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Equation 13 · Part 2 · The Corner of the Equivalence Principle No Experiment Has Touched

Symbol hateta_A

⟨η^AB⟩≠⟨η^A⟩+⟨η^B⟩\langle\hat\eta_{AB}\rangle \neq \langle\hat\eta_A\rangle + \langle\hat\eta_B\rangle
η^A\hat\eta_A

What this part means

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

Its job in the formula

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

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 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. η^sup\hat\eta_{sup} depends on the system’s…

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