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.”
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.”
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.”