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$\ell=1\,\mathrm{cm}$

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which at the horizon itself scales as $\ell$ $c^6$ /(4 $G^2$ $M^2$ ) — falling as the inverse square of the mass. For a processor of laboratory size $\ell$ =1\, $\mathrm{cm}$ at the horizon of a black hole with the mass measured for the progenitors of the first LIGO gravitational-wave detection, around 30\, $M_\odot$ , this tidal stress is already about 1.1 $\times$ 10^5\, $\mathrm{m\,s^{-2}}$ , 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 $\times$ 10^{-6}\, $\mathrm{m\,s^{-2}}$ across the same centimeter: negligible, and consistent with the…

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\ell=1\,\mathrm{cm}

Equation 81 · Evolutionary Physics

A Horizon Is a Toll Booth, Not a Loophole

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

which at the horizon itself scales as $\ell$ $c^6$ /(4 $G^2$ $M^2$ ) — falling as the inverse square of the mass. For a processor of laboratory size $\ell$ =1\, $\mathrm{cm}$ at the horizon of a black hole with the mass measured for the progenitors of the first LIGO gravitational-wave detection, around 30\, $M_\odot$ , this tidal stress is already about 1.1 $\times$ 10^5\, $\mathrm{m\,s^{-2}}$ , 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 $\times$ 10^{-6}\, $\mathrm{m\,s^{-2}}$ across the same centimeter: negligible, and consistent with the…

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