Special relativity and the A-theory

I've been thinking about (Special) Relativity Theory and the A-theory of time. The A-theory of time requires an absolute simultaneity. Relativity theory seems to deny an absolute simultaneity.

But need it? Why not instead say this? Relativity theory never even talks about simultaneity. It talks about a different relation: simultaneity relative to a frame. Likewise, relativity theory never talks about spatial or temporal distances. It talks about spatial or temporal distances relative to a frame. These are different concepts: simultaneity, spatial distance and temporal distance are binary relations. Simultaneity relative to a frame, spatial distance relative to a frame and temporal distnace relative to a frame are ternary relations (the frame is a relatum). All the stuff Relativity says about simultaneity relative to a frame, spatial distance relative to a frame and temporal distnace relative to a frame may very well be true. But the A-theorist need not worry at all about this, because that's not what she is talking about.

But wouldn't it follow, then, that contrary to relativity theory there is a privileged reference frame? There are two questions here: (a) Does it follow that there is a privileged reference frame? (b) Would this be contrary to relativity theory? And neither question has a clearly positive answer.

The standard answer to (a) is this. If we have absolute simultaneity and a Minkowski spacetime, then we can define a privileged frame as the inertial frame whose simultaneity relation matches the absolute simultaneity relation. But nothing that was said so far guarantees that any inertial frame has a simultaneity relation that matches our absolute simultaneity relation. Suppose, for instance, that there are two points, a and b, that are absolutely simultaneous but where b is in the forward light-cone of a. Then not only will there be no inertial frame according to which a and b are simultaneous, but there won't be any foliation by spacelike hypersurfaces (which I guess could be our General Relativistic version of a reference frame) according to which they are simultaneous. Granted, that would be weird. But so far nothing has ruled this out. To get a positive answer to (a) we would need a posit that bridges between metaphysics and physics, namely that the absolute simultaneity relation agrees with the simultaneity relation of some frame.

What about (b)? Is it contrary to Relativity for there to be a privileged reference frame? It surely depends on the way in which the frame is privileged. Suppose, for instance, that earth is the only inhabited planet in the universe. Then the reference frame of the earth is privileged as the reference frame of the reference frame of the only inhabited planet in the universe. While earth may not be the only inhabited planet in the universe, it is no business of Relativity Theory to decide that question. So it had better not be contrary to Relativity for one reference frame to be privileged in this way.

Now, it is essential to Einstein's project that no reference frame be privileged with respect to the fundamental laws of nature. But I don't see that the A-theorist need hold anything that implies some reference frame is privileged in this way. The fundamental laws of motion, perhaps, talk only about what moves relative to reference frames, and say nothing about what moves simpliciter.

If the answer to (a) is positive, then presumably our A-theorist should hold that there is no metaphysically privileged reference frame. But Einstein's Principle of Relativity appears to be a (second-order) law of physics rather than a law of metaphysics. Why should we read it as denying a metaphysically privileged frame? Granted, Einstein so read it. But did he have reason to assert such a strengthened Principle?

All that said, while there is no incoherence between the A-theory and Relativity Theory, I think there is a plausibilistic argument from Relativity against the A-theory. On any sensible A-theory, the events that appear commonsensically simultaneous are at least approximately simultaneous, and the events that appear commonsensically far from simultaneous are not simultaneous. Moreover, our normal commonsensical measurements of distance (with meter sticks) and time (with clocks) had better approximately match up with the correct absolute distance and absolute time measurements. Now, these ordinary life judgments and measurements match up with those provided by our Relativistic science, relative to some reasonable reference frame. Such a match would be a surprising and vast coincidence if there were no deeper connection between absolute simultaneity, distance and time and simultaneity, distance and time according to a frame.

So, it seems that if we are to have a sensible A-theory, we will want to say that there is some frame whose simultaneity relation at least approximately matches absolute simultaneity, and likewise for temporal and spatial difference. But this sort of global coincidence is precisely the sort of thing for laws of nature to explain. So our sensible A-theorist should have fundamental laws of nature that entail that there is a frame whose simultaneity and distance relations approximately match the absolute ones. But these laws will violate Einstein's strictures against the laws not privileging a frame. For such laws privilege those frames whose relativized relations approximately match the absolute ones over those frames where this does not happen. And so such laws are improbable by Einstein's inductive argument for the Principle of Relativity.

There is also a perhaps more direct argument. On the supposition that there is an absolute simultaneity relation, it is surprising that frames whose simultaneity relation do and do not match are treated equally in the laws of motion. On the supposition that there is no such simultaneity relation, there is no surprise there. So, the laws of motion favor there not being an absolute simultaneity relation in a familiar Bayesian way.