On 10 April 2015 at 13:17, Bruce Kellett <[email protected]> wrote:
> I thought I had explained that. But there is a problem about how > probabilities are determined that might make it clearer. I haven't found a > clear account of this from Bruno, but the following from a discussion of > Step 3 in his 2013 paper might be relevant. > > He is talking about the fact that duplication leads to FPI. "Likewise, it > is easy to see that if such a self-duplication experiment is iterated, say > n times, the majority of the 2n reconstituted people will be unable to > compress algorithmically the information bits the got after finally > perceiving where they actually were reconstituted. In fact, from their > perspectives, via this protocol, the number of times they reach Tokyo > (resp. London) will follow the binomial distribution. [...] It leads to an > objective probability applied to subjective (first person) outcomes." > Later, he says that he will use P(Tokyo) = P(London) = 0.5, "if only to > settle on a determination." > > There are a couple of mistakes in this, but they may not be terminal. In > the first place it is not clear what Bruno means by iterations of the > experiment. If each 'person' is to accumulate a sequence of experiences of > Tokyo or London, then after each duplication run, the resulting 'persons' > must be returned to Brussels and duplicated again, one copy of the second > duplication to Tokyo and one to London. So after the second run there will > be 4 copies, not just 2. Likewise, after 3 iterations there will be eight > copies; after n iterations there will be 2^n copies, not 2n. These copies > will all have distinct sequences of T or L experiences. In fact, every > possible sequence, from TTTTTT... to LLLLLL... will be represented. Over > this set, the distribution will indeed follow the binomial with p = 0.5. > The fact the the probability is 1/2 is simply a result of the fact that > there was one duplication with two possible outcomes for each 'person' at > each step. > > If we compare this to FPI in the MW Interpretation of quantum mechanics we > see that this is just a branch counting account of quantum probabilities. > Now it is well-known that this fails to reproduce the correct quantum > probabilities in MWI. So FPI as via Step 3 and FPI as in MWI are > intrinsically different. > Does the MWI predict an infinite number of branches from any given measurement? I'm not sure (from FOR) that the MWI predicts branches at all, so much as differentiation within a continuum? Maybe you could expand on this. Why (to keep it simple) would a quantum experiment with two possible outcomes not reproduce the correct probabilities in the MWI? (Or is that a special case where it would?) When we go to the full dovetailer stage we get multiple copies of the same > conscious instant. If we interpret these as repetitions of the same quantum > experiment (say a Stern-Gerlach spin measurement), we get some sequences of > Up and Down results. I'm not sure I understand this. Why do we need to interpret these copies (an infinite number, if the UD is able to run for an infinite time) as repetitions of the experiment? Personally, I have only compared the MWI with step 3 for John Clark's benefit, since he insists there is some problem with pronouns in step 3, but not in the MWI. The extent to which they are the same is that they produce both FPI from splitting or differentiation of fungible observers. But at this stage there is no need to take this any further. I'm just trying to help Mr Clark get his head around this particular point, and since comp assumes classical computation I wouldn't expect it to reproduce quantum probabilities "simplistically" - if it's going to work, it needs to produce them as an end result, not be expected to produce them until the entire logic of the argument has been examined. (Bruno claims to have produced some sort of quantum results at the far end of the comp argument, but I haven't got that far myself.) > But in so far as the duplication ideas of Step 3 are involved, the Born > Rule of quantum probabilities will not be reproduced, since that cannot be > obtained by branch counting in the MWI. OK. I believe that this is not the intention of step 3. It's only a metaphorical comparison for people who suffer from pronoun trouble, or only an exact comparison to the extent that both give a form of FPI. To assume this is the final result is to be "too quick". -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
