Measurement of the Transverse Doppler Effect in an Accelerated System

Using an ultracentrifuge rotor, the shift of the 14.4-keV Mössbauer absorption line of ${\mathrm{Fe}}^{57}$ in a rotating system was measured as a function of the angular velocity $\omega$. An ${\mathrm{Fe}}^{57}$ absorber was placed at a radius of 9.3 cm from the axis of the rotor. A ${\mathrm{Co}}^{57}$ source was mounted on a piezoelectric transducer at the center of the rotor. By applying a triangularly varying voltage to the transducer, the source could be moved relative to the absorber. This arrangement makes possible the observation of the entire resonance line at various values of $\omega$. The measured transverse Doppler shift agrees within an experimental error of 1.1% with the predictions of the theory of relativity. Possible sources of systematic errors are discussed.