On Mon, Jan 6, 2025 at 7:49 PM Russell Standish <li...@hpcoders.com.au> wrote:
> On Mon, Jan 06, 2025 at 12:44:05PM +1100, Bruce Kellett wrote: > > On Mon, Jan 6, 2025 at 12:02 PM Russell Standish <li...@hpcoders.com.au> > wrote: > > > > On Sun, Jan 05, 2025 at 04:47:00PM -0800, Brent Meeker wrote: > > > > > > What he fails to explain is how probabilities are realized in > these worlds. As > > > Bruce pointed out, except for 50-50 cases the overwhelming number > of worlds > > > find QM to be empirically falsified; so branch counting doesn't > work. It > > > appears that the Born rule adds another axiom; it's not just the > Schroedinger > > > equation. > > > > > > Brent > > > > > > > Bruce's argument is too coarse. He is assuming that all worlds have > > equal representation in the original experimental preparation, > whereas > > the preparation process can clearly set things up such that there is > > 90% up 10% down in the original sample, after which measurement is > > performed. "Branch counting" can easily explain something like the > > 90/10 Stern Gerlach case. > > > > > > No, that does not work, even if you make the extreme assumption that > > measurement is a process of discrimination between already existing > worlds (a > > point of view for which we have no evidence whatsoever.) > > In Everettian many worlds, every outcome is realized on every trial. So > after > > one trial, there are two branches; after two trials, 4 branches; and so > on; so > > that after N trials, there are 2^N branches. > > Why do you think that just because there are two outcomes (up/down, > say), there will be precisely two branches generated? > That is what the theory says. There is a separate branch for each possible outcome. The fact that decoherence might spread this outcome over many further branches is not relevant here. We are counting outcomes, not final branches. It can only be guaranteed if there is a fundamental symmetry in the > system between the two outcomes. That is when you get equal branches > for each outcome. > Nonsense. You have no basis to assume that. The theory says the opposite. It is quite easy to concoct an example where 3 branches are up and 1 > down, giving a 75/25 ratio. Just perform a second binary measurement > if the down measurement is observed in the first measurement, but just > record if an up was seen in either measurement, or not. This can be > easily generalised to any ratio representable by a finite binary > expansion. > We are not doing branch counting as an explanation of probability here. The point is counting experimental outcomes. And the number of possible outcomes is determined by the initial wave function, which is a superposition of the possible eigenstates. Each eigenvalue is realized as an outcome on some branch. Not sure if you can squeeze the Stern Gerlach experiment into that > role, but my hunch is maybe. Positions of magnets are limited to the > accuracy of our rulers and protractors. > My point about S-G magnets to measure spin values was that they can easily be rotated away from the 50/50 position. The exact values do not matter in this context. You still get either an UP or a DOWN result along the axis of the magnet in its final position. The only thing that changes are the probabilities for each outcome. Let us consider a more realistic experimental situation. We set up a source of spin-half particles in the x-spin-left state, (easily done by a preliminary state preparation magnet.) Then pass these prepared particles through a further S-G maget in some orientation and record the result -- either UP or DOWN. Do this N times and look at the records of all copies of the experimentalist. According to the Everettian theory, each copy will have recorded some sequence of UP/DOWN results, but each copy will have a different sequence. In total, there are 2^N copies and 2^N different output records. In fact, these 2^N records will cover all possible binary sequences of length N. The additional branches coming from decoherence do not come into play here. We are considering only the records of recorded measurement results. The final point to be made is that regardless of the orientation of the S-G magnet, we must get the same set of 2^N possible sequences. Each set of results will converge to 50/50 UP vs DOWN as N becomes very large. This contradicts the Born probability for all but a very limited number of magnet orientations. But I do suspect that pure branch counting does fail to describe more > complex scenarios, such as Bell inequality violating ones, but I > haven't seriously looked into it. > Branch counting certainly fails as an account of probability. Decoherence involves an unknown number of branches, and this number is not controlled for different amplitude coefficients or Born probabilities. Branch counting is a washout as an account of probability via self-locating uncertainty. Also, branch counting has nothing to do with Bell's theorem. 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 everything-list+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/everything-list/CAFxXSLRWBsnHHZbF75NzxNj%3D9ePw6jiU7D%3DyC7ynsu4gYfRuhA%40mail.gmail.com.
