Drag in Dynamical Spatial Frames: Flow–Time Integration and Photon Propagation on Galactic Scales

A kinematic formulation of light propagation in the presence of a geometric flow field is introduced under the name Moving-Frame Optics (MFO). The model assumes that light propagates locally at speed (c) relative to a comoving spatial frame, while this frame has a velocity (u(x,t)) relative to the observer’s coordinate system. The observed photon trajectory results from the combination of local null propagation and transport by the flow field. The direct integral of the transverse flow velocity is interpreted as an accumulated transverse displacement rather than, by itself, an angular deflection. Directional changes depend on spatial gradients of the flow and can be obtained from ray equations derived from a Painlevé–Gullstrand-type effective metric. This distinction provides a rigorous formulation of the flow–time integration principle: a weak flow may produce an observable effect when acting coherently over an extended trajectory, whereas a uniform flow produces no gravitational lensing regardless of exposure time. The relevant magnitude depends on the amplitude, gradients, spatial extension, symmetry, and coherence of the field. The framework is proposed as a testable description of galactic-scale lensing using a flow field derived exclusively from the baryonic distribution. It can only be regarded as an alternative to dark-matter halos if the same independently determined field reproduces rotation curves, deflection, convergence, shear, and time-delay observations without additional lensing parameters. Differential predictions, consistency conditions, and explicit falsification criteria are presented. This manuscript is a theoretical preprint and has not undergone formal peer review.