(adsbygoogle = window.adsbygoogle || []).push({}); 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).

http://arxiv.org/abs/0801.0861

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."

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# My thoghts on Quantum Graphity: a model of emergent locality

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