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

Why this formula appears here

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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η^AB\hat\eta_{AB}

Symbol hateta_AB

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

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η^A\hat\eta_A

Symbol hateta_A

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

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η^B\hat\eta_B

Symbol hateta_B

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

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Published contexts (1)

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

Equation 13 · Quantum Relativity

The Corner of the Equivalence Principle No Experiment Has Touched

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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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