Equation 58 · Part 9 · The Bend an Elevator Cannot Fake

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\Delta t_e = (2/c^2)\,\boldsymbol\Omega \cdot \mathbf A_e

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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.

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The passage around this formula

A loop opens, instead, whenever some edge’s own realization is not simply a difference of two corotating nodes’ W . The clearest documented case is the relativistic Sagnac effect: a synchronization or comparison signal that does not itself corotate with the network — a one-way satellite time transfer, or any path analyzed against a non-rotating inertial frame — picks up an explicit timing correction $\Delta$ $t_e$ = (2/ $c^2$ )\, $\boldsymbol\Omega$ $\cdot$ $\mathbf A_e$ , where $\mathbf A_e$ is the area swept by that specific link’s path, projected onto Earth’s equatorial plane. That expression carries units of time, while an edge datum is a dimensionless log frequency ratio, so what actually enters the…

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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 surrounding passage

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