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Equation 66 · The Bit Comes Back Before the Bearing

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β≈1.24×10−4 s\beta \approx 1.24\times10^{-4}\,\mathrm s

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This equation gives an approximation: it relates the quantities while allowing an approximation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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β\beta

Symbol β

β 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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ss

Symbol s

s 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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≈

≈

Approximately equal to; the equality is not exact.

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superscript

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.

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where the second equality for a Schwarzschild hole follows directly from Hawking’s temperature formula [ 7 ] and S = A/4ℓP2\ell_P^2 is the Bekenstein-Hawking entropy [ 6 ] . For a solar-mass hole, β\beta ≈\approx 1.24×\times10^{-4}\,s\mathrm s and ln⁡\ln S ≈\approx 177 , giving t∗t_* ≈\approx 3.5\,ms\mathrm{ms} — an exact evaluation of the stated formulas, illustrative of the scrambling scale and not a claim about any particular measured hole.

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