Equation 14 · Part 7 · The Bend an Elevator Cannot Fake

=

y_{ij} := \ln(\nu_j/\nu_i) = \phi(\mathbf x_i) - \phi(\mathbf x_j).

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

Full expression=Article 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 follows from the timelike Killing vector generating t -translations, and one on which the standard treatments of relativity in a geodetic or navigational setting already rely [ 10 , 14 ] . The dependence on endpoints only, never on the path connecting them, is not an approximation: because $\partial$ / $\partial$ t generates a…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

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