Effective Observer-Split Source Terms in Rotating Frames and Gravitomagnetic Backgrounds in Extended Aharonov-Bohm Electrodynamics

Abstract

We examine whether the observer split of a covariantly conserved electric current in a rotating finite system can provide a physically constrained effective source for the scalar sector of extended Aharonov--Bohm electrodynamics. We first recall that rotation, a stationary gravitomagnetic background, or a change of coordinates cannot by themselves generate genuine microscopic charge non-conservation for standard locally $U(1)$-invariant matter; this simple no-go statement is used to delimit the phenomenological context. In a $3+1$ decomposition adapted to a rotating apparatus, the transport continuity equation contains the exact observer-split term $I_{\mathrm{split}}=N^{-1}{D}_i(\rho {\beta }^i)$, which reduces for weak rigid rotation to $I_G=\Omega {\partial }_{\varphi }\rho$. We propose to use this restricted, congruence-dependent source as a phenomenological input to the extended scalar sector. The relevant observer/evolution structure is not an arbitrary coordinate choice: the laboratory synchronization and readout protocol select the foliation, while the rotor motion fixes the evolution field relative to it. We characterize which features of a genuine extra-current can and cannot be represented by this construction, and discuss falsifiable signatures, including rotation reversal, axisymmetric-source suppression, gradient scaling, and a recently proposed optically gated rotating-disc test. Analogue-gravity systems are also identified as a possible future setting in which a preferred material flow naturally selects the observer congruence.

16 pages, 3 figures; 2 code sources uploaded. Final journal version

References in corpus (9)

• Analogue Gravity
• The Sagnac Effect in curved space-times from an analogy with the Aharonov-Bohm Effect
• Electrodynamics and spacetime geometry I: Foundations
• Generalized Maxwell equations and charge conservation censorship
• Gauge waves generation and detection in Aharonov-Bohm electrodynamics
• Oscillating dipole with fractional quantum source in Aharonov-Bohm electrodynamics
• A new theory of tensor-scalar gravity coupled to Aharonov-Bohm electrodynamics
• Scalar-tensor gravity and Aharonov-Bohm electrodynamics with bosons: applications to superconductors
• Quantum collapse, local conservation of charge, and possible experimental consequences