The recent observation of single spins flips with a single proton in a Penning trap opens the way to measure the proton magnetic moment with high precision. Based on this success, which has been achieved with our apparatus at the University of Mainz, we demonstrated recently the first application of the so called double Penning-trap method with a single proton. This is a major step towards a measurement of the proton magnetic moment with ppb precision. To apply this method to a single trapped antiproton our collaboration is currently setting up a companion experiment at the antiproton decelerator of CERN. This effort is recognized as the Baryon Antibaryon Symmetry Experiment (BASE). A comparison of both magnetic moment values will provide a stringent test of CPT invariance with baryons.
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