Equation 9 · Part 3 · A Horizon Is a Toll Booth, Not a Loophole

Symbol H

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

H

What this part means

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

Its job in the formula

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

Full expressionSymbol HArticle meaning

The passage around this formula

The baseline is the quantum speed limit. 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 $E_0$ …

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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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