This question was asked by a grade 12 learner Xavier and I am asking it on his behalf.
General expectation is that antimatter should be gravitationally attractive, both with itself and with ordinary matter, for a number of reasons. But this has yet to be proven experimentally.
Testing this proposition is one of the goals of CERN's ATHENA Experiment [re: http://athena.web.cern.ch/athena/]. It is considered highly unlikely anti matter will exhibit any anti gravity effects. We know we can accelerate anti matter particles [e.g. positrons] just like ordinary matter particles. It would seem logical to expect they would exhibit anti inertial properties if endowed with anti gravity properties.
Indeed, a breaking of the union between inertial and gravitational mass (which is puzzling to begin with!) would be quite striking. Particle physics would have a lot to answer for if this were the case.
The current version of CERN's anti-matter / gravity test is called AEGIS. Here is a recent report the project status http://cdsweb.cern.ch/record/1416071/files/SPSC-SR-096.pdf
In this paper italian physicist Massimo Villata claims that it is theoretically consistent that matter and antimatter would exert antigravity to eachoter.
Anyone can comment on its validity? (I'm not skilled enough)
Just to translate. CPT invariant, means reverse charges, spin, and time. The idea is that if you reverse those three at the same time, then situation which is allowed in the original theory will also be allowed in they "reversed" world. This is important, because anything that isn't CPT invariant makes field theory impossible.
I think the argument is wrong. Yes having an effective negative mass will allow the repulsion without violating CPT, but having an effective negative mass is going to break a lot of other things. Namely I don't see how you can statisify various energy constraints.
One big problem is photons. A photon is it's own anti-particle so if you have a photon interact with matter, it's always going to be attractive, which doesn't make sense if you have repulsive antimatter.
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