$$\boldsymbol\Omega$$

Equation 53 · Evolutionary Physics

The Bend an Elevator Cannot Fake

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Real terrestrial clocks are not simply static; they corotate with Earth, and their genuinely single-valued potential is the geopotential W($\mathbf x$) := $\Phi_{\rm grav}(\mathbf x)$ - $\tfrac12$|$\boldsymbol\Omega$ $\times$ $\mathbf r$|^2 , gravitational potential combined with the centrifugal term for Earth’s rotation rate $\boldsymbol\Omega$ . Because W is a smooth, single-valued function of position in the corotating frame for any fixed $\Omega$ , folding it into the node potential $\phi$ := W/$c^2$ 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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