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Equation 9 · Part 1 · The Corner of the Equivalence Principle No Experiment Has Touched

Symbol hateta_diag

η^diag\hat\eta_{diag}
η^diag\hat\eta_{diag}

What this part means

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.

Its job in the formula

hatetada_diag is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

η^diag\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.

The passage around this formula

ηcl\eta_{cl} is an ordinary number, the same for every state — MICROSCOPE’s slot. η^diag\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. η^coh\hat\eta_{coh} is off-diagonal…

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Sources cited in the article section

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