Another framing of the issue with negative inertial+gravitational mass is that it would result in perpetual acceleration. E.g. assume two bodies, one with mass

Another framing of the issue with negative inertial+gravitational mass is that it would result in perpetual acceleration. E.g. assume two bodies, one with mass M, the other with mass -M. The standard gravitational model describes a "repulsive" force on each of these objects, in the direction opposite each other. However, since the object of mass -M has negative inertial mass, this force would cause it to accelerate toward the object of mass M. This results in these objects not accelerating relative to each other, and perpetually accelerating relative to an independent observer. One might attempt to explain this by saying that the negative mass has a growing negative kinetic energy level, but (it seems as a layman) this would violate the second law of thermodynamics. Edit: Actually just negative inertial mass does this all by itself; it is just in the opposite direction if the gravitational mass is positive.