Improved Test of Time Dilation in Special Relativity

An improved test of time dilation in special relativity has been performed using laser spectroscopy on fast ions at the heavy-ion storage-ring TSR in Heidelberg. The Doppler-shifted frequencies of a two-level transition in ${}^7\mathrm{L}\mathrm{i}^{+}$ ions at $v=0.064c$ have been measured in the forward and backward direction to an accuracy of $\Delta \nu /\nu =1\times {10}^{-9}$ using collinear saturation spectroscopy. The result confirms the relativistic Doppler formula and sets a new limit of $2.2\times {10}^{-7}$ for deviations from the time dilation factor ${\gamma }_{\mathrm{S}\mathrm{R}}=(1-v^2/c^2{)}^{-1/2}$.