Wedge Dislocation in the Geometric Theory of Defects

TL;DR

This paper demonstrates that the geometric theory of defects can quantitatively replicate elasticity theory results for wedge dislocations by introducing a specific gauge condition linked to the Poisson ratio, revealing a privileged reference frame.

Contribution

It establishes a connection between the geometric theory of defects and elasticity theory through a gauge condition dependent on the Poisson ratio, providing a new perspective on the theory's foundations.

Findings

Geometric theory reproduces elasticity results in linear approximation.

The gauge condition depends on the Poisson ratio, which is measurable.

A privileged reference frame is suggested, challenging the relativity principle.

Abstract

We consider a wedge dislocation in the framework of elasticity theory and the geometric theory of defects. We show that the geometric theory reproduces quantitatively all the results of elasticity theory in the linear approximation. The coincidence is achieved by introducing a postulate that the vielbein satisfying the Einstein equations must also satisfy the gauge condition, which in the linear approximation leads to the elasticity equations for the displacement vector field. The gauge condition depends on the Poisson ratio, which can be experimentally measured. This indicates the existence of a privileged reference frame, which denies the relativity principle.