We will discuss a new proof of the fact that an initial data set with null ADM energy-momentum must have zero ADM energy-momentum, and consequently it must be a slice of Minkowski space. Previous work by Beig-Chrusciel and Chrusciel-Maerten established this result in the spin case. Our argument applies to any manifold on which the spacetime positive mass theorem applies. The main idea is to use a Lagrange multipliers argument together with the modified constraint operator. The is joint work with Lan-Hsuan Huang.