The basic Lorentz vector is the spacetime displacement. Any other quantity that has the same behavior under rotations and boosts is also a valid Lorentz vector.
In classical mechanics, Newton’s second law relates momenta and forces, through the time derivative of the momentum. In relativity, we’ll therefore simply define the force four-vector as the derivativ...In classical mechanics, Newton’s second law relates momenta and forces, through the time derivative of the momentum. In relativity, we’ll therefore simply define the force four-vector as the derivative of the energy-momentum four-vector with respect to the proper time.
In Newtonian mechanics, position in space can be indicated with a three-dimensional vector. In Special Relativity, however, events are indicated using four coordinates: x=(t,x,y,z).
