Abstract
We report the status of an experimental test of time dilation in Special Relativity. This is accomplished by simultaneously measuring the forward and backward Doppler shifts of an electronic transition of fast moving ions, using high-precision laser spectroscopy. From these two Doppler shifts both the ion velocity β = v/c and the time dilation factor can be derived. From measurements based on saturation spectroscopy on lithium ions stored at β = 0.03 and β = 0.06 in the TSR heavy-ion storage ring, we achieved an upper limit for a \U0001d4aa[β2] deviation from Special Relativity of . In recent measurements on a β = 0.34 Li+ beam in the ESR storage ring we used optical-optical double-resonance spectroscopy which, in combination with the TSR result, gives improved sensitivity on the \U0001d4aa[β4] term of . We discuss current limitations and possible improvements that promise an enhancement of the sensitivity by at least one order of magnitude in the future.
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