It's an accepted á priori postulate of all types of physics ( Galileo, Newton, Einstein's Special and General relativity ) that the form of all of these mathematical physics laws maintain the same invariant form in all reference frames, whether inertial ( non - accelerating ) as in Special Relativity or the more generalized non - inertial frames ( accelerating ) for General Relativity.
So the problem is that in the case of ordinary E3 spacial coordinates for time and velocities, nothing really is Lorentz form - invariant especially as regards time and velocity, all of which will be overcome by enlisting proper time τ first and foremost in all future special and general relativity equations regarding time, velocity, energy, momentum and acceleration for the motion of bodies of matter possessing mass along world timelines in four - dimensional space and time.
Hence, the 4-velocity, 4-acceleration, 4-force, and 4-momentum vectors are brought into the realm of General Relativity mathematics.
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