> On 5 Mar 2020, at 05:52, Bruce Kellett <[email protected]> wrote: > > On Thu, Mar 5, 2020 at 3:23 PM 'Brent Meeker' via Everything List > <[email protected] <mailto:[email protected]>> > wrote: > On 3/4/2020 7:54 PM, Bruce Kellett wrote: >> On Thu, Mar 5, 2020 at 2:02 PM 'Brent Meeker' via Everything List >> <[email protected] <mailto:[email protected]>> >> wrote: >> On 3/4/2020 6:45 PM, Bruce Kellett wrote: >>> On Thu, Mar 5, 2020 at 1:34 PM 'Brent Meeker' via Everything List >>> <[email protected] >>> <mailto:[email protected]>> wrote: >>> On 3/4/2020 6:18 PM, Bruce Kellett wrote: >>>> >>>> But one cannot just assume the Born rule in this case -- one has to use >>>> the data to verify the probabilistic predictions. And the observers on the >>>> majority of branches will get data that disconfirms the Born rule. (For >>>> any value of the probability, the proportion of observers who get data >>>> consistent with this value decreases as N becomes large.) >>> >>> No, that's where I was disagreeing with you. If "consistent with" is >>> defined as being within some given fraction, the proportion increases as N >>> becomes large. If the probability of the an even is p and q=1-p then the >>> proportion of events in N trials within one std-deviation of p approaches >>> 1/e and N->oo and the width of the one std-deviation range goes down at >>> 1/sqrt(N). So the distribution of values over the ensemble of observers >>> becomes concentrated near the expected value, i.e. is consistent with that >>> value. >>> >>> >>> But what is the expected value? Does that not depend on the inferred >>> probabilities? The probability p is not a given -- it can only be inferred >>> from the observed data. And different observers will infer different values >>> of p. Then certainly, each observer will think that the distribution of >>> values over the 2^N observers will be concentrated near his inferred value >>> of p. The trouble is that that this is true whatever value of p the >>> observer infers -- i.e., for whatever branch of the ensemble he is on. >> >> Not if the branches are unequally weighted (or numbered), as Carroll seems >> to assume, and those weights (or numbers) define the probability of the >> branch in accordance with the Born rule. I'm not arguing that this doesn't >> have to be put in "by hand". I'm arguing it is a way of assigning measures >> to the multiple worlds so that even though all the results occur, almost all >> observers will find results close to the Born rule, i.e. that self-locating >> uncertainty will imply the right statistics. >> >> But the trouble is that Everett assumes that all outcomes occur on every >> trial. So all the branches occur with certainty -- there is no "weight" that >> differentiates different branches. That is to assume that the branches occur >> with the probabilities that they would have in a single-world scenario. To >> assume that branches have different weights is in direct contradiction to >> the basic postulates the the many-worlds approach. It is not that one can >> "put in the weights by hand"; it is that any assignment of such weights >> contradicts that basis of the interpretation, which is that all branches >> occur with certainty. > > All branches occur with certainty so long as their weight>0. Yes, Everett > simply assumed they all occur. Take a simple branch counting model. Assume > that at each trial a there are a 100 branches and a of them are |0> and b are > |1> and the values are independent of the prior values in the sequence. So > long as a and b > 0.1 every value, either |0> or |1> will occur at every > branching. But almost all observers, seeing only one sequence thru the > branches, will infer P(0)~|a|^2 and P(1)~|b|^2. > > Do you really disagree that there is a way to assign weights or probabilities > to the sequences that reproduces the same statistics as repeating the N > trials many times in one world? It's no more than saying that one-world is > an ergodic process. > > > I am saying that assigning weights or probabilities in Everett, by hand > according to the Born rule, is incoherent.
I think that it is incoherent with a preconception of the notion of “world”. There are only consistent histories, and in fact "consistent histories supported by a continuum of computations”. You take Everett to much literally. Bruno > > Consider a state, |psi> = a|0> + b|1>, and a branch such that the > single-world probability by the Born rule is p = 0.001. (Such a branch can > trivially be constructed, for example, with a^2 = 0.9 and b^2 = 0.1). Then > according to Everett, this branch is one of the 2^N branches that must occur > in N repeats of the experiment. But, by construction, the single world > probability of this branch is p = 0.001. So if MWI is to reproduce the > single-world probabilities, we have with certainty a branch with weight p = > 0.001. Now this is not to say that we certainly have a branch with p = 0.001; > it is, rather, the conjunction of two statements: (a) the branch probability > is p = 0.001, and (b) the branch probability is p = 1.0. These two statements > are incompatible, so any assignment of weights to Everettian branches is > incoherent. > > Bruce > > -- > 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAFxXSLS%3DLTwRWURF_Tmv-3ThXNGE7TqwGo927sCdnYW5cAw_dw%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAFxXSLS%3DLTwRWURF_Tmv-3ThXNGE7TqwGo927sCdnYW5cAw_dw%40mail.gmail.com?utm_medium=email&utm_source=footer>. -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/F728ABE1-0F02-4015-A035-D234B9BDB636%40ulb.ac.be.
