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.
This is indeed the standard thought, but be careful not to make a mountain out of a molehill.
"You'll never actually die" only holds if you define "you" to be "you who doesn't die." If you include "you who does die" as also you, then you do die! In short, both the mind-blowing and confusifying powers of quantum immortality are related to the fact that it is a tautology in disguise. It's a question of definitions and not a property of the universe because the universe doesn't really care whether you're alive or dead; dead bodies make great quantum observers, they interact with their environment just fine. But we choose to divide up the possible universes into "us alive" and "us dead," and then only look at what happens in one of those groups, making the answer predetermined by our fairly arbitrary choice of which universes to look at.
The standard response to that fact is "yes, but we choose to care about the universes where we live for a very special reason: you can't think about yourself being dead when you're dead. Cogito ergo sum."
And then I would say: "This is true, but just be careful. Though by definition we won't perceive ourselves as dead, that doesn't mean we can't die, unless we redefine 'we.' Pronouns beyond here become confusing; for a clearer view try to think of things following fuzzy worldlines in spacetime, with events being points in spacetime."
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To make quantum immortality not confusing is to make the mountain back into a molehill, relatively speaking at least. "The big complicated space that we exist in can be thought of like parallel universes, and in some of those parallel universes you'll live forever." Cool!