I think there’s a subtle but important difference between saying that time travel can be represented by a DAG, and saying that you can compute legal time travel timelines using a DAG.
There’s one possible story you can tell about time turners where the future “actually” affects the past, which is conceptually simple but non-causal.
There’s also a second possible story you can tell about time turners where some process implementing the universe “imagines” a bunch of possible futures and then prunes the ones that aren’t consistent with the time turner rules. This computation is causal, and from the inside it’s indistinguishable from the first story.
But if reality is like the second story, it seems very strange to me that the rules used for imagining and pruning just happen to implement the first story. Why does it keep only the possible futures that look like time travel, if no actual time travel is occurring?
The first story is parsimonious in a way that the second story is not, because it supposes that the rules governing which timelines are allowed to exist are a result of how the timelines are implemented, rather than being an arbitrary restriction applied to a vastly-more-powerful architecture that could in principle have much more permissive rules.
So I think the first story can be criticized for being non-causal, and the second can be criticized for being non-parsimonious, and it’s important to keep them in separate mental buckets so that you don’t accidentally do an equivocation fallacy where you use the second story to defend against the first criticism and the first story to defend against the second.
I think there’s a subtle but important difference between saying that time travel can be represented by a DAG, and saying that you can compute legal time travel timelines using a DAG.
There’s one possible story you can tell about time turners where the future “actually” affects the past, which is conceptually simple but non-causal.
There’s also a second possible story you can tell about time turners where some process implementing the universe “imagines” a bunch of possible futures and then prunes the ones that aren’t consistent with the time turner rules. This computation is causal, and from the inside it’s indistinguishable from the first story.
But if reality is like the second story, it seems very strange to me that the rules used for imagining and pruning just happen to implement the first story. Why does it keep only the possible futures that look like time travel, if no actual time travel is occurring?
The first story is parsimonious in a way that the second story is not, because it supposes that the rules governing which timelines are allowed to exist are a result of how the timelines are implemented, rather than being an arbitrary restriction applied to a vastly-more-powerful architecture that could in principle have much more permissive rules.
So I think the first story can be criticized for being non-causal, and the second can be criticized for being non-parsimonious, and it’s important to keep them in separate mental buckets so that you don’t accidentally do an equivocation fallacy where you use the second story to defend against the first criticism and the first story to defend against the second.