From: *Brent Meeker* <[email protected] <mailto:[email protected]>>
On 7/6/2018 4:54 PM, Bruce Kellett wrote:
I am not sure I understand the idea of being in the same world when
space-like separated.
Who said anything like that? They end up in the same world when they
meet. Or do you disagree with that as well?
Certainly the two people who meet are in the same quasi-classical
world. But when decoherence happened to the two people who were
space-like separated wasn't that decoherence at Alice in general
different from the decoherence at Bob? From Zurek's quantum Darwinism
view, at each end there will be a very large number of different
states reached by decoherence (Zurek proposes to recover the Born rule
as statistices over these) but the decoherence effects will spread at
roughly the speed of light and eventually overlap. When they overlap
they will in general be incompatible so the Alice and Bob
corresponding to those, can never meet. Only those, if there are any,
which decohered compatibly AND have the contra-Bell correlations in
their notebooks can meet. What happened to those that decohered
incompatibly?...they are traced out to zero?
Decoherence is a local phenomenon, spreading at the speed of light or
less. But that does not necessarily mean that the spacelike separated
people are in different worlds. At any particular instant of GMT, you in
California are spacelike separated from me in Australia. But that does
not mean we are in different worlds, and does not prevent us from
meeting at some time in the future. Consequently, when the decoherence
from an event at Alice meets the decoherence from another event at Bob,
they may or may not be in the same world. It is not the compatibility of
the decoherence that is at issue, but the branches of the wave function
on which the particular measurement results put them that can be
incompatible. Separate decohered branches can never meet. It is not that
they are traced out to zero -- it is that they are separate disjoint worlds.
There is an additional complication present in the measurements on EPR
pairs. Given that Alice measured 'up', either 'up' or 'down' for Bob is
compatible if the polarizers are aligned at some intermediate angle. So
Alice _up and Bob_up can be in the same world. And Alice_up and Bob_down
can be in the same world. But since Bob has split, these cannot be the
same worlds overall. The crucial point for recovering the quantum
correlations is the corresponding probabilities -- the probability for
Bob to have recorded 'up' when Alice's lab book shows 'up' is generally
different from the probability that Bob's book shows 'down' in this
situation. For any particular trial, there is no way of knowing these
probabilities, or of knowing which of the two Bob-worlds are compatible
with the Alice-world. This only shows up in the expectation values over
a large sequence of trials. It is explaining the origin of these
probabilities that is the challenge for any proposed local account of
the EPR correlations. And many-worlds signally fails to provide any such
explanation. Many-worlders are content with waving their hands over
multiple entanglements and incompatible worlds, but they never get down
to the nitty-gritty of explaining the probabilities.
Bruce
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