Equation 14 · Part 9 · The Bend an Elevator Cannot Fake

subscript

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

subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

Full expressionsubscriptArticle 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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

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