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Equation 52 · Part 2 · The Bend an Elevator Cannot Fake

Symbol x

W(x):=Φgrav(x)−12∣Ω×r∣2W(\mathbf x) := \Phi_{\rm grav}(\mathbf x) - \tfrac12|\boldsymbol\Omega \times \mathbf r|^2
xx

What this part means

x is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

x is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

Real terrestrial clocks are not simply static; they corotate with Earth, and their genuinely single-valued potential is the geopotential W(x\mathbf x) := Φgrav(x)\Phi_{\rm grav}(\mathbf x) - 12\tfrac12|Ω\boldsymbol\Omega ×\times r\mathbf r|^2 , gravitational potential combined with the centrifugal term for Earth’s rotation rate Ω\boldsymbol\Omega . Because W is a smooth, single-valued function of position in the corotating frame for any fixed Ω\Omega , folding it into the node potential ϕ\phi := W/c2c^2 preserves exact loop closure for any network of clocks that are themselves at rest relative to the rotating Earth — precisely the convention already standard in relativistic geodesy [ 4 , 3 ] .

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A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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