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Equation 101 · Part 3 · The Bend an Elevator Cannot Fake

superscript

1 E=10−9 s−21\,\mathrm E = 10^{-9}\,\mathrm{s^{-2}}
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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

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 to the factor U2U^2 ≈\approx 1 negligible at the one-part-in- 10^9 level for any terrestrial network, it is c2c^2 times the frame component RiR^i{}_{0j0} of the Riemann tensor in the static observers’ own rest frame — a…

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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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Sources cited in the article section

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