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Equation 14 · Part 4 · The Bend an Elevator Cannot Fake

Symbol phi

yij:=ln⁡(νj/νi)=ϕ(xi)−ϕ(xj).y_{ij} := \ln(\nu_j/\nu_i) = \phi(\mathbf x_i) - \phi(\mathbf x_j).
ϕ\phi

What this part means

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

Its job in the formula

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

The passage around this formula

…own location, so a network’s fitted node potential can be compared against a measurement made over any convenient physical route without first specifying which route was used. Define the dimensionless node potential ϕ(x)\phi(\mathbf x) := ln⁡\ln U(x\mathbf x) and the edge observable actually recorded between linked clocks i and j , yij:=ln⁡(νj/νi)=ϕ(xi)−ϕ(xj)y_{ij} := \ln(\nu_j/\nu_i) = \phi(\mathbf x_i) - \phi(\mathbf x_j). 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…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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