Sebastian:
I see your point that given the atoms are what they are, they are 'the same person', but can't get around the sense that it still matters on some level.
What if cryonics were phrased as the ability to create an identical twin from your brain at some point in the future, rather than 'you' waking up. If all versions of people are the same, this distinction should be immaterial. But do you think it would have the same appeal to people?
Suppose you do a cryogenics brain scan and create a second version of yourself while you're still alive. Each twin might feel strong regard for the other, but there's no way they would actually be completely indifferent between pain for themselves and pain for their twin. They share a past up to a certain point, and were identical when created, but that's it. If another 'me' were created on mars and then got a bullet in the head, this would be sad, but no more so than any other death. It wouldn't feel like a life-extending boon when he was created, nor a horrible blow to my immortality when he was destroyed. How is cryogenics different from this?
I can understand why creating a reconstruction of a frozen brain might still be considered 'you'. But what happens if multiple versions of 'you' are created? Are they all still 'you'? If I create 4 reconstructions of a brain and put them in four different bodies, punching one in the arm will not create nerve impulses in the other three. And the punched brain will begin to think different thoughts ('who is this jerk punching me?').
In that case, all 4 brains started as 'you', but will not experience the same subsequent thoughts, and will be as disconnected from each other as identical twins.
This is basically the first Parfit example, which I note you don't actually address. Is the 'you' on mars the same as 'you' on Earth? And what exactly does that mean if the 'you' on earth doesn't get to experience the other one's sensations first hand? Why should I care chat happens to him/me?
I can think of a few reasons why you would do this, although I'm not sure which one you had in mind.
Primarily, it's to evaluate the extent to which we commenters accept what you say on face value, particularly when we're not well informed to begin with. I don't mean picking at the specifics of examples, but whether we're evaluating what you're saying for internal consistency between posts.
For instance, the 'many worlds' argument you've presented DOES seem more plausible that collapse, but it certainly still seems mysterious. Having universes sprouting in all directions is bad enough, but something like 'mangled worlds' whereby there are arbitrary cutoffs that make a world disappear is even worse. It may be an improvement, but it sure doesn't feel like the final word, even though it's presented as such.
I think this in part gets to the heart of why the mistake was unspotted for so long. Because Bohr and Shrodinger and the rest said that collapse was what was going on, and people tend to take these things on face value. Who wants to be the first guy to publicly disagree with Bohr? We didn't have 30 years of physicists forming bad judgments, we had a couple of early physicists with bad judgments and 30 years of people taking their word on face value because they didn't understand the problem exactly themselves.
Sebastian:
Take this as a further question. One of the key distinctions between the 'you you' and the 'identical twin you' is the types of sacrifice I'll make for each one. Notwithstanding that I can't tell you why I'm still the same person when I wake up tomorrow, I'll sacrifice for my future self in ways that I won't for an atom-exact identical twin.
If you truly believe that 'the same atoms means its 'you' in every sense', suppose I'm going to scan you and create an identical copy of you on mars. Would you immediately transfer half your life savings to a bank account only accessible from mars? What if I did this a hundred times? If the same atoms make it the same person, why wouldn't you?
And if you don't really have the same regard for a 'copy' of yourself while you're still alive, why should this change when the original brain stays cryogenically frozen and a copy is created?