Equation 36 · Part 8 · A Horizon Is a Toll Booth, Not a Loophole

subscript

\tau_{\rm ML}(\tau) = \pi\hbar/[2(\langle H(\tau)\rangle-E_0(\tau))]

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

The dossier for this paper flags something the two equations above do not, by themselves, settle: the periodic-evolution bound above was derived for a Hamiltonian with a genuinely time-independent spectrum. A real computation drives H( $\tau$ ) through a sequence of different instantaneous Hamiltonians, one per gate, and nothing guarantees in advance that a chain of instantaneously applied bounds sums to a valid bound on the whole chain. The condition that licenses treating $N_\perp$ [ $\Gamma$ ] as a legitimate partition into instantaneously static Levitin-Toffoli steps is a quasi-static one: over one local orthogonalization time $\tau_{\rm ML}(\tau)$ = $\pi$ $\hbar$ /[2( $\langle$ H( $\tau$ ) $\rangle$ - $E_0(\tau)$ )] ,…

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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 →

Sources cited in the article section

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