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Equation 80 · Part 4 · A Horizon Is a Toll Booth, Not a Loophole

superscript

ℓc6/(4G2M2)\ell c^6/(4G^2M^2)
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What this part means

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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The passage around this formula

which at the horizon itself scales as ℓ\ell c6c^6/(4G2G^2M2M^2) — falling as the inverse square of the mass. For a processor of laboratory size ℓ\ell=1\,cm\mathrm{cm} at the horizon of a black hole with the mass measured for the progenitors of the first LIGO gravitational-wave detection, around 30\,M⊙M_\odot , this tidal stress is already about 1.1×\times10^5\,m s−2\mathrm{m\,s^{-2}} , on the order of ten thousand Earth gravities across a single centimeter — enough to disassemble ordinary hardware well before the horizon is reached [ 16 ] . For the Sagittarius A* mass used above, the same formula gives roughly 6×\times10^{-6}\,m s−2\mathrm{m\,s^{-2}} across the same centimeter: negligible, and consistent with the…

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An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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