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Equation 47 · A Horizon Is a Toll Booth, Not a Loophole

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Δτ\Delta\tau

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Δτ\Delta\tau

Symbol Δτ

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

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change

change

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

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What the article says around this equation

That second identity is the entire resolution in miniature, and it is worth deriving N⊥N_\perp[Γ\Gamma] both ways to see it operate. Hold the local energy budget fixed at ElocE_{\rm loc}=E0E_0' (a battery physically at the processor, delivering a fixed amount of locally measured energy) over a proper interval Δ\Deltaτ\tau :

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