In this book frequency measurements on fast lithium ions as a test of time dilation are presented. The measurements are carried out at the Max Planck Institute for Nuclear Physics in Heidelberg using the storage ring TSR. The transition frequency of a two-level system in the lithium ion is measured using a Doppler-free fluorescence saturation spectroscopy. The spectroscopy is realized by two counter-propagating lasers that are collinearly aligned with the stored ion beam. Two measurements are carried out, one at a ion velocity of 3% speed of light and one at 6.4% speed of light. The measured transition frequencies are compared with the prediction of Special Relativity. The influence of magnetic fields and light forces are also discussed. The results are expressed as parameter, that describes the deviation from the time dilation of Special Relativity, introduced by the test theory of Robertson-Mansouri-Sexl.

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