Demystification of the Aharonov-Bohm Effect and Bohmian Mechanics: Vector Potential as Substrate Shear Velocity and the Hydrodynamic Origin of the Quantum Potential in a Pre-Stressed Vacuum

The Aharonov-Bohm (AB) effect is widely heralded within orthodox Copenhagen quan- tum mechanics as direct proof of irreducibly non-local topology and the physical supremacy of abstract gauge potentials over observable force fields. Building upon our foun- dational series on the physical vacuum as an elastically pre-stressed, fully occupied continuum, we present a deterministic and strictly local resolution of the AB effect and Bohmian mechanics. We demonstrate that the magnetic vector potential⃗ A is not an ungrounded mathematical abstraction, but represents the physical shear dis- placement velocity ⃗vsub and circulating momentum density of the underlying vacuum substrate. In a shielded solenoid configuration where the classical magnetic force vanishes (⃗B= ∇ ×⃗ A = 0), the surrounding continuum is not quiescent; it supports an irrotational, circulating strain velocity field. An electric charge—modeled as a lo- calized topological strain soliton—undergoes an entirely local phase shift as it tra- verses this flowing substrate, mediated directly by the elementary action quantum h= P0ℓ40/c. Furthermore, we demonstrate that David Bohm’s enigmatic “quantum po- tential” Q=−(¯h2/2m)(∇2R/R) originates naturally from the hydrodynamic Bernoulli pressure gradient and elastic curvature tension of the pre-stressed substrate. This uni- fies quantum phase phenomena with classical continuum mechanics under Occam’s razor without invoking action-at-a-distance.