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Featured A Ed Witten on Symmetry and Emergence

  1. Nov 11, 2017 #41

    Fra

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    Fearing the discussing is diverging too much, i will try to keep the follow up short. As speculations arent allowed here.
    IMO the physical essence of gauge theory is the concept of "observer equivalence". Ie the law of physics "must"(or must they? see below) be the same to all observers. This constraint as a constructing implies the transformations EXPLAINING the "apparent" disagreements.

    In SR and GR, when you apply this to two sub-classes of valid equivalent gedanken observers. However in classical physics the observers is imagined to be able to make gedanken experiments without interacting with the system. The "physics" is contained here in the entire equivalence classes and their internal relations.

    QM improves this by describing the "PHYSICS of measurementprocess", not just imaging gedanken experiments, like you can go in classical physics. Also in QM, the gageu equivalences are not as always as CLEARLY interpreted as observer equivalence as they relate to "internal symmetries". But in the below these are unified. There is no principal difference. to understand how spacetime splits off from internal structurs is a different discussion.

    However, the measurement process is only PART of the complete what i call inference process.

    So howto combined these?

    Now, if we try to understand the old contstraint of observer equivalence in terms of inference, what does this mean? That means to say that any observer "must" infer the same laws of physics. IF you think about this, you realize soon that this is not a logical constraint, and its not generally true. It rather corresponds to an kind of equilibrium, steady state or attractor point, where interacting observers are in supporting agreement. The scenario which they do not agree, means that they exert a kind of evolutionary selctive pressure to each other so as to - "revise or die". Ie. evolution. the concept of intertia in spacetime and internal spaces, also gets it unification here. In inference the correspondence of intertia is simply the confidence in the prior, that shows resistance to conflicting new information. In this view, there is now placeholder for timeless law - it is considered "speculative" in the strict inference view.

    This is just brief description, as an answer to the question. A longer attemp at explanation would be wrong. Formally all i do here is to hint, and stimulate reflections in the direction. If the above doesnt give you a hint, then cross your fingers that i will be able to work this out an publish something.

    /Fredrik
     
  2. Nov 12, 2017 at 5:12 PM #42
    I was puzzled by this passage in Witten paper referenced in the first thread myself...

    "To put it differently, global symmetry is a property of a system, but gauge symmetry in general
    is a property of a description of a system. What we really learn from the centrality of gauge
    symmetry in modern physics is that physics is described by subtle laws that are “geometrical.”
    This concept is hard to define, but what it means in practice is that the laws of Nature are subtle
    in a way that defies efforts to make them explicit without making choices. The difficulty of making
    these laws explicit in a natural and non-redundant way is the reason for “gauge symmetry."


    To others besides Fra, how do you understand the passage? What did Witten mean the centrality of gauge symmetry in modern physics is that physics is described by subtle laws that are “geometrical.”. He said the concept was hard to define and he only spent 2 sentences for it. At least a paragraph would be more descriptive.. kindly rewords what it means (or the way you understand it). Thanks.
     
    Last edited: Nov 12, 2017 at 6:52 PM
  3. Nov 15, 2017 at 3:36 AM #43
    If no one really understands that passage of Witten either.. here's a simpler question.. what can serve as possible boundary/bulk in reality (in our actual universe).. can the boundary be located inside the planck scale?
     
  4. Nov 16, 2017 at 4:51 PM #44

    Fra

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    I assume you mean an explicit example where both the bulk side and boundary side has a standard interpretation without exotic stuff?
    I am not aware of any, because no standard things seems to have a natural interpretation as AdS, and this is the only bulk form where i think there is an explicit duality known? Someone correct me if i am wrong.

    On one hand the principle is just a mathematical duality, where one version is easier to solve or work with.

    But as such a mathematical tool, one need not worry about the physical reality of the dual side, no more than one need to worry about the physical basis of changing dependet varibles. Its just a computational trick, where the boundary version is more strongly coupled and harded to compute things with.

    Here is a paper with a very pragmatic name.

    AdS/CFT Duality User Guide
    "...The AdS/CFT duality originated from string theory, so it had been discussed in
    string theory. But the situation is changing in recent years, and AdS/CFT has been
    discussed beyond theoretical particle physics. This is because AdS/CFT is be-
    coming a powerful tool to analyze the “real-world.” Examples are QCD, nuclear
    physics, nonequilibrium physics, and condensed-matter physics..."
    -- https://arxiv.org/abs/1409.3575

    And one the other hand one cant help but to ponder about if there is any conceptual generalized meaning of the principle. Geometrical interpretations is one thing, cool as it is, beeing the basis for alot, it does not add anything to my intuition, because i do not think of reality in terms of geometry, that maybe einstein did. I seek an an inferential interpretation, as that is the task i see at hand.

    IMO, i see the holographic (boundary) side of things as a compressed code, that is the result of trying to encode more information in the same physical memory capacity. Obviously a compressed code is more tricky to work with, having stronger and stranger couplings between parts, than the uncompressed version. So while the bulk version may be easier to work with - it takes up more storage. So there seems to be an interplay between computation complexity and a kind of compression. These two fight each other. This is also intutive for computer users. Sometimes you have to choose between space or speed. And in an inference perspective, both this things are important. There is also lots of research on these things which fringes to computer science, but few approaches make what i think are the right combination of things.

    I think we need more cross-sub-discipline thinking to solve this, and some ideas unfortunately get stuck inbetween chairs.

    /Fredrik
     
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