In one earlier post, I suggested the principle the basic laws of morality, just like those of physics, should be reference frame invariant. In that post, I offered some examples of the application of this theory, albeit ones that were not of much interest. In a later post, I have offered an application of the principle to the abortion debate, but the principle did not really decide any issue, but simply deepened the discussion. But now I have what is to me a much more interesting pair of applications.
I promise you never to sit on your late wife's favorite bench which happens to be on my front lawn. I thus create an obligation for myself (an amazing power, isn't it, the power to create obligations?). A while later you release me from the promise. Your release destroys the obligation (so a part of my power of promising was a power to give you the power to make the obligation cease to obtain).
But when did these things happen? When did the obligation not to sit on the chair come into existence? When I promised I wouldn't, or only when the promise reached you? And when did the obligation cease? When you said you release me, or only when the release reached me? Of course, if we're speaking face to face, the question is only of theoretical interest—but, still, it is a genuine interest, I think. But what if you live four light-years away, and we speak by radio? Then, did I become bound when I made the promise, or only four years later, when you heard the promise? And did I become released when you uttered the words releasing me from the promise, or only four years later? In such a case, the question is not just of theoretical interest.
It turns out that there is a very natural way to decide this question when we apply invariance, assuming that making promises and releasing from them is a matter of basic laws of morality. Suppose that we said that the obligation comes to exist when you hear my promise. But then the law would not be invariant. For five minutes after I have sent my words to you over the radio, it will be true in some but not all reference frames that you have already received the message. So, it will depend on reference frame whether I may sit on the bench then or not. Invariance will be violated. (Note that it will not help much to say that what is relevant is my reference frame. For extended substances do not in general define a unique reference frame. Besides, if my reference frame matters so much then, absurd, I'll be able to affect when the obligation applies simply by running really fast in some direction or other.)
If, on the other hand, I say that the promise is binding on me as soon as I have made it, then this rule is invariant. For the rule, basically, says that the obligation obtains when I am in the forward light-cone of the promise-making, and this is a reference-frame invariant relationship.
One might think that just as I am bound as soon as I sent the promise, so too am I released as soon as you sent the release. But here things are quite the opposite. For if I were released as soon as you sent the release, invariance would be violated—for, we would have to ask, in which reference frame is the "as soon as" measured. But invariance will obtain if I specify that my obligation ceases as soon as the release gets to me.
So we have a pretty good argument, based on invariance, for when promises come to bind and when we are released from them. The obligations, as it were, exist at the site of the promiser, and hence come to exist when the promiser speaks, and cease to exist when the promisee's release arrives at the promiser. Of course, further questions can be asked—when is the exact moment of sending, for instance. But those questions, I think, do not concern the basic practice of promise making/keeping itself—maybe answers to those questions can be left to custom or the prudent legislator.
Here is a different application. When a legislature passes a law, when does the law become morally binding on me? (I don't care about the question when it becomes legally binding, since only moral normativity matters in the end.) When the law is passed? Or when the law is promulgated? Or when the promulgation arrives? Intuitively, it would seem unfair if I were bound as soon as the law were passed, since I would have no way of knowing about the law as soon as it were passed, and surely the law is to be a guide to my rational deliberation. I think Aquinas makes something like this argument. But it would be nice to have an argument without so much that is controversial. Well, that's easy. The rule that the law is binding morally on me when promulgated violates invariance (imagine that the law is one of the Galactic Empire, and there is no faster than light travel, so it can take years and years to reach me), since we would have to ask: "In which reference frame?" The same problem obtains for the question: "When the law is promulgated?" (e.g., when the legislature radios it out to the subjects). But "When the promulgation arrives to me" is invariant, since it is a question of my being bound.
Now there is a problem with this answer. Generally, it is taken that ignorance of the law is no excuse. So, it seems, I can be bound by laws that were never communicated to me. Three answers are available. The first is that the "ignorance" saying only applies to legal binding—morally, ignorance of positive law is a perfectly fine excuse. The second is to modify my initial formulation: I am bound at the first time at which it was reasonably possible for me to have found out about the legislation had I set my mind to it. This, too, is invariant. The third is to combine the first two answers. Certain basic laws, such as laws proclaiming the constitution of a new nation, only become morally binding when the subjects hear of them. As part of the proclamations of these laws, the subjects hear how and where they can find out about additional laws. But then further laws becoming binding when one can reasonably find out about them. This, too, is invariant.
In any case, the answer "When the legislator makes the law" is not a good one. So we have an argument for Aquinas' thesis that promulgation is essential to the bindingness of a law. Secret treaties do not bind those ignorant of them, at least not morally.
I think it's pretty cool that one can get such fairly specific answers to difficult normative questions simply out of relativity theory. I think one could probably also get similar answers if one had a causal theory of time (whether it was relativistic or not). And that is not a coincidence because I think the relativistic theory of time is, basically, a causal theory of time.