On Mon, Jan 06, 2025 at 09:50:47PM +1100, Bruce Kellett wrote:
> 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.
All papers I've read on branch counting rely on symmetry to get the
50/50 result.
>
>
> 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.
I thought that is exactly what we're doing. The aim is to reproduce
the Born rule.
> 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.
>
Yes - and my point is that branch counting will probably explain the
variation in probability in this experiment too. But my main point is
that your argument fails, and that is most clearly seen when creating
outcomes that are simple logical functions of the 50/50 case.
> 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 the setup is _not_ symmetric with respect to the set of possible
outcomes. You have to further subdivide the measured "worlds" (by
adding in additional unobserved observables) until you end with a set
of symmetric outcomes, which you can then apply
branch-counting. Summing over the unobserved observables leads to the
nonuniform probability distribution.
--
----------------------------------------------------------------------------
Dr Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders hpco...@hpcoders.com.au
http://www.hpcoders.com.au
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