On Mon, Feb 10, 2025 at 10:52 AM Russell Standish <[email protected]> wrote:
> On Mon, Feb 10, 2025 at 10:06:12AM +1100, Bruce Kellett wrote: > > On Mon, Feb 10, 2025 at 9:51 AM Russell Standish <[email protected]> > wrote: > > > > On Mon, Feb 10, 2025 at 09:25:57AM +1100, Bruce Kellett wrote: > > > On Mon, Feb 10, 2025 at 8:49 AM Russell Standish < > [email protected]> > > wrote: > > > > > > On Thu, Feb 06, 2025 at 11:38:52AM +1100, Bruce Kellett wrote: > > > > > > > > Many worlds theory does not have any comparable way of > relating probabilities > > > > to the properties of the wave function. In fact, if all > possibilities are > > > > realized on every trial, the majority of observers will get > results that > > > > contradict the Born probabilities. > > > > > > > > > > I'm not sure what you mean by "contradict", but the majority of > > > observers will get results that lie within one standard > deviation of > > > the expected value (ie mean) according to the distribution of > Born > > > probabilities. If this is what you mean by "contradict", then > you are > > > trivially correct, but uninteresting. If you mean the above > statement > > > is false according to the MWI, then I'd like to know why. It > sure > > > doesn't seem so to me. > > > > > > > > > It does depend on what value you take for N, the number of trials. > In the limit > > > of very large N, the law of large numbers does give the result you > suggest. But > > > for intermediate values of N, MWI says that there will always be > branches for > > > which the ratio of successes to N falls outside any reasonable > error bound on > > > the expected Born value. > > > > > > This problem has been noted by others, and when asked about it, > Carroll simply > > > dismissed the poor suckers that get results that invalidate the > Born Rule as > > > just poor unlucky suckers. Sure, in a single world system, there > is always a > > > small probability that you will get anomalous results. But that is > always a > > > small probability. Whereas, in MWI, there are always such branches > with > > > anomalous results, even for large N. The difference is important. > > > > > > > Yes, but the proportion of "poor unlucky suckers" in the set of all > > observers becomes vanishingly small as the number of observers tend > to > > infinity. > > > > > > The number of trials does not have to tend to infinity. That is just the > > frequentist mistake. > > > > I wasn't talking about the number of trials, but the number of > observers. That is either astronomically large or an actual infinity. > There are only ever 2^N branches under consideration, so only ever 2^N observers. Additional branches due to decoherence can be disregarded for these purposes since all such observers only duplicate some that have already been counted. > As JC says, we don't know if the number of observers is countably > > infinite (which would be my guess), uncountably infinite or just > plain > > astronomically large. In any case, the proportion of observers seeing > > results outside of one standard deviation is of measure zero for > > practical purposes. If that is not the case, please explain. > > > > > > The number of anomalous results in MWI is not of measure zero in any > realistic > > case. > > > > I'm trying to see why you say that. > Read Kent. > > The other point is that the set of branches obtained in Everettian > many worlds > > > is independent of the amplitudes, or the Born probabilities for > each outcome, > > > so observations on any one branch cannot be used as evidence, > either for or > > > against the theory. > > > > > > > We've had this discussion before. They're not independent, because > the > > preparation of the experiment that defines the Born probabilities > > filters the set of allowed branches from which we sample the > > measurements. > > > > > > I don't know what this means. > > > > In preparing the experiment, you are already filtering out the > observers who choose to observe something different. And that > definitely changes the set of worlds, or branches under > consideration. So you cannot say (as you did) "the set of branches > obtained in Everettian many worlds is independent of the > amplitudes". Whether the set of branches changes in precisely the way > to recover the Born rule is a different question, of course, and > obviously rather hard to prove. > There is no such selective state preparation. Nobody gets filtered out in this way. You are just making things up. > > See the articles by Adrian Kent and David Albert in "Many Worlds: > Everett, > > > Quantum Theory, and Reality"(OUP, 2010) Edited by Saunders, > Barrett, Kent, and > > > Wallace. > > > > > > > I've already got a copy of Kent's paper in my reading stack. > Albert's paper > > appears to be behind a paywall, alas :(. > > > > In any case, it'll be a while before I get to the paper - just > > wondering if you had a 2 minute explanation of the argument. What > I've > > heard so far on this list hasn't been particularly convincing. > > > > > > A quote from Kent (p. 326 of the book) > > " After N trials, the multiverse contains 2^N branches, corresponding to > all N > > possible binary string outcomes. The inhabitants on a string with pN > zero and > > (1-p)N one outcomes will, with a degree of confidence that tends towards > one as > > N gets large, tend to conclude that the weight p is attached to zero > outcomes > > branches and weight (1-p) is attached to one outcome branches. In other > words, > > everyone, no matter what outcome string they see, tends towards complete > > confidence in the belief that the relative frequencies they observe > represent > > the weights." > > That is true. And the observers observing something like an all zero > sequence, or alternating 1s and 0s, are living in what we called a > "wabbity universe" some years ago on this list. Those observers become > vanishingly small as N→∞ in the space of all observers. > > I'm still not convinced there is a problem here... > We don't have to take N to infinity to get a problem. The trouble is that since the set of branches obtained is the same for all values of p (in Ken't's example), and the dominant ratio of zeros to ones is 50/50 in every case as N becomes large, it is always the case that the majority of observers get results that disagree with the Born rule. In most cases, observers find that QM is disconfirmed. 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 visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQ84kjf0_bOZppezK8n_%2B4ymEvc-graH3-Wm6ovAZpLkA%40mail.gmail.com.
