Jesse Mazer wrote: > Hal Finney wrote: > >Measure is important. It is what guides our life every day. > >We constantly make decisions so as to maximize the measure of good > >outcomes, as nearly as we can judge. I don't think we can neglect it > >in these thought experiments. > > What type of "measure" are you talking about? I had gotten the impression > reading this list that the measure on "everything", however it's > defined--all possible computations, for example--was an open question, and > that different TOEs might disagree.
That's true, but the important point is to consider why we are searching for a measure, or why we even think there might be a measure that is relevant to our experience. The reason is because our own existence is not chaotic, but ordered. Presumably there are observers who see universes that are much more chaotic than ours, universes where there are no natural laws but the observers just manage to hang together somehow. Why do we see a lawful universe? And in our own universe, why do more probable things happen more often than less probable ones? It's not tautological! Remember our discussion of the magical universe where dice always come up "6" but everything else works OK. Why don't we live in one of those universes? The same thing happens in the MWI. If you send almost-vertically- polarized photons through a vertical polarizer then 99 times out of 100 they go through. Each time, the universe splits into two branches. After 100 photons, only one universe in 2^100 of them will see the right statistics. By sheer numbers of universes, almost all of them will see about 50% go through. Why aren't we in one of those universes? The answer to all of these puzzles must be that fundamentally, some universes are more likely to be experienced than others. This is the concept which we refer to as measure. It is a weighting factor that somehow must make some universes more important in the grand scheme of things. You are right that there are many different ideas about how measure works and how it could apply, in both the MWI and in the larger multiverse. But this uncertainty doesn't mean that we can reject or ignore the concept of measure. Its reality is forced upon us by every observation we make. > Are you talking about a type of measure > specific to the MWI of quantum mechanics? I thought there was supposed to be > a problem with this due to the "no preferred basis" problem. The proper manner for incorporating measure into the MWI is indeed an open question at this point. The simplest is to just introduce it ad hoc and define the measure of a branch as the square of its amplitude. Others claim that they can derive this from more elementary and/or obvious assumptions. But it's got to be there. > In any case, if there is some sort of theory that would give objective > truths about first-person probabilities in splitting experiments (and I'm > not sure if you believe in continuity of consciousness or that such a theory > is out there waiting to be found), Well, I do believe in continuity of consciousness, modulo the issues of measure. That is, I think some continuations would be more likely to be experienced than others. For example, if you started up 9 computers each running one copy of me (all running the same program so they stay in sync), and one computer running a different copy of me, my current theory is that I would expect to experience the first version with 90% probability. However I don't see any way at this point to test this model. > then if first-person probabilities > disagree with "measure", however it's defined, I think most people would > care more about maximizing the first-person probabilities of good outcomes > as opposed to measure. Our experiences every day prove that first person probabilities do correspond to measure, but that is because we define measure to correspond to what we experience. That is where the amplitude-squared formula for probability came from in QM; it is there to make theory match experience. > The main reason to care about measure would be for > altruistic reasons, that you don't want friends and families to have a high > probability of suffering because they see you die, but even this could be > stated in terms of maximizing the subjective probability of happy outcomes > for other people. It seems that for QS to be an attractive option, you have to believe that measure applies all the time, except when you die. What is the justification for making an exception, when all the rest of the time you act as if you believe in measure? You would take a good bet rather than a bad bet, but if your death is involved you'll stop caring? Hal