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Could there be spin particles in spin networks?

  1. Jul 24, 2010 #1

    MTd2

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    Would it make sense to think of excitations of a node as it they were made of particles of spin occupying states just like electrons in atoms?
     
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  3. Jul 25, 2010 #2

    marcus

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    MTd2, it does not make sense to me. I find the idea incomprehensible. But fortunately there are several other people who know the current formulation of LQG quite well. Such as Tom.Stoer, francesca, f-h, maybe others too. They may be able to help.

    I don't want to sidetrack your thread. If I tell you a little of how I understand of spin networks it will be enough different from what you asked about that it could be distracting to you. Please, if I say something, don't let it distract from your line of questioning.

    =============
    In my view what is most important is that spin networks are the eigenvectors of the area and volume operators---and they form a basis for the Hilbert space.
    ...Therefore intuitively the labeling on each link must have something to do with area. Since any surface's area operator measures the area of that surface by looking at the labels of all the links through which the surface cuts. That's probably enough to say for now.
     
  4. Jul 25, 2010 #3

    MTd2

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    I don't see the problem with area and volume operator, since in the case of an atom the occupation of levels is what gives it or the lattice geometry, basically. I just tried to pull a very rough analogy. If you have an electron and a lattice, sometimes you have phonons...
     
  5. Jul 25, 2010 #4
    Interesting seond post MTD. Now I see what you are getting at.

    At first, moving from geometry to particles seemed like a bigger step.... your lattice and phonon idea contrasts with spin networks because yours are fixed with periodic vibrational patterns where the spin networks are not...they are evolving rather than fixed.

    Could it be that such evolving spin networks 'pause" long enough to evolve phonons??? Or maybe they create a related type phonon during transitions?? not so crazy to imagine.
     
  6. Jul 25, 2010 #5

    MTd2

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    I don't know about a pause, but if spin foams had a tendency to nest in higher density planes with low spins, the orthogonal direction to the plane could work as a vibration element for each node. So, there could be bound states between orthogonal vibration states of that plane. What do you people think? Is there any relation between asymptotic safety, which gives 2 dimensional planes on UV, and spin foams?
     
  7. Jul 25, 2010 #6

    MTd2

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    I am sorry, it should be a string like surface, so that the analogy holds with AS. The spin evolves. The worldsheet would be the plane.
     
  8. Jul 25, 2010 #7

    marcus

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    If you don't want me to put in my two cents---about a different heuristic viewpoint----because it interferes with your thread, please just say. I'm happy either way.

    QG (quantum geometry) is essentially about information. I will speak in an extremely unrigorous heuristic way for now. Area is one measure of the capacity of a channel---the size of the window that exists between node A and node B.
    The graphs or triangulations of this or that approach are not real objects, they describe geometry (how the world responds to geometrical measurements.)

    So in this case we are talking about spin networks and a spin j is the size of a Hilbert space. Remember that 2j+1 is the dimension of the Hilbert space of the j-irrep.
    The size of a Hilbert space shows the capacity of a channel. The dimensionality of the space of signals that can flow along that link.

    The j label on the link, or the size of the Hilbert along that link, tells me the thickness of the link. Capacity=area. Call that link's Hilbert Hj, technically it is the Hilbert of the j-irrep that was assigned to that link.

    Now I want to think about the INTERTWINER Hilbert at the node where some links come together.

    You know how to take the tensor product (TP) of some finite dimensional vectorspaces, which can be of several different dimensions. We will take the TP of all the incoming and outgoing Hj at some particular node.

    Now we have a special action of the group G=SU(2) where we screw around at the source node before we go along the link, and then we screw around afterwards, at the target node.
    "Rotating" by an element of G before and after shouldn't affect the flow of information.

    So at each node we want the G-invariant subspace of the tensor product of all the incoming and outgoing Hj at that node. That will be a nice little finite-dimensional Hilbert (called the intertwiner Hilbert).

    The thickness of the links that have to meet at a node will determine the volume or chunkiness of the node. If big dimension Hilberts meet at the node, then the node itself will have to be big. That is, the dimension of the intertwiner Hilbert will be correspondingly large.

    What I was just talking about was equations (10) and (11) on page 3 of Rovelli's April paper "1780". You know the one.

    Any quantum theory is about information and measurement, not about ontology hardware gimmicks. What the observer can measure and what info he can get about the system, ideally. So we have to think of geometry in terms of information and how different measurements entrain and connect to each other. The Hilbert space is the fundamental way information is represented, so we have to think of how geometric information is to be coded in a family of Hilberts. And then finally each graph Γ has its own graph Hilbert HΓ. And as you see in equation (1) on page 1, the whole Hilbert is the direct sum of all the separate graph Hilberts.
    Spin networks are simply the natural basis elements of that construction.
     
    Last edited: Jul 25, 2010
  9. Jul 25, 2010 #8

    MTd2

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    Marcus, how anything besides spin is measured through those channels?
     
  10. Jul 25, 2010 #9

    marcus

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    I think you mean how is something transmitted through a channel or a network link.

    The world sends info about itself to itself---info about one place affects another place.
    Measuring is different--it is done by an outside observer.

    Well clearly information travels along a network link by parallel transport.

    The j determines the dimensionality of the vector that you can send along the track.
    And a vector's dimensionality relates to amount of information. Bigger j means more information.

    I am only talking heuristically to give you my intuitive feel in case you are interested. This is enough for me to say about this for now.

    Did you ever read 1998 article called LQG:a Primer by Rovelli Upadhya?
    http://arxiv.org/abs/gr-qc/9806079
    If anyone is unfamiliar with the word "primer" in textbooks it means the absolute most basic introduction. It is a good article, parts of it are still quite useful.
     
    Last edited: Jul 25, 2010
  11. Jul 25, 2010 #10

    marcus

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    There is insight to be gotten by comparing the April paper with the 1998 "Lqg Primer".

    They are consistent but different enough so that they complement each other.
    For example compare equation (3) on page 2 of the new paper
    with the first paragraph of Section B Gauge Transformations, of the old 1998 paper.

    2010: http://arxiv.org/abs/1004.1780
    1998: http://arxiv.org/abs/gr-qc/9806079

    In a sense the old paper, LQG Primer, is more explanatory. It starts with the space of connections (parallel transport functions on a manifold) take as the configuration space of geometry.
    Then a "wave function" on the configuration space would be a complex valued function defined on the connections. So the hilbert of quantum states of geometry is defined by constructing the "cylindrical functions" which are natural easy-to-understand functions of a connection A. Plug in any connection and the cylinder function will spit out a number for you. That's equation (1) and the inner product of two of them is equation (2).

    Then you see how spin networks are motivated. Why they emerge as the basis of the Hilbert space of functions defined on connections---the Hilbert space of geometric quantum states.

    Because a spin network gives a function defined on connections in a natural way. Basically you run along the links of the network, using the parallel transport of the connection. Just like doing holonomy around a loop, except the network is slightly more complicated than a single loop.

    The new treatment (vintage 2010) does not require the connections on a manifold, as a place to start. It is more streamlined, combinatorial, and algebraic. It is not based on so much differential manifold hardware. But it constructs the same Hilbert space of quantum states.
     
  12. Jul 25, 2010 #11

    MTd2

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    spin network stands for su(2) spinorial representation quantum mechanical network, right?

    But why not thinking really of spin 1/2 particles and each rep as something like a Hartree-Fock matrix of said particles?
     
  13. Jul 25, 2010 #12

    marcus

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    You can think about it whatever way works best for you, MTd2. Penrose formulated a mathematical construction with one purpose in mind. Rovelli took over the same construction and found that it just happens to be suitable for an entirely different purpose. With a math construct, there is no unique "right" way to use it, or to think about it.

    I simply want to let you know how I think about spin networks. As presented by
    Rovelli in 1998 they do not have physical existence. They are not hardware. They are a convenient basis of a certain vector space---the vector space of functions defined on something more basic (the connections on a manifold.) A spin network is analogous to a wave function defined on a space of configurations.

    You can go on exploring the idea that a spin network might be a real thing with particles running around on it. I should be quiet now, since I've given you my concept and it is useless to argue the comparative merits.
     
  14. Jul 25, 2010 #13

    MTd2

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    Non existent, yet they count the entropy of gravity?
     
  15. Jul 25, 2010 #14

    marcus

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    Well, in the sense that information exists, they exist. They are not (as I understand it) hardware.

    And entropy is an information theoretic concept. It may in fact depend on the observer (as Padma says) and what he is able to know about what is inside the box or beyond his horizon. And the different microstates he can (or cannot) distinguish. This is about information.

    Spin networks are about what we can measure and how the world responds to measurements of geometric quantities and relations.

    What do you think Feynman diagrams are? Are they real hardware? Made of some special kind of wire? :biggrin:

    Please, I want to get out of this thread because I have given my viewpoint sufficiently clearly, I think, and contrasted it with yours. We should not argue about what viewpoint on spin networks is "right".
     
  16. Jul 25, 2010 #15

    MTd2

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    But Feynman diagrams would be spin foams...
     
  17. Jul 26, 2010 #16

    Fra

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    The last discussion between Marcus and MTd2 reminds me about some objections I have to the way rovelli presents LQG. Some parts are attractive, and some parts doesn's seem to fit, so the overall pictures is to me incoherent.

    Marcus describes that on one hand, one could see the spin-networks as an underlying sort of information theoretic abstraction, a priori void of things like "geometry notions" etc. So that instead the notions of geometry somehow emerges from a deeper picture. This part is I think plausible, and it's the vision I had when I first learned about LQG.

    But when you analyse the notion of information, interaction, and measurement more carefully rovelli IMO avoids the harder questions. Instead he at some points, just throws in the statement that "this is described by quantum mechanics as we know it" - something he also described clear enough in his RQM paper. Both the good and the "not so good" parts are IMO reasonbly clearly exposed in that paper.

    The summary is IMO, that he has not made a construction in the clean deeper relational spirit he gave the impressoin of in the beginning, it seems to be only a way ot motivate a construction that was already decided, that essential was geometric after all.

    I think this objection is related to the question of wether spin-networks, or information in general is "real".

    My vision, that I had before lookin into LQG, was that the entire spin-network is rather ENCODED within an observer view, and in that sense to speak about a spin-network we need a context. An obsrrver. And a REAL inside observer. This is what I think is a possible connection to particles and matter in LQG - that the information one piece of matter, have about it's own environment could (maybe) be represented by something like an spin-network. But I personally don't like the name SPIN-network as it's a way to sneak in geometric notions that aren't (yet) justified. I think the name action-network is better. This would could represents inferred relations between distinguishable events in the environment. But this entire "relations-networks" would then itself be subjective, and depending on the observer.

    Maybe "spin" would be better though of as a "directed" action, in the sense that the preferred direction is related to an entropic flow.

    In this sene I think that what is a to one observer, just a "transition", could do antother observer be a state. The sense of objectivity that I think exists in LQG about the spin networks is IMO hard to justify, and they just come from how rovelli postulated that the communication in his "relatiional view" simply are obeyed by the mathematical structure of QM. This is a vert strong statement, and I IMO he has not motivated it beyond the level that "otherwise he doesn't know what to do".

    /Fredrik
     
  18. Jul 26, 2010 #17

    Fra

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    Yes, this makes perfect sense. Entropy is observer dependent.

    Shouldn't it be what an observer can measure, rather than "we"? If so - I would conclude that also a spin-network has to be observer dependent? Because rovelli once said there are "no absolute relations" - then I expect that relations as well as subject to inference. IE. a physical observer, can have "information" about what relations (between distinguishable thinkgs in it's environment) that is seen, and this too has to be a result of physical processes? or?

    I respect that we have differing view here but I'm curious if that would that make sense in your view?

    /Fredrik
     
  19. Jul 26, 2010 #18

    Fra

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    Isn't this the inconsistency of how we normally do "relativity".

    Absolute states are replaced by relative states, but instead we find an absolute transformation between the relative states. So it's a "reformulation" into the "same form", isn' it?

    It's what smolin also points out in the evolving law arguments, that most of current physics have the same form. The difference between newtons mechanics, relativity and QM is not really that big in this sense.

    /Fredrik
     
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