World Crystal
Encyclopedia
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
. 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
). 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
. More studies of the World Crystal are here.
The existence of a shortest length at the Planck level has interesting consequences for quantum physics at at ultrahigh energies. For example, the uncertainty relation
will be modified as discussed in. The World Crystal implies specific modifications whose consequences are investigated here.
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
.
The World Crystal model is an alternative which exploits the fact that crystals with defects
Crystallographic defect
Crystalline solids exhibit a periodic crystal structure. The positions of atoms or molecules occur on repeating fixed distances, determined by the unit cell parameters. However, the arrangement of atom or molecules in most crystalline materials is not perfect...
have the same non-Euclidean geometry
Non-Euclidean geometry
Non-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...
as spaces with curvature
Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...
and torsion
Torsion tensor
In differential geometry, the notion of torsion is a manner of characterizing a twist or screw of a moving frame around a curve. The torsion of a curve, as it appears in the Frenet-Serret formulas, for instance, quantifies the twist of a curve about its tangent vector as the curve evolves In the...
. Thus the world crystal represents a model for Emergent or Induced Gravity
Induced gravity
Induced gravity is an idea in quantum gravity that space-time background emerges asa mean field approximation of underlying microscopic degrees of freedom, similar to the fluid mechanics approximation of Bose–Einstein condensates...
in an Einstein–Cartan theory
Einstein–Cartan theory
In theoretical physics, the Einstein–Cartan theory, also known as the Einstein–Cartan–Sciama–Kibble theory or the Cartan–Sciama–Kibble theory is a classical theory of gravitation similar to general relativity but relaxing the assumption that the metric be torsion-free. Introducing torsion allows...
of gravitation (which embraces Einstein's theory of General Relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
). The model illustrates that the world may have, at Planck distances, quite different properties from those predicted by string theorists
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
. In this model, matter creates defects in spacetime which generate curvature and all the effects of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
. More studies of the World Crystal are here.
The existence of a shortest length at the Planck level has interesting consequences for quantum physics at at ultrahigh energies. For example, the uncertainty relation
will be modified as discussed in. The World Crystal implies specific modifications whose consequences are investigated here.