> On 6 Sep 2020, at 08:15, Bruce Kellett <bhkellet...@gmail.com> wrote: > > On Sun, Sep 6, 2020 at 3:37 PM 'Brent Meeker' via Everything List > <everything-list@googlegroups.com <mailto:everything-list@googlegroups.com>> > wrote: > On 9/5/2020 6:07 PM, Bruce Kellett wrote: >> On Sun, Sep 6, 2020 at 10:25 AM 'Brent Meeker' via Everything List < >> <mailto:everything-list@googlegroups.com>everything-list@googlegroups.com >> <mailto:everything-list@googlegroups.com>> wrote: >> On 9/5/2020 4:59 PM, Bruce Kellett wrote: >>> >>> So why do you defend Carroll and Everett? Even self-locating uncertainty is >>> an essentially probabilistic idea. >> >> I don't defend them. I criticize your argument against them because I think >> it is unconvincing for the reasons I have given; essentially because you cut >> off the MWI interpretation before the step in which it extracts >> probabilistic statements by using self-locating uncertainty in the ensemble >> of worlds. >> >> >> I think that the only way this comment makes sense is if the number of >> worlds multiplies in proportion to the Born probabilities on each >> interaction. > > Or if you postulate some kind of weighting as Carroll does. > >> That is an even bigger departure from Everett than anything you might have >> accused me of doing. > > I didn't mean Everett himself. He didn't even propose multiple worlds; he > talked about the relative state of the observer (meaning relative to the > observed value).
According to some biographer, Everett did mentioned the “many-worlds” in the title of his first paper, but was asked by the publisher to use something less shocking, and that is why he used the notion of relative state. I was a bit disappointed by this, as “relative state” is more general a priori, and help to avoid taking the “world” notion to much seriously or ontologically. > I was saying you were not attacking the argument actually put forward by > Everttians, i.e. MWI advocates. > >> >> Let us revisit this problem using David Albert's example of Captain Kirk's >> transporter malfunction, so that when Kirk is beamed down to the surface of >> a planet, two "Kirks" arrive, one dressed in blue and the other in green. >> (One could make the same argument in terms of Bruno's WM duplication >> experiment.) >> >> If, after transportation, the Kirks re-ascend to the Enterprise and each >> copy again transports down: being duplicated in the same way. After N >> iterations, there are 2^N Kirks on the surface of the planet. If each >> carries a notebook in which he has recorded the sequence of colours of his >> outfits, all possible binary sequences of B and G will be recorded in some >> book or the other. A simple application of the binomial distribution shows >> that the notebook records peak around sequences showing approximately equal >> numbers of blue and green outfits. This is experimental verification of the >> probability of p(blue) = 0.5 = p(green). >> >> Now let us try to vary the probabilities, say to p(blue) = 0.9 and p(green) >> = 0.1. How do we do this? >> >> OK, we transport Kirk and, with probability p = 0.9, we colour one of the >> uniforms blue. The other must, therefore, be coloured green. But then we >> simply have two Kirks on the surface of the planet, one in a blue uniform >> and one in a green uniform -- exactly as we had before. It is easy to see >> that, no matter how we imagine that we have changed the relative >> probabilities of uniform colours, we must always end up with just one blue >> uniform and one green uniform. Our attempt to change the probabilities has >> failed. >> >> There is a way out, however. If, instead of simply duplicating the Kirks on >> transportation, the transporter manufactures 10 copies on the surface of the >> planet. Then we can suppose that 9 of these have blue uniforms, and the >> remaining Kirk is dressed in green. Iterating this procedure, we end up with >> 10^N Kirks on the surface of the planet, the vast majority of whom are >> dressed in blue. We have, thereby, changed the probability of a blue uniform >> for Kirk to 0.9 -- in the majority of cases. >> >> The trouble with this is that such a scenario cannot be reproduced with the >> Schrodinger equation. > > I agree. That's why MWI advocates must resort to "weights", which are just > amplitudes. Or add some structure like an infinite or very large ensemble of > already existing worlds that just get distinguished by results. > > > Don't you see that the argument I have made above shows that the idea of > adding 'weights' to the branches does not work?: you cannot consistently > graft the Born rule on to a model in which every possible outcome occurs on > every trial. The set of 2^N possible branches resulting from N repetitions of > the binary measurement is independent of the original amplitudes or weights. If you define the frequency operator, like in Preskill’s course, or Selesnick book, or Graham in the DeWitt-Graham selected papers, there is arguably some explanation of why we have to weight the relatives states, or the Griffith-Omnes consistent and relative histories. > I think I made that point months ago -- it was, in effect, my starting point. > The idea of a large ensemble of pre-existing worlds that just get > distinguished by results has never been taken seriously by anyone outside of > this list. Nor in this list, I think. Except by you, perhaps. > It has never been worked through in detail, and it is doubtful if it even > makes sense. It certainly has nothing to do with the Schrodinger equation. It has to do with the superposition principle. > > I suppose you can explore such ideas if you wish, but my purpose was more > limited -- I merely wished to show that MWI as advocated by the likes of > Carroll, Zurek, and Wallace, is incoherent. Since I have shown that adding > weights, or multiplying branches, is inconsistent with the Born rule and/or > the Schrodinger equation, I have made my point. All else is idle chatter. I think that your argument only shows that a naive conception of “world” should be abandoned. That happens already when we assume only mechanism in the cognitive science, due to the mathematical fact that all universal machine state is accessed in infinitely many computations (in arithmetic). Bruno > > Bruce > > >> If the universal wave function is represented by a vector in Hilbert space, >> for a two-outcome experiment the Hilbert space is two-dimensional, and we >> cannot fit 10 independent basis vectors into such a two-dimensional space. >> So the multiple branches for each outcome solution is not available in >> quantum mechanics. We might be able to dream up a theory in which this >> multiplication of branches would work, but that is not Everett, and it is >> not quantum mechanics as we know it. (Carroll and Zurek attempt to get >> around this by expanding the dimensionality of the operative Hilbert space >> by "borrowing" degrees of freedom from environmental decoherence. I doubt >> that this is actually convincing, or even possible. Whatever, it is a >> hopelessly ad hoc violation of the underlying dynamics.) >> >> I can, therefore, see no way in which the Born rule can be made compatible >> with strictly deterministic Everettian Schrodinger evolution. >> >> Note that (pace Bruno) this conclusion does not depend on any 1p/3p >> confusion. It depends only on the details of the assumed dynamics. >> >> 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAFxXSLTUxo8Jduo7fHeuAPpdNpbJ_b8SUoJhnAJOyanqQzomwA%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAFxXSLTUxo8Jduo7fHeuAPpdNpbJ_b8SUoJhnAJOyanqQzomwA%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 everything-list+unsubscr...@googlegroups.com. 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