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Equation 65 · The Bit Comes Back Before the Bearing

What does this equation mean?

S=A/4ℓP2S = A/4\ell_P^2

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Inputs and operationsA/4ell_P^2
Result or conditionS
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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SS

Symbol S

S is part of the quantity the equation computes from the expression on the right.

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AA

Symbol A

A is an input to the expression that computes the quantity on the left.

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P2P^2

Symbol P^2

The square of P: multiply P by itself.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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subscript

subscript

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.

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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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How to interpret it

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What the article says around this equation

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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