causality and time ordering

I had a nice chat with David Blei (Columbia) at the end of the day about the question of whether causal inference (a subject in statistics) can be re-phrased in terms of making predictions about the time-ordering of events. He was not extremely positive about that project! But we talked about the causal-inference approaches. I don't like many of them! Because many of them somehow assume that it is possible to intervene on the situation, and how can you intervene on a unitary system (like, say, the Universe)? Does causality not exist in physics? Does the force cause the acceleration or does the acceleration cause the force? There isn't an answer to that in physics.