  The dynamics of defect excitations in crystalline solids is necessary to
understand the macroscopic low-energy properties of elastic media. We use
fracton-elasticity duality to systematically study the defect dynamics and
interactions in the linear isotropic medium. We derive the explicit expressions
for the dual gauge potentials for moving dislocations and the resulting
Jefimenko equations. We also compute stresses and strains. The paper includes
two physical situations: when the vacancy number is fixed and when the number
is fluctuating. If defects are present we show a constraint that needs to be
satisfied by them when they climb perpendicularly to their Burgers vector.
Next, we extend the classic result of Peach and Koehler for the force between
two dislocations and show that, similarly, to moving charges in
electrodynamics, it is non-reciprocal, when one dislocation is moving. We argue
that our formalism can be extended beyond Cauchy's elasticity by exploiting the
simplifications provided by the dual gauge formulation of elastic stresses.
