In the particular case of particles having equal masses, it can be verified by direct computation from the result above that the scalar product of the velocities before and after the collision are the same, that is ⟨ ⟨ v 1 ′ , v 2 ′ ⟩ ⟩ = ⟨ ⟨ v 1 , v 2 ⟩ ⟩ . Although this product is not an additive invariant in the same way that momentum and kinetic energy are for elastic collisions, it seems that preservation of this quantity can nonetheless be used to derive higher-order conservation laws.