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Equation 19 · The Bend an Elevator Cannot Fake

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e=(i,j)e = (i,j)

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Inputs and operations(i,j)
Result or conditione
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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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ee

Symbol e

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

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ii

Symbol i

i is an input to the expression that computes the quantity on the left.

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jj

Symbol j

j is an input to the expression that computes 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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What the article says around this equation

At weak field this reduces to the familiar yijy_{ij} ≈\approx (Φi\Phi_i - Φj\Phi_j)/c2c^2 for Newtonian potential Φ\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 = Bϕ\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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