≈

The passage around this formula

The bill here is tidal, not electromagnetic or mechanical, and it is the one place this construction is bounded directly by what has actually been observed rather than by an idealization. A rigid processor of size $\ell$ falling radially experiences a stretching tidal acceleration between its two ends of approximately $a_{\rm tidal}(r) \approx \frac{2GM}{r^3}\,\ell$. 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…

Read this part in the article →