What is the relation beween Granger causality and Rubin's causality? Granger proposed a test for causality based on time series, is there any relation with the notion of causality by Rubin that seems prevalent on applied micro work. The latter deals with the notion of counterfactual and how we can use an experimental set-up to capture the expected value of this parallel world situation to infer about the average effect of the intervention.
In short, not really.  Prof. John Cochrane offers an astute example of Granger causality by stating that a weatherman Granger-causes the weather.  We know that a weatherman has no measurable role in causing the weather, but there is indeed an intertemporal correlation between what the weatherman says today and what happens tomorrow.