> On 14 Feb 2020, at 21:15, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > > > On 2/14/2020 6:35 AM, Bruno Marchal wrote: >> >>> On 13 Feb 2020, at 23:59, Bruce Kellett <[email protected] >>> <mailto:[email protected]>> wrote: >>> >>> On Tue, Feb 11, 2020 at 11:16 PM Bruno Marchal <[email protected] >>> <mailto:[email protected]>> wrote: >>> On 7 Feb 2020, at 12:07, Bruce Kellett <[email protected] >>> <mailto:[email protected]>> 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" but >>> couldn't find the reference. >> >> I have given it. It is in Graham paper in the selected papers by DeWitt 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 infinite >>> ensemble of electrons, where each of the electrons in the ensemble is >>> initially prepared in the state (alpha|x-up> + beta|x-down>). Then it can >>> easily be shown that in the limit as the number of measurements already >>> performed goes to infinity, the state of the world approaches an eigenstate >>> of the frequency of (say) up-results, with eigenvalue |alpha|^2. And note >>> that the limit we are dealing with here is a perfectly concrete flat-footed >>> limit of a sequence of vectors in Hilbert space, not a limit of >>> probabilities of the sort that we are used to dealing with in applications >>> of the probabilistic law of large numbers. And the though has occurred to a >>> number of investigators over the years that perhaps all it *means* to say >>> that the probability of an up-result in a measurement of the x-spin of an >>> electron in the state (alpha|x-up> + beta|x-down>) is |alpha|^2 is that if >>> an infinite ensemble of such experiments were to be performed, the state of >>> the world would with certainty approach an eigenstate of the frequency of >>> (say) up-results, with eigenvalue |alpha|^2. >> >> Yes, that is the idea. I think it was shown (with some rigour) first by >> Paulette Février (a student of De Broglie), but unfortunately, her master >> (De Broglie) came back to the hidden variable theory the “onde pilote”), and >> the work by Paulette Février has remained forgotten. >> >> >> >>> But the business of parlaying this thought into a fully worked-out account >>> of probability in the Everett picture quickly runs into very familiar 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 is after all >>> very unlikely ever to be in an eigenstate of my undertaking to 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 this >>> particular 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 it shows >> how to derive relativity from quantum logic, but I have never completely >> understood. Selesnick (an expert in quantum logic) wrote an entire book on >> this idea by Finkelstein, and make the square law derivation (Born Rule) >> already in the first pages of the first chapter, then the math get a bit too >> much high for a classical logician, but I progress in it. Selesnick has >> written important paper in Quantum logic which can be used to show that the >> physics that I extract from the “dream of number” contains a quantum nor (I >> don’t bother you with a precise technical rendering of this theorem, and to >> be sure some lemma still needs some consolidation). >> >> I am not sure why you say that such line of thinking never gone anywhere, >> 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 (in the >> simplest case of sharp measurement). But don’t hesitate to take a look 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 square law. >> It is not important, you can define Everett by MW+born rule, as with >> mechanism, we have to derive the whole formalism for what is at the 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.
That is why we do math, and thought experiences, and why sometimes I use the virtual environment to assure the numerical identity. In real life, the probability is given by the UD, and it asks, to be computed exactly, the entire run of the UD, + some non provable arithmetical truth, so no probabilities are exactly computable in practice, but they can (only) be approximated through simplification. Note that it is the same for QM, or most applied science. Bruno > > 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 [email protected] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/6f06779f-a7c2-61a8-3578-ea93826a64d2%40verizon.net > > <https://groups.google.com/d/msgid/everything-list/6f06779f-a7c2-61a8-3578-ea93826a64d2%40verizon.net?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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/04BB1CBD-FDD0-43A1-B5BF-EF3764B88BEA%40ulb.ac.be.
