On 18/04/2016 5:25 am, Jesse Mazer wrote:
"A and B perform their measurements at spacelike separation, but each
chooses the measurement orientation outside the light cone of the
other. There are four possible combinations of results, corresponding
to four worlds in the MWI: |+>|+'>, |+>|-'>, |->|+'>, and |->|-'>.
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."
I don't think this is how it's supposed to work for those who argue
the MWI is local like Deutsch. Rather the idea is that "splitting"
into worlds is local, not global; so one experimenter locally splits
into copies that see |+> and |-> when they measure their particle,
likewise the other experimenter splits into copies that saw |+'> and
|-'>. But until their future light cones overlap there are no "worlds"
containing facts about what *both* experimenters saw. And once they do
overlap--say, because they both sent signals about their results to an
experimenter at the midpoint between them
The future light cones of the observers will overlap at a time
determined by their initial separation, regardless of whether they send
signals to each other or not.
Consider the following: Alice and Bob perform their experiments on the
entangled pair and record the results (magnet orientation and outcome)
in their lab books. They then go on with other things. Some weeks later
they meet up at a cafe down the street for a coffee, and there compare
their results. This is the first time that any explicit information
about magnet orientations and results has ever been exchanged. And yet
Alice and Bob meet in the same world -- they are both the result of the
fully decohered separation of worlds after their quantum experiments,
and they both ended up in the same branch in the MWI (else they could
not meet up). How do you prevent the situation in which, when they
compare their lab books, they find that they both used the same magnet
orientation and both recorded |+>? The world which they both inhabit was
already fully formed before they met -- otherwise the could not have
met. So the world in which they both measure |+> at the same orientation
could never have formed. What prevented it? Recall that neither they
(nor their magnets) knew the other's orientation until the met for
coffee several weeks later -- that information was simply not
transferred in any other way (unless you believe in magic????)
--then they can be matched up appropriately based on information in
the past light cone of the overlap region, including information about
what detector setting each copy of each experimenter used. So if both
experimenters used the same detector setting, then if we consider the
copy of the middle observer who gets matched up with the copy of the
left experimenter that got |+>, he must also be matched up with the
copy of the right experimenter that got |-'>, and likewise the copy of
the middle observer who gets matched up with the copy of the left
experimenter who got |-> must be matched up with the copy of the right
experimenter that got |+'>.
This so-called "matching up" is pure fantasy. Who does this matching? If
the central umpire is to do the matching, he has to have the power to
eliminate cases that disagree with the quantum prediction. Who has that
power?
The situation before even more bizarrely extreme if you consider the
situation in which Bob and Alice do a long series of trials of the
experiment before they meet to compare notes. They each have a series of
|+> and |-> results, with corresponding orientations, But the
probabilities calculated from these sequences must match the quantum
predictions, even though no intermediate exchange of orientation
information ever took place. Note also that if the initial separation is
sufficient, or if the repeat rate was sufficiently high, they could both
accumulate these long sequences of results before their future light
cones ever intersected. The records are fixed and unchangeable before
any information exchange ever takes place.
Bruce
You could design a cellular-automata like system that keeps track of
multiple copies of each system at a given "cell" in this sort of way,
and reproduces the statistics seen in Bell experiments, so the idea is
at least in principle consistent (I described a simple toy model at
http://www.physicsforums.com/threads/does-mwi-resolve-locality-problems-with-entanglement.206291/#post-1557143
). Although from what I've read, the "preferred basis problem" means
the current formulation of the MWI has trouble getting probabilities
from the universal wavefunction in any simple frequentist way (one
where you have a well-defined "fraction of copies with property X vs.
fraction with property Y" for each local region of spacetime, and
probability is simply interpreted in terms of this fraction), instead
probabilities are usually derived in non-frequentist ways using things
like decision theory. Maybe in the future a nice frequentist version
of the Everett interpretation will be found though...I don't
understand the details, but I think Mark Rubin has been trying to get
closer to something like this in the papers at
http://arxiv.org/abs/quant-ph/0204024 and
http://arxiv.org/abs/quant-ph/0511188 and http://arxiv.org/abs/0909.2673
Jesse
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