[UPSC IFoS 2024] Special Theory of Relativity (Q324, 10+5=15M)

Consider two inertial frames S and S'. S is at rest and S' is moving along x - x' direction with constant speed v. (i) Find how different components of momentum four-vector in S and S' frames are related. (ii) Show that p^\mu p_\mu is Lorentz invariant.