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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 a RMS parameter in the RMS framework. The best test to date comes from spectroscopy of lithium ions in a storage ring [249Jump To The Next Citation Point]. In this experiment, 7 + Li ions are trapped in a storage ring at a velocity of 0.064 c. 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 |a |< 2× 10-7 RMS 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]
p p p |cXX + cYY - 2cZZ |< 10-11, (69) |cp + cp |< 10-8, (70) e e TJ eJT -5 |cXX + cYY - 2cZZ |< 10 , (71) |ce + ce |< 10-2, (72) TJ JT
where J = X, Y,Z in a heliocentric frame. In the photon sector, the limit - 5 ~ktr < O(10 ) can also be set from this experiment [269].
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