Researchers will use the unique ability of the European Organization for Nuclear Research (CERN) to produce and store antimatter to test an idea that has so far belonged entirely in the realms of science fiction.
According to some theories, antimatter may generate a gravitational field that repels anything around it rather than attracting it in the way that normal matter does.
If proven, such a discovery would revolutionise physics - and might have radical practical applications, ranging from aircraft that need scarcely any fuel to space drives that could reach other star systems, 'The Sunday Times' reported.
"We know that it is like the mirror image of matter, with many of its key properties reversed. What we want to find out is whether that includes its gravitational properties.
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"Put simply, if we put antimatter into a gravitational field like that of the Earth, does it fall upwards or downwards? If it falls upwards, repelled by the Earth, then we would have discovered something very new and exciting," he was quoted by the paper as saying.
ALPHA was the first experiment to trap atoms of antihydrogen - neutral antimatter atoms held in place with a strong magnetic field for up to 1000 seconds.
The problem is that this field is so powerful that scientists cannot measure the effect of gravity.
Current theoretical arguments predict that hydrogen and antihydrogen atoms have the same mass and should interact with gravity in the same way. If an atom is released, it should experience a downward force whether it's made of matter or antimatter.
The CERN team plans to trap up to 100 antihydrogen atoms in a magnetic field - and then gently turn it off.
The experiment will be done in a vacuum so the antiatoms will move under gravity alone. If they go up, then physicists would have found antigravity.
"In the unlikely event that antimatter falls upwards, we would have to revise our view of the way the universe works," said Joel Fajans, a member ALPHA at the University of California, Berkeley.