World crystal

In physics, world crystal is a theoretical model of spacetime consistent with general relativity but based on a lattice with the dimensions of the Planck length. Defects in the crystal cause the curvature effects of mass-energy on spacetime. Proposed ^[1] by Hagen Kleinert, it provides an alternative understanding of gravity and an alternative to the extra-dimensional concepts of string theory. ^[2]

Overview

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. ^[3] Thus the world crystal represents a model for emergent or induced gravity in an Einstein–Cartan theory of gravitation (which embraces Einstein's theory of General Relativity). ^[4] The model illustrates that the world may have, at Planck distances, quite different properties from those predicted by string theorists. ^[2] In this model, matter creates defects in spacetime which generate curvature and all the effects of general relativity. ^[5]

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. ^[6] The world crystal implies specific modifications. ^[7]

See also

• Quantum cosmology
• Non-standard cosmology

References

1. H. Kleinert (1987). "Gravity as Theory of Defects in a Crystal with Only Second-Gradient Elasticity". Annalen der Physik . 44 (2): 117. Bibcode:1987AnP...499..117K. doi:10.1002/andp.19874990206.
2. Kleinert, Hagen (June 2016). "Chapter 11: World Crystal Model of Gravity". In Licata, Ignazio (ed.). Beyond Peaceful Coexistence. IMPERIAL COLLEGE PRESS. pp. 299–306. doi:10.1142/9781783268320_0012. ISBN   978-1-78326-831-3.
3. Hagen Kleinert (2000). "Nonholonomic Mapping Principle for Classical and Quantum Mechanics in Spaces with Curvature and Torsion". General Relativity and Gravitation. 32: 769–839. doi:10.1023/A:1001962922592. ISSN   0001-7701.
4. Abdel Nasser Tawfik; Eiman Abou El Dahab (2015). "Corrections to entropy and thermodynamics of charged black hole using generalized uncertainty principle". International Journal of Modern Physics A. 30. doi:10.1142/S0217751X1550030X.
5. Danielewski, M. (2007). "The Planck-Kleinert Crystal" (PDF). Zeitschrift für Naturforschung A . 62 (1–2): 56. Bibcode:2007ZNatA..62...56M. doi:10.1515/zna-2007-10-1102.
6. Magueijo, J.; Smolin, L. (2003). "Generalized Lorentz invariance with an invariant energy scale". Physical Review D . 67 (4): 044017. arXiv: gr-qc/0207085 . Bibcode:2003PhRvD..67d4017M. doi:10.1103/PhysRevD.67.044017.
7. Jizba, P.; Kleinert, H.; Scardigli, F. (2010). "Uncertainty Relation on World Crystal and its Applications to Micro Black Holes". Physical Review D . 81 (8): 084030. arXiv: 0912.2253 . Bibcode:2010PhRvD..81h4030J. doi:10.1103/PhysRevD.81.084030.

Literature

• 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.