Differential Geometry, Dislocations and Einstein's TeleparallelismEinstein's teleparallel theory is based on the so-called torsion tensor, which has become a quantity equally important as curvature in differential geometry. At that time, however, is was difficult to get an intuitive picture what torsion means. This changed in the 1950s when Kröner - after the pioneering work of Kondo and Bilby Bullough and Smith - developed a theory of dislocations in crystalline bodies and demonstrated that the density of dislocations piercing through a surface is equivalent to torsion. Thus with discolations we got a very nice tool to understand Einstein's teleparallelism !
Surprisingly, the theory of dislocations showes many similarities with electrodynamics, including a relativistic behaviour of moving dislocations. Not enough here, this 'electromagnetical' behaviour of dislocations was discovered even before the relation to torsion and thus the relation to Einstein's unified theory was revealed - you may believe this is just coincidence, I don't !
Thus Einstein's attempt, after all, may be not that wrong as it seems today.
My activities in this field
- What can Physics Learn from Continuum Mechanics ? (gr-qc/001164)
- Teleparallel space-time with defects yields geometrization of electrodynamics with quantized sources (gr-qc/9612061),
- paper (revised 10/97), old version(12/96),dvi.
- Einsteins Teleparallelism Attempt and its Relation to Topological Defects in an Elastic continuum,
- talk given at the Gravitation group meeting of the Italian Physical Society in Rome 09/01 (abstract)
- Einsteins Veröffentlichung zum Fernparallelismus 1930: Betrachtung mit Differentialformen,
- talk given at the Gravitation group meeting of the DPG in Bad Honnef 9/99 (abstract)
- Maxwellgleichungen als geometrische Identitäten in einer Raumzeit mit Fernparallelismus und topologischen Defekten,
- talk given at the DPG meeting in Regensburg 3/98 (abstract)
- Einstein's teleparallelism attempt and the theory of dislocations,
- talk given at the differential geometry conference in Budapest 7/96 (abstract)
- Dislocations in crystalline bodies and non-riemannian geometry,
- talk given at the University of Munich 1/95
Jose G. Vargas published a series of papers that are related to Einstein's teleparallelism and Finsler geometry you find in the literature. Of very recent experimental interest is the paper 'The Cartan--Einstein Unification with Teleparallelism and the Discrepant Measurements of Newton's Constant G' in Foundation of Physics 29 (1999), p. 145.