From: *Brent Meeker* <[email protected] <mailto:[email protected]>>
On 7/6/2018 8:38 PM, Bruce Kellett wrote:
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.
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.
That can't be right. The number of copies of a result left in the
environment cannot determine the probability of that result. The
probability is given by the square of the amplitude in the wave
function. And if the environment is sparse, the system may not even
properly decohere. I think that Zurek's quantum Darwinism is much more
about establishing robust classical states after a quantum event.
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.
That is regarding the lab book as a classical object. But it always was
a decohered classical onject -- unaffected by the measurements Alice
makes, at least until she write her result in the book. The decoherence
is in the pointer state that reveals up or down, and many copies of this
result are written to the environment, making it stable and classical.
But this does not affect probabilities, or what ALice writes in her book/
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.
No, this idea is quite wrong. Once the measurements have been made and
the results recorded, everything between Alice and Bob is completely
classical. There are not some mystical "quantum threads" that reach out
into the environment to determine probabilities. That is a total
misreading of Zurek.
The statistics of the joint results that form the correlations are a
result of the original singlet wave function itself, They have nothing
to do with the subsequent decoherence and onset of classicality. Unless
the probabilities of 'up' and 'down' at the two ends of the experiment
are properly correlated from the start, nothing in the environment is
going to make things come out right. The trace over ignored
environmental degrees does not make the 'incorrect' matches between the
lab books 'zero out'. Because for an individual pair of measurements at
some angle, other than perfect alignment or misalignment, is going to
give all four combinations of results. It is getting these result in the
correct proportions that is the non-local trick. You just have to look
at the standard quantum calculation of the correlations to realize this.
As an exercise, consider the fact that in many-worlds, all possible
sequences of results for Alice occur, from '111111...' to '00000....',
all 1s or all 0s, and everything in between. The correlations have to
come out correctly for every sequence that Alice could get (or better,
there is an Alice corresponding to each possible sequence). All of these
Alices must match up with a corresponding set of results from their
partner Bob to give the correct quantum correlations. Explain how this
happens, particularly for the 'Monster' sequences that at least some
copies of Alice must get.
Bruce
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