Suppose I find out that tomorrow I will make you a certain promise (maybe God tells me; or maybe I know this by induction, having made you that promise on the second Wednesday of every year for as long as I remember). Moreover, when I think about it, I realize that I can only keep the promise if I do some preparatory work today. What sort of a reason do I have to do the preparatory work today? If I had to do some preparatory work to fulfill a past promise, I would have a reason grounded in the promise--in promising to do something, I become obliged (at least prima facie) to do what it takes to do what was promised. But does this obligation extend backwards in time?
I clearly have some reason to do the preparatory work. I do, after all, have reason to be a keeper of promises. This is, however, a self-interested reason (though the self-interest here is of the unsordid, Aristotelian virtue ethics sort), and is a different kind of reason from the kind of reason I have to keep a promise. I keep a promise to you because I owe it to you, rather than to be a certain kind of person.
Suppose now one of my children makes you a promise, and I know that she will be unable to keep it unless I do something. I then have some reason to do that, and my reason now does concern you. I owe it to you insofar as I am responsible for my children's actions. It seems to me that my reason for doing the preparatory work for keeping my future promise to you is similar to my reason for doing what makes it possible for my child to keep her promise to you. In both cases, the promise is made by someone for whose actions I am responsible. But in both cases, the reason that I have for acting seems different from the reason I have when I have made you a promise in the past.
Does analysis of promises thus show that there is some metaphysical asymmetry of time, with the past metaphysically different from the future? Maybe not. For it may be that promises bind us over the time period over which they are intended to bind us. Promises create consented-to obligations. Typically, when we make a promise, we are not consenting to bind ourselves in the past, because we typically have no way of communicating the fact of the promise to the past. If backwards causation were possible to us, however, then maybe it would not be so absurd to suppose that a promise could pastly bind. Suppose I have a transtemporal communicator. In the morning I come across a note from the future: "Alex: Send George a check for $100 per the promise of February 16, 2043. Best wishes, Alex". Maybe I really would be bound?