World Crystal

Theoretical models of the universe are valid only at large distances. The properties of spacetime at ultrashort distances of the order of the Planck length are completely unknown since they have not been explored by any experiment. At present there is one major theory which tries to predict what happens at these distances: string theory.

The World Crystal model is an alternative which exploits the fact that crystals with defects have the same non-Euclidean geometry as spaces with curvature and Torsion Field torsion used in Einstein–Cartan theory of gravitation(which embraces Einstein's theory of General Relativity).The model illustrates that the world may have at
Planck distances quite different properties than those predicted by
string theorists. The World Crystal is also called Planck-Kleinert crystal (see paper cited below).In this model, matter creates defects in spacetime which generate curvature and all the effects of general relativity.

Literature

*Hagen Kleinert, "Gravity as Theory of Defects in a Crystal with Only Second-Gradient Elasticity", Annalen der Physik, Bd.44, 1987, S.117 (online [http://www.physik.fu-berlin.de/~kleinert/172/172.pdf here] ).
*Hagen Kleinert and Jan Zaanen, "World nematic crystal model of gravity explaining the absence of torsion", Physics Letters A 324, 2004, S.361 (online [http://arxiv.org/abs/gr-qc/0307033 here] )
*Hagen Kleinert, "Multivalued Fields in in Condensed Matter, Electrodynamics, and Gravitation", [http://www.worldscibooks.com/physics/6742.html World Scientific (Singapore, 2008)] (online [http://www.physik.fu-berlin.de/~kleinert/re.html#B9 here] ). See Chapter 12.
* Marek Danielewski: "Defects and diffusion in the Planck-Kleinert Crystal: The matter, gravity and electromagnetism", 2005 (online [http://ceram.agh.edu.pl/~icmmagh/artykuly/237%20PLANCK%20CRYSTAL%20DSL%20final.pdf here] ).
*Gerardus 't Hooft, "Crystalline Gravity", [http://www.ccsem.infn.it/ef/emfcsc2008/pdf/Poster_ISSP2008.pdf Erice Lectures] 2008 and [http://www.icra.it/ICRA_Networkshops/INW25_Stueckelberg3/Welcome.htm 3rd Stueckelberg Workshop] at [http://www.icranet.org/ ICRANet Center] , Pescara 2008.