Brent, In Everettian QM, the Born rule applies to coarse-grained outcomes, not to individual fine-grained sequences treated as equiprobable. The amplitudes are not just bookkeeping: their squared norm defines the measure, which determines how observer-instances are distributed.
Think of a lottery with one million tickets, but where 400,000 of them are identical copies of the same number. All tickets "exist," but they are not equally weighted when predicting what a typical observer will see. Similarly, in your N=6 example, 011000 and 001010 belong to the same coarse-grained class of "2 successes out of 6," and the combined measure of all such sequences follows the Born rule. Assuming each branch has equal weight and uniform observer sampling creates the contradiction, Everett’s formulation does not require that assumption. Quentin All those moments will be lost in time, like tears in rain. (Roy Batty/Rutger Hauer) Le mer. 27 août 2025, 21:16, Brent Meeker <[email protected]> a écrit : > I think some specificity would help this debate. Suppose N=6, so there > are 64 different sequences in 64 different worlds. The number of observers > is irrelevants; we can suppose the results are recorded mechanically in > each world. Further suppose that a=b so there is no question of whether > amplitudes are being respected. Then in one of the worlds we have 011000. > Per the Born rule its probability is 0.2344. In MWI it is 1/64=0.0156. > The difference arises because the observers applying the Born rule looks at > it as an instance of 2 out of 6 successes. > > So why can't the MWI observer do the same calculation? He certainly can. *He > can apply the Born rule.* But when he does so, it can't be interpreted > as a probability of his branch since such probabilities would add up to > much more than 1.0 when summed over the 64 different worlds. From the > standpoint of statistics 011000 is the same as 001010 and their > probabilities sum. Their difference is just incidental, but they are > different worlds in MWI and summing them makes no sense. > > Brent > > On 8/26/2025 11:39 PM, Quentin Anciaux wrote: > > Bruce, > > Everett’s original formulation describes a universal wavefunction evolving > unitarily, not discrete worlds with one observer per branch. Your argument > assumes this mapping, but it is an interpretative choice, not a result > derived from the Schrödinger equation. > > Also, your claim that all 2^N sequences have equal measure only holds if > amplitudes are treated as irrelevant. In standard quantum mechanics, > amplitudes directly determine observed frequencies via the Born rule, which > has strong experimental support. Ignoring amplitudes means you are no > longer analyzing Everett’s framework but a different model where the Born > rule indeed fails. > > To refute Everett with Born included, you would need to show that even > when squared amplitudes define a natural measure, the predicted observed > frequencies still fail. Assuming uniform sampling over sequences does not > establish that. > > This is why your derivation is not accepted: it relies on a hidden > premise, one observer per branch with uniform sampling, which is not part > of Everettian quantum mechanics. > > Quentin > > All those moments will be lost in time, like tears in rain. (Roy > Batty/Rutger Hauer) > > Le mer. 27 août 2025, 07:32, Bruce Kellett <[email protected]> a > écrit : > >> On Wed, Aug 27, 2025 at 3:26 PM Quentin Anciaux <[email protected]> >> wrote: >> >>> Bruce, >>> >>> If your derivation is as solid as you claim, then a skeptical referee is >>> exactly who you should want to convince. Repeating the same argument here >>> without engaging with the role of amplitudes will not make it any stronger. >>> You cannot dismiss amplitudes entirely and then claim to have explained why >>> measure must be uniform, that is circular. >>> >>> If you truly believe your reasoning refutes the Born rule within >>> Everett’s framework, then publishing it is the only way to settle the >>> matter. Otherwise, endlessly asserting it here looks less like confidence >>> and more like avoidance. >>> >>> Your entire argument hinges on assuming uniform observer sampling by >>> postulating one observer per branch. >>> >> >> The argument does not depend on this. This shows nothing more than that >> you have not understood the argument. >> >> But that is precisely the point under debate, not a derived result. If >>> you ignore the role of amplitudes in defining the structure of the >>> wavefunction, you're not engaging with Everett's formulation, only with >>> your own simplified model. >>> >>> Until you demonstrate why amplitudes should be irrelevant within unitary >>> evolution, claiming equal weights is just assuming your conclusion. >>> >> >> I think, rather, that you should show how the argument I have made >> depends on amplitudes when it clearly does not. It depends merely on the >> proportion of zero outcomes in each sequence. And that does not depend on >> the amplitudes. >> >> 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/CAFxXSLTqmwjWPL45KfJwEJRqr5_VOZETJZKZaCE3tZamgVBXbg%40mail.gmail.com >> <https://groups.google.com/d/msgid/everything-list/CAFxXSLTqmwjWPL45KfJwEJRqr5_VOZETJZKZaCE3tZamgVBXbg%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 [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/everything-list/CAMW2kAp6jiQmTmu%3D%2Bd1p0XFf1axT6%2BBSp4EMbna1ZJ5%2BvDp4jQ%40mail.gmail.com > <https://groups.google.com/d/msgid/everything-list/CAMW2kAp6jiQmTmu%3D%2Bd1p0XFf1axT6%2BBSp4EMbna1ZJ5%2BvDp4jQ%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 [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/everything-list/f3274fef-f07c-498b-b19e-b4c742e064ed%40gmail.com > <https://groups.google.com/d/msgid/everything-list/f3274fef-f07c-498b-b19e-b4c742e064ed%40gmail.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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