World crystal
The world crystal is a model of the universe in which the fact is exploited that crystals with defects have the same internal geometry as non-Euclidean spaces , especially spaces with curvature and torsion , which are used in the Einstein-Cartan theory of gravity (which the Einstein Theory includes). The model is also called the Planck-Kleinert crystal. More recently it has also been discussed by Gerardus' t Hooft (Nobel Prize 1999) (see below).
The model is intended to illustrate that the world at ultrashort distances of the order of Planck length can look completely different from what string theorists assume. If in string theories a fundamental length of the order of magnitude of the Planck length is assumed and the elementary particles including the graviton are modes of vibration of the strings, matter in the world crystal model creates curvature defects on a microscopic level and thereby reproduces the results of the general theory of relativity , in which the Energy-momentum tensor of matter determines the geometrical curvature of space-time.
literature
- Hagen Kleinert : Gravity as Theory of Defects in a Crystal with Only Second-Gradient Elasticity , Annalen der Physik, Vol. 44, 1987, p. 117, online here: number 172 of Kleinert's list of publications
- Hagen Kleinert, Jan Zaanen : World nematic crystal model of gravity explaining the absence of torsion , Physics Letters A 324, 2004, p. 361 ( online preprint and abstract )
- Hagen Kleinert: Multivalued Fields in Condensed Matter, Electrodynamics, and Gravitation , World Scientific (Singapore, 2008) (also available online here ). See chapter 12
- Marek Danielewski: Defects and diffusion in the Planck-Kleinert Crystal: The matter, gravity and electromagnetism . 2005. Full text as pdf (English); 300 KB
- Gerardus' t Hooft : Crystalline Gravity , Erice Lectures (PDF; 1.7 MB) 2008 and 3rd Stueckelberg Workshop at ICRANet Center , Pescara 2008.
swell
- ↑ Danielewski ( Memento of August 13, 2011 in the Internet Archive ) (PDF; 304 kB)