Einsteins Teleparallelism Attempt and its Relation
Einsteins Teleparallelism Attempt and its Relation to
Topological Defects in an Elastic continuum
Alexander Unzicker
Pestalozzi-Gymnasium München
Abstract
"... theoreticians aim to
find natural generalizations or extensions of Riemannian
geometry that are richer of concepts, hoping to get to
a logical construction that unifies all physical field
concepts..." (Einstein, 1928).
The geometry of Einstein's teleparallelism attempt,
grown out of discussion with E. Cartan
in the 20ies, is visualized by means of the
continuum theory of dislocations (Kröner, 1960).
Starting from the quantitiy Einstein proposed for the
electromagnetic field, a physical interpretation of
one torsion component is given that represents a defect
density in the continuum theory of dislocations.
Given the fact that a kind of Special Relativity emerges from the motion
of dislocations in a crystal, further analogies
between an elastic medium filled with topological defects
and a spacetime with particles are developed.
In opposition to the common idea of the incompatibility
of Einstein's attempts and quantum mechanics, it will be
demonstrated with some simple
examples that topological defects in many cases behave
like quantum mechanical particles.
File translated from TEX by TTH, version 2.00.
On 24 Feb 2003, 22:33.