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yij≈(Φi−Φj)/c2y_{ij} \approx (\Phi_i - \Phi_j)/c^2

Why this formula appears here

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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yijy_{ij}

Symbol y_ij

yiy_ij 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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Φi\Phi_i

Symbol Phi_i

Phiii_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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Φj\Phi_j

Symbol Phi_j

Phiji_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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Published contexts (1)

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yij≈(Φi−Φj)/c2y_{ij} \approx (\Phi_i - \Phi_j)/c^2

Equation 15 · Evolutionary Physics

The Bend an Elevator Cannot Fake

This equation gives an approximation: it relates the quantities while allowing an approximation.

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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