I think the weirdness is, the distance between masses wouldn't change, they'd just accelerate together, in the same direction, indefinitely. Both mass would ex

I think the weirdness is, the distance between masses wouldn't change, they'd just accelerate together, in the same direction, indefinitely. Both mass would experience negative repulsive force: F=Gm(-m)/r^2 =-Gm^2/r^2 The positive mass accelerates away from the negative mass, because F=ma => ma=-Gm^2/r^2 => a=-Gm/r^2 Now here's the kicker. If inertial mass (the m in F=ma), is the same thing as gravitational mass. Then, the negative mass accelerates towards the positive mass. Because F=(-m)a => F=-ma => -ma=-Gm^2/r^2 => a=Gm/r^2 So accelerates in same direction as positive mass. Technically, conservation of energy & momentum is maintained, because the negative kinetic energy of negative mass would cancel out positive energy of positive mass. But I think the above can't be natural, because the magnitude of kinetic energy would grow to infinity, leading to even more impossibilities. So you'd need to 'hack' the theory of gravity and make inertial mass different to gravitational mass. So the particle has negative gravitational mass, but positive inertial mass, to make laws of physics stay sane :)