Equation 76 · A Horizon Is a Toll Booth, Not a Loophole
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol Δ r
Δ r is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol m
m is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
change
Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.
superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
See an illustrated explanation →How to interpret it
Read this expression with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
[ 11 ] . Setting equal to a demanding but realistic dilution-refrigerator base temperature of 10\, and solving for the required clearance gives r2.810^{-14}\, — 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…
Read the full surrounding passage
[ 11 ] . Setting equal to a demanding but realistic dilution-refrigerator base temperature of 10\, and solving for the required clearance gives r2.810^{-14}\, — 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 the item that kills the claim; the strut rig fails first, by an enormous margin.
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
Return to A Horizon Is a Toll Booth, Not a Loophole