Symbol t_L
the scrambling time, and it is worth deriving in real units rather than only in the abstract.
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is exact [ 4 ] . Fixing m=2 (a single qubit) and letting n — the effective size of everything else the qubit could be entangled with — grow gives = 0.5095 nats, = 0.6465 nats, and = 0.6814 nats, closing in on the ceiling 2 = 0.6931 nats. The residual gap to that ceiling shrinks by a factor of 3.94 when n quadruples from 4 to 16 , and by 3.98 when it quadruples again from 16 to 64 — converging, as more radiation-sized dimension is added two qubits at a time, on a clean factor of four per doubling of collected qubits, or two per single qubit. This is an exact, hand-computable corroboration of the folklore “each extra…
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Symbol epsilon
epsilon is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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Equation 87 · Evolutionary Physics
The Bit Comes Back Before the Bearing
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
is exact [ 4 ] . Fixing m=2 (a single qubit) and letting n — the effective size of everything else the qubit could be entangled with — grow gives = 0.5095 nats, = 0.6465 nats, and = 0.6814 nats, closing in on the ceiling 2 = 0.6931 nats. The residual gap to that ceiling shrinks by a factor of 3.94 when n quadruples from 4 to 16 , and by 3.98 when it quadruples again from 16 to 64 — converging, as more radiation-sized dimension is added two qubits at a time, on a clean factor of four per doubling of collected qubits, or two per single qubit. This is an exact, hand-computable corroboration of the folklore “each extra…
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Equation guide → · Article →Equation 153 · Evolutionary Physics
The Bit Comes Back Before the Bearing
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.
Sorting the claims above by what actually supports them: that an old black hole’s radiation is close to maximally entangled with its remaining interior, that scrambling proceeds no faster than a chaos bound saturated by horizons, and that a small system thrown in becomes recoverable from a matching small sample of later radiation are OBSERVED-theory baselines, DERIVED and inherited whole from Page, Hayden and Preskill, Sekino and Susskind, and Maldacena, Shenker, and Stanford [ 5 , 1 , 2 , 3 ] . That a global symmetry delays and partially obstructs that same recovery is likewise inherited, from Nakata, Wakakuwa, and Koashi’s direct analysis of the symmetric case [ 8 ] . What is PROPOSED, and…