Quantum geometry
The term quantum geometry math concepts are summarized, with which a common description of phenomena of general relativity and quantum field theory is attempted. Such an approach is needed in the research fields of quantum gravity, for example, for the treatment of effects in the orders of magnitude of the Planck scale, ie in the range of very low lengths ( 10-35 m). This is relevant for some aspects of singularities of general relativity, the properties of black holes and the very early universe ( "big bang ").
A problem for a common treatment between general relativity and quantum mechanics is that the usual methods of quantum mechanics, space and time ( summarized in the theory of relativity as four-dimensional space-time ) as an immutable sizes require. By contrast, according to the general theory of relativity of space dynamically matter affects the spacetime by the gravitational field.
A space-time is described in the general theory of relativity by a Lorentz manifold. With regard to the link target of general relativity with quantum mechanics, the quantum geometry is not necessarily a classic space (or a space-time ) describe, but a generalized form of the geometry from which the properties of the physical space-time arise in special cases. As basic objects nichtvertauschende sizes are accepted instead of point sets often, quantum geometry is then a non- commutative geometry.
Theories of quantum geometry are still in development. An early attempt was made by John Archibald Wheeler, who coined the term Quantengeometrodynamik for a quantum mechanics metric sizes, which should also explain the properties of elementary particles, if possible. With the results of Yang-Mills theory, the task to include the internal degrees of freedom of the particles of the standard model of quantum field theory in the analyzes presented. Meanwhile, several concepts were developed in theoretical physics, none has so far gone beyond the mathematical description of a few specific problems. Examples of such approaches are the loop quantum gravity and string theory. The latter is usually based on a " conventional " ( continuous ) geometry, but at least 10 or 11 space space and time dimensions, are observed of which only four spacetime.
In many concepts of quantum geometry (eg in the loop quantum gravity ) the structure of space-time is in the range of the Planck scale is not continuous but quantized (ie, discrete). Has not fulfilled the hope that by the discretization of a natural limit of very small lengths, the shortest periods and thus the highest energies comes about, which dissolves the problem of infinite expressions in quantum field theory and the consequent need renormalization.