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Zureck's Quantum Darwinism Paper

  1. Mar 9, 2015 #1

    bhobba

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    Hi Guys

    Quantum Darwinism came up in another thread so I thought I would go through Zurecks paper on it.
    http://arxiv.org/pdf/0903.5082v1.pdf

    Went through it years ago but know quite a bit more about the foundations of QM now.

    What struck me this time was his postulates:

    'Quantum physics is based on several “textbook” postulates The first two; (i) States are represented by vectors in Hilbert space, and; (ii) Evolutions are unitary – give complete account of mathematics of quantum theory, but make no connection with physics. For that one needs to relate calculations made possible by the superposition principle of (i) and unitarity of (ii) to experiments. Postulate (iii) Immediate repetition of a measurement yields the same outcome starts this task. This is the only uncontroversial measurement postulate (even if it is difficult to approximate in the laboratory): Such repeatability or predictability is behind the very idea of “a state”. In contrast to (i)-(iii), collapse postulate (iv) Outcomes correspond to eigenstates of the measured observable, and only one of them is detected in any given run of the experiment, is inconsistent with (i) and (ii). Conflict arises for two reasons: Restriction to a preferred set of outcome states seems at odds with with the egalitarian principle of superposition, embodied in (i). This restriction prevents one from finding out unknown quantum states, so it is responsible for their fragility.'

    My concern has to do with Gleason's theorem. Starting from Von Neumann measurements (the probability of outcome i is described by a resolution of the identity Ei, such that outcome i depends only on Ei) one applies Gleason and you get; first, states must exist (and they obey by fiat the principle of superposition since pure states form a vector space), and secondly, the Born rule he asserts is in conflict with the first. That however is logically not possible. I am not worried about the unitary thing since that falls out of Wigners Theorem.

    Really scratching my head here.

    What do others think?

    Thanks
    Bill
     
  2. jcsd
  3. Mar 9, 2015 #2

    atyy

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    He's just stating things very loosely. He can state it more properly, but he knows and his audience knows that the problems don't go away, so he sticks to the naive form of the postulates in the Copenhagen interpretation for simplicity. Because of the Born rule, in order to describe successive measurements in the Schroedinger picture, the state evolution must be random after after the Born rule has been applied when a measurement is made. Since there are two rules of time evolution - one deterministic and one random, in order to avoid a contradiction, they must be applied at different times. An external observer is needed to decide when a definite outcome is obtained, which is the measurement problem.
     
  4. Mar 10, 2015 #3

    bhobba

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    Hi Atty

    Mate I think you nailed it.

    I had to take a trip since I posted it and thought about it during the drive and that's the conclusion I pretty much reached.

    Thanks
    Bill
     
  5. Mar 10, 2015 #4
    Bill. After reading Zurek quantum Darwinism papers for 5 years.. I still can't understand how it is connected to Copenhagen so let me ask this so it's clear up once and for all. I know it is about (Maximillian page 86) "Thus the role of environment is now broadened, namely, from the selection of preferred states for the system of interest and the delocalization of local phase coherence between these states to the transmission of information about the state of the system. The key question, first spelled out by the Los Alamos group, is then the following. How, and which kind of information is both redundantly and robustly stored in a large number of distinct fragments of the environment in such a way that multiple observers can retrieve this information without disturbing the state of the system, thereby achieving effect classicality of the state?"

    Why does Zurek worry about how multiple observers can retrieve this information without disturbing the state of the system. For example. You measure the electron using the position operator while atyy measure it using the momentum operator. You two will get different answers. This is commonly done in laboratory so what's the problem. So why propose quantum Darwinism where you and atyy has to both read the same state of the electron? This is the reason if I thought this had to do with macroscopic object like window as we discussed. And you two said it didn't.. so for microscopic object, what's the deal if you two read different results since you use different instrument (and hence shift the operators)?
     
  6. Mar 10, 2015 #5

    bhobba

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    Think to Schroedingers Cat. You can tell if the particle detector clicked by looking at if the vial was broken or if the cat was alive or dead. They are different observations, part of the particle detectors environment - different fragments as he says. But they should all agree - which is a central concern he has.

    Thanks
    Bill
     
  7. Mar 10, 2015 #6
    You told me the window won't change by each person looking at it because it's locked to the eigenstates of positions. So it really can change (without quantum Darwinism)? But how does it and the cat eigenstates of positions change (hence changing the window shape)? Why didn't you say so, I was perplexed by it for a week.
     
  8. Mar 10, 2015 #7

    atyy

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    Yes, Quantum Darwinism does make sense in Copenhagen. In Copenhagen, one can place the classical/quantum cut at different locations along the von Neumann chain of different observers and get consistent results. Decoherence and Quantum Darwinism show this consistency.
     
  9. Mar 10, 2015 #8
    without quantum darwinism, you would see a cat sleeping and bhobba would see the same cat that is jumping up and down? can you give other examples for macroscopic object if quantum darwinism didnt exist.. like would you literally see window that is square while bhobba would see a triangle window? or is it all valid only for quantum object in coherence? but bhobba mentioned a cat...
     
  10. Mar 10, 2015 #9

    bhobba

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    I didn't say that.

    I said in my interpretation its not an issue because I put collapse immediately after decoherence and everything is classical after that. And I specifically pointed out Zureck has a different view and you have to read his paper to understand it rather than the limited account in Schlosshauer.

    Again, as I said, there is a tacit assumption in decoherence accounts that every observer observes the same thing which Zureck does not assume and proves it.

    To be exact in ignorance ensemble it is assumed its a proper mixed state so its actually in the state that's observed - since it really is in that state all observers must agree on it.

    Thanks
    Bill
     
    Last edited: Mar 10, 2015
  11. Mar 10, 2015 #10

    bhobba

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    That's incorrect.

    First Zureck proves that observations of fragments leads to exactly the same result for all observers. There is no interpretive assumption in doing that. Secondly most interpretations like ignorance ensemble, Copenhagen etc etc make that assumption anyway because they assume a classical world observations appear in. Its an assumption of classicality all observers observe the same thing.

    Zurek specifically states it:
    'Bohr bypassed conflict of (i) and (ii) with (iv) by insisting that apparatus is classical, so unitarity and the principle of superposition need not apply to measurements. But this is an excuse, not an explanation. We are dealing with a quantum environment, and redundancy of previous section strengthened motivation for postulate (iii) – repeatability. Let us see where this demand takes us in a purely quantum setting of postulates (i), (ii), and (iii)'

    There is no inconsistency in Copenhagen. It simply assumes something Zurek proves.

    Thanks
    Bill
     
    Last edited: Mar 10, 2015
  12. Mar 10, 2015 #11
    In other words, Zurek quantum Darwinism has made an extra prediction.. in that if you can suppress quantum Darwinism, you can change the macroscopic object and make each window change shape everytime a new tourist interact with it? Do you agree with this?
     
  13. Mar 10, 2015 #12

    bhobba

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    No.

    Its simple - you are making something complex and opaque from something simple.

    Most interpretations have an explicit or implicit hidden assumption that all observers will see the same thing. Such does not invalidate QM or create the issues you mentioned - in fact it specifically denies them. All Zureck does is simply prove, from the axioms of QM he states, that must be the case. It doesn't in anyway have issues with any other interpretation.

    My post simply had to do with some comments he made about his axioms and his second two are somehow in conflict with the first two. That's not logically possible since the second two in fact determine the first two. But thinking about it I agree with Atty - he is being a bit loose here because he wants to show QM basically just needs his two axioms. Unfortunately Wigners theorem can't be used at this stage to get axiom 2 because probabilities haven't been introduced. Its a nice idea, and may even be true, but its not the only way to proceed eg it can be done from from just one axiom (see post 137):
    https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

    Which way is better? That's hard to say. I think from an understanding point of view Zureck is better because it elucidates better exactly what an observation is. The other approach is along the lines of Fuchs Quantum Information:
    http://arxiv.org/abs/quant-ph/0205039

    There - as in the link I gave - observations are the primitive - for Zureck states are the primitive. I personally side with Fuchs - but others may not see it that way.

    Thanks
    Bill
     
    Last edited: Mar 10, 2015
  14. Mar 10, 2015 #13
    Has it occurred to you that quantum Darwinism is redundant? For example.. we know the window is decohered by thermal bath into eigenstates of positions, so the shape is fixed. Therefore even without different observers intercepting the photons, they would still see the same thing even by directly interacting with the window. It won't re-prepare the window because it's already decohered, so what's the purpose of quantum Darwinism, it's redundant, do you get my what I'm saying?
     
  15. Mar 10, 2015 #14

    bhobba

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    I believe its redundant by simply saying its in a proper mixed state. If that what you are saying then sure.

    But you can't use that to derive Born's rule which is a biggie for Zurek. Some done think his derivation is incorrect but I don't really want to get into that - its a whole new thread.

    Thanks
    Bill
     
  16. Mar 11, 2015 #15
    MWI, Bohmian treat it as in proper mixed state and so is Hansen ignorant ensemble so can you confirm here quantum Darwinism is superfluous (redundant)?
    What do you make of kashner partioning or factoring critique of classical pointer states. You think the reasoning is valid or just an attempt to push at her CI? Zurek just ignored it totally. I spent a lot of time reading her work yesterday.
     
  17. Mar 11, 2015 #16

    bhobba

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    Don't know Hansen ignorant ensemble - but I can confirm the ignorant ensemble ensemble does not require a proof that observations of environment fragments give the same result.

    Don't know that one.

    But the factoring issue has been hashed out ad-nausium in many threads. It completely exacerbates me - it's the last gasp of those that wont accept progress IMHO. Its a tacit assumption of many areas of physics. Still proofs are required that show regardless of how a system is factored you get the same result. I don't want to rehash it though - its all there in the previous threads.

    Thanks
    Bill
     
  18. Mar 11, 2015 #17

    naima

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    In this paper the author writes that the no cloning theorem is not troublesome. That the cloned things are the observables not the states. Have you the beginning of an idea on what he wants to say?
     
  19. Mar 11, 2015 #18

    bhobba

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    You observe a system in a certain state with an observable. In decoherence the environment acts like the observable and then you observe different fragments of the environment.

    Thanks
    Bill
     
  20. Mar 11, 2015 #19
    Bill, so you basically agree that quantum Darwinism is attempt to turn improper mixed state to proper mixed state? or is it just all about explaining why pointer states are classical? And if something can explain why pointer states are classical, does it automatically explain how improper turn to proper mixed state?
     
  21. Mar 11, 2015 #20

    bhobba

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    Quantum Darwinism is simply Zurek's attempt to reduce QM to the first two axioms he talks about in his paper. Since that doesn't include the concept of observation he has to give a fully quantum account of it, which he does via his idea of observing fragments.

    Other approaches such as mine start from a different primitive - observations themselves. A tacit assumption of such an approach, even though its not explicitly stated, is that observational outcomes are objective ie everyone agrees on what it is eg if a number of people look at a readout everyone agrees its the same thing. This is really the assumption of classicality that observations are assumed to appear in.

    It's two different approaches with two different primitives - in Zureck the quantum state is the primitive and observations defined from that. In the other observation leads to states via Gleason.

    Take your pick - I am with observations being the primitive. But the choice isn't science - just like interpretations its simply what appeals better.

    Thanks
    Bill
     
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