Till today no such thing has been found even the tinest particle has mass. May be it is possible therotitically because of the negative sign and which has to be violated since there is no such thing called negative mass.
Mass is possessed by the gravitational force, and in space that is beyond gravity mass is zero.
There is no such thing called mass zero everything which is matter will have mass in presence of gravity and in absence of gravity that is in vacume will have zero mass but negative mass is not possible even in futuru there wont be anything called negative zero.
For a particle to have negative mass, it would have to have properties that cause it to react in opposition to the laws of physics, mass, and gravity that are understood today. Even neutrinos have some mass, but it is so infinitesimal that it has proved impossible to measure; to simplify things, neutrinos are commonly said to have "zero mass," but in actual calculations they must have mass or they would not exist. All particles, though the simple fact of existing as objects in three-dimensional space, have some level of mass, and so exert some level of gravity on other particles; a particle with negative mass would repel all other particles as it worked against their positive mass. Today, negative mass has only been speculated for certain classes of theoretical exotic matter, and has never been demonstrated or proven.
No. Negative mass is not possible. Certainly no such thing has ever been observed. Dirac predicted the existence of anti-matter as an interpretation of the negative energy eigenvalue solutions to the Schroedinger equation. I beleive ( and I need to verify this) that there are no such equivalent solutions to Einstein's GR equations or to Hamiltonian formulations of classical mechanics.
Although photons are massless, they do feel the influence of gravity. In GR, gravity couples not to an object with a non-zero rest mass, but to an object with momentum and energy. Photons may have a zero rest mass, but they do have momentum and energy, and feel the influence of gravity.
This isn't to say the idea of negative mass is totally off the wall (only partially off the wall). It might explain some aspects of dark energy (although this is outside my area of expertise). The main argument against it is that:
A) It would require a total reformulation of GR that is not obviously necessary.
B) There is no observational evidence that would suggest it.
A proposed adapted theory of General Relativity leads to simple mathematical formulas for BOTH the radius of the observable Universe AND the neutrino mass. www.hugsleftbrain.com