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Equation 136 · The Bend an Elevator Cannot Fake

What does this equation mean?

σy=1×10−18\sigma_y = 1\times10^{-18}

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Inputs and operations1 × 10^-18
Result or conditionsigma_y
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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σy\sigma_y

Symbol sigma_y

sigmaya_y is part of the quantity the equation computes from the expression on the right.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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subscript

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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superscript

superscript

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.

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How to interpret it

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What the article says around this equation

Take each edge’s fractional-frequency comparison uncertainty to be σy\sigma_y = 1×\times10^{-18} , the stability optical clocks have already demonstrated is what centimetre-level geodesy requires [ 8 ] . The combined noise on the independent-edge difference y2y_2-y1y_1 is 2\sqrt2\,σy\sigma_y . Setting signal equal to noise, ϕ,zz\phi_{,zz}\,h2h^2 = 2\sqrt2\,σy\sigma_y , gives

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Sources cited in the surrounding passage

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