Confinement of antihydrogen might help provide a future answer. http://arxiv.org/abs/1104.4982
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Anti-hydrogen and gravity are also discussed here: https://physics.stackexchange.com/q/1190/2451 – Qmechanic May 02 '11 at 14:11
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Also see this article: http://arxiv.org/abs/0909.3456 – Zo the Relativist Sep 01 '11 at 14:03
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at least what i can comment is that gravity is strange in itself....Being lowest to such an extent that m-theory researchers say that it is actually escaping from our universe! – Vineet Menon Sep 02 '11 at 10:07
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I want to give this link for experiment running at CERN to test the behavior of antimatter to gravity https://home.cern/news/news/experiments/new-antimatter-gravity-experiments-begin-cern . – anna v Dec 07 '19 at 06:59
3 Answers
Never seen any good reason to think that antimatter is affected any differently.
Light and anti neutrinos (from supernovas) seem to be affected by gravity the same as regular mass, and the theory of gravity (general relativity) doesn't distinguish mass and any other energy. If we beam a gamma photon down the gravitational well (from space to ground, for example), it gets blue shifted a little bit - it gains energy. If we use that gamma photon to produce matter antimatter pair and send the pair up the gravitational well, unless the antimatter is affected by gravity exactly the same as matter (and light), the conservation of energy will be violated. It makes absolutely no sense for antimatter to be affected by gravity differently than light, when the matter is affected by gravity the same as light. (note: no, there is no anti-light)
I guess it is the usual opportunistic fundraising, exploiting the ignorance. It is hard to raise funds for real research, realistically presented - it sounds obscure and layman has no idea what it is for - and it is easy to raise funds for something that layman thinks is a huge question with good likehood of something extremely awesome, like antigravity. When one is perfectly ignorant then the likehood is fifty-fifty.

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See the paper http://arxiv.org/abs/1103.4937 by M. Villata for an argument for antimatter falling up. However, see D.J. Cross at http://arxiv.org/abs/1108.5117 for powerful rebuttal arguments, asserting that Villata misapplied the CPT theorem, resulting in an incorrect sign for the matter-antimatter gravitational interaction.
See http://lss.fnal.gov/archive/test-fn/0000/fermilab-fn-0822-cd-t.pdf for a general review of the previously existing experimental evidence from Etvos and other experiments such as accelerometers, Kaons, astrophysical neutrino's from SN1987A.

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You're of course right. Experimentally established, known laws of physics - especially the equivalence principle - are enough to be certain that antimatter has the same gravitational properties - including universal attraction - as ordinary matter.
http://motls.blogspot.com/2010/09/can-antimatters-gravity-be-repulsive.html
The justification of further experiments by "tests of antimatter's gravity" is partly based on ignorance and partly on deliberate deception to get funding.

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16I think you are being unfair about the funding. It is more the Nobel effect than anything else. There are still experimentalists going for the unexpected so as to make a big splash and that is why they pursue funding for such experiments. In addition your certainty of experimentally established laws of physics has not filtered down to experimentalists, who tend to be measuring limits and pushing them as far as possible.. – anna v May 02 '11 at 17:24
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I see, Anna, but the Nobel prize also comes with some funding, doesn't it? :-) – Luboš Motl May 02 '11 at 17:28
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2There is an ancient greek proverb : "many despise money, nobody despises glory". It was spoken of generals in the colonial wars of the time. – anna v May 02 '11 at 18:11
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6Unless I've missed something I don't buy your argument about the nucleon sea. Every $\bar{u}$ is paired with a $u$, every $\bar{d}$ with a $d$... . If we assume some (bizzar!) theory that support anti-matter anti-gravity those contributions cancel out. Not that I expect a surprise here. I know the PIs on at least one proposed experimental test and they expect antimatter to be gravitational attracted to matter. But it remains an important untested prediction. Interesting stuff is rarely found in the well tested parts of theories, but rather when in obscure corners. Dot the i's cross the t's. – dmckee --- ex-moderator kitten May 04 '11 at 02:44
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1I believe there is a strong justification for tests of the gravitational interaction of antimatter. You speak of "experimentally established, known laws of physics", but strictly speaking in most cases they have only been tested with matter, not with antimatter. For example, there is not even a test of the equivalence principle with antimatter. So in the end, there is still a possibility that matter and antimatter behave differently. Antimatter gravity probably can't be repulsive, but the force of gravity could differ by a few percent from matter gravity. – Sentry Sep 25 '16 at 23:12
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The effect of gravity on antimatter has been tested many times. If you want some really specific, naive experiments, check e.g. http://www.zmescience.com/science/physics/matter-antimatter-same-properties-043243/ - But even without these experiments, it's spectacularly obvious that gravity is equally attractive for antiparticles. Each normal object contains some admixture of antimatter, too - which depends on the material etc. (virtual antiquarks etc.). If there were a repulsion, it would be easier to see violations of the equivalence principle. – Luboš Motl Sep 27 '16 at 10:30
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2The experiment in the article you linked did not test the influence of gravity on antimatter. Though there are no details, it seems like it just tested the equality of the strong force for matter and antimatter, which is a completely different question. Second, I did not say that antimatter gravity was repulsive. This case can indeed be considered excluded. The interesting question is if the strength is equal, or if it differs by a small amount. And this has not been conclusively tested, so there is still a good justification for the above experiment – Sentry Oct 10 '16 at 18:40