Block Universe Ontological Models: A Framework for Realist Accounts of Quantum Theory That Allows for Retrocausality*

In light of Bell's theorem, it has been suggested that one way of maintaining locality is to violate the measurement independence assumption, i.e. to allow the hidden variables to depend on the choice of measurement settings. This is variously viewed as retrocausality, superdeterminism, or a violation of free choice. However, when we drop measurement independence, it is not clear that the other assumption of Bell's theorem - local causality - still captures the intended sense of locality. I will argue that it does not and that, in this context, it needs to be upgraded to a stronger assumption called Λ-mediation. I derive how probabilities should decompose in a model that satisfies Λ-mediation, but not measurement independence, and show that such models can reproduce the correlations in a Bell experiment. The Λ-mediation assumption can be generalized to arbitrary causal structures, and the corresponding decomposition of probabilities can be derived, leading to a graphical model that has some similarities to Markov Networks and Factor Graphs.