Equation 11 · A Horizon Is a Toll Booth, Not a Loophole

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E_0

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the ground-state energy of H [ 2 , 1 ]. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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E_0

Symbol E_0

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

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subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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What the article says around this equation

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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