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 ${\gamma }_{\mathrm{S}\mathrm{R}}=(1-v^2/c^2{)}^{-1/2}$.

Figure 1

Setup of the experiment at the ion storage ring TSR.

Figure 2

Fluorescence signal observed with PMT3 for a multiple scan of the Lamb dip. Spectrum (b) is taken with both lasers interacting with the ions simultaneously. Spectrum (a), plotted with an offset for clarity, is the sum of the spectra taken with the lasers applied separately and reflects the Doppler background. The pure Lamb dip spectrum (c) is obtained by subtracting (a) from (b). The zero of the frequency scale corresponds to the position of the P(10)14-1 $a$ component.

Figure 3

Frequency offset of the Lamb dip from the ${\mathrm{I}}_2$ reference line as a function of the total laser intensity.