Equation 67 · Part 8 · The Bend an Elevator Cannot Fake

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\Delta t = 2\Omega A/c^2 \approx 2(7.292\times10^{-5})(2.5\times10^{11})/(8.988\times10^{16}) \approx 4.1\times10^{-10}\,\mathrm s

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What this part means

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

Its job in the formula

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

Full expressionchangeArticle meaning

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

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 surrounding passage

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