We present a new generation of experiments using cryogenic optical resonators(COREs) to test the foundations of relativity. The experiments test the isotropy of the speed of light (Michelson-Morley experiment), the independece of the speed of light from the velocity of the laboratory (Kennedy-Thorndike experiments), and the gravitational redshift for clocks based on an electronic transition. Compared with the best previous results, our tests have already yielded improvements up to a factor of three. Future versions promise significant improvements.
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Müller et al. (2002) studied this question.