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Wetterich's derivation of QM from classical

  1. Jun 28, 2009 #1

    marcus

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    We know of Christof Wetterich because much cited by Martin Reuter in papers about Asymptotic Safe approach to quantum gravity (invited talks at Loops 2005, Loops 2007, and other QG conferences.) But actually Wetterich has a much broader reputation.

    So here is my puzzle. It seems unlikely that anyone could derive QM from classical statistical physics. If it were valid wouldn't this give a deeper understanding of the foundations. Kind of thing 't Hooft has asked for in Chapter 2 of Oriti's book. Can this thing of Wetterich be right?
    Is there some catch?

    I hope some other people can help out here.

    http://arxiv.org/abs/0906.4919
    Quantum mechanics from classical statistics
    Christof Wetterich
    31 pages
    (Submitted on 26 Jun 2009)

    "Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer."

    I just checked Spires and Wetterich has 5 papers of topcites 250+ class.
    He has 258 published papers in Spires and 18 of them are in the 100+ cites category. His home is the Heidelberg ITP.
    I mention this in case someone needs these objective measures. My awareness of him is that his work forms the basis for one of a halfdozen active live non-string approaches to QG (where you find a UV fixed point in the renormalization group flow---idea proposed by Steven Weinberg and carried out by Reuter Percacci Litim and others. This approach, like Loll's and Horava's also shows a decline in dimensionality from 4D towards 2D with scale---the spatial and space-time dimension runs.)

    Because Wetterich is at the root of a live approach to QG, he is a big deal for me. But I don't know how to evaluate what he says about deriving QM from statistical physics. It seems too cute to be true. Can anyone put this in perspective for me?
     
    Last edited: Jun 28, 2009
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  3. Jun 28, 2009 #2

    marcus

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    Here is Oriti's book
    Approaches to Quantum Gravity: Toward a New Understanding of Space, Time and Matter
    http://www.amazon.co.uk/Approaches-Quantum-Gravity-Toward-Understanding/dp/0521860458

    Here is Gerard 't Hooft's Chapter 2 of Oriti's book
    The Fundamental Nature of Space and Time
    www.phys.uu.nl/~thooft/gthpub/QuantumGrav_06.pdf

    Here also is Carlo Rovelli's Chapter 1 of the book
    Unfinished Revolution
    http://arxiv.org/abs/gr-qc/0604045

    I think both of these are important essays that we could take as signposts. But I have always thought I understood Rovelli's essay very easily and clearly, whereas I was puzzled by the essay of 't Hooft. He seems to be saying that QM is not fundamental and there is some deeper classical structure. I didn't like this, so I couldn't get into his way of thinking. Now I am wondering if there was something correct in 't Hooft essay that I missed.

    Please let me know if I am wrong, and if there is no possible bearing of Wetterich's work on what is discussed in that Chapter 2 essay.
     
    Last edited: Jun 28, 2009
  4. Jun 28, 2009 #3

    atyy

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    Zee has a comment in his nutshell textbook that there are coincidences between stat mech and QM that may come from a deep relationship, but it's in his wild speculations about the future section - I don't remember his exact words.

    Also came across some wild speculation from Vedral here http://arxiv.org/abs/quant-ph/0701101.
     
  5. Jun 28, 2009 #4

    atyy

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  6. Jun 29, 2009 #5

    Fra

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    Marcus, thanks for reporting about new people. At least I never heard of him before.

    I'll try to check that paper and see if I can connect to anything.

    /Fredrik
     
  7. Jun 29, 2009 #6

    Fra

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    I skimmed it quickly, and decided that it's worth reading more properly.

    I like and can related to some parts, but other things worry me. In either case it seems like an interesting paper. Thanks for posting it!

    /Fredrik
     
  8. Jun 29, 2009 #7
  9. Jun 30, 2009 #8

    Demystifier

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    Marcus, I have skimmed through the Wetterich's paper. Here are some of my impressions.

    First, the Wetterich's approach is quite different from those of 't Hooft. 't Hooft insists on determinism, while Wetterich explicitly says that his approach is not deterministic.

    In my view, the basic assumption of the Wetterich's approach is that both classical and quantum physics are purely probabilistic theories. The difference between the two lies in different statistics: quantum statistics is different from classical statistics. What Wetterich claims is that quantum statistics of a finite number of degrees of freedom can emerge from classical statistics of an infinite number of degrees of freedom. He does not propose a concrete underlying classical "theory of everything", but only claims that it is possible in principle and supports it by some toy models. The main reason why, according to him, it works is his INCOMPLETE STATISTICS hypothesis. I am not saying that I completely understand it, but it does make some sense to me. For example, the so called nonlocal correlations among measured degrees of freedom are possible because there are in fact many unmeasured classical degrees of freedom that prepared (by purely local mechanisms) the system before the measurement to make an illusion of nonlocal correlations. While it is possible in principle, it does not look to me as a natural hypothesis. Instead, it looks to me more like a conspiracy.

    To summarize, I would say that in principle the world might work in the way Wetterich proposes, but it is not very likely that it is so.
     
    Last edited: Jun 30, 2009
  10. Jun 30, 2009 #9

    Fra

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    I went through the paper again and here are some brief comments of my impression, judged through my own view.

    I tend to prefer to get the overall motivation and context first, and there I don't see their exact level of ambition is beyond shedding new light on the conceptual interpretation of QM. Perhaps I need to also read some of the references.

    It seems they want to give a different way of introducing some of the quantum logic, expcet as the ordinary axioms of QM.

    They do this by means of conditional probabilities and incomplete statistics. This could make great sense to me if it wasn't for the fact that some things regarding the context is unclear to me. Their context seems to be the entire environment, and I have a little hard to see how they would introduce space and time into that, and how they explain the interactions. But then I don't know what their ambition is.

    What I think incomplete statistics could mean, is simply that the action of any subsystem, is based ONLY on the information contained in the system itself, which is admittedly an incomplete decision base. But this incompleteness will be reflected in the action. Ie. the CONTEXT of the probability space, is the subsystem itself. Thus this leads to a sort of "subjective conditional probability". I think this is partly what they are saying, which is very close to my own thinking, but if so, something is missing I think in their context. They seem to hold a probabilistic realism, and am doubtful that this picture would be possible, in particular if you also aim to explain diversification of interactions and spacetime dynamics.

    About natures preference for QM logic they write

    "The question why Nature shows a strong preference for subsystems that are described by quantum mechanics can now be addressed within the general framework of classical statistics which allows, in principle, also subsystems without the characteristic features of quantum physics. We conjecture that the answer is related to particular stability properties for the time evolution of subsystems with a quantum character"

    I think their conjecture is correct but I don't see any explanation for this conjecture. I expect there to be one. They seem to arrive at their conclusion by adding various constraints and conditions - I expect to see a plausability argument for their uniqueness. I personally think that it takes an evolving context to do so.

    Also, they do not address the physical basis of probability in the sense I wish for. Instead they adopt a probabilistic realism. I don't think that can be maintained if you have the ambition to complement this also with the space and time, and unification of interactions.

    I think in short my main objection is their lack of contex for the probabiliy ~ probabilistic realism. I think this will cause problems when they take this further. I'm against also probabilistic realism. Instead I think the context - which they consider to be an infinite environment, is rather another observer, and thus usually bounded. This is also the "home" of the probability, and I think the only way to compare these contextes, are by letting the observers interact. This could be an alternative continuation to rovellis RQM when he throwed in that "communication is decribed by QM". Instead one could there do soemthing like these guys are doing, but with the addition that the context is bounded, but the observers complexity?

    /Fredrik
     
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