How Does Quantum Darwinism Relate to the Born Rule and Observer Agreement?

[PeterDonis]

As far as I know they are standard terms.

I assume you mean, with the particular definitions you are giving them (which are not the same as the ones cube137 was using earlier).

It means that there's no experiment we can do to distinguish between 'proper' and 'improper'

I assume you mean, no experiment on the particles you sent. Of course in the second case you can do experiments involving the other particles in each pair that will tell you about the global state and hence will distinguish it from the first case.

 

[Simon Phoenix]

I assume you mean, no experiment on the particles you sent. Of course in the second case you can do experiments involving the other particles in each pair that will tell you about the global state and hence will distinguish it from the first case

Yes - oops I should have been clearer. Original post now fixed (I hope)

 

[Simon Phoenix]

In other words, when you think of yourself as "measuring the wood directly", you aren't really; you are really interacting with the same "fragments" that are part of the environment and are storing copies of information about the wood.

Yes, and clearly that can contain only a very limited amount of information about the wood - so the environment isn't keeping a whole load of copies of $|wood \rangle$, but just copies of limited information (the 'observables'). Have I interpreted that correctly?

I was intrigued by Zurek's allusion to error-correcting codes and Shannon's theorem. If we look at the 'noisy typewriter' channel then we have a channel that is like a broken typewriter so that if we hit the B key then we could get A,B or C being printed with equal probability, and so on for every key. If we only ever use the B,E,H,... keys then we can communicate error-free on this noisy channel. So in a very loose way I'm thinking that if B is the observable - then 'environment' states A,B or C contain the same information (about B).

 

[PeterDonis]

the environment isn't keeping a whole load of copies of $|wood \rangle$, but just copies of limited information (the 'observables').

Yes, I agree. Zurek seems to be suggesting that the environment is keeping many copies of information about the position of the block of wood as a whole--which basically means the position of its center of mass and its size. That is certainly a small fraction of all the possible information about the $10^{25}$ or so atoms in the wood. (This is still true even if we also imagine the environment to be storing many copies of information about the wood's surface color, texture, etc.)

 

[secur]

I'm actually not sure that's the general strategy he's trying to describe. For one thing, it doesn't work with coefficients that don't square to rational numbers; for example, $\sqrt{\pi}$ and $\sqrt{1 - \pi}$. But I need to look into this aspect more; I agree there's certainly something missing from the paper we've been looking at.

If probabilities (meaning, of course, squares of the coefficients - assuming Born rule) are irrational or transcendental he'll use converging sequence of rationals.

Extension of this proof to the case where probabilities are commensurate is conceptually straightforward but notationally cumbersome.

Probabilities being commensurate, meaning the ratios of them are rational. (Which is, actually, equivalent to the probabilities themselves being rational.)

The case of noncommensurate probabilities is settled with an appeal to continuity.

If they're incommensurate there are non-rationals involved, like $\sqrt{1/\pi}$ and $\sqrt{1 - 1/\pi}$. In that case he'll rely on the density of rationals in the reals.

See this paper https://arxiv.org/pdf/quant-ph/0405161.pdf:

D. Born’s rule: the case of unequal coefficients

We now introduce a counterweight / counter C. It can be thought of either as a subsystem extracted from the environment E, or as an ancilla that becomes correlated with E so that the combined state is: {formula} where {C k} are orthonormal. Moreover, we assume that {C k} are associated with subspaces of {The Hilbert Space} of sufficient dimensionality so that the ‘fine-graining’ represented by {formula} is possible.
...
This is Born’s rule. The extension to the case where {the probabilities} are incommensurate is straightforward by continuity as rational numbers are dense among reals.

(BTW I should use LaTex.) Here he goes into the strategy in more detail. It seems there's a vital piece missing, why should the subspace dimensions be related (at least, so directly) to probabilities / coefficients?

Note that reproducing Born rule constitutes one of the major difficulties in MWI. AFAIK it's never been solved. So I was particularly interested in how he'd handle it. The discussion preceding this, involving Schmidt decomposition and "swapping" to establish equiprobabilities, is fine and interesting. But is it a smokescreen, to cover this fine-graining, which is key to the whole approach? If it really works, it's an MWI breakthrough.

 

[cube137]

Yes, I agree. Zurek seems to be suggesting that the environment is keeping many copies of information about the position of the block of wood as a whole--which basically means the position of its center of mass and its size. That is certainly a small fraction of all the possible information about the $10^{25}$ or so atoms in the wood. (This is still true even if we also imagine the environment to be storing many copies of information about the wood's surface color, texture, etc.)

For those of us indoctrinated into Many worlds... so Zurek fragments only belong to one world or branch.. and the reasons we can't perturb the quantum object directly is akin to the reason we can't influence or affect all the worlds or branches at once?? This is especially apparent in Zurek own words at page 8 of https://arxiv.org/pdf/1412.5206v1.pdf "Quantum Darwinism, Decoherence, and the Randomness of Quantum Jumps"

"Repeatability leads to branch-like states, Eq. (13),
suggesting Everettian `relative states' [19]. There is no
need to attribute reality to all the branches. Quantum
states are part information. As we have seen, objective
reality is an emergent property. Unobserved branches
can be regarded as events potentially consistent with the
initially available information that did not happen. Information
we gather can be used to advantage|it can lead
to actions conditioned on measurement outcomes [5]."
<snip>
"Quantum Darwinism explains why we see only one
branch. One can dismiss other branches, e.g. with an appeal
to Everett [19]. So we can account for a perception
of collapse. Thus, while unitarity precludes fundamental
collapse, local observables that reveal branches do not
commute with the global observable whose eigenstates
are coherent superpositions of all the branches, Eq. (13).
Therefore, local observers have no way to probe (hence,
cannot perceive) the global state vector."

For all the superposition experiments that have been performed. Is the idea that superposition is just quantum information compatible or do both copies really exist at same time (such as spin up or spin down that is in superposition.. is there really a copy of spin up and spin down or can superposition of it be simply quantum information and is this compatible with all data so far??)

 

[secur]

is there really a copy of spin up and spin down or can superposition of it be simply quantum information and is this compatible with all data so far?

It could be "simply quantum information" or both copies could "really exist". Neither of those statements is well-defined (since they're philosophy not science) but they're both possible, and so are other interpretations.

What counts is the physics and math. That starts with mainstream QM math, interpretation-free. But also "What does Zurek (or whoever) mean here"? "Is his math consistent"? "Does it really work"? - are good questions. My advice, avoid the question "Is it true?" - leave that to philosophy forums.

It's also not worth debating "what is Zurek's stance" but FWIW I think it's MWI.

There is no need to attribute reality to all the branches.

That doesn't sound like MWI.

unitarity precludes fundamental collapse ...

But that does. FWIW I think he's an MWI believer making a commendable effort to kick the habit, knowing such belief is scientifically unjustifiable. But it doesn't matter, of course.

My advice: don't either believe or disbelieve a particular interpretation. Also, don't care what someone else's beliefs are. It's worth discussing interpretations, but only with the goal of making sure they really are valid. That brings me back to your question. Yes, the superpositions could be "really real" or they could be "quantum information" - whatever those two phrases mean. Both are vague enough to be compatible with the facts of QM.

And that's my last word - literally - concerning the "truth" of interpretations!

 

[cube137]

Is the reason many of you guys dislike interpretations is because you can still turn it the other way around and say that the classical world is all there is and everything is just observation effect and Zurek stuff is just all imagination? Prior to the 1970 before the time of Zeh there was no discussion about decoherence. So can those pre-Zeh, pre decoherence period still be correct in that in the buckyball experiment where different thermal condition can affect the interference. It is really all classical world with the observation effect. This means in spite of all evidences of decoherences.. it doesn't prove that Zurek is correct but Bohr could still be correct about the classical and quantum world?

How many of physicists believe in Bohr and believe in Zurek?
For those who only want to focus on the mathematics like Peterdonis, does it mean either Bohr or Zurek could still be correct and all the evidences of decoherences don't prove (or disprove) any of them?

 

[PeterDonis]

the reason many of you guys dislike interpretations

The reason interpretations are not good topics for discussion here on PF is that they are experimentally indistinguishable; they all make exactly the same predictions for the results of all experiments. So any difference between them is not a matter of physics; it's a matter of "philosophy", or whatever you want to call it, but it not being a matter of physics is what makes it an unsuitable topic for PF discussion (at least in the physics forums).

does it mean either Bohr or Zurek could still be correct and all the evidences of decoherences don't prove (or disprove) any of them?

No evidence can "prove" or "disprove" any interpretation relative to any other, since, as above, they all make exactly the same predictions for all experimental results.