Testing Time Dilation on Fast Ion Beams

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 beta = v/c and the time dilation factor gamma = gamma SR (1+ (alpha) over cap beta(2) +(alpha) over cap (2)beta(4)) can be derived. From measurements based on saturation spectroscopy on lithium ions stored at beta = 0.03 and beta = 0.06 in the TSR heavy-ion storage ring, we achieved an upper limit for a O[beta(2)] deviation from Special Relativity of vertical bar(alpha) over cap vertical bar <= 8 x 10(-8). In recent measurements on a beta - 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 O[beta(4)] term of vertical bar(alpha) over cap (2)vertical bar <= 1.2 x 10(-5). We discuss current limitations and possible improvements that promise an enhancement of the sensitivity by at least one order of magnitude in the future.