Testing Einstein's time dilation under acceleration using Mössbauer spectroscopy

Abstract

The Einstein time dilation formula was tested in several experiments. Many trials have been conducted to measure the transverse second-order Doppler shift by Mössbauer spectroscopy using a rotating absorber, to test the validity of this formula. Such experiments are also able to test if the time dilation depends only on the velocity of the absorber, as assumed by Einstein's clock hypothesis, or whether the present centripetal acceleration contributes to the time dilation. We show here that because the experiment requires γ-ray emission and detection slits of finite size, the absorption line is broadened, by geometric longitudinal first-order Doppler shifts immensely. Moreover, the absorption line is non-Lorentzian. We obtain an explicit expression for the absorption line for any angular velocity of the absorber. The analysis of the experimental results in all previous experiments which did not observe the full absorption line itself were wrong and the conclusions doubtful. The only proper experiment was done by Kündig (1963 Phys. Rev.129 2371), who observed the broadening, but associated it with random vibrations of the absorber. We establish necessary conditions for the successful measurement of a transverse second-order Doppler shift by Mössbauer spectroscopy. We indicate how the results of such an experiment can be used to verify the existence of a Doppler shift due to acceleration and to test the validity of Einstein's clock hypothesis.