Equation 7 · Part 3 · The Bend an Elevator Cannot Fake

Symbol U

\nu_j/\nu_i = U(\mathbf x_j)/U(\mathbf x_i)

U

What this part means

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

Its job in the formula

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

Full expressionSymbol UArticle meaning

The passage around this formula

For a static observer at position $\mathbf x$ in a stationary spacetime, define U( $\mathbf x$ ) := d $\tau$ /dt , the local rate of proper time relative to coordinate time. Two clocks compared through any phase-coherent link that depends only on their respective proper frequencies report the ratio $\nu_j$ / $\nu_i$ = U( $\mathbf x_j$ )/U( $\mathbf x_i$ ) — a fact about stationary spacetimes that…

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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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