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The passage around this formula

$\eta_{cl}$ is an ordinary number, the same for every state — MICROSCOPE’s slot. $\hat\eta_{diag}$ is diagonal in the internal energy basis: it can make a clock in one internal state fall differently from the same species in another, which is what a clock-redshift test or a test comparing atoms prepared in different hyperfine states actually probes. $\hat\eta_{coh}$ is off-diagonal in that same basis — it couples the coherences between internal states to free fall, so it only shows up in an experiment that keeps a system in superposition of two internal states long enough for gravity to act on the superposition itself, rather than on each state separately. $\hat\eta_{sup}$ depends on the system’s…

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