# Is 'Measure' infinitely divisible?

```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.)```
```
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.)

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

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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