Equation 136 · Part 4 · The Bend an Elevator Cannot Fake

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\sigma_y = 1\times10^{-18}

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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

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The passage around this formula

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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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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

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