Because this 4-vector removes the factor of rest mass, which distinguishes objects. Putting back the rest mass converts 4-velocity to 4-momentum, which does not have the same magnitude for all objects--the magnitude is the rest mass.
Because this 4-vector removes the factor of rest mass, which distinguishes objects. Putting back the rest mass converts 4-velocity to 4-momentum, which does not have the same magnitude for all objects--the magnitude is the rest mass.