According to the Emitter theory, the velocity of an emitted particle is influenced by the velocity of its source. Obviously yes, this is what commonsense predicts.
So when a photon gets emitted from a decaying pion (travelling at velocity ‘v’), relativists predict that the photon should travel at a speed of ‘c+v’. But the emitted photons were ‘seen’ to travel at just ‘c’ irrespective of the pion’s velocity. Hence relativists concluded that the speed of light is constant and is not affected by that of the source.
But we will soon realise that a decaying pion can’t be used to verify the emitter theory.
Imagine a bee that can fly at a speed of 10mt/sec. If this is used to ‘drive’ a mass, it can only do that at a slower speed, say 8 meters/sec. If we recruit more bees to do the job, together they probably move the mass faster (say 9 meters/sec) but this can’t be more than their own individual speed. Imagine that at this point, a bee frees itself from the ‘flying mass’. As this bee gets ‘released’ from the flying mass, it only flies at its original speed of 10mt/sec. It is wrong to expect this bee to travel at 9+10mt/sec (as per the emitter theory).
Imagine that a spaceship (pion) is flying at a speed of say 1000meters/sec with the help of 4 rocket engines (photons). If one of the rockets gets detached, this detached rocket will fly at its own speed and will not get ‘boosted’ by the spaceship’s motion.
Photons are the fundamental particles of energy. These particles ‘impart’ energy and thus provide the driving force to various particles in the quantum world, let it be an electron or a neutral pion. They are the engines of the quantum world. When a particle decays, photons do not get ‘ejected’ but just get freed. So the photon’s velocity is uninfluenced by that of the decaying particle.