On 2/17/2020 2:11 AM, Bruce Kellett wrote:
On Mon, Feb 17, 2020 at 6:04 PM 'Brent Meeker' via Everything List
<[email protected]
<mailto:[email protected]>> wrote:
On 2/16/2020 9:48 PM, Bruce Kellett wrote:
On Mon, Feb 17, 2020 at 4:13 PM 'Brent Meeker' via Everything
List <[email protected]
<mailto:[email protected]>> wrote:
But exactly the same reasoning applies for any given true
value of p. There will be different estimates by different
experimenters and they can't all be right. Each will infer
that any proportion other than the one he observed will have
zero measure in the limit N->oo.
Exactly right. That is what my example of spin measurements on an
ensemble of equally prepared spin states comes into play. If all
2^N bit strings are realized for one orientation of the S-G
magnet, then exactly the same 2^N bit strings are realized for
every other orientation.
?? Suppose the ensemble is equally prepared in spin-up. What does
it mean to say all 2^N bit strings are realized for the S-G
oriented left/right? We may expect they will be for any number of
trials >>N. But certainly not for the S-G oriented up/down.
I think we are beginning to argue at cross-purposes, and I may not
have understood you correctly. Let me try to restate the position
clearly, and see if you can agree.
Take a spin-half state, and prepare a linear combination in the x-basis:
|psi> = (alpha*|x-spin up> + beta*|x-spin down>),
where we assume that neither alpha nor beta is equal to zero. We can
now measure this state in the x-direction and assume Everett, so that
every result is obtained in a separate branch on every trial. Coding
these results as zero and one, a run of N experiments will give 2^N
binary strings of results, consisting of the set of all 2^N binary
strings of length N. Now rotate the S-G magnet from the x-direction
by, say, 10 degrees. Your results are again the set of all binary
strings of length N. Similarly for any other angle (except those for
which alpha or beta rotates to zero). Since the set of results is the
same in all cases, even though rotation of the S-G magnet is
equivalent to changing alpha and beta in the superposition, the
individual sets of results must be independent of alpha and beta.
However, the Born rule states that the probabilities depend on
|alpha|^2 and |beta|^. But we have seen that the many-worlds data are
actually independent of alpha and beta. The Born rule for
probabilities is thus disconfirmed in this Everettian case.
That is the crux of what I am trying to get across -- Everettian QM is
disconfirmed by experiment, since experiments show results that depend
on the coefficients alpha and beta, in accordance with the Born Rule.
There are other points that I have been making, but let's get this
straight first.
Yes, I agree with that. It's another way of expressing my objection
that while alpha=0.5 produces a split into two worlds, alpha= 0.499
produces a split into a thousand worlds.
But proponents of MWI like Sean Carroll and Bruno, essentially assume
there are already (infinitely?) many branches which, prior to the
measurement, are identical at the macroscopic level, but which get
projected (split) onto orthogonal subspaces by a measurement.
Brent
Bruce
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