Brent, Consider a simple computational analogy: if consciousness is a program, running multiple instances of it doesn’t create different "people"—it just creates more instances of the same subjective experience.
Now, imagine we take a program that simulates an observer. We run it 9 times on computers that display "1" on the screen and once on a computer that displays "0". Each instance of the program experiences seeing either "1" or "0", but the overwhelming majority experience "1". This mirrors how observer instances distribute in MWI: more instances exist in high-amplitude branches. The program has no way to distinguish whether it's in a "common" or "rare" instance, but if you were to randomly select an instance, it would most likely be one that sees "1". This is the key distinction: probability in MWI doesn’t come from counting branches; it comes from the relative number of observer instances in each. The Born rule follows naturally if amplitude determines observer frequency—just as in the example, where the majority of observer instances see "1" despite both outcomes occurring. Quentin Le ven. 21 févr. 2025, 23:10, Quentin Anciaux <allco...@gmail.com> a écrit : > Brent, > > I’m not just repeating that the Born rule works—I’m pointing out that any > valid interpretation must explain why it works. You keep arguing as if I’m > assuming it, but the argument is that measure provides a natural way to > account for it without assuming it outright. > > The lottery analogy illustrates this: more copies of an observer in a > high-measure branch means an observer is overwhelmingly likely to > experience that outcome. This is not about assuming the Born rule—it’s > about showing how a distribution naturally arises from the structure of the > wavefunction. > > You seem to interpret "more observers" as meaning entirely separate people > in the same world. That’s not what’s being said. If the wavefunction > remains a continuous superposition, then what we call "a branch" isn’t a > single, discrete entity—it’s a coarse partition in an underlying structure. > More observers in a branch means more instances of the same observer, not > more independent individuals. > > If you think this fails to explain the Born rule, then the burden is on > you to show why. Just stating that the Schrödinger equation doesn’t > explicitly derive it ignores the fact that all interpretations rely on > additional reasoning to connect math to experience. Dismissing this as > "assuming what needs to be proven" without engaging with how measure > distributes observer instances doesn’t resolve anything. > > Quentin > > Le ven. 21 févr. 2025, 22:59, Brent Meeker <meekerbr...@gmail.com> a > écrit : > >> >> >> On 2/20/2025 11:30 PM, Quentin Anciaux wrote: >> >> Brent, >> >> The Schroedinger equation governs the evolution of the wavefunction, but >> decoherence determines the effective structure of branches. >> >> A branch is defined the result of the measurement. If the electron spin >> is UP, then that defined the UP branch. Decoherence presumably spreads >> from the SG detector and makes a world around UP that's orthogonal to the >> world around DWN. "Effective structure" beyond this is just your invention. >> >> When I say a branch isn’t a single discrete unit, I mean that what we >> call a “branch” is an approximation—a macroscopic, emergent structure from >> the underlying quantum evolution. >> >> Why isn't it single in the sense that it is the branch that originated >> from a single measurement value. "emergent structure from the underlying >> quantum evolution" is just obfuscation. >> >> The wavefunction never truly “splits” into countable, independent worlds; >> rather, it evolves into a superposition of decohered, non-interfering >> components, which we approximate as separate branches. >> >> If they are non-interfering they are in a superposition. They're >> orthogonal. >> >> >> The fact that different results are orthogonal doesn’t mean each result >> corresponds to exactly one observer copy. >> >> The UP world originated from the single UP measurement. How many people >> observe it is irrelevant. They're all in one world. >> >> The amplitudes still dictate relative frequencies, just as they do in >> standard QM. The mechanism isn’t imposed externally—it’s in the structure >> of the wavefunction itself. You ask what equation determines that branches >> aren’t uniform: the answer is the same equation that governs quantum >> amplitudes. The measure of an outcome isn’t arbitrary—it follows from the >> squared amplitude of that outcome, just as it does in any quantum >> experiment. >> >> Here you spend three sentences to say the Born rule is instantiated. But >> why and how is nothing but assertion and hand waving. Bruce and I have >> both challenged you to provide the mathematics. You say the equation that >> governs quantum amplitudes. But in an SG experiment the probability >> amplitude for UP is proportional to cos(phi) where phi is the angle between >> the beam polarization and the instrument's "UP". The electron however >> doesn't carry that information to the detector; the electron just registers >> on the counter as 0 or 1. Which is Bruce's point that the "a" and "b" in >> a|up>+b|dwn> are NOT part of information available in the experimental >> record. The structure of the wave-function just determines the sequence of >> 0s and 1s. You know the answer you want, the Born rule, so you just >> suppose it must be in there somewhere. But it's not as Bruce's example >> shows and also the many failures by smart people to try to derive the Born >> rule. >> >> >> Your example about performing an experiment in a Superbowl crowd vs. an >> undergrad lab misunderstands what’s being discussed. The measure isn’t >> about the number of classical humans performing an experiment—it’s about >> how many instances of an observer are instantiated in a given outcome due >> to the structure of the wavefunction. >> >> Yes, I know what you meant, I'm just cautioning you against using >> misleading language. What you meant is the SG detector, when registering >> an electron UP instead of decoherence producing one UP-branch it produces a >> whole lot, a bush of UP-branches *and the number of branches in this >> bush is proportional the b^2 in Bruce's example.* It's this last that >> is the problem. There is no mechanism for it. It is just your gratuitous >> assumption to get the Born rule by branch counting. >> >> The classical analogy would be a lottery where some numbers are printed >> in greater quantities than others; if you pick a ticket randomly, you are >> overwhelmingly likely to pick a more common one. >> >> If branch count alone determined probability, we wouldn’t see Born’s rule >> in experiments. >> >> We would if you just assume the right number of branches. But as JKC >> pointed out, doing so requires retro-causation to change the past. >> >> Since we do, that means any valid interpretation of QM must account for >> why low-amplitude branches contribute less to observer experiences. If you >> believe MWI fails to do this, then you need to provide a counterargument >> that doesn’t assume what it wants to prove—that all branches contribute >> equally regardless of amplitude. >> >> You are the one claiming that the Born rule follows from the Schroedinger >> equation. Above you just repeat that we know it applies. Yes, we know it >> applies empirically and for more that two results is implied by Gleason's >> theorem. But that's not a derivation or a proof. You just repeating you >> it must be so because we know it workds doesn't add anything. >> >> 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 visit >> https://groups.google.com/d/msgid/everything-list/f28334e0-ed0e-424b-8e99-725eb0d29a27%40gmail.com >> <https://groups.google.com/d/msgid/everything-list/f28334e0-ed0e-424b-8e99-725eb0d29a27%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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