2026/05/09 by R. Pullano, G. Modanese · 1 voice
Physics and Astronomy · #physics.gen-ph
We discuss a formal and physical connection between the Bohm quantum potential and the scalar mode of the Aharonov-Bohm extension of electrodynamics. The analysis is motivated by the effective non-relativistic bosonic model recently proposed by Minotti and Modanese, in which the electromagnetic field is coupled to a conserved current while the field equations contain an additional source term. In the Madelung representation ψ=Rexp(iθ/ℏ), the Bohm quantum potential QB=-(ℏ2)/(2m)(∇2 R)/(R) is determined by the relative curvature ∇2R/R of the amplitude profile R. In the same bosonic model, the scalar electromagnetic mode S=∂μAμ is sourced by the extra-current I=∂μjμ, which contains the density-weighted electromagnetic combination ∇⋅(R2\mathbf A). Thus QB does not act as a direct source of S; rather, the two quantities probe different differential aspects of the same amplitude profile: QB is sensitive to the relative curvature of R, whereas the source of S is sensitive to its density and gradient content through R2 and ∇ R. We show that, once boundary and normalization data are fixed, this observation may be written as a mediated functional dependence of S on QB through R. We also clarify the physical status of QB: although it is state-dependent and should not be interpreted as an autonomous external potential, its density-weighted integral gives the amplitude-gradient energy, equivalently a Fisher-information contribution. This makes QB a compact diagnostic of quantum pressure, rigidity, and inhomogeneity of a bosonic condensate. The resulting link with S is therefore best understood as a structural relation between the order-parameter amplitude profile of the condensate and the scalar sector of the extended electromagnetic theory.