On 17/04/2016 7:35 am, John Clark wrote:
On Fri, Apr 15, 2016 Bruce Kellett <[email protected]
<mailto:[email protected]>>wrote:
>
Consider the usual case of a spin singlet that splits into two
spin-half components that separate and are measured by A and B at
spacelike separation. There are two possible measurement results
for each observer, call them |+> and |->.
The entangled state can then be written as:
|psi> = (|+>|-> - |->|+>).
You can write it however you like but in many worlds it means there
are 4 different outcomes and a observer will see each one.
>
The first ket applies to observer A and the second to observer B.
OK but keep in mind that in Many Worlds there must be some difference
between A and B for the universe to split; if there is no difference
between them then it is meaningless to talk about two separate entities.
A and B are shorthand for the conventionally named experimenters, Alice
and Bob. These two are different, regardless of the orientations they
choose for their magnets.
>
A and B perform their measurements at spacelike separation, but
each chooses the measurement orientation outside the light cone of
the other.
In other words they choose it for reasons that don't exist inside
their lightcone, in other words they choose it for no reason, in
other words they choose it at random.
There are four possible combinations of results, corresponding to
four worlds in the MWI: |+>|+'>, |+>|-'>, |->|+'>, and |->|-'>.
OK. All those results could happen and in many worlds everything
that can happen does happen.
Since each observer has a 50% chance of getting |+> and 50% of
getting |->, and the two measurements are completely independent
of each other, it would seem that each of these four worlds is
equally likely.
OK.
>
But this conclusion is contradicted by quantum mechanics:
It is?! Then
which of those four outcomes does quantum mechanics predict is more
likely to happen??
Read on......
>
if the two observers, by chance, have their magnets aligned, then
the |+>|+'> and |->|-'> combinations are impossible.
If A and B are identical BEFORE the measurement then there were not 2
experimenters there was only one, and in Many Worlds
only when different results are observed does the universe split and
only then would it make sense to talk about A/* and*/ B . If on the
other hand A and B were different
BEFORE the measurement
and they observed identical results then A and B would still
be different and thus be in different universes.
But A and B are different, regardless of this experiment. And there are
copies of both A and B in every universe that might be generated by
their respective experimental results.
>
In general, the probabilities of the four possible joint outcomes
depend explicitly on the relative orientation of the magnets of
the A and B -- they are seldom all equal. How is this taken into
account in the formalism?
In any formalism that corresponds to reality a spinning particle going
through a Stern–Gerlach
magnet will be deflected either either up or down from the center line
by the same amount, and the probability of observing either is exactly
50%. And from that experiment, depending on how the magnet is
oriented, you can determine the part of the original particle's spin
that was in the z axis or the part that was along the x y axis but NOT
both.
If the world is realistic then the spin axis of the original particle
had a exact orientation before the measurement you just didn't know
what it was, before you a made a measurement for all you knew the
north pole of the spin axis could have been pointing to any point on
the inner surface of a sphere, after the measurement you've narrowed
things down to any point on a circle but you still don't know what
point on the circle.
This is counterfactual determinism. Unfortunately, quantum mechanics
violates CFD in many situations, particularly EPR and the Kochen-Specker
result.
If the world is not realistic then the spin axis did not point to
anything before the measurement was taken because the spin axis did
not even exist before the measurement.
Right.
>
After the measurements are complete, A and B communicate their
results to each other,
Then, assuming A and B were different to begin with and assuming the
MWI is correct, the universe
splits into 4 strands with a observer in each one.
Sometimes: sometimes only two strands.
>
So MWI does not give a local account of the EPR results on
entanged states.
I think that's right, some would disagree but they can only so by
giving a somewhat tortuous meaning to the word "local", and when they
do that they just increase the difficulty in making MWI realistic and
deterministic. No quantum interpretation can get rid of quantum
weirdness and make things realistic local and deterministic as common
sense demands because common sense is just dead wrong.
It seems that we agree, then.
I like many worlds because, at least to me, it seems a little bit less
ridiculous than any other quantum interpretation I know of. Maybe
someday a better one will come along but I would bet money it will
still be weird because we live in a weird place.
I don't like many worlds because it is baroque and unnecessary.
Bruce
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