I had an incredibly frustrating conversation this morning trying to explain the idea of quantum immortality to someone whose understanding of MWI begins and ends at pop sci fi movies. I think I've identified the main issue that I wasn't covering in enough depth (continuity of identity between near-identical realities) but I was wondering whether anyone has ever faced this problem before, and whether anyone has (or knows where to find) a canned 5 minute explanation of it.
You think of your life as a branching tree of possibilities rather than a single line in time. And the immortality is supposed to happen because according to MWI, every possibility, no matter how improbable, actually happens, so there's always a branch of the tree that keeps growing - a possibility where the cancer goes away by itself, the bullet goes astray, and so on.
One possible attitude to quantum immortality would be that no matter what happens to you, there's always another copy of you who survives. But it seems that people who are really into quantum immortality want to identify with their copies - they have decided to think of the whole tree of possibilities as themselves, and not just the current branch. Wikipedia puts it like this: "Over time, the experimenter would therefore never perceive his or her own death." That's a little retarded, because if you're going to identify with the whole tree of possibilities, then you should identify with every death. So "quantum immortality" actually means that you die infinitely many times and in every possible way, but there's no final death.