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

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

Equation 101 · Evolutionary Physics

The Bend an Elevator Cannot Fake

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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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