Improved Test of Time Dilation in Special Relativity

Abstract

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 $\ensuremath{\Delta}\ensuremath{\nu}/\ensuremath{\nu}=1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ using collinear saturation spectroscopy. The result confirms the relativistic Doppler formula and sets a new limit of $2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ for deviations from the time dilation factor ${\ensuremath{\gamma}}_{\mathrm{S}\mathrm{R}}=(1\ensuremath{-}{v}^{2}/{c}^{2}{)}^{\ensuremath{-}1/2}$.