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We have carried out a modern version of the Kennedy-Thorndike experiment by searching for sidereal variations between the frequency of a laser locked to an l₂ reference line and a laser locked to the resonance frequency of a highly stable cavity. No variations were found at the level of 210^-13. This represents a 300-fold improvement over the original Kennedy-Thorndike experiment and allows the Lorentz transformations to be deduced entirely from experiment at an accuracy level of 70 ppm.
Hils et al. (Mon,) studied this question.