In physics we cannot easily imagine “negative” energy for a particle (not a field) in order to have “negative” mass, although the first concept of Dirac for antiparticles was that they were “holes” that were opposite to particle existence and there was a minus in front of mc2.Regardless of whether we use the Dirac sea interpretation, a negative-energy particle in field theory is always interpreted as an antiparticle. Here we can also give an answer to the problematic feature of "negative rest energy" if we regard that Eo=(-mo)c2<0 comes from E2=m2c4 +c2p2 so for rest mass and zero momentum we truly have Eo2=(-mo)2c4 which gives back the well known Eo=(mo)c2>0 In the beginning we have to distinguish inertial mass, active gravitational mass, and passive gravitational mass. Active and inertial mass of course can be negative, meaning that the motion will be opposite than expected. If we regard, as until today is accepted, that these 3 are one and only feature, we could also solve the problem of equations of motion of a negative mass particle (-m). We will just add a minus in acceleration too (either as opposite motion, or as negative length). Experimentally found here https://m.phys.org/news/2017-04-physicists-negative-mass.html Theoretically fits to the notion that in GR spacetime is the "field" of mass, so negative gravitational charge (mass) gives negative field(spacetime). As for "negative" time, in physics we cannot accept time travelling backwards, but we can accept opposite arrow of time for antiparticles in Feynman diagrams and also conversion of a particle to antiparticle in case it changes sides (or time evolution…) in the particle equation. So F = (-m) (-a) = G (-m) M /r2 => a = -GM/r2. (Either we use r or -r, the result stays the same) It seems to accelerate away from a positive passive mass particle, opposite than normal mass does. In the case of the positive mass charge close to a negative mass' field (passive mass) F = ma = G m (-M) /r2 => a = -GM/r2. The positive charge/mass seems also to run away from a negative passive one. Perhaps it is opposite mass repelling and not an unknown "dark energy" that is causing the universe to expand at an ever increasing rate. We will also in this way solve the baryon asymmetry problem, where all antimatter seems vanished. Of course for both negative masses we have usual behavior of same positive mass F = (-m) (-a) = G (-m) (-M) /r2 => a = GM/r2. In GR the important quantity is the energy, not the mass, so the appropriate question would be, "are there negative energy states"? We could accept opposite/negative curvature in spacetime. We have not accepted the correlation between covariant-contravariant with matter-antimatter respectively, but we can accept that changing sides of the equation changes contra-variant to co-variant and vise versa, or when we have contravariant vector instead of covariant, the Christoffel symbol changes signs, which means opposite curvature. When we multiply a covariant metric with its contravariant one, the result is the unit tensor or the Cronecker Delta, that means flat space (no curvature)! Matter with antimatter gives us no matter (particle annihilation), like opposite curvatures cancel (destructive interference). In QFT negative mass doesn't make much difference. For a scalar (spinless) object, the expression in the Lagrangian (ie. the physical description) is always m2, so if m<0 you get the same thing. Therefore whether or not the mass is positive or negative is just a matter of definition. For a fermion, the mass in the Lagrangian is linear but you can just redefine your fermion field to make it positive. All antiparticles have all features opposite (charges/quantum numbers & spin direction) except mass. All particles have antiparticles except these with no mass and no charge. Finally seems impossible, at least yet, for our experiments to distinguish gravitational repelling while gravity is 1038 times weaker than any EM field close. Can anybody think of a reason not to regard negative mass as existent and not to correlate it to antimatter?