On Tue, Jan 7, 2025 at 9:33 AM Russell Standish <li...@hpcoders.com.au>
wrote:
> On Tue, Jan 07, 2025 at 09:12:26AM +1100, Bruce Kellett wrote:
> > On Tue, Jan 7, 2025 at 8:42 AM Russell Standish <li...@hpcoders.com.au>
> wrote:
> >
> > On Mon, Jan 06, 2025 at 09:50:47PM +1100, Bruce Kellett wrote:
> >
> > > 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.
> >
> >
> > Then you have misunderstood what I am arguing here. I am not trying to
> derive
> > the Born rule; I am just pointing out that if every outcome occurs for
> any
> > measurement, then you get results that contradict the Born rule
> probabilities.
> >
>
> So you're trying to do the opposite - that the theory cannot reproduce
> the Born rule. It is still the same thing - Proof by contradiction is
> still a valid form of proof.
>
> >
> >
> > > 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.
> >
> >
> > You have not understood the argument. It has nothing to do with branch
> > counting, although you seem to be insisting that that is what this is all
> > about.
> >
> >
> > > 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.
> >
> >
> > That is not what is going on here. I do not have to "further subdivide
> the
> > measured worlds (by adding in additional unobserved observables) until
> you end
> > with a set of symmetric outcomes". I have no interest in symmetric
> outcomes or
> > branch counting. You are confusing my argument with obscure thoughts of
> your own.
> > The point is that, according to Everett, if there are two possible
> outcomes for
> > each trial, then each is realized on any measurement. This leads to the
> same 2^
> > N sequences for any magnet orientation, contradicting the expectation
> from the
> > Born rule which is that the proportion of, say, UP results, should
> follow a cos
> > ^2(theta/2) distribution, where theta is the angle between the
> x-direction and
> > the magnet orientation. The probability of an UP result depends on the
> magnet
> > orientation, which is not what is found if every outcome is realized in
> every
> > trial.
> >
>
>
> You are applying an "indifference principle" as Sebens and Carroll
> call it when you say that each world of distinct N bit sequence is
> equally likely.
I am making no assumptions about probabilities or the likelihood of each
branch.
The Schrodinger equation is insensitive to the amplitudes, so it treats the
amplitudes corresponding to different magnet orientations all in the same
way. There is no probability associated with this. When I claim that the
sets of 2^N sequences are equivalent for all orientations, all that is
being claimed is that each set contains all possible sequences of UP/DOWN
results. It is the number of UP and DOWN that is relevant for each
sequence, not the Born rule probability of that sequence. A sequence will
have n_up UP results and n_down DOWN results. If, at a given magnet
orientation, the amplitude for UP is a_up and the amplitude for DOWN is
a_down, then the overall sequence has a coefficient
a_up^n_up*a_down^n_down
and this value will be different for each orientation and for each
sequence. This gives the Born probability for a sequence. But the number of
UP/DOWN results is the same for all magnet orientations. That is crucial
here. I am not using the Born weights for each sequence, nor am I assuming
some 'principle of indifference' to assign equal probabilities to each set
of sequences, but for the majority of sequences, the probability that one
would assign by counting the number of UPs, say, as a proportion of the
total number of results (N), will be different from the Born probability as
assigned by the coefficient a_up^n_up. That is the crux of the argument.
The results at each magnet orientation are equivalent, not because of some
'principle of indifference", but because the number of UP/DOWN results that
make up each sequence is the same for all orientations. The equivalence is
a matter of the way in which the set of sequences is constructed, not a
matter of some arbitrary assumptions about probabilities.
And you are applying it inappropriately, as that is
> only justified when each outcome corresponds to physically symmetric
> situations.
>
> In order to generalise to non-symmetric situations, then you need to
> some sort of branch counting, contra your claim this has nothing to do
> with branch counting.
>
> Please - lets focus on genuine problems of the MWI, rather than making up
> problems that don't exist.
>
This problem certainly exists, even if it is not generally recognized.
Others (such as Adrian Kent in various articles) have pointed to similar
problems with MWI, but they have been largely ignored.
Bruce
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