On 2/14/2020 6:35 AM, Bruno Marchal wrote:

On 13 Feb 2020, at 23:59, Bruce Kellett <bhkellet...@gmail.com<mailto:bhkellet...@gmail.com>> wrote:On Tue, Feb 11, 2020 at 11:16 PM Bruno Marchal <marc...@ulb.ac.be<mailto:marc...@ulb.ac.be>> wrote:On 7 Feb 2020, at 12:07, Bruce Kellett <bhkellet...@gmail.com <mailto:bhkellet...@gmail.com>> wrote:I don't think you have fully come to terms with Kent's argument. How do you determine the measure on the observed outcomes? The argument that such 'outlier' sequences are of small measure fails at the first hurdle, because all sequences have equal measure -- all are equally likely. In fact, all occur with unit probability in MWI.Each individual sequence of head/tail would also occur with probability, in the corresponding WM scenario, and in the coin tossing experience. In the MWI, what you describe is what has motivated the introduction of a frequency operator, and that is the right thing to do in QM.I remembered reading something about such a "frequency operator" butcouldn't find the reference.I have given it. It is in Graham paper in the selected papers byDeWitt and Graham on the MW (Princeton, 1973).I see it was in a paper by David Albert, who writes:"Here's an idea: suppose we measure the x-spin of each of an infiniteensemble of electrons, where each of the electrons in the ensemble isinitially prepared in the state (alpha|x-up> + beta|x-down>). Then itcan easily be shown that in the limit as the number of measurementsalready performed goes to infinity, the state of the world approachesan eigenstate of the frequency of (say) up-results, with eigenvalue|alpha|^2. And note that the limit we are dealing with here is aperfectly concrete flat-footed limit of a sequence of vectors inHilbert space, not a limit of probabilities of the sort that we areused to dealing with in applications of the probabilistic law oflarge numbers. And the though has occurred to a number ofinvestigators over the years that perhaps all it *means* to say thatthe probability of an up-result in a measurement of the x-spin of anelectron in the state (alpha|x-up> + beta|x-down>) is |alpha|^2 isthat if an infinite ensemble of such experiments were to beperformed, the state of the world would with certainty approach aneigenstate of the frequency of (say) up-results, with eigenvalue|alpha|^2.Yes, that is the idea. I think it was shown (with some rigour) firstby Paulette Février (a student of De Broglie), but unfortunately, hermaster (De Broglie) came back to the hidden variable theory the “ondepilote”), and the work by Paulette Février has remained forgotten.But the business of parlaying this thought into a fully worked-outaccount of probability in the Everett picture quickly runs into veryfamiliar and very discouraging sorts of trouble. One doesn't know(for example) about finite runs of experiments,That is not correct, or correct for most practical use of probability.and one doesn't know what to say about the fact that the world isafter all very unlikely ever to be in an eigenstate of my undertakingto carry out any particular measurement of anything.”That does not make sense to me.Such reflections as those of David Albert here are probably why thisparticular line of thinking has never gone anywhere.The frequency operator approach has been refined by different people,and generalised for non sharp partial measurement of subsystem.Now, a quite similar idea has been developed by Finkelstein, and itshows how to derive relativity from quantum logic, but I have nevercompletely understood. Selesnick (an expert in quantum logic) wrote anentire book on this idea by Finkelstein, and make the square lawderivation (Born Rule) already in the first pages of the firstchapter, then the math get a bit too much high for a classicallogician, but I progress in it. Selesnick has written important paperin Quantum logic which can be used to show that the physics that Iextract from the “dream of number” contains a quantum nor (I don’tbother you with a precise technical rendering of this theorem, and tobe sure some lemma still needs some consolidation).I am not sure why you say that such line of thinking never goneanywhere, except that you dislike both Everett MWI, and the simplest(conceptually) arithmetical MWI.I might later make a post on how Finkelstein derived the Born rule (inthe simplest case of sharp measurement). But don’t hesitate to take alook on Graham paper.Usually, though, I prefer to mention Gleason theorem (or even Kochen &Specker) to justify the necessity of the MWI together with the squarelaw. It is not important, you can define Everett by MW+born rule, aswith mechanism, we have to derive the whole formalism for what is atthe start clearly an infinite set of histories/computations.Just to be clear, are you OK with P(W) = 1/2 in the WM-duplicatipon,when “W” refers to the first person experience?Bruno

`What if P(W) = 0.499999 ? We can't expect perfection in duplication`

`machines.`

Brent -- 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. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/6f06779f-a7c2-61a8-3578-ea93826a64d2%40verizon.net.