On Thu, Mar 5, 2020 at 10:05 PM Bruno Marchal <[email protected]> wrote:
> 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]> 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]> 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]> 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. > I thought you were the one that claimed that Everett had essentially solved all the problems...... But actually, all I need for my proof is that every outcome occurs on every trial, which is a very slim version of Everett. The proof of the impossibility of a sensible notion of probability works just as well for the classical deterministic case, such as your WM-duplication scenario. 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]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLRD6ZXhDWW7N1UiOwX4moEHcBreeQYYdpSJM_H3LM3Dmg%40mail.gmail.com.
