Jeremy and I pretty much share our philosophy of time, the so-called "consistent" theory of time I think it is called. As much as I like this theory and hold it to be true, there is one Achilles' heel to it that I can see. Imagine the following scenario:
In 2002, Alice receives a present from Bob. The present is a watch or some other suitably complex object that must have been man-made. Alice goes back in time to 2001. She meets Bob at some point and gives him the watch.
Dilemma: who made the watch? Notice that the watch only exists from the years 2001-2002. That's spontaneous creation and destruction of matter (which might be OK on quantum scales with elemental particles, but is not so OK large, complex items).
With the "consistent theory" of time, there is no praticular reason why such a scenario could not arise. ("Branching theories" can sweep this kind of problem under the rug along with any other "inconsistencies" that go along with personal timelines trumping world timelines.) My only out seems to be that time travel (in the backwards direction) is not possible.
[Edited to swtich names around so that the example makes sense now. Kudos to Jonathan for catching the mistake.]