On 7/6/2018 11:27 PM, Bruce Kellett wrote:
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.
But he also proposes to recover the Born rule. A classical world is an
equivalence class over many quantum states. We don't suppose that every
K40 decay in your blood puts you into a different world, even though it
decoheres into a definite decayed state. When a quantum measurement
gets recorded in its environment, that environment consists of many
classically equivalent, but quantum inequivalent, states. So the
decoherence with these states can realize relative measures satisfying
the Born rule.
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.
Unaffected by the measurement we're considering. But it is maintained
as being classical by continual measurement-like interactions with the
environment.
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.
I don't think so. But whether it is or not, you need to take into
account that the "completely classical" is somehow constructed from the
underlying quantum. I don't think you can just isolate the quantum to
the lab measurement, and use decoherence to get a needle state, but
neglect the constraints that puts on decoherence, i.e. that the
classical (decohered) results satisfy certain statistics.
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'.
But if you assume each measurement is local, i.e. not influenced by the
spacelike measurement of it's partner, then something must zero out
enough of certain ones in order that the right statistics be realized,
in those worlds that Alice and Bob share, whether they meet or not.
Brent
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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