Brent, The Schroedinger equation governs the evolution of the wavefunction, but decoherence determines the effective structure of branches. 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. 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.
The fact that different results are orthogonal doesn’t mean each result corresponds to exactly one observer copy. 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. 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. 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. 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. Quentin Le ven. 21 févr. 2025, 07:16, Brent Meeker <[email protected]> a écrit : > > > On 2/20/2025 9:48 PM, Quentin Anciaux wrote: > > Brent, > > The key point is that a branch isn’t a single, discrete unit—it’s a > coarse-grained structure emerging from decoherence. > > It must emerge from the thing measured; from a discrete result. There's > no mechanism for creating a "coarse grained structure". > > The fact that a branch has "only one result" is an approximation because, > in reality, the wavefunction remains a superposition of countless > micro-branches. > > But they all agree on the measurement result; otherwise they would be a > branch. > > What we call "a branch" is just a region where interference is negligible, > > ?? It's interference that eliminates the superposition of different > results. > > but within that, there are still subtler partitions based on amplitude. > > Yes, observer instances are in orthogonal branches, but the partitioning > isn’t uniform. > > Why not? What mechanism, defined in what equation makes them not uniform, > i.e. one per result. I know you would like there to be mechanism, but that > doesn't make it so; and it certainly doesn't make the Schroedinger equation > that mechanism. > > The measure of a branch corresponds to the number of observer instances > experiencing that outcome, > > So if I perform an experiment in from a Superbowl crowd my results will be > more probable than those in undergrad lab on the 3rd floor of the physics > building. > > not to the number of distinct sequences. This means that instead of "one > observer per branch," there are exponentially more copies of an observer in > high-amplitude branches than in low-amplitude ones. > > The difference is subtle but crucial: If you assume one observer per > branch, you get branch counting and no Born rule. But if you recognize that > branches are not discrete and observer instances scale with measure, you > naturally recover Born probabilities. > > Do you? Let's see you do that math. > > 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]. > To view this discussion visit > https://groups.google.com/d/msgid/everything-list/3d482f4c-901e-47b7-890f-0769ebd6f2e5%40gmail.com > <https://groups.google.com/d/msgid/everything-list/3d482f4c-901e-47b7-890f-0769ebd6f2e5%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/CAMW2kAoAPV4256m4geuY93FDVGCg%3DcGP3TBhRAgcEHChM6_3cg%40mail.gmail.com.
