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Equation 64 · Part 3 · The Bit Comes Back Before the Bearing

Symbol pi

t∗  ∼  β2π ln⁡S,β≡ℏkBTH=8πGMc3,t_* \;\sim\; \frac{\beta}{2\pi}\,\ln S, \qquad \beta \equiv \frac{\hbar}{k_BT_H} = \frac{8\pi GM}{c^3},
π\pi

What this part means

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

Its job in the formula

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

The passage around this formula

The natural timescale for tLt_L is the scrambling time, and it is worth deriving in real units rather than only in the abstract. Sekino and Susskind conjectured that black holes are the fastest scramblers nature permits, mixing information across all their degrees of freedom in a time growing only logarithmically with entropy [ 2 ] . Maldacena, Shenker, and Stanford later proved the sharp version of the bound this conjecture leans on: the exponential growth rate of an out-of-time-order correlator, the operational signature of chaos, cannot exceed λL\lambda_L ≤\le 2π\pi/β\beta for a thermal system at inverse temperature β\beta , with a black hole horizon saturating the bound [ 3 ] . Combining a…

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