the measurement device, behave so differently? In particular, how can lenient causality be brought about in a detailed model of a detector, with signal causality for the outcome coexisting with future-input dependence for the internal variables? This problem will be tackled in a sequel to the present work.

— Ontic and epistemic states in the theory of spacetime-local beables  (2609.00848 - Argaman, 1 Sep 2026) in Section 4, subsection “Conclusions”