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Ω≈7.292×10−5 rad s−1\Omega \approx 7.292\times10^{-5}\,\mathrm{rad\,s^{-1}}

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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 Δ\Delta tet_e = (2/c2c^2)\,Ω\boldsymbol\Omega ⋅\cdot Ae\mathbf A_e , where Ae\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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Ω\Omega

Symbol Omega

Omega is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Published contexts (2)

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Ω≈7.292×10−5 rad s−1\Omega \approx 7.292\times10^{-5}\,\mathrm{rad\,s^{-1}}

Equation 66 · Evolutionary Physics

The Bend an Elevator Cannot Fake

This equation gives an approximation: it relates the quantities while allowing an approximation.

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 Δ\Delta tet_e = (2/c2c^2)\,Ω\boldsymbol\Omega ⋅\cdot Ae\mathbf A_e , where Ae\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…

Equation guide → · Article →
Ω≈7.292×10−5 rad s−1\Omega \approx 7.292\times10^{-5}\,\mathrm{rad\,s^{-1}}

Equation 150 · Evolutionary Physics

The Bend an Elevator Cannot Fake

This equation gives an approximation: it relates the quantities while allowing an approximation.

Earth’s own centrifugal contribution is the concrete case worth sizing, precisely because it is not negligible enough to ignore by assumption. With Ω\Omega ≈\approx 7.292×\times10^{-5}\,rad s−1\mathrm{rad\,s^{-1}} fixed by astrometry to far more figures than any clock network could hope to determine on its own [ 10 ] , the centrifugal Hessian has magnitude Ω2\Omega^2 ≈\approx 5.32×\times10^{-9}\,s−2\mathrm{s^{-2}} — smaller than the radial tidal magnitude computed above by a factor of nearly six hundred, but not so much smaller that a network aiming to certify the 2:{-1}:{-1} ratio to good precision can skip subtracting it. Left in, it would masquerade as roughly a fifth of one percent of the genuine tidal…

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