  Explaining observations in terms of causes and effects is central to all of
empirical science. Correlations between entangled quantum particles, however,
seem to defy such an explanation. To recover a causal picture in this case,
some of the fundamental assumptions of causal explanations have to give way.
Here we consider a broad class of models where one of these assumptions, Bell's
local causality, is relaxed by allowing a direct influence from one measurement
outcome to the other. We use interventional and observational data from a
photonic experiment to bound the strength of this causal influence in a
two-party Bell scenario and test a novel Bell-type inequality for the
considered models. Our results demonstrate the incompatibility of quantum
mechanics with an important class of nonlocal causal models, which includes
Bell's original model as a special case. Recovering a classical causal picture
of quantum correlations thus requires an even more counter-intuitive
modification of our classical notion of cause and effect.
