On 7/6/2018 8:38 PM, Bruce Kellett wrote:
From: *Brent Meeker* <meeke...@verizon.net <mailto:meeke...@verizon.net>>
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.
As I understand Zurek's quantum Darwinism there are many (e.g. ~10^30)
quantum threads corresponding to each sequence of entries in Alice's
notebooks. A probable entry sequence has more threads and hence more
measure than an improbable one. So "Alice and her notebook reading
u,u,d,u...d,u,d,d,d" is a classical thing that exists as many quantum
threads that are classically indistinguishable and so constitute one
FAPP classical world. Similarly for Bob. So where the forward light
cones of their last measurements overlap, most of these quantum threads
must trace out to zero and leave only those whose measures satisfy both
the Born rule and the correlations that violate Bell. This "tracing
out" is what adjusts the relative proportion of Alice/Bob pair meetings
so that the proper statistics are realized.
Brent
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