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Differential Geometry, Dislocations and Einstein's Teleparallelism
Einstein'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
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.
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