Equation 75 · Part 4 · The Bend an Elevator Cannot Fake

Symbol g

\phi(Z) = \ln U(Z) = \ln(1 + gZ/c^2)

g

What this part means

the observer under constant proper acceleration.

Its job in the formula

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

Full expressionSymbol gArticle meaning

Where the article explains it

Consider a uniformly accelerated laboratory in otherwise empty, flat spacetime — Einstein’s elevator, given by the exact Rindler metric in coordinates comoving with an observer under constant proper acceleration g : d $s^2$ = -U(Z)^2\,d $x_0^2$ + d $Z^2$ + d $x^2$ + d $y^2$ , $\qquad$ $x_0$ := ct, $\qquad$ U(Z) := 1 + $\frac{gZ}{c^2}$ .

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 d $\tau$ = U(Z)\,dt exactly, so two such clocks compare frequencies as $\nu_2$ / $\nu_1$ = U( $Z_1$ )/U( $Z_2$ ) to all orders — the same exact redshift formula an accelerating rocket produces for light climbing or falling inside it. The node potential is $\phi(Z)$ = $\ln$ U(Z) = $\ln(1 + gZ/c^2)$ , and its first derivative at Z=0 is $\phi$ ' = g/ $c^2$ : 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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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

[14] General Relativity ↗

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