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

--
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Reply via email to