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Equation 76 · Part 3 · A Horizon Is a Toll Booth, Not a Loophole

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Δr≈2.8×10−14 m\Delta r\approx2.8\times10^{-14}\,\mathrm m
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What this part means

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

Its job in the formula

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

The passage around this formula

​ [ 11 ] . Setting TlocT_{\rm loc} equal to a demanding but realistic dilution-refrigerator base temperature of 10\,mK\mathrm{mK} and solving for the required clearance gives Δ\Delta r≈\approx2.8×\times10^{-14}\,m\mathrm m — a few nuclear radii from the horizon. For a supermassive hole, in other words, the ambient Hawking bath stays colder than any laboratory cryostat until the processor is closer to the horizon than an atomic nucleus, twenty-odd orders of magnitude closer than the point at which the support-acceleration bill already becomes unpayable. Cooling is a genuine, non-negotiable line item — it is what ties this construction to horizon thermodynamics at all — but for this mass scale it is not…

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the surrounding passage

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