Equation 15 · Part 10 · A Horizon Is a Toll Booth, Not a Loophole

Numerator: 2

N \leq \frac{2}{\pi\hbar}\left(\langle H\rangle-E_0\right) t

2

What this part means

The complete quantity above the fraction bar.

Its job in the formula

2 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Full expressionNumerator: 2Article 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…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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