To appear in Chance in Physics: Foundations and Perspectives, edited by

Abstract. It is argued, using a relativistic space-time view of the Universe, that Reichenbach’s “principle of the common cause ” provides a good basis for understanding the time direction of a variety of time-asymmetric physical processes. Most of the mathematical formulation is based on a probabilistic model using classical mechanics, but the extension to quantum mechanics is also considered. 1.1 Does time have a direction? When we speak of “the direction of time ” we are not really saying that time itself has a direction, any more than we would say that space itself has a direction. What we are saying is that the events and processes that take place in time have a direction (i.e. they are not symmetrical under time reversal) and, moreover, that this time direction is the same for all the events. To see the distinction, imagine that you look into a body of water and see some fish all facing in the same (spatial) direction. You would not attribute the directedness of this fish population to any “direction of space”; it would be much more natural, assuming the body of water to be a river, to attribute th