Gravitational properties of antimatter

Quantum gravity is at the forefront of modern particle physics, yet there are no direct tests, for antimatter, of even the principle of equivalence. We note that modern descriptions of gravity, such as fibre bundles and higher dimensional spacetimes, allow violations of the commonly stated form of the principle of equivalence, and of CPT. We review both indirect arguments and experimental tests of the expected gravitational properties of CPT-conjugate states. We conclude that a direct experimental test of the gravitational properties of antimatter, at the 1% (or better) level, would be of great value. We identify some experimental reasons which make the antiproton a prime candidate for this test, and we strongly urge that such an experiment bo done at LEAR