From: *Bruno Marchal* <[email protected] <mailto:[email protected]>
On 12 Jul 2018, at 04:04, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
There are no up' or down' branches.
? (That contradicts directly what you just said). A up-branch is just
a branch where Alice saw or would see “up”.
You were the one who introduce up-prime and down-prime branches. I
maintain that there are only two branches on each and every measurement,
an up-branch and a down-branch.
......
Each measurement splits a branch, but branches never meet or recombine.
Because they both measure in the same direction (not sure how they do
that btw), but for Bell’s inequality, some measurement are not
“orthogonal”. Partial fusion is in play, which forbids ti associate
each personal experience with any definite Alice (Bob) in the branching.
Perhaps I was not sufficiently clear. I am considering a series of N
trials in which both Alice and Bob independently choose random magnet
orientations. So if the relative angle is theta, the probabilities for
combined results are:
Alice gets up: then Bob has probability sin^2(theta/2) for up, and
probability cos^2(theta/2) for down.
Alice gets down: then Bob has probability cos^2(theta/2) for up, and
probability sin^2(theta/2) for down.
If theta = 0, then if Alice gets up then Bob down 100%.; Alice down then
Bob up 100%.
If theta = 120 degrees, then if Alice gets up, then Bob gets up 75%
probability, and down 25% probability.
And so on for other angles and combined results. It is these
probabilities that are crucial for getting the correct correlations when
Alice and Bob meet.
Now if you can get these correlations without the non-local knowledge of
this relative angle, then you have a local explanation. But you will
never be able to produce such a set of probabilities locally -- the
relative angles are set at random: non-locally at space-like separations.
So the Alice that meets a Bob over coffee after the N trials is the
Alice with one particular branching history.
Again, this begins to be too much ambiguous, if not non sensical for me.
This is the heart of the matter. If you don't understand this, then you
don't understand how the correlations are formed.
The Bob she meets is necessarily in the same world,
At the moment of the meeting, yes. But that is a far cry to say that
it is the “physical Bob” she started with, in the case of "non
orthogonal measurements”. But OK, for this scenario.
We assume randomly non-orthogonal measurements. And neither Alice nor
Bob can switch between branches, so the Bob that Alice meets has a set
of measurement made all in this same world -- the world in which Alice
has made her measurements. In fact, the multi-branching tree forms a
giant superposition, and we have just singled out one component of this
superposition. There is nothing at all mysterious in this -- it is what
physicists do all the time when they perform calculations in momentum
space -- on just one component of the superposition that makes up a wave
packet.
and he has a similar particular branching history corresponding to
just one world. There are 2^N such meetings, each with unique
branching histories. The wonder of the singlet state is that for all
these Alice/Bob meetings, comparison of the data recorded in their
lab books /always/ gives correlations that agree with quantum theory
and violate the Bell inequalities.
To get them, they need non orthogonal measurement, with different
probabilities (cos^2(some angle)), and your identity relations does no
more work.
We have assumed non-orthogonal measurements, ones with the relative
angles set randomly at spacelike separation, ie., non-locally.
Bruce
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