Equation 137 · The Bend an Elevator Cannot Fake

What does this equation mean?

y_2-y_1

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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y_2

Symbol y_2

$y_2$ 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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y_1

Symbol y_1

$\sqrt2$ \, $\sigma_y$ .

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subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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What the article says around this equation

Take each edge’s fractional-frequency comparison uncertainty to be $\sigma_y$ = 1 $\times$ 10^{-18} , the stability optical clocks have already demonstrated is what centimetre-level geodesy requires [ 8 ] . The combined noise on the independent-edge difference $y_2$ - $y_1$ is $\sqrt2$ \, $\sigma_y$ . Setting signal equal to noise, $\phi_{,zz}$ \, $h^2$ = $\sqrt2$ \, $\sigma_y$ , gives

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Sources cited in the surrounding passage

[8] Atomic Clock Performance Enabling Geodesy Below the Centimetre Level ↗

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