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Equation 15 · Part 8 · The Bend an Elevator Cannot Fake

superscript

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

What this part means

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.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

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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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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