"The problem of the arrow of time owes its origin to the intuitive asymmetry between past and future. We experience the time order of the world as “directed”: if two events are not simultaneous, then one of them is earlier than the other one. Moreover, we view our access to past and future quite differently: we remember the past and predict the future. The problem of the arrow of time arises when we seek a physical correlate of this intuitive asymmetry: does physics pick out a preferred sense of time?

The main difficulty to be encountered in answering this question lies in our anthropocentric perspective: the difference between past and future is so deeply rooted in our language and our thoughts that it is very difficult to shake off these asymmetric assumptions. In fact, philosophical discussions around the question are usually subsumed under the label “the problem of the direction of time”, as if we could find an exclusively physical criterion for singling out the direction of time, identified with what we call “the future”. But there is nothing in physics that distinguishes, in a non-arbitrary way, between past and future as we conceive them. It might be objected that physics implicitly assumes this distinction with the use of asymmetric temporal expressions, like “future light cone”, “initial conditions”, “increasing time”, and so on. However this is not the case, and the reason can be understood in simple conceptual terms.

Two entities are formally identical when there is a symmetry transformation between them that does not change the properties of the system to which they belong or in whose description they are involved. In physics it is usual to work with formally identical entities: the two lobes of a light cone, the two spin senses, etc. When we call two formally identical entities by different names, we are establishing a conventional difference between them; this is the case, for instance, when we call the two lobes of a light cone “past lobe” and “future lobe”, or the two spin senses “up” and “down”. By contrast, the difference between two entities is substantial when they are not formally identical: we assign different names to them in virtue of such a difference. When asymmetric temporal expressions appear in the discourse of fundamental physics, they are used in a completely conventional way: if we exchanged each of them for its symmetric correlate, the resulting discourse would be indistinguishable from the original one, at least to the extent that the “directionality” of time is not introduced from the outside, that is, from our natural language.

Once this point is accepted, the problem cannot yet be posed in terms of singling out the future direction of time: the problem of the arrow of time becomes the problem of how to find a temporal asymmetry only grounded on physical arguments. But if this is our central problem, we cannot project our independent intuitions about past and future for solving it without begging the question. In spite of the fact that these observations are simple, they are usually ignored in the philosophical discussions. This is particularly evident in the widespread reductionistic attitude regarding the arrow of time, whose ambition consists in identifying or reducing the relation of temporal priority to some lawlike or de facto feature of the physical world: it is supposed that there is a non-temporal asymmetric relation R between events such that R(e1, e2) holds iff E(e1, e2) holds, where E is the temporal relation “is earlier than”. For some reductionists, the connection between R and E is a lawlike association. For others, the connection between R and E has a definitional nature. Nevertheless, both approaches rely on assuming our previous intuitions about what “earlier” means."