On 1/6/2025 2:33 PM, Russell Standish 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<[email protected]> 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. And you are applying it inappropriately, as that is
only justified when each outcome corresponds to physically symmetric
situations.
No. He's not saying each bit sequence is equally likely. Probabilities
have not been introduced. He's saying that in every measurement of UP
or DWN, *both* results occur per MWI, and so in N repetitions there will
be N occurrences of UP and N occurrences of DWN and this obtains
independent of the probability of UP. Then for every observer who sees
p*N Ups then there will also be an observer who sees (1-p)*N UPs (by
simple symmetry).And if p has a Born rule value other than 0.5 then one
observer will find QM confirmed and the other will see it contradicted.
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.
My example above shows branch counting can't work. To make MWI work you
must either have something different than both UP and DWN occurring at
every measurement, OR you must have weights assigned to the UP and DWN
instead of just counting the numbers.
Please - lets focus on genuine problems of the MWI, rather than making up
problems that don't exist.
What do you consider the genuine problems?
Brent
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