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Equation 143 · Part 5 · The Bend an Elevator Cannot Fake

subscript

h∝σyh \propto \sqrt{\sigma_y}
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.

The passage around this formula

It is worth being honest about how far current best precision still has to travel to make a genuinely compact version of this measurement realistic. The most precise fractional frequency resolution reported to date, 7.6×\times10^{-21} , comes from comparing atoms at different heights inside a single shared optical lattice, where systematic effects common to both heights cancel almost completely [ 13 ] . If that exact resolution were ever achieved between two independently operated, physically separated network clocks — which is not what was demonstrated, and which faces a substantially harder common-mode-rejection problem — the same scaling gives h ∝\propto σy\sqrt{\sigma_y} and a required…

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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.

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Sources cited in the surrounding passage

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