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Equation 48 · Part 8 · A Horizon Is a Toll Booth, Not a Loophole

subscript

N⊥=2πℏE0′ Δτ.N_\perp = \frac{2}{\pi\hbar}E_0'\,\Delta\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.

The passage around this formula

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 : N⊥=2πℏE0′ ΔτN_\perp = \frac{2}{\pi\hbar}E_0'\,\Delta\tau. Now hold the asymptotic Killing energy fixed instead, at E∞E_\infty = f\sqrt{f}\,E0E_0' (the amount of energy it would cost a distant experimenter, at infinity, to deliver that same physical resource down to radius r ), and integrate over the corresponding coordinate interval Δ\Delta t = Δ\Deltaτ\tau/f\sqrt f :

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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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