Effect of local scale invariance in Aharnov-Bohm setup using non-hermitian pilot-wave (deBroglie-Bohm) theory

We show that Weyl's abandoned idea of gauge as local scale invariance has a natural implementation at the quantum level in pilot-wave (deBroglie-Bohm) theory. The current density is given by the local scale invariant, trajectory-dependent expression $|ψ|²/ 1²[C], where 1[C] is a scale factor that depends on the pilot-wave trajectory C in configuration space. We show that in Aharanov-Bohm experiment our theory predicts modified probabilities that depend on the which-way information. These predictions, testable in regimes of extreme flux and space-time curvature, render non-hermitian pilot-wave theory empirically distinguishable from orthodox quantum theory and other quantum formulations.