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Equation 56 · Part 4 · The Bend an Elevator Cannot Fake

=

ϕ:=W/c2\phi := W/c^2
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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