Hm, perhaps I should try to flesh out the parallels in measurement theory between MW and Copenhagen, and see if you agree.
Before measurement is considered, one possible outcome in Copenhagen is exactly identical to one point in world-space in MWI.
And even for the act itself, measurement is measurement. You find the wavefunction of your detector at some time, and this gives you a probability distribution over your Hilbert space, with each point in Hilbert space being one possible outcome/one world.
The difference is in (surprise) interpretation and surrounding procedures. MWI only lets you measure the wavefunction of the entire universe, but in exchange it lets the universe just evolve deterministically. Copenhagen lets you measure small parts of the universe, simplifying many computations, but this 1) often requires the complicated machinery of collapse and entanglement and 2) treats these parts of the universe as real.
Since we don't know the state of the universe, MWI makes predictions by conditioning on the statement of the problem at hand, e.g. "given that the spin of an electron points along x at t=0..." This makes it trickier to talk about "you." The machinery of the Copenhagen interpretation lets us talk about "you" quite easily, you're handled as a part of the universe, and our classical experience translates nicely. But MW makes it a bit harder - the most useful approach I know is to just to construct a hypothetical "you" state, relying on empirical evidence that you have one. But what is the "real you" with known distribution in Hilbert space that gets conditioned on in order to actually predict things? Which points in this very general space still qualify as a possible "you?"
Fortunately, for most applications we can dodge the hard questions by just answering "me from 5 minutes ago" and "everything with reasonable probability is still me." A long series of this simplification gives the familiar image of a tree-ish volume in you-space plus time, all "you" at different times.
But notice that one point in MW's you-space equals one possible you in Copenhagen, just like one point in the Hilbert space of the universe can be either a possible state or a point in world-space. So "you" in MW corresponds to the entire set of possible yous in Copenhagen. Similarly, you in Copenhagen corresponds to one point in you-space.
Surely "you" could tell if you were a spread out function or a single point, right? Well, no. Why not? Because whenever you're measured, what matters are the properties of a single point in you-space, which are identical between MW and Copenhagen, as long as the statement of the problem was the same.
So you cannot tell by any measurement whether you are you(M) or you(C). That's what I meant by "a definition change to "you" that is... totally undetectable."
The question of which of the copies is "you" doesn't define a correct answer
So if you want to go from MWI to Copenhagen, what you do is make a measurement, thus choosing one point from the Hilbert space, and then treat that point as real. So there are no "copies," really, there are only "possible yous that didn't turn out to be you when measured."
A practical albeit fictional application of the philosophical conclusion that free will is compatible with determinism came up today in a discussion about a setting element from the role-playing game Exalted
(5:31:44 PM) Nekira Sudacne: So during the pirmodial war, one Yozi got his fetch killed and he reincarnated as Sachervell, He Who Knows The Shape of Things To Come. And he reincarnated asleep. and he has remained asleep. And the other primordials do all in their power to keep him asleep. and he wants to be asleep.
For you see, for as long as he sleeps, he dreams only of the present. should he awaken, he will see the totaltiy of exsistance, all things past and future exsactly as they will happen. quantumly speaking he will lock the universe into a single shape. All things that happen will happen as he sees them happen and there will be no chance for anyone to change it. effectivly nullifying chance for change. Even he cannot alter his vision for his vision takes into account all attempts to alter it.
And there's a big debate over rather or not this is a game ending thing. Essentially, does predestination negate freewill or not
(5:32:17 PM) Nekira Sudacne: and this is important, because one of the requirements for Exaltation to function is freewill. if Sachervell is able to negate freewill, then Exaltations will cease to function
(5:32:44 PM) Nekira Sudacne: and maddenly enough the game authors are also on the thread arguing because THEY don't agree where to go with it either :)
(5:38:02 PM) rw271828: ah, well I happen to know the answer :-)
(5:39:23 PM) rw271828: one of the most important discoveries of 20th-century mathematics is that in general the behavior of a complex system cannot be predicted -- or rather, there is no easier way to predict it than to run it and see what happens. Note in particular:
(5:39:41 PM) rw271828: 1. This is a mathematical fact, so it applies in all possible universes, including Exalted
(5:40:01 PM) rw271828: 2. Humans and other sentient lifeforms are complex systems in the relevant sense
(5:41:33 PM) rw271828: so if you postulate an entity that can actually see the future (as opposed to just extrapolate what is likely to happen unless something intervenes), the only way to do that is for that entity to run a perfect simulation, a complete copy of the universe
(5:42:50 PM) rw271828: if you're willing to postulate that, well fine, continue the game, and just note that you are running it in the copy the entity is using to make the prediction - the people in the setting still have free will, it is their actions that determine the future, and thus the result of the prediction ^.^
(5:43:04 PM) Nekira Sudacne: Hah. nice one