From: *Brent Meeker* <meeke...@verizon.net <mailto:meeke...@verizon.net>>
It is early Sunday evening in midwinter Melbourne, and I have been out
all afternoon drinking with friends. so a couple of bottles of prime
Australian red wine later, I will try to answer you points sensibly......
On 7/6/2018 11:27 PM, Bruce Kellett wrote:
From: *Brent Meeker* <meeke...@verizon.net <mailto:meeke...@verizon.net>>
On 7/6/2018 8:38 PM, Bruce Kellett wrote
From: *Brent Meeker* <meeke...@verizon.net
<mailto:meeke...@verizon.net>>
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.
Zurek does not try to recover the Born rule from quantum Darwinism. His
idea is that the Born rule comes from entanglement assisted invariance,
or envariance. When a state can be transformed by a unitary operator
acting on that state, the action can be undone by another unitary
operator acting on the environment states. This leads to swaps of states
and equal probabilities. He develops this to establish the Born rule
from envariance. Quantum Darwinism is totally different, and is
concerned with the transition from the quantum to the classical state.
So I think your contention here is a misreading of Zurek.
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.
That may be the case, but it is irrelevant in this context.
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.
There are no such constraints on decoherence. The statistics satisfied
by the state are a property of the state itself, not a property of
decoherence.
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.
But that is exactly the point that I am contesting. The measurements are
not completely local. The assumption of locality is shown to break down
in that the quantum statistics cannot be reproduced with purely local
interactions. Since the original quantum state is non-local, we do not
need anything to "zero out" the states that do not have the right
statistics. There are no such states. All states have the right
statistics. There is nothing that needs to be zeroed out. When Alice
gets up, Bob can get either up or down. There is nothing to be removed.
The only thing that is important is that the probabilities for Bob's up
or down must obey the quantum rules, and there is no way that this is
possible with purely local interactions. The probabilities for Bob's up
or down are set by the relative orientation of the magnets, and that
cannot be known locally. Decoherence reaching out into the environment
cannot help here. I urge you to look at the derivation of the quantum
correlations in standard quantum theory. This will convince you that
decoherence and quantum Darwinsim have nothing to do with it. The
correlations can only be formed non-locally. I though you had actually
seen the point of my original argument in terms of Alice and Bob's lab
books after a long series of measurements.
Bruce
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