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. > > > 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. > > > 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. > > > 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... -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders [email protected] http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- 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/Z6k_s1Mi5jYDaHFm%40zen.
