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Equation 7 · Part 3 · The Corner of the Equivalence Principle No Experiment Has Touched

Symbol hateta_diag

η^=ηcl+η^diag+η^coh+η^sup+η^ent\hat\eta = \eta_{cl} + \hat\eta_{diag} + \hat\eta_{coh} + \hat\eta_{sup} + \hat\eta_{ent}
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 one of the signed contributions combined to compute the quantity on the left.

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

…joint, Hilbert space. Expand that operator and, the paper argues, exactly five structurally distinct pieces fall out: η^=ηcl+η^diag+η^coh+η^sup+η^ent\hat\eta = \eta_{cl} + \hat\eta_{diag} + \hat\eta_{coh} + \hat\eta_{sup} + \hat\eta_{ent}. 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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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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