When considering possible continuations of "observer-moments", one speaks of dividing one's measure among them such that any succeeding observer-moment has a relative proportion consistent with the quantum amplitude of its wave function. (Or something like that.)

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My first question is: Can this go on indefinitely? Based on my understanding of MWI, the answer is yes, but I haven't seen this addressed before. I think another way to ask this is, can the amplitude of a wave function ever go to zero for all values of it's dependent variable? (Forgive me if this is an ill-formed question, I'm still sorting out in my own mind what I'm trying to figure out.) Secondly, there are value-judgment arguments made here on the list about the desirability of taking certain actions based on the anticipated observer-measure that would result from them, such as implied by Lee Corbin's recent comment: > Not sure I entirely understand, but it seems to me that we survive in > "Harry potter like universes", but only get very little runtime there > (i.e. have very low measure in those). I can understand the argument that one's present expectation value of an possible outcome is related to the proportion of one's measure that would continue in that "branch" of the wave function. But here is where my first question has implications--if "measure" has some finite lower bound, then eventually, all roads lead to zero at some point. An observer would have a strong motivation to take actions which maximize one's future measure "integral", to stave off this impending non-existence as long as possible. If, on the other hand, measure is infinitely divisible, then there will always be a branch that will continue. Finally, here's my second question: Does being in a "low" measure branch somehow "feel different" from being in a "high" measure branch? To take the canonical example, let's say one is next to that 20 megaton H-Bomb when it detonates. In one branch, with a very very tiny fraction of one's current measure, one will find himself magically tunneled and reformed somewhere away from the danger. The expectation value of this happening, of course is tiny, but is non-zero, so it does happen somewhere in the multiverse. Now, finding oneself, after the fact, having survived the blast by quantum tunneling, one realizes one is in a low measure branch of his wave function. But does it really matter? If measure is infinitely divisible, I don't think it does. But if measure can "run out", then I've just brought that point in time much closer. (Of course, one could then also argue that the quantum amplitude of surviving the blast would likely fall below this threshold, so there would be no continuer at all.) I've seen references to something called the "no cul-de-sac theorem", which sounds like what I'm talking about, but I can't seem to find out more about it in Google or Wikipedia. I also think what I've been discussing is related to the RSSA and ASSA concepts, but I don't understand those well enough. I think I've been assuming RSSA here in my argument though. Thoughts? -Johnathan

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