Pruss recently wrote an intriguing post on his blog where he argued that time travel might be possible on the A-theory. I used to disagree (and am not now sure), but I think his post can help clarify why time travel is not possible, to my mind, on the B-theory, if one means by time travel that it is mind-independently true that any subject S traveled through time (away from the present).
He introduces the idea that a necessary condition for time travel is that there be a distinction between internal and external time. He argues that if external time is governed by the A-theory, internal time could still be governed by the B-theory and “there is no more need for these two series to line up than there would be a need for the two series to line up if the external series were a B-series.” I thought this may have been mistaken, since if the A-theory is correct then one’s internal conscious experience of time is constrained by what time it is externally, so that even if somebody’s internal sense of time doesn’t always seem to advance at the rate of time’s flow (whatever that happens to be, assuming that’s a coherent concept) it will always only be able to track what is present. In other words, it is not possible, if A-theory is true of external time, for some mind to be conscious of that which is not objectively present, since what is not objectively present is not real. I cannot be appeared to pastly.
Perhaps one could argue that if one rejected presentism and adopted growing block theory that one could travel backwards to the past because the past, on that A-theoretic view, is as real as is the present (though, then, one could never travel forward in time beyond the ‘present’). I don’t think such a solution allows for time travel since suppose that I want to travel backwards in time from the present t1 to the past t0, before t1 was actual there was no cause of my travelling back to t0, and so if there is no cause then there is no effect. At t0 I will not appear having traveled from the future. But then how could I travel from t1 to t0? This would involve changing the past. However, changing the past is not logically possible, it is a completely incoherent idea. Ergo, etc. Moreover, if one adopted what Pruss has called the moving spotlight view of A-theory (which could take the shape of what Rasmussen and Tallant call ersatz presentism, for example), then one could travel forwards or backwards in time, and there would be no need to be conscious of what time it is. I remain unsure of this solution, but the point is that time travel requires a distinction between internal time and external time.
The B-theory allows for no such distinction. The ‘present’ is not public property, and simply cannot be. Even if some time t1 were present to most or all conscious persons, it would no more, by reason of that, become the external present, than if all monads (assuming Leibniz’ monadology) perceived t1 as present. If the B-theory is true, then all experiences of presentness are incommensurable. In no way could there be an external mind-independent present, and that just is to say that the B-theory doesn’t allow for a mind-independent present.
Perhaps if God experiences time internally A-theoretically, and external time is B-theoretic, one could argue that whatever time is present to God is the preferred reference frame for the present (the external present). However, this would land us with all the problems theists have in the first place with the A-theoretic problems associated with divine temporality (such as that God cannot be simple, cannot be immutable, and so on). I argue, therefore, that this is not a live option. Morever, I fail to see why/how God would/could experience time A-theoretically if the B-theory is true.
In the end, I think any account of time travel on the B-theory has to come down to a phenomenal experience (as I tried to argue here), and just cannot B-theoretically appeal to the distinction of internal and external time.
So it seems to me.