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Equation 100 · Part 2 · The Bend an Elevator Cannot Fake

Symbol c^2

Tij:=c2(ϕ,ij+ϕ,i ϕ,j),\mathcal T_{ij} := c^2\left(\phi_{,ij} + \phi_{,i}\,\phi_{,j}\right),
c2c^2

What this part means

The square of c: multiply c by itself.

Its job in the formula

c2c^2 is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

…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 genuine curvature quantity, reported honestly as one stated-frame component rather than a coordinate-free scalar invariant, exactly the caveat this construction owes a reader.

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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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