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Published equation contexts

Δte=(2/c2) Ω⋅Ae\Delta t_e = (2/c^2)\,\boldsymbol\Omega \cdot \mathbf A_e

Why this formula appears here

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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Δte\Delta t_e

Symbol Δ t_e

Δ tet_e is part of the quantity the equation computes from the expression on the right.

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Published contexts (1)

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Δte=(2/c2) Ω⋅Ae\Delta t_e = (2/c^2)\,\boldsymbol\Omega \cdot \mathbf A_e

Equation 58 · Evolutionary Physics

The Bend an Elevator Cannot Fake

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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…

Meanings in this article

  • AeA_e: the area swept by that specific link’s path, projected onto Earth’s equatorial plane.
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