Thank you for clear explanation. I wonder how changes in 4-vector velocity relate to "energy & momentum" 4-vector? Does that vector also have fixed magnitude?
It's magnitude is called 'mass' (or 'rest mass'/'invariant mass' if you want to differentiate it from the concept of 'relativistic mass', which probably should be retired).
This means we have
four-momentum = mass * four-velocity
three-momentum = gamma * mass * three-velocityMy layman's research suggest these are, respectively, "electric charge" and "current"?