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Equation 36 · Part 4 · A Horizon Is a Toll Booth, Not a Loophole

Symbol H

τML(τ)=πℏ/[2(⟨H(τ)⟩−E0(τ))]\tau_{\rm ML}(\tau) = \pi\hbar/[2(\langle H(\tau)\rangle-E_0(\tau))]
HH

What this part means

H is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

H is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

…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(τ\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⊥N_\perp[Γ\Gamma] as a legitimate partition into…

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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