A Theory We're Incapable to Understand?

[ensabah6]

LQG as of now is no candidate for a ToE by construction. The LQG approach is restricted to quantum gravity. It is compatible with matter interaction, the mathamtical formulation (gauge theory) is rather close in a certain sense. But there are no direct attempts to unify gravity with matter.

There are some ideas how particles could emergy from "braided" or "twisted" spin networks, but that seems to be highly speculative. If you like I can give you some references.

There is the idea to harmonize non-commutative geometry with the LQG approach which could lead to standad model matter emerging in the LQG framework; again this is an idea, not a fully developed research program. You can get references if you like.
.

Could particles in LQG be both braiding (a la Sundance) AND noncommutative geometry?

 

[tom.stoer]

I would say no. Or to be more precise: yes, could be, but I see no good reason for it. Either braiding itself is powerful enough to let SM particles emergy from spin networks (I think you need a quantum deformation on a boundary Hilbert space according to Chern-Simons, Smolin's ideas etc. in order to define braids). Or NC is the way to go. Doing both for me means doing too much. One concept should be sufficient.

Braiding is fascinating as it - if it works - requires nothing else but "quantum geometry".

To be honest: in the modern physics literature there is a trend towards mathematically involved constructions w/o physical results. Noncommutative geometry with topological aspects of supergravity AdS/CFT quantum deformations in compactified extra-dimensions derived from M-theory motivated 3-algebras ... This is not how physics works (in my opinion) A theory must be simple enough in order to be true.

As a reference look at these papers:

http://arxiv.org/abs/1005.1057
Spin Foams and Noncommutative Geometry
Domenic Denicola (Caltech), Matilde Marcolli (Caltech), Ahmad Zainy al-Yasry (ICTP)
48 pages, 30 figures
(Submitted on 6 May 2010)
We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the encoding of the gravitational field via holonomies. We then describe convolution algebras of spin networks and spin foams, based on the different ways in which the same topology can be realized as a branched covering via covering moves, and on possible composition operations on spin foams. We illustrate the case of the groupoid algebra of the equivalence relation determined by covering moves and a 2-semigroupoid algebra arising from a 2-category of spin foams with composition operations corresponding to a fibered product of the branched coverings and the gluing of cobordisms. The spin foam amplitudes then give rise to dynamical flows on these algebras, and the existence of low temperature equilibrium states of Gibbs form is related to questions on the existence of topological invariants of embedded graphs and embedded two-complexes with given properties. We end by sketching a possible approach to combining the spin network and spin foam formalism with matter within the framework of spectral triples in noncommutative geometry.

http://arxiv.org/abs/0907.5510
On Semi-Classical States of Quantum Gravity and Noncommutative Geometry
Authors: Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke, Ryszard Nest
(Submitted on 31 Jul 2009)
We construct normalizable, semi-classical states for the previously proposed model of quantum gravity which is formulated as a spectral triple over holonomy loops. The semi-classical limit of the spectral triple gives the Dirac Hamiltonian in 3+1 dimensions. Also, time-independent lapse and shift fields emerge from the semi-classical states. Our analysis shows that the model might contain fermionic matter degrees of freedom.
The semi-classical analysis presented in this paper does away with most of the ambiguities found in the initial semi-finite spectral triple construction. The cubic lattices play the role of a coordinate system and a divergent sequence of free parameters found in the Dirac type operator is identified as a certain inverse infinitesimal volume element.

 

[member 11137]

The proof.

... reloaded ... (no change)

 

[ZapperZ]

Closed pending moderation.

Zz.