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Equation 87 · Part 1 · The Bit Comes Back Before the Bearing

Symbol t_L

tL(ϵ)t_L(\epsilon)
tLt_L

What this part means

the scrambling time, and it is worth deriving in real units rather than only in the abstract.

Its job in the formula

tLt_L is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Where the article explains it

Where the Qubit’s Bill Comes Due The natural timescale for tLt_L is the scrambling time, and it is worth deriving in real units rather than only in the abstract.

The passage around this formula

…qubit. This is an exact, hand-computable corroboration of the folklore “each extra collected qubit roughly halves what is left to recover,” not a re-derivation of Hayden and Preskill’s original bound, and it is why tL(ϵ)t_L(\epsilon) depends on ϵ\epsilon only logarithmically: driving ϵ\epsilon from 10^{-1} to 10^{-9} costs on the order of thirty extra qubits of radiation, a negligible addition to t∗t_* for any astrophysically sized hole. None of this requires the hole’s dynamics to be literally Haar-random for an…

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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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