I disagree. You have to recast GR into an initial value problem and then pick a foliation to model interesting physical phenomena, like stellar collapse and black hole collision. Completely independent of any underlying ontology. There is no intent to "sustain A-theory", that's just silly. You want to know how to detect the dying cry of a star torn apart by a supermassive black hole in the center of a galaxy, not whether to pick A or B from some book.
None of these amounts to picking a single foliation and stating, "This (and no other) is the correct foliation of space-time." A-theory requires a single privileged foliation. The fact that we often use foliations when modeling physical phenomena has nothing to do with sustaining A-theory, you're right, but I didn't say that any use of a foliation would have that role.
Are you saying that this A-theory predicts that there is a preferred foliation? By that logic, wouldn't B-theory predict that no foliation is possible at all? Or that all foliations are equal, whether they are timelike, null or spacelike?
No. The B-theory predicts that there is no single preferred foliation. That is not equivalent to saying that no foliation is possible. Nor is it equivalent to saying that all foliations are equal.
This seems like a major category error to me, mixing qualia ("experience of the passage of time") with statistical mechanics. They are about a dozen of abstraction and energy levels removed from each other.
There is, of course, a mystery about how (or even if) particular qualia are produced by physical processes. I don't claim that statistical mechanics can answer that mystery, but that is not a mystery that A-theory claims to answer, either. However, if you grant (as I think you should) that our experience of the passage of time is related to the way in which our brain performs various computations, then stat. mech. becomes immediately relevant, and isn't dozens of levels removed. There is a rich literature applying statistical mechanics to understand constraints on computational processes.
The beauty of stat. mech. methods is that they are not constrained to a particular energy level. They can be applied to understand the behavior of molecules in a gas, but also to understand the behavior of galaxies in a supercluster. In any case, my mention of stat. mech. in this context wasn't just a throwaway. Part of my dissertation was about understanding the experience of time direction (in particular, the fact that cognitive systems record memories in one temporal direction and intervene in the opposite temporal direction) in statistical mechanical terms. I'd be happy to summarize the argument if you'd like, when I have the time.
What requires us to "complicate our best physical understanding of the world", such as recast the beautiful Einstein equation into an ugly ADM form, is the drive to explain and predict what we see or will see.
As I said before, the motivations and consequences of the ADM formalism (at least when applied to obtain numerical solutions to initial value problems) are quite distinct from those of the A-theory. Now it may turn out that in our ultimate theory of quantum gravity, we do have to specify a single preferred foliation of space-time, in which case I will readily admit that this particular objection to A-theory no longer holds. But that just highlights how this debate is responsive to empirical confirmation and disconfirmation.
This was almost verbatim the Hoyle's criticism of the Big Bang model, wasn't it?
Perhaps it was, I don't know. But if it was, then he was wrong, because the criticism certainly doesn't seem to apply to the Big Bang model as we know it. Just because the criticism can be misapplied doesn't mean it's never valid.
Part of my dissertation was about understanding the experience of time direction (in particular, the fact that cognitive systems record memories in one temporal direction and intervene in the opposite temporal direction) in statistical mechanical terms. I'd be happy to summarize the argument if you'd like, when I have the time.
Drool - I would very much like to get a copy of this part of your dissertation, or the whole thing, or a summary, whatever and whenever is convenient to you. I think I sorta get it on an intuitive level, but to fill in more of the physics would be wonderful.
I've always been puzzled by why so many people have such strong intuitions about whether the A-theory or the B-theory1 of time is true. [ETA: I've written "A-theory" and "B-theory" as code for "presentism" and "eternalism", but see the first footnote.] It seems like nothing psychologically important turns on this question. And yet, people often have a very strong intuition supporting one theory over the other. Moreover, this intuition seems to be remarkably primitive. That is, whichever theory you prefer, you probably felt an immediate affinity for that conception of time as soon as you started thinking about time at all. The intuition that time is A-theoretic or B-theoretic seems pre-philosophical, whichever intuition you have. This intuition will then shape your subsequent theoretical speculations about time, rather than vice-verse.
Consider, by way of contrast, intuitions about God. People often have a strong pre-theoretical intuition about whether God exists. But it is easy to imagine how someone could form a strong emotional attachment to the existence of God early in life. Can emotional significance explain why people have deeply felt intuitions about time? It seems like the nature of time should be emotionally neutral2.
Now, strong intuitions about emotionally neutral topics aren't so uncommon. For example, we have strong intuitions about how addition behaves for large integers. But usually, it seems, such intuitions are nearly unanimous and can be attributed to our common biological or cultural heritage. Strong disagreeing intuitions about neutral topics seem rarer.
Speaking for myself, the B-theory has always seemed just obviously true. I can't really make coherent sense out of the A-theory. If I had never encountered the A-theory, the idea that time might work like that would not have occurred to me. Nonetheless, at the risk of being rude, I am going to speculate about how A-theorists got that way. (B-theorists, of course, just follow the evidence ;).)
I wonder if the real psycho-philosophical root of the A-theory is the following. If you feel strongly committed to the A-theory, maybe you are being pushed into that position by two conflicting intuitions about your own personal identity.
Intuition 1: On the one hand, you have a notion of personal identity according to which you are just whatever is accessible to your self-awareness right now, plus maybe whatever metaphysical "supporting machinery" allows you to have this kind of self-awareness.
Intuition 2: On the other hand, you feel that you must identify yourself, in some sense, with you-tomorrow. Otherwise, you can give no "rational" account of the particular way in which you care about and feel responsible for this particular tomorrow-person, as opposed to Brittany-Spears-tomorrow, say.
But now you have a problem. It seems that if you take this second intuition seriously, then the first intuition implies that the experiences of you-tomorrow should be accessible to you-now. Obviously, this is not the case. You-tomorrow will have some particular contents of self-awareness, but those contents aren't accessible to you-now. Indeed, entirely different contents completely fill your awareness now — contents which will not be accessible in this direct and immediate way to you-tomorrow.
So, to hold onto both intuitions, you must somehow block the inference made in the previous paragraph. One way to do this is to go through the following sequence:
One potential problem with this psychological explanation is that it doesn't explain the significance of "becoming". Some A-theorists report that a particular basic experience of "becoming" is the immediate reason for their attachment to the A-theory. But the story above doesn't really have anything to do with "becoming", at least not obviously. (This is because I can't make heads or tails of "becoming".)
Second, intuitions about time, even in their primitive pre-reflective state, are intuitions about everything in time. Yet the story above is exclusively about oneself in time. It seems that it would require something more to pass from intuitions about oneself in time to intuitions about how the entire universe is in time.
1 [ETA: In this post, I use the words "A-theory" and "B-theory" as a sloppy shorthand for "presentism" and "eternalism", respectively. The point is that these are theories of ontology ("Does the future exist?"), and not just theories about how we should talk about time. This shouldn't seem like merely a semantic or vacuous dispute unless, as in certain caricatures of logical positivism, you think that the question of whether X exists is always just the question of whether X can be directly experienced.]
2 Some people do seem to be attached to the A-theory because they think that the B-theory takes away their free will by implying that what they will choose is already the case right now. This might explain the emotional significance of the A-theory of time for some people. But many A-theorists are happy to grant, say, that God already knows what they will do. I'm trying to understand those A-theorists who aren't bothered by the implications of the B-theory for free will.