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Equation 75 · Part 3 · The Bend an Elevator Cannot Fake

Symbol U

ϕ(Z)=ln⁡U(Z)=ln⁡(1+gZ/c2)\phi(Z) = \ln U(Z) = \ln(1 + gZ/c^2)
UU

What this part means

U is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

U is one of the signed contributions combined to compute 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…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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