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?
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.
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.
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.
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.
--
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Principal, High Performance Coders hpco...@hpcoders.com.au
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