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Studies in History and Philosophy of Science Part A

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

Patrícia Kauark-Leite, Romeu Rossi Junior, Pablo L. Saldanha

Published Sep 9, 2026• 0 citations

Abstract

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.

DOI: 10.1016/j.shpsa.2026.102211

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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.

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Explaining observations in terms of causes and effects is central to empirical science. However, correlations between entangled quantum particles seem to defy such an explanation. This implies that some of the fundamental assumptions of causal explanations have to give way. We consider a relaxation of one of these assumptions, Bell's local causality, by allowing outcome dependence: a direct causal influence between the outcomes of measurements of remote parties. We use interventional data from a photonic experiment to bound the strength of this causal influence in a two-party Bell scenario, and observational data from a Bell-type inequality test for the considered models. Our results demonstrate the incompatibility of quantum mechanics with a broad class of nonlocal causal models, which includes Bell-local models as a special case. Recovering a classical causal picture of quantum correlations thus requires an even more radical modification of our classical notion of cause and effect.

Demonstrations of quantum entanglement (QE), which confirm the violation of Bell’s inequality, indicate that under certain conditions action at a distance is possible. This consequence seems to contradict the relativistic principle of causality, which asserts that an effect never precedes its cause, in any reference frame. By analyzing a numerical example of Bell’s experiment with entangled pairs of photons, we show how observers in two inertial reference frames can disagree about the causality relation between two events. One observer claims that event 1 is the cause of event 2, while the other claims that event 1 is the result of event 2. The solution we suggest to the paradox is that in entangled systems, one can find pairs of “entangled events” which have symmetrical causality relations. Each of the events can serve as a cause or as an effect, depending on the frame of reference in which they are observed.

We investigate the role of time ordering in entanglement experiments involving unstable particles, focusing on

\mu^+ \mu^-

pairs produced in a maximally-entangled spin state. We analyse the correlations between measurements performed by two experimenters, Alice (who measures

\mu^-

spin) and Bob (who measures

\mu^+

decay products). Remarkably, the observed correlations persist irrespective of whether Bob's muon decays before or after Alice's spin measurement. We further discuss different interpretations of the same empirical results depending on the observer's reference frame. The findings reinforce the viewpoint that the Copenhagen interpretation of measurement is a mathematical tool rather than a literal account of physical reality.

The existence of a global causal order between events places constraints on the correlations that parties may share. Such 'causal correlations' have been the focus of recent attention, driven by the realization that some extensions of quantum mechanics may violate so-called causal inequalities. In this paper we study causal correlations from an entropic perspective, and we show how to use this framework to derive entropic causal inequalities. We consider two different ways to derive such inequalities. Firstly, we consider a method based on the causal Bayesian networks describing the causal relations between the parties. In contrast to the Bell-nonlocality scenario, where this method has previously been shown to be ineffective, we show that it leads to several interesting entropic causal inequalities. Secondly, we consider an alternative method based on counterfactual variables that has previously been used to derive entropic Bell inequalities. We compare the inequalities obtained via these two methods and discuss their violation by noncausal correlations. As an application of our approach, we derive bounds on the quantity of information—which is more naturally expressed in the entropic framework—that parties can communicate when operating in a definite causal order.