[snarfy]

Ah, if my understanding is correct then this makes sense.

In my initial argument I bring in relativity and the invariant speed of light. What I neglected is everything else in relativity, like lorentz transformations.

I mentioned a discontinuity between invariant speed of light and summing velocities to calculate momentum. The discontinuity is distance. Velocity is distance x time, but under lorentz transformations distance is relative. The discontinuity is resolved if you include length contraction (and time dilation).