Equation 20 · Part 3 · A Horizon Is a Toll Booth, Not a Loophole

Symbol E_0

\langle H(\tau)\rangle - E_0(\tau)

E_0

What this part means

the ground-state energy of H [ 2 , 1 ].

Its job in the formula

$E_0$ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol E_0Article meaning

Where the article explains it

For a system with a fixed, time-independent Hamiltonian H evolving from a state $\lvert$ $\psi$ $\rangle$ toward any state orthogonal to it, the minimum time required is bounded below by the tight, unified Margolus-Levitin/Mandelstam-Tamm result of Levitin and Toffoli: $\tau_\perp$ $\geq$ $\frac{\pi\hbar}{2\left(\langle H\rangle - E_0\right)}$ , where $\langle$ H $\rangle$ is the mean energy in the evolving state and $E_0$ is the ground-state energy of H [ 2 , 1 ] .

The passage around this formula

Define the object this paper needs: for a worldline $\Gamma$ traced by a processor, with instantaneous mean energy above its own ground state $\langle$ H( $\tau$ ) $\rangle$ - $E_0(\tau)$ measured in the processor’s own comoving rest frame at proper time $\tau$ , the cumulative orthogonalization count is

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Learn the underlying idea

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Sources cited in the article section

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