According to Quantum theory there exists a distinct, albeit small probability that a particle can tunnel it’s way through a barrier. That probability exponentially declines with the barrier’s thickness.
A particle tunneling has to borrow energy to overcome the barrier it is penetrating. In effect the particle’s energy runs an energy deficit while it is tunneling – it possesses a negative kinetic energy. Classically Ke is related to the square of the speed, thus if energy is negative, the speed will be the square root of a negative number.
Few if any results could come about to bring about negative matter from a Quantum mechanical investigations of Gravity alone. Gravity is inherent to a particle as energy in debt to G. Accordingly there should be two types of mass - the first type positive mass, which retains all the properties of ordinary mass.
The second type; negative mass differs only in that it’s mass is an inherently negative quantity. Consideration of the Quantum mechanical effects of the existence of these two types of mass is erroneous because their separate existences are not of an isolatable nature with respect to a single particle.
Hypothetically speaking negative mass cannot be plausible without time travel, especially where isolation is concerned, salvaging that back into the positive would prove difficult.
Why negative mass has never been “observed” (not particles) is due to the same reason why Ke and Pe are interdependent, is because of gravity.