mg < . Competitive bounds on the mass of the graviton have also been obtained from solar system measurements by space missions such as Cassini and MESSENGER, which instead give the constraint λg > or mg < . Linearized massive gravity At the linear level, one can construct a theory of a massive spin-2 field propagating on Minkowski space. This can be seen as an extension of linearized gravity in the following way. Linearized gravity is obtained by linearizing general relativity around flat space, , where is the Planck mass with the gravitational constant. This leads to a kinetic term in the Lagrangian for which is consistent with diffeomorphism invariance, as well as a coupling to matter of the form where is the stress–energy tensor. This kinetic term and matter coupling combined are nothing other than the Einstein–Hilbert action linearized about flat space. Massive gravity is obtained by adding nonderivative interaction terms for . At the linear level (i.e., second order in ), there are only two possible mass terms: Fierz and Pauli showed in 1939 that this only propagates the expected five polarizations of a massive graviton (as compared to two for the massless case) if the coefficients are chosen so that . Any other choice will unlock a sixth, ghostly degree of freedom. A ghost is a mode with a negative kinetic energy. Its Hamiltonian is unbounded from below and it is therefore unstable to decay into particles of arbitrarily large positive and negative energies. The Fierz–Pauli mass term, is therefore the unique consistent linear theory of a massive spin-2 field. The vDVZ discontinuity In the 1970s Hendrik van Dam and Martinus J. G. Veltman and, independently, Valentin I. Zakharov discovered a peculiar property of Fierz–Pauli massive gravity: its predictions do not uniformly reduce to those of general relativity in the limit . In particular, while at small scales (shorter than the Compton wavelength of the graviton mass), Newton's gravitational law is recovered, the bending of light is only three quarters of the result Albert Einstein obtained in general relativity. This is known as the vDVZ discontinuity. We may understand the smaller light bending as follows. The Fierz–Pauli massive graviton, due to the broken diffeomorphism invariance, propagates three extra degrees of freedom compared to the massless graviton of linearized general relativity. These three degrees of freedom package themselves into a vector field, which is irrelevant for our purposes,