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Φ/c2\Phi/c^2

Why this formula appears here

Two known limits anchor it. First, the elevator: Tij\mathcal T_{ij} ≡\equiv 0 for any uniformly accelerated frame, proven directly above — the “uniform potential difference is not curvature” claim, derived rather than asserted. Second, weak-field gravity: expanding ϕ\phi ≈\approx Φ\Phi/c2c^2 for small Φ\Phi/c2c^2 , the quadratic term ϕ,i\phi_{,i}ϕ,j\phi_{,j} is second order in the already-small ratio Φ\Phi/c2c^2 and negligible next to the first-order term ϕ,ij\phi_{,ij} ≈\approx Φ,ij\Phi_{,ij}/c2c^2 , so Tij\mathcal T_{ij} →\to Φ,ij\Phi_{,ij} , exactly the ordinary Newtonian tidal tensor of tower and satellite geodesy [ 15 , 14 ] . The first derivative alone, meanwhile, recovers the textbook gravitational redshift these networks…

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Φ\Phi

Symbol Phi

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Φ/c2\Phi/c^2

Equation 110 · Evolutionary Physics

The Bend an Elevator Cannot Fake

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

Two known limits anchor it. First, the elevator: Tij\mathcal T_{ij} ≡\equiv 0 for any uniformly accelerated frame, proven directly above — the “uniform potential difference is not curvature” claim, derived rather than asserted. Second, weak-field gravity: expanding ϕ\phi ≈\approx Φ\Phi/c2c^2 for small Φ\Phi/c2c^2 , the quadratic term ϕ,i\phi_{,i}ϕ,j\phi_{,j} is second order in the already-small ratio Φ\Phi/c2c^2 and negligible next to the first-order term ϕ,ij\phi_{,ij} ≈\approx Φ,ij\Phi_{,ij}/c2c^2 , so Tij\mathcal T_{ij} →\to Φ,ij\Phi_{,ij} , exactly the ordinary Newtonian tidal tensor of tower and satellite geodesy [ 15 , 14 ] . The first derivative alone, meanwhile, recovers the textbook gravitational redshift these networks…

Equation guide → · Article →
Φ/c2\Phi/c^2

Equation 112 · Evolutionary Physics

The Bend an Elevator Cannot Fake

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

Two known limits anchor it. First, the elevator: Tij\mathcal T_{ij} ≡\equiv 0 for any uniformly accelerated frame, proven directly above — the “uniform potential difference is not curvature” claim, derived rather than asserted. Second, weak-field gravity: expanding ϕ\phi ≈\approx Φ\Phi/c2c^2 for small Φ\Phi/c2c^2 , the quadratic term ϕ,i\phi_{,i}ϕ,j\phi_{,j} is second order in the already-small ratio Φ\Phi/c2c^2 and negligible next to the first-order term ϕ,ij\phi_{,ij} ≈\approx Φ,ij\Phi_{,ij}/c2c^2 , so Tij\mathcal T_{ij} →\to Φ,ij\Phi_{,ij} , exactly the ordinary Newtonian tidal tensor of tower and satellite geodesy [ 15 , 14 ] . The first derivative alone, meanwhile, recovers the textbook gravitational redshift these networks…

Equation guide → · Article →