Relative causal order in Grete Hermann's retrodictive causality applied to Bell's inequalities violation.

In 1935, Grete Hermann proposed a way to conciliate causality and quantum mechanics, detaching causality from determinism. In her view, a causal explanation for quantum phenomena can be inferred in a retrodictive way, after the corresponding measurements were performed, and verified via the obtained (non-deterministic) predictions for the future behavior of the system. Here we discuss the violation of Bell's inequalities, where pairs of entangled particles are measured by two parties named Alice and Bob in spacelike intervals, in view of retrodictive causality. We concluded that the causal order of the events is relative to the observer. For some observers, Alice's measurement occurs first and, combined with the physical laws that govern the production of the entangled state, can be retrodictively considered as an explanatory cause, though not a real cause, of Bob's observations. But for other observers, Bob's measurement occurs first and can be considered as an explanatory cause for Alice's observations. So, which event is the explanatory cause and which one is its consequence depends on the observer. But this odd conclusion does not conflict with Hermann's view, since for her the causal law is epistemic rather than ontological. We illustrate these ideas describing the quantum correlations between two spin-1/2 particles, when these particles are produced by the decay of a spin-0 particle, and the polarization quantum correlations of photons generated by parametric downconversion.