We defined a (Lorentz) invariant as a quantity that was unchanged under rotations and Lorentz boosts. A uniform scaling of the coordinates (t,x,y,z)→(kt,kx,ky,kz) , which is analogous to a change of u...We defined a (Lorentz) invariant as a quantity that was unchanged under rotations and Lorentz boosts. A uniform scaling of the coordinates (t,x,y,z)→(kt,kx,ky,kz) , which is analogous to a change of units,1 is all right as long as k is nonzero. A quantity that stays the same under any diffeomorphism is called a scalar. Since a Lorentz transformation is a diffeomorphism, every scalar is a Lorentz invariant. Not every Lorentz invariant is a scalar.
