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.


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On 24 Feb 2003, 22:33.