Source-velocity dependence of light and the velocity-composition law: a unified test framework, current bounds and new tests

Special relativity (SR) states that the speed of light does not depend on the velocity of its source and that velocities compose by the relativistic addition law. Emission (ballistic) theories state instead that light inherits the velocity of its source. We embed both ideas in one kinematic test framework, the source-velocity composition (SVC) framework. One parameter, ε, sets the invariant speed C = c(1 − ε)−1/2 of massive-particle kinematics, while light moves at c in the rest frame of its last emitter. The framework reduces to SR at ε = 0 and to Galilean kinematics with Ritz emission at ε = 1. A second element, the memory closure, specifies how matter erases the source velocity through forward re-radiation. We derive velocity composition, light speed, Doppler shifts, aberration, time dilation, energy–momentum relations, decay kinematics and propagation over astrophysical distances. Laboratory data exclude ε = 1 by more than three orders of magnitude. Ion-clock Doppler data give ε < 4 × 10−8 for any memory closure, and gamma-ray-burst timing gives ε below about 10−17 for the Ewald–Oseen closure. The framework predicts two signatures that SR and standard Lorentz-violation models lack: a thickness-dependent arrival delay of radiation behind a thin foil, and an energy-dependent memory edge in astrophysical photon arrival times. We propose three archival analyses and two laboratory experiments that test these signatures, and we quantify their statistical power.