Invariance under the charge, parity, time-reversal (CPT) transformation 1 is one of the fundamental symmetries of the standard model of particle physics. This CPT invariance implies that the fundamental properties of antiparticles and their matter-conjugates are identical, apart from signs. There is a deep link between CPT invariance and Lorentz symmetry-that is, the laws of nature seem to be invariant under the symmetry transformation of spacetimealthough it is model dependent 2 . A number of high-precision CPT and Lorentz invariance tests-using a co-magnetometer, a torsion pendulum and a maser, among others-have been performed 3 , but only a few direct high-precision CPT tests that compare the fundamental properties of matter and antimatter are available [4][5][6][7][8] . Here we report high-precision cyclotron frequency comparisons of a single antiproton and a negatively charged hydrogen ion (H 2 ) carried out in a Penning trap system. From 13,000 frequency measurements we compare the charge-to-mass ratio for the antiproton (q=m) p to that for the proton q=m ð Þ p and obtain q=m ð{12 . The measurements were performed at cyclotron frequencies of 29.6 megahertz, so our result shows that the CPT theorem holds at the atto-electronvolt scale. Our precision of 69 parts per trillion exceeds the energy resolution of previous antiproton-toproton mass comparisons 7,9 as well as the respective figure of merit of the standard model extension 10 by a factor of four. In addition, we give a limit on sidereal variations in the measured ratio of ,720 parts per trillion. By following the arguments of ref. 11, our result can be interpreted as a stringent test of the weak equivalence principle of general relativity using baryonic antimatter, and it sets a new limit on the gravitational anomaly parameter of a g {1 , 8.7 3 10 27 . The standard model is the theory that describes particles and their fundamental interactions, although without taking into account gravitation. However, this model is known to be incomplete, which has inspired searches for physics beyond the standard model, such as tests of CPT invariance that compare the fundamental properties of matterto-antimatter equivalents at the lowest energies and with the greatest precision [12][13][14][15] . For leptons, for example, the magnetic anomalies of electron and positron were compared with a fractional uncertainty of about 2 parts per billion 4 , and by applying similar techniques to protons and antiprotons, the resulting g-factor (a proportionality constant which links the spin of a particle to its magnetic moment) comparison reached a precision of 4.4 parts per million 8 . We are planning to improve this measurement by at least a factor of a thousand 16,17 . In this context, we recently reported the most precise and first direct high-precision measurement of the proton magnetic moment, with a fractional precision of 3.3 parts per billion 18 . Complementary to these efforts, spectroscopic comparisons of hydrogen and antihydrogen are underway; recent progress has been...