Equation 9 · Part 4 · A Horizon Is a Toll Booth, Not a Loophole

Symbol E_0

\tau_\perp \geq \frac{\pi\hbar}{2\left(\langle H\rangle - E_0\right)},

E_0

What this part means

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

Its job in the formula

$E_0$ occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Full expressionSymbol E_0Article meaning

Where the article explains it

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

…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 ] . Inverting this gives a maximum rate of orthogonal state changes per unit proper time, 2( $\langle$ H $\rangle$ - $E_0$ )/ $\pi$ $\hbar$ , and Giovannetti, Lloyd, and Maccone showed that for a periodic evolution this rate integrates cleanly: a system with mean energy…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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