### 5.6 Doppler shift of lithium

If Lorentz invariance is violated, then the transformation laws for clocks with relative velocity will be
different from the usual time dilation. The RMS framework of Section 3.2 provides a convenient
parameterization of how the Doppler shift can deviate from its standard relativistic form. Comparisons of
oscillator frequencies under boosts therefore can constrain the parameter in the RMS
framework. The best test to date comes from spectroscopy of lithium ions in a storage ring [249].
In this experiment, ions are trapped in a storage ring at a velocity of . The
transition frequencies of the boosted ions are then measured and compared to the transition
frequencies at rest, providing a bound on the deviation from the special relativistic Doppler shift of
in the RMS framework. Recently, the results of [249] have been reinterpreted in
the context of the mSME. For the electron/proton sector the approximate bounds are [197]
where in a heliocentric frame. In the photon sector, the limit can also be set
from this experiment [269].