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 are various approaches which try to predict what happens at these distances: Quantum Gravity.

The World Crystal model[1] is an alternative which exploits the fact that crystals with defects have the same non-Euclidean geometry as spaces with curvature and torsion. Thus the world crystal represents a model for emergent or induced gravity[2] in an 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 from those predicted by string theorists. In this model, matter creates defects in spacetime which generate curvature and all the effects of general relativity.[3]

The existence of a shortest length at the Planck level has interesting consequences for quantum physics at ultrahigh energies. For example, the uncertainty relation will be modified.[4] The World Crystal implies specific modifications.[5]

• Kleinert, H. (2008). Multivalued Fields in Condensed Matter, Electrodynamics, and Gravitation (PDF). World Scientific. pp. 338ff. ISBN 978-981-279-170-2.
• Danielewski, M. (2005). "Defects and Diffusion in the Planck-Kleinert Crystal: The Matter, Gravity, and Electromagnetism" (PDF). Proceedings of the 1st International Conference on Diffusion in Solids and Liquids.
• Kleinert, H.; Zaanen, J. (2004). "World Nematic Crystal Model of Gravity Explaining the Absence of Torsion". Physics Letters A. 324 (5–6): 361–365. arXiv:gr-qc/0307033. Bibcode:2004PhLA..324..361K. doi:10.1016/j.physleta.2004.03.048.
• t' Hooft, G. (2008). "Crystalline Gravity" (PDF). Erice Lectures 2008.