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Equation 100 · Part 7 · The Bend an Elevator Cannot Fake

addition

Tij:=c2(ϕ,ij+ϕ,i ϕ,j),\mathcal T_{ij} := c^2\left(\phi_{,ij} + \phi_{,i}\,\phi_{,j}\right),
addition

What this part means

Add the term after the plus sign to the term or group before it.

Its job in the formula

Add the term after the plus sign to the term or group before it.

The passage around this formula

Define the network’s curvature-diagnosing observable directly from this result, restoring physical units through the relation between coordinate acceleration and proper time for a static observer, Tij:=c2(ϕ,ij+ϕ,i ϕ,j)\mathcal T_{ij} := c^2\left(\phi_{,ij} + \phi_{,i}\,\phi_{,j}\right). a symmetric rank-two tensor in the local spatial frame of the static observers, with units of inverse time squared — the Eötvös units already standard in gravity-gradient surveying, where 1\,E\mathrm E = 10^{-9}\,s−2\mathrm{s^{-2}} . Under a rotation of the local spatial axes it transforms as an ordinary rank-two tensor; under a change of which node is used as the additive reference for ϕ\phi it is unchanged, because it depends only on derivatives of ϕ\phi , never its value; and up…

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the article section

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