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Equation 74 · Part 4 · The Bend an Elevator Cannot Fake

Symbol Z_1

ν2/ν1=U(Z1)/U(Z2)\nu_2/\nu_1 = U(Z_1)/U(Z_2)
Z1Z_1

What this part means

Z1Z_1 is an input to the expression that computes the quantity on the left.

Its job in the formula

Z1Z_1 is an input to the expression that computes the quantity on the left.

The passage around this formula

This is an exact solution describing flat Minkowski spacetime in non-inertial coordinates, not a weak-field approximation. A clock held static at height Z has dτ\tau = U(Z)\,dt exactly, so two such clocks compare frequencies as ν2\nu_2/ν1\nu_1 = U(Z1Z_1)/U(Z2Z_2) to all orders — the same exact redshift formula an accelerating rocket produces for light climbing or falling inside it. The node potential is ϕ(Z)\phi(Z) = ln⁡\ln U(Z) = ln⁡(1+gZ/c2)\ln(1 + gZ/c^2) , and its first derivative at Z=0 is ϕ\phi' = g/c2c^2 : a nonzero, entirely real, measurable slope. A network of clocks bolted to this elevator’s walls would report exactly the nonzero edge data a network in a genuine gravitational field reports at the same order. If…

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