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My thoghts on Quantum Graphity: a model of emergent locality

  1. Jan 12, 2008 #1
    my thoughts on "Quantum Graphity: a model of emergent locality"

    I want to thank Marcus for bringing this to my attention.

    One thing I've wanted to see is a rigorous derivation of Wen's string net condensation, which gives rise to both U(1) gauge charge and electrons, with LQG's spin networks. Wen's model is desirable as it is modelled after condense matter systems, which are experimentally verified, and the mechanism and analogy being applied to Sm particles, and in addition to giving rise to U(1) gauge charge and electrons, it also explains fermi statistics, identical particles, gauge interactions in one comprehensive theory. Can LQG appropriate these results within LQG's framework?

    While string nets may not be directly testable when applied to SM vacuum, it may be possible to use certain materials to create artificial electrons, to test the soundness of the proposed mechanism (emergence)

    This is the second paper on quantum graphity, which is LQG + Wen's string net condensation, and here they establish more rigorously that LQG's spin networks, arranged in a hexagonal (not cubic in Wen's more simpler model) plaquette, and dynamical (not static in Wen's model) give rise to U(1) gauge charge and possibly electrons through physics of emergence, studied in condense matter physics.

    Historically, it seems LQG is inspired by the idea of matter as geometry, such as Wheeler's geometrodyanimcs program, of explaining matter in terms of geometry.

    Condense matter physics is an entire branch unto itself, and there is some similarity between phonons and quasiparticles in CDM physics, and SM physics. Since LQG has a candidate spacetime atom, personally, I think this research direction is one of the most promising directions for an TOE based on LQG. It appears that while LQG started out as a purely gravitational theory, since it has spacetime atoms, the mechanism of string nets can give LQG SM U(1) gauge and possibly SU(3) gauge (although I'm not aware of Wen-Levin offering a SU(3) paper). (Alexander's isogravity program may show how to give SU(2) gauge bosons). Wen and Levin also offer a string net mechanism that gives rise to gravitons.

    The paper quantum graphity shows that LQG has the capability of producing some SM physics. They speculate, but do not show, that a certain configuration of this hexagonal lattice gives rise to 3 large spatial dimensions.

    I see a future where condense matter physics principles are applied to LQG's spacetime atoms to give rise to U(1) and SU(3) gauge charges and particles (leptons and quarks).

    Quantum Graphity: a model of emergent locality
    Tomasz Konopka, Fotini Markopoulou, Simone Severini
    25 pages
    (Submitted on 6 Jan 2008)

    "Quantum graphity is a background independent model for emergent locality, spatial geometry and matter. The states of the system correspond to dynamical graphs on N vertices. At high energy, the graph describing the system is highly connected and the physics is invariant under the full symmetric group acting on the vertices. We present evidence that the model also has a low-energy phase in which the graph describing the system breaks permutation symmetry and appears to be ordered, low-dimensional and local. Consideration of the free energy associated with the dominant terms in the dynamics shows that this low-energy state is thermodynamically stable under local perturbations. The model can also give rise to an emergent U(1) gauge theory in the ground state by the string-net condensation mechanism of Levin and Wen. We also reformulate the model in graph-theoretic terms and compare its dynamics to some common graph processes."
    Last edited: Jan 12, 2008
  2. jcsd
  3. Jan 19, 2008 #2
    It is a nice piece of work but there is a problem with it that they do not seem to have looked at. Simply put, they have broken the permutation symmetry too far. They want to break it down to a diffeomorphism invariance but they have broken it down to the symmetry of a flat hexagonal lattice. They can have local perturbations away from flat space but they cannot make it curve over extended distances without dislocations in the hexagonal lattice.

    If they think they can get diffeomorphism invariance from such a lattice they need to discuss how the dislocations would affect the physics. It seems likely to me that they need to break the symmetry differently so that their vacuum acts more like a liquid or glass than a crystal.

    I posted more comments about it on my blog here:
  4. Jan 19, 2008 #3
    I read your blog post, thanks. Would you prefer I comment here or on your blog?

    re: "What is needed is a network that behaves less like a solid crystal and more like a liquid with fluid random triangulations. Then space-time would behave more like the curving surface of a liquid bubble."

    While the authors Markapolou et al, suggest this (page 23 "...important open problems....)"

    I personally have wondered whether this is necessarily true. What exactly is the physical relationship between spin networks and classical spacetime? Your premise seems to imply that spin networks directly participate in classical spacetime, and as atoms are in motion in liquid bubbles, so a network should be allowed to evolve to create curvature.

    But there are physical systems where this is not directly the case.

    A superconducting magnet consists of atoms frozen at liquid nitrogen temperatures, but the magnetic field that is induced by an external magnetic field is dynamical.
    So maybe a frozen non-dynamical hexagonal 3D + 1 lattice of spin networks could, by their interactions and mechanisms like BCS theory give rise to a classical "continuous" dynamical spacetime.
  5. Jan 19, 2008 #4


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    Er.. no they're not! Just because a cuprate superconductor becomes superconducting at such a temperature doesn't mean the atoms are "frozen". It only means that there are strong couplings between the electron and possibly a bosonic mode (magnetic origin or phonons) to induce paring a condensation. The lattice vibration is still present at such a temperature. One only needs to look at the quasiparticle widths in ARPES experiments that extract out the phonon contribution to the scattering rate at these temperatures.

  6. Jan 19, 2008 #5
    the atoms are frozen "at liquid nitrogen temperatures", but of course there is some motion at these temperatures, there is even motion at near absolute zero temperatures.

    The analogy I draw is that a relatively rigid lattice of spin networks could have properties that allows for a spacetime condensation that is dynamical.
  7. Jan 20, 2008 #6
    I'll link from the blog to here

    They mention the need to look at string-net condensation on irregular graphs but this is in order to understand the higher temperature dynamics. They do not discuss any problem with having a regular structure for the vacuum.

    Yes, people have done all kinds of interesting things with spin networks e.g. spin foam approaches and group field theory but the point is that those ideas are not being used here. There have also been discussions of the role of superconductivity on space-time networks (e.g. Finkelstein's superconduncting causal nets) but again they are not being invoked here and there is no indication that the author are thinking that way.
  8. Jan 20, 2008 #7
    I agree that there is no indication that the author are thinking that way, nor do they not discuss any problem with having a regular structure for the vacuum, but what I'm arguing is a response to your blog

    "re: "What is needed is a network that behaves less like a solid crystal and more like a liquid with fluid random triangulations. Then space-time would behave more like the curving surface of a liquid bubble.""

    and my suggestion is that it's not necessarily true that a network (spin network or here hexagonal plaquettes) that behaves less like a solid crystal is needed, and that a network that behaves like a solid crystal could still give rise to an emergent 4D spacetime "that would behave more like the curving surface of a liquid bubble"
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