You could put something sorta like a Time Turner in MWI. But I don’t see any way to do it that would reliably result in consistent time-loops, as opposed to people observing different results in their second pass than they remember from the first.
You sure can! It’s a bit hard on the complexity, but probably less so than spontaneous collapse.
there are a bunch of different versions, the most obvious (but not only) class consists of proceeding the simulation as if time travel didn’t exist then pruning paradoxical branches retroactively. There’s tweaks and hacks needed to figure out how that actually works with interference, and to fix the problem of any branch where time travel is invented at all losing all it’s measure in effect acting as a probability pump preventing it, but you’re smarter than me and can probably work out better versions.
Can’t you have mixed states that are stable or at least self-consistent? Something like there’s a 50% chance you go back and kill your grandfather and there’s then a 50% chance you don’t exist? I seem to remember David Deutsch discussing something similar at one point.
You can if nearby Everett branches reinforce each other and ‘bleed over’ into each other. Then you wind up with a bifurcation diagram, with each path’s “weight” based on the number of other paths that are close/similar enough to reinforce it, and some paths can converge into the internal appearance of a stable time loop.
It may be better to put it like this: “if there are many worlds, then time travel would generally create loops across worlds; it does not force consistency within a single world”.
However, if the Source of Magic is careful how it sets up the loops, it can force a consistent outcome, or at least force one of the consistent outcomes to become much more probable than any inconsistent outcome (one which loops between worlds). In particular this still allows any NP problem, or indeed any PSPACE problem, to be solved in polynomial time using tricks like Harry’s factorisation attempt (though perhaps with a small probability of failure). See Scott Aaranson’s wonderful lecture here.
So the fact that Harry always observes a consistent single-world loop doesn’t by itself imply a single world interpretation, or any non-computability. It simply means that the Source of Magic is a PSPACE oracle!
I think a simulation (Y) is a process of mimicking something else (X). In which case we should not observe in Y something (Z) that couldn’t happen in X.
So maybe we should rather say that Y is a game with otherwise X-like rules, but additional rules that allow Z, rather than calling it simulation. Or at least I think if “simulation” Y is not an accurate simulation of X, we should use some explicit qualifier to indicate its non-accuracy.
I might be missing something obvious, but I don’t think it implies single world quantum mechanics. It certainly makes it messier thou.
You could put something sorta like a Time Turner in MWI. But I don’t see any way to do it that would reliably result in consistent time-loops, as opposed to people observing different results in their second pass than they remember from the first.
You can’t have a “stable time loop” without a single future.
You sure can! It’s a bit hard on the complexity, but probably less so than spontaneous collapse.
there are a bunch of different versions, the most obvious (but not only) class consists of proceeding the simulation as if time travel didn’t exist then pruning paradoxical branches retroactively. There’s tweaks and hacks needed to figure out how that actually works with interference, and to fix the problem of any branch where time travel is invented at all losing all it’s measure in effect acting as a probability pump preventing it, but you’re smarter than me and can probably work out better versions.
Just think about it for 5 minutes. ;p
Can’t you have mixed states that are stable or at least self-consistent? Something like there’s a 50% chance you go back and kill your grandfather and there’s then a 50% chance you don’t exist? I seem to remember David Deutsch discussing something similar at one point.
Yes, but that’s not a “stable time loop” as portrayed in either cannon or MoR.
You can if nearby Everett branches reinforce each other and ‘bleed over’ into each other. Then you wind up with a bifurcation diagram, with each path’s “weight” based on the number of other paths that are close/similar enough to reinforce it, and some paths can converge into the internal appearance of a stable time loop.
It may be better to put it like this: “if there are many worlds, then time travel would generally create loops across worlds; it does not force consistency within a single world”.
However, if the Source of Magic is careful how it sets up the loops, it can force a consistent outcome, or at least force one of the consistent outcomes to become much more probable than any inconsistent outcome (one which loops between worlds). In particular this still allows any NP problem, or indeed any PSPACE problem, to be solved in polynomial time using tricks like Harry’s factorisation attempt (though perhaps with a small probability of failure). See Scott Aaranson’s wonderful lecture here.
So the fact that Harry always observes a consistent single-world loop doesn’t by itself imply a single world interpretation, or any non-computability. It simply means that the Source of Magic is a PSPACE oracle!
As soon as I saw the stable time loop in HPMOR, I thought, “Oh, they’re all in a simulation.”
I think a simulation (Y) is a process of mimicking something else (X). In which case we should not observe in Y something (Z) that couldn’t happen in X.
So maybe we should rather say that Y is a game with otherwise X-like rules, but additional rules that allow Z, rather than calling it simulation. Or at least I think if “simulation” Y is not an accurate simulation of X, we should use some explicit qualifier to indicate its non-accuracy.