From: *Bruno Marchal* <[email protected] <mailto:[email protected]>>
On 12 Jul 2018, at 14:09, Bruce Kellett <[email protected]
<mailto:[email protected]>> wrote:
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.
In which direction?
In the direction in which the measurement is made. One of your enduring
mistakes is to confuse the rotational symmetry of the singlet state with
the single basis corresponding to the direction in which the measurement
will be made. Once a direction is chosen, the state can be represented
as a superposition of up and down eigenvectors /in that direction/.
Other directions are irrelevant to the measurement. The state is not in
a superposition of eigenvectors of every possible orientation. Quantum
mechanics does not have any such superposition. The state is a
superposition of just two eigenvectors, although which eigenvectors
depends on the direction chosen.
......
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.
But the result of the measurement are determined by the singlet state.
They just cannot known there local angles.
Of course they know their local angles -- they choose them! The point is
that Alice does not know Bob's chosen angle when she makes her
measurement, and neither does Bob know Alice's angle when he makes his
measurement. The fact that the probabilities depend on the relative
angle between these random non-local choices is the conundrum to be
answered.
When they measure in non orthogonal “direction”, the probabilities
depends, for all Alice-Bod couples, of that state, which is unknown to
both of them.I am OK that it is non-local, but that does not entail
that when Alice makes a measurement, she influence Bob’s outcome by a
FTL influence. They just get aware locally of which sub partition they
both belong.
That is just avoiding the issue. 'Sub-partition' as you use it here has
no meaning. Alice and Bob both know what world they are in -- the world
in which they got up that morning and had their breakfast..... And they
are in that same world when they later meet after a series of trials --
they cannot change worlds!
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.
From entanglement.
That is meaningless without further explication. The straightforward
explication in quantum physics is that the probabilities for each
outcome are determined by the non-local relative angle between their
measurements. If you want a local account, you have to give it
explicitly -- stop just waving your hands about and appealing to some
'entanglement' magic.
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,
? They don’t know which branches they are in, right at the start.
Rubbish. There are no branches until they make a measurement. And then
each tracks along a particular branching tree as recorded by the
sequence of up/down results recorded in their lab books. There is
absolutely no ambiguity here because neither Alice nor Bob can switch
between branches -- they must always be in the same branch.
That is equivalent to belonging to many threads at once.
This is your 'comp' nonsense. It has nothing to do with quantum
mechanics, especially not the quantum mechanics of Everett. Branches
arise only from existing superpositions, and there are no infinite
superpositions in this problem.
Only later will they get more precision on this. The singlet state
explains why they will observe the correlations when coming back
together, without having to have any FTL.
Once more the appeal to magic. You have to spell out how this happens.
Once a superposition exist, it never disappear, and the correlations
just reflect the type of interaction they did have to prepare the
singlet state.
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.
But there is an infinity of such world, where Alice find any possible
results. Same for Bob. The results are correlated, because they are in
the right corresponding relations, in all of them.
There are not an infinity of worlds, there are only 2^N of them. Of
course the correlations come out right for every Alice/Bob pair when
they meet. But you have not explained this locally.
My feeling is that you introduce some collapse somewhere.
I don't have to introduce a collapse: I just choose one branch from the
superposition of 2^N such branches. Since the branch I choose is
typical, the same result obtains for all 2^N such branches. Because each
branch is just a single world, it looks exactly the same as the collapse
model of Copenhagen or some such interpretation. I know you find
collapse an anathema, but collapse is just the same as picking one
typical branch from the many-worlds superposition. In that sense,
many-worlds and collapse models are identical.
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.
That makes sense.
That is what I have been saying all along, and this is what removes your
worry about 'collapse models' -- they are just a branch from the
many-worlds superposition.
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.
No problem with this. Still not see why we would need single branch
physical FTL when we look at the “giant superposition”.
The "giant superposition", in so far as it exists, has been spirited
away by just looking at a single branch. There is nothing the "giant
superposition" can add to the conclusions obtained from just one branch.
I don’t see at all why and how any FTL would be needed once we agree
that both the evolution and the tensor product are linear.
Stop worrying about FTL. There is no physical FTL mechanism. It is just
that non-separability of the singlet state means that non-local
measurements will be correlated. There is no deeper explanation than
this. In particular, there is no local explanation.
I see only local interaction, shared by people belonging to the
(infinitely many) corresponding states described by the singlet state.
Sure, the interactions are local, but at non-local positions. Get over
the nonsense about infinitely many corresponding states -- that is your
private fantasy and nothing to do with quantum mechanics.
Bruce
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
