In this talk I will reconsider the problem of comparing initial data to a reference solution for the vacuum Einstein field equations is considered. To this end I will analyse the analogous construction for valence 1 spinors solving the so-called twistor equation. This yields an invariant that measures how much the initial data deviates from Minkowski data. Furthermore, we prove that this invariant vanishes if and only if the mass vanishes. Hence, we get a spinorial proof of the positivity of mass. This proof involves solving a second order elliptic equation, thus providing greater flexibility in the prescription of boundary conditions than the original spinorial proof of the positivity of the mass by Witten. This observation is the suggest a new strategy for the construction of geometric inequalities in General Relativity.
