Equation 120 · The Bend an Elevator Cannot Fake

What does this equation mean?

y_1 = \phi(0)-\phi(-h)

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Inputs and operationsphi(0)-phi(-h)

Result or conditiony_1

How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

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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y_1

Symbol y_1

$\sqrt2$ \, $\sigma_y$ .

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\phi

Symbol phi

phi is one of the signed contributions combined to compute the quantity on the left.

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h

Symbol h

h is one of the signed contributions combined to compute the quantity on the left.

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=

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

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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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How to interpret it

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What the article says around this equation

An exact analytic evaluation, not a simulation, fixes the scale this actually requires. Take three clocks stacked vertically at heights -h , 0 , and +h near Earth’s surface, giving two edges $y_1$ = $\phi(0)$ - $\phi(-h)$ and $y_2$ = $\phi(h)$ - $\phi(0)$ . Their difference is an exact finite-difference identity up to a Taylor remainder of order $h^4$ :

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Sources cited in the article section

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