The Aharonov-Bohm Effect in a Micropolar Vacuum: A Topological Phase Application

This preprint presents a direct application of the "World Crystal" (micropolar vacuum) framework to one of the most fundamental quantum topological phenomena: the Aharonov-Bohm effect. Building upon the foundational exact duality between Cosserat elasticity and gauge theories (established in Part I and II of this research program), this work demonstrates that the electromagnetic vector potential A is not merely a mathematical auxiliary construct, but represents the physical, internal microrotation field ϕ of the vacuum substrate. Key highlights of this paper: Mechanical Interpretation of Quantum Phase: The quantum phase shift experienced by an electron in a magnetic-field-free region is mathematically derived as a purely mechanical holonomy. It is modeled as the topological friction experienced by a physical defect (dislocation) moving through a locally twisted vacuum lattice. Macroscopic Decoupling: To ensure consistency with experimental bounds, the paper provides a rigorous dimensional analysis argument. It proves why macroscopic rotating neutral masses (generating a standard "Cosserat slip" or Lense-Thirring drag) do not induce an Aharonov-Bohm phase, owing to a massive gravitational-to-gauge suppression factor of ∼10−43. This analog model successfully bridges the gap between classical continuum mechanics and topological quantum phases, offering a tangible physical interpretation of gauge potentials without violating macroscopic experimental constraints. Note: This is an application paper extending the theoretical foundations laid out in "Emergent Gauge and Gravity Fields from the Asymmetric Distortion of a Cosserat Vacuum" (Part I) and its extension to non-Abelian fields (Part II).