Brent, Yes, and that’s exactly the problem—Gleason’s theorem doesn’t apply to two-dimensional Hilbert spaces, which means it doesn’t universally derive the Born rule. So if MWI fails for not deriving the Born rule, then standard QM faces the same issue unless you introduce additional postulates.
Branch counting doesn’t work, but my example isn’t branch counting—it’s asymmetric duplication, where observer distribution follows measure, just like amplitudes in MWI. The issue is whether we can derive probability weights from unitary evolution without assuming the Born rule. Partitioning an infinite multiverse by amplitude might work, but only if it doesn’t presuppose Born’s rule. Instead, something like compression, complexity, or Speed Prior could explain why some outcomes dominate observer experiences. If reality emerges from an infinite computational structure (UDA-style), then probability might arise from the structure of computations rather than being inserted ad hoc. The real challenge is showing that observer-weighted probabilities emerge naturally—not just assuming them. Quentin Le mer. 19 févr. 2025, 02:40, Brent Meeker <[email protected]> a écrit : > I noted the exception in my comment. > > Brent > > On 2/18/2025 2:45 PM, Quentin Anciaux wrote: > > Brent, > > Gleason’s theorem only works for Hilbert spaces with more than two > dimensions, so it doesn’t universally derive the Born rule. If the Born > rule were truly fundamental, it should emerge naturally even in the > two-outcome case. Instead, it must be assumed in single-world views or > justified through additional reasoning in MWI. Pointing to Gleason’s > theorem avoids addressing the very case where the issue is most crucial. > > Quentin > > Le mar. 18 févr. 2025, 23:13, Brent Meeker <[email protected]> a > écrit : > >> >> >> On 2/17/2025 2:01 PM, Quentin Anciaux wrote: >> >> >> >> Le lun. 17 févr. 2025, 22:53, Brent Meeker <[email protected]> a >> écrit : >> >>> >>> >>> On 2/17/2025 5:15 AM, John Clark wrote: >>> >>> On Sun, Feb 16, 2025 at 8:33 PM Brent Meeker <[email protected]> >>> wrote: >>> >>> *>> There must be a fundamental reason why we can't make predictions >>>>> better than those allowed by HUP, and self-locating uncertainty is that >>>>> reason.* >>>> >>>> >>>> *>**?? Most physicist think it's because conjugate operators don't >>>> commute. * >>>> >>> >>> >>> *That is true but of no help whatsoever in explaining what's actually >>> going on. I want to know WHY momentum and position, and energy and time are >>> conjugate operators, I want to know why Schrodinger's equation and the Born >>> rule describe what we see in experiments. * >>> >>> Seems more explanatory than "There are other worlds where....what?" >>> >>> >>> >>> *>> If you make a record of which slit an electron went through in the >>>>> two slit experiment then you will not see an interference pattern on a >>>>> screen, but if you don't make a record of it then you will. And if you >>>>> make >>>>> a record and place the screen a light year away from the slits but erase >>>>> that record one second before the electrons hit the screen then you will >>>>> see an interference pattern. This is certainly odd but it poses no >>>>> problem >>>>> for Many Worlds.* >>>> >>>> >>>> *> You only see the interference pattern after you know the identity of >>>> the ones whose partner was erased. Otherwise you could use it for faster >>>> than light signalling. * >>>> >>> >>> *Also true but irrelevant to the subject at hand. * >>> >>> *> But it's not subjective; the pattern is really there for anyone to >>>> see.* >>>> >>> >>> *I agree, it's not subjective. Anyone could see the pattern, anyone who >>> is in a universe where the information about which slit the electrons went >>> through before they hit the screen does NOT exist. But anyone in a universe >>> where that information DOES exist will NOT see an interference pattern.* >>> >>> *> **It's curious that you criticize QBism because it's not explaining >>>> what's "actually going on"* >>>> >>> >>> *I respect QBism, a.k.a. Shut Up And Calculate, more than Copenhagen >>> because it's more honest, it doesn't even attempt to explain what's >>> actually going on, Copenhagen attempts to do so but the result is a >>> ridiculous convoluted mess. Copenhagen fans can't agree, even among >>> themselves, what it's saying. * >>> >>> >>> >>>> *> but you like MWI versus spontaneous collapse**. Yet spontaneous >>>> collapse does explain what's "actually going on". * >>>> >>> >>> *That's why I think MWI and spontaneous collapse are the two least bad >>> quantum hypotheses that attempt to explain what's actually happening; they >>> may both be wrong but at least they're clear and at least they try; the >>> others just give up or hide behind an opaque fog of bafflegab.* >>> >>> It's a probability, so some things happen and others don't. A lot >>> clearer than "Everything happens and we don't know how it's a probability." >>> >>> Brent >>> >> >> Brent, >> >> Sure, but saying “some things happen and others don’t” is just labeling >> an outcome, not explaining why probability follows the Born rule. If you >> take that as fundamental, fine, but that’s just postulating rather than >> deriving it. >> >> Once you accept probabilistic interpretation of Schoredinger's equation, >> Gleason's theorem gives the Born rule for any number of possible outcomes >> greater than two. >> >> Brent >> >> >> MWI doesn’t deny probability; it just reframes the question. The >> challenge isn’t that “everything happens,” it’s understanding why observers >> experience frequencies matching the Born rule. That’s what self-locating >> uncertainty and measure attempts to address. If you reject those >> approaches, what exactly is the alternative explanation for why >> probabilities follow Born’s rule, rather than just assuming they do? >> >> Quentin >> >> >>> >>> >>> -- >>> 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/cb2ba399-6fcf-41eb-adb0-20011e74b8e3%40gmail.com >>> <https://groups.google.com/d/msgid/everything-list/cb2ba399-6fcf-41eb-adb0-20011e74b8e3%40gmail.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/CAMW2kArEOkzBUNkTncM3zEfwUjQi_0O719kjhZFYAHDe3ioUnw%40mail.gmail.com >> <https://groups.google.com/d/msgid/everything-list/CAMW2kArEOkzBUNkTncM3zEfwUjQi_0O719kjhZFYAHDe3ioUnw%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/568c5149-bae1-418a-abbb-3712e50d68b4%40gmail.com >> <https://groups.google.com/d/msgid/everything-list/568c5149-bae1-418a-abbb-3712e50d68b4%40gmail.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/CAMW2kAqfLWhHAPsPNscGWKgEYqhJxtSBEEJZKhhukn3BGaqyOw%40mail.gmail.com > <https://groups.google.com/d/msgid/everything-list/CAMW2kAqfLWhHAPsPNscGWKgEYqhJxtSBEEJZKhhukn3BGaqyOw%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/a35c64d5-0e94-4393-85f6-06903b5b9059%40gmail.com > <https://groups.google.com/d/msgid/everything-list/a35c64d5-0e94-4393-85f6-06903b5b9059%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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