Equation 10 · Part 1 · A Horizon Is a Toll Booth, Not a Loophole

Symbol H

\langle H\rangle

H

What this part means

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

Its job in the formula

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

Full expressionSymbol HArticle meaning

The passage around this formula

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 $\langle$ H $\rangle$ - $E_0$ above its ground state can pass through at most

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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