Lamb Shift Measurement
According to the Schrödinger theory 2 times the 2S-4S transition frequency should be half of the 1S-2S transition frequency. By longitudinal Doppler-free two-photon excitation of a cold hydrogen beam we have observed the beat frequency between the frequency doubled IR radiation, used to drive the 2S-4S transition, and the blue light used to drive the 1S-2S transition after being frequency doubled. If the well-known fine and hyperfine structure and the first order correction of the Dirac energies due to the finite nuclear mass is subtracted, this beat contains a combination of Lamb shifts of the involved levels. On the other hand, if one believes in QED, a more accurate value of the proton charge radius can be extracted from those frequencies.