Does an atom of antihydrogen ( H ¯ ) have the same energy levels as its charge conjugate, the hydrogen atom? Yes, according to the venerable CPT theorem, which proclaims the invariance of the laws of physics under the simultaneous operation of charge conjugation (C), parity inversion (P), and time reversal (T). Does antimatter fall at the same rate as ordinary matter in a gravitational field? It should, if the equivalence principle of general relativity holds. Although CPT invariance has been tested to high precision in several systems, its importance impels us to explore its limits: Comparing H to H ¯ should provide the most sensitive test yet of a system involving both a baryon and a lepton. As for gravitational properties, they have not yet been measured on antimatter. To conduct either test, though, one needs large quantities of H ¯...

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