Setting aside whatever Sean thinks he's talking about with cross-branch travel, let me refer back to my original description. My point is that based on my current (and somewhat recent) understanding, the "branching fractal tree" perspective on quantum histories is subtly incorrect, and the flaw becomes particularly apparent in the context of time travel.
Essentially, I think that the branching tree concept is based on the idea of locality: that whatever is going to happen next is based on what happens here and now. Locality is absolutely true in some sense, but there are ways in which it's not the whole story. Specifically, you'll never recognize different topological sectors if you only look at local branches, any more than you could deform a clay ball into a doughnut without ever linking two points that weren't touching to begin with.
My claim is that in relativity, a space-time that allows a time traveler is topologically different than one that doesn't (in some sense because time travel would create a closed loop of causality, and closed loops are like doughnuts). So one isn't just a small deformation of the other resulting from a different outcome of a single event: your sum over histories has to include not just local branching on a single tree but also a sum over entirely distinct trees. And each instance of time travel requires its own distinct tree.
That's still viewing time travel as something that happens within a single space-time, though. My issue with the notion of traveling from one branch to another (whether you view that as moving back down a branch of a tree or swapping two branches or whatever else) is that I can't even come up with a way for the idea to make sense on a technical level. (Contrast that with relativity, where I can easily describe a space-time that includes time travel even if understanding it is a challenge.) I think my sense of "history" is tied closely to the space-time manifold picture, while my sense of time in quantum mechanics is simply "unitary evolution" of information. Time travel seems to make more sense in the former picture than the latter.
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Essentially, I think that the branching tree concept is based on the idea of locality: that whatever is going to happen next is based on what happens here and now. Locality is absolutely true in some sense, but there are ways in which it's not the whole story. Specifically, you'll never recognize different topological sectors if you only look at local branches, any more than you could deform a clay ball into a doughnut without ever linking two points that weren't touching to begin with.
My claim is that in relativity, a space-time that allows a time traveler is topologically different than one that doesn't (in some sense because time travel would create a closed loop of causality, and closed loops are like doughnuts). So one isn't just a small deformation of the other resulting from a different outcome of a single event: your sum over histories has to include not just local branching on a single tree but also a sum over entirely distinct trees. And each instance of time travel requires its own distinct tree.
That's still viewing time travel as something that happens within a single space-time, though. My issue with the notion of traveling from one branch to another (whether you view that as moving back down a branch of a tree or swapping two branches or whatever else) is that I can't even come up with a way for the idea to make sense on a technical level. (Contrast that with relativity, where I can easily describe a space-time that includes time travel even if understanding it is a challenge.) I think my sense of "history" is tied closely to the space-time manifold picture, while my sense of time in quantum mechanics is simply "unitary evolution" of information. Time travel seems to make more sense in the former picture than the latter.