Equation 15 · The Bend an Elevator Cannot Fake

What does this equation mean?

y_{ij} \approx (\Phi_i - \Phi_j)/c^2

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This equation gives an approximation: it relates the quantities while allowing an approximation. 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_{ij}

Symbol y_ij

$y_i$ j 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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\Phi_i

Symbol Phi_i

Ph $i_i$ 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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\Phi_j

Symbol Phi_j

Ph $i_j$ 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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c^2

Symbol c^2

The square of c: multiply c by itself.

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≈

Approximately equal to; the equality is not exact.

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subtraction

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

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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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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

Its accuracy depends on the assumptions and range of use described in the article.

What the article says around this equation

At weak field this reduces to the familiar $y_{ij}$ $\approx$ ( $\Phi_i$ - $\Phi_j$ )/ $c^2$ for Newtonian potential $\Phi$ , exactly the quantity real fibre-linked clock comparisons already report [ 1 , 7 ] . Collect every measured edge into a vector y , one entry per link, and encode the network’s topology in an incidence matrix B : row e = (i,j) has a +1 in column i , a -1 in column j , and zero elsewhere. The model is y = B $\phi$ + n for measurement noise n with covariance C , and the standard weighted least-squares estimate of the node potentials is

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