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. 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/CAFxXSLQRb1FGgGT-%2Bt%2Bb6FCzoU_PN9xB82bmK8zY5K1X4DNxCw%40mail.gmail.com.
